Ph.D. Thesis 2009 Biomedical Engineering D. Keng – Whispering Gallery Mode bioparticle sensing and transport - i - WHISPERING GALLERY MODE BIOPARTICLE SENSING AND TRANSPORT DISSERTATION Submitted in Partial Fulfillment Of the Requirements for the Degree of DOCTOR OF PHILOSOPHY (BIOMEDICAL ENGINEERING) at the POLYTECHNIC INSTITUTE OF NEW YORK UNIVERSITY by Ta Kang (David) Keng May 2009 Approved by: ____________________________________ Department Head ____________________________________ Date Copy No. _____
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Ph.D. Thesis 2009 Biomedical Engineering
D. Keng – Whispering Gallery Mode bioparticle sensing and transport
- i -
WHISPERING GALLERY MODE BIOPARTICLE
SENSING AND TRANSPORT
DISSERTATION
Submitted in Partial Fulfillment
Of the Requirements for the
Degree of
DOCTOR OF PHILOSOPHY (BIOMEDICAL ENGINEERING)
at the
POLYTECHNIC INSTITUTE OF NEW YORK UNIVERSITY
by
Ta Kang (David) Keng
May 2009
Approved by:
____________________________________
Department Head
____________________________________
Date
Copy No. _____
Ph.D. Thesis 2009 Biomedical Engineering
D. Keng – Whispering Gallery Mode bioparticle sensing and transport
D. Keng – Whispering Gallery Mode bioparticle sensing and transport
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GUIDANCE COMMITTEE APPROVALS
Ph.D. Thesis 2009 Biomedical Engineering
D. Keng – Whispering Gallery Mode bioparticle sensing and transport
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MICROFILM OR OTHER COPIES OF THIS DISSERTATION
MAY BE OBTAINED FROM:
UMI Dissertations Publishing
Bell & Howell Information and Learning
300 North Zeeb Road
P.O. Box 1346
Ann Arbor, Michigan 48106-1346
Ph.D. Thesis 2009 Biomedical Engineering
D. Keng – Whispering Gallery Mode bioparticle sensing and transport
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VITA
Ta Kang (David) Keng was born on June 17, 1983 in Moorhead, Minnesota. He obtained
a B.S. in Electrical Engineer in 2005, and a M.S. in Biomedical Engineering in 2007 from
Polytechnic University. As an undergrad, he took Prof. Stephen Arnold’s honor’s physics
class and then he joined Arnold’s MicroParticle PhotoPhysics Lab (MP3L) in summer
2002 as a research assistant. He was particularly interested in the instrumentation and
automation of the Whispering Gallery Mode Biosensor (WGMB) system. He developed
many gadgets turning the WGMB into a robust research tool for discovery. During his
MS studies, he developed a microfluidic system enabling the WGMB to perform in situ
surface chemistry for unlabeled specific detection of virus. He was accepted into the
Polytechnic-SUNY Downstate Biomedical Engineering PhD program in 2007, after
obtaining his MS degree. His PhD thesis topic was WGM single bioparticle sensing and
transport. He co-authored a publication on single Influenza A virus detection in the
summer of 2008. After that, he focused his research on the WGM Carousel, which
utilizes the cavity enhanced nearfield optical force to sense and actively trap individual
particles. The WGMC effect is revolutionary and it solves numerous biosensing
challenges in one shot, including: Active transport within the boundary layer (enhanced
detection rate), uniform sensor response (particle mass spectrometer in liquid), and
particle-surface interaction (surface probe with nanometer resolution). During his MP3L
stay, he generated seven refereed publications, one book chapter, one provisional patent,
and possibly more.
June 11, 2009
Ph.D. Thesis 2009 Biomedical Engineering
D. Keng – Whispering Gallery Mode bioparticle sensing and transport
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DEDICATION
TO
MY FELLOW HOMO SAPIENS SAPIENS
Ph.D. Thesis 2009 Biomedical Engineering
D. Keng – Whispering Gallery Mode bioparticle sensing and transport
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ACKNOWLEDGMENT
I would like to give special thanks to my thesis advisor Prof. Stephen Arnold for giving
me a chance to join the cutting edge research. I thank him for his academic and non-
academic guidance, his dedication to science, and his kindness to his students and lab
members. He is the best guidance professor.
I would like to also give special thanks to thesis co-advisor Prof. Iwao Teraoka for his
care to his student.
I would like to thank my co-workers and affiliates in the MP3L and in the Polytechnic:
(in approximate chronological order in which I met them)
Prof. Neil Wotherspoon, Dr. Mazia Khoshsima, Dr. Mayumi Noto, Dr. Frank Vollmer,
Dr. Steve Holler, Dr. Jason Guan, Dr. Ivan Selesnick (committee), Dr. Ravi Ramjit, Dr.
Volkan Otugen, Dr. Richard Seasholtz, Dr. Grigory Adamovsky, Ophir Gaathon, Dr.
Charles Martucci, Momchil Mihnev, Jelena Culic- Viskota, Dr. Noel L.Goddard, Dr.
Kolchenko, Dr. Bruce Garetz (committee), Minnie Chan, Dr. Subrata Saha (committee),
Suzy McAnanama, Monica Agarwal, Dr. Siyka Shopova, Dr. Walter Zurawsky
(committee), Raaj Rajmangal, Mariya Gelman, and many others.
I would like to thank my parents, my sister, and the rest of the family members for their
full support, special thanks to my aunt Jenny Chen, who died of cancer and who made me
set my goal to be a biomedical engineer. I would like to thank all my friends, and special
thanks to my girlfriend Ying Chen for her support.
Ph.D. Thesis 2009 Biomedical Engineering
D. Keng – Whispering Gallery Mode bioparticle sensing and transport
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ABSTRACT
We are in a constant battle with viral-born diseases.1 (eg. Swine flu, avian flu, HIV,
HepC, West Nile, smallpox, and etc.) To prevent worldwide pandemics, rapid
identification and sensitive detection are keys to intervention. Here we present a label-
free, real-time single virus detection platform derived from a fusion between physics,
telecom fiber-optics, microfluidics, and biochemistry. The result, the Whispering Gallery
Mode (WGM) biosensor, has demonstrated real-time single Influenza-A virion
detection,2 and this on-going development may be the most sensitive gadget ever built for
identifying individual virions.3 The WGM biosensor detects the virus by transducing the
virus’ optical polarizability into an optical resonance shift. The virus binds to the
antibody decorated sensor surface, and the natural interaction allows the virus particle to
be sensed without the need for labeling. The individual virus’ mass is also obtained from
the measured polarizability and adds an additional dimension in identifying the virus. In
addition, the resonant nature of the WGM allows the light to build up inside the sensor,
and the accumulated light forms a near-filed optical tweezers. This intense optical field
breaks the limitation of the diffusing-only transport within the boundary layer, and
actively grabs the particle in the surrounding fluids into the sensing region and
contributes to enhancing the particle detection rate by >100 fold.4 This active force gives
WGM biosensor unmatched advantages in guaranteeing the uniform sensor response, and
provides a new method for studying surface binding in real time using WGM
fluctuations.5
1 P.W. Ewald, “Mastering Disease in the Next Fifty Years,” Ed. John Brockman, (Vintage Books, 2002). 2 F. Vollmer, S. Arnold, D. Keng, Proc. National Academy of Science, 105, 20701-20704 (2008) 3 S. Arnold, R. Ramjit, D. Keng, V. Kolchenko, I. Teraoka, Faraday Discussion, 137, 65-83 (2008) 4 S. Arnold, D. Keng, S.I. Shopova, S. Holler, W. Zurawsky, and F. Vollmer, Optics Express, 17, 6230-
6238 (2009) 5 D. Keng, S.R. McAnanama, I. Teraoka, and S. Arnold, Appl. Phys. Lett., 91, 103902 (2007)
Ph.D. Thesis 2009 Biomedical Engineering
D. Keng – Whispering Gallery Mode bioparticle sensing and transport
1.1 THE GENERAL THEME FOR THIS THESIS .........................................................................................1 1.2 THE FOCUS OF THE THESIS.............................................................................................................1
9.1 BASIC FUNCTION OF THE MACROFLUIDIC SYSTEM.......................................................................58 9.2 PUMP AND TUBING SELECTION ....................................................................................................59 9.3 PUMP CONTROL SOFTWARE AND HARDWARE ..............................................................................62
10 LABVIEW PROGRAM – DIP TRACKING ....................................................... 64
10.1 BASIC FUNCTION OF THE PROGRAM.............................................................................................64 10.2 PROGRAM STRUCTURE ................................................................................................................64 10.3 SOFTWARE/HARDWARE INTERFACE............................................................................................65 10.4 TRIGGER TIMING AND NOISE REDUCTION ....................................................................................70 10.5 DIP DETECTION AND WAVELENGTH CONVERSION .......................................................................71 10.6 DIP TRACKING CORE ALGORITHM................................................................................................72 10.7 LASER TEMPERATURE CONTROL AND INTERFACE .......................................................................74 10.8 RUN TIME UTILITY – LOG KEEPER ...............................................................................................74 10.9 CHANGING LASER WITH MATCHING CALIBRATION FILE...............................................................75 10.10 OVERVIEW AND PRECISION .........................................................................................................75
11 PUMP PROBE COUPLING AND COMPACT MICROFLUIDIC .................. 76
11.1 CONTINUOUS FIBER COUPLING METHOD .....................................................................................76 11.2 PUMP PROBE COUPLING METHOD ................................................................................................77 11.3 DROP CHANNEL ON THE PLANAR SURFACE..................................................................................78 11.4 HIGH Q – TUNABLE COUPLING ....................................................................................................78 11.5 ZERO BACKGROUND ...................................................................................................................79 11.6 MINIATURIZATION OF THE MICROFLUIDIC...................................................................................80 11.7 CONSTRUCTION...........................................................................................................................80
Ph.D. Thesis 2009 Biomedical Engineering
D. Keng – Whispering Gallery Mode bioparticle sensing and transport
The pump-probe approach is very useful for detecting WGM which normally cannot be
coupled to a through fiber because of the resonator-waveguide refractive index mismatch.
Below is a spectrum comparison of Zirconia (Zr) coated silica microsphere using
the pump-probe approach and the conventional through fiber coupling approach.
Figure 11-13 : Fiber coupling to a ZrO2 coated silica microsphere in air. Note the shallow dip.
Ph.D. Thesis 2009 Biomedical Engineering
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As one can see, the fiber offers poor coupling because of the index refraction mismatch.
Since little light is coupled into the microsphere, there is not enough light returning to the
fiber to produce a strong interference at the coupling region, and therefore the dip is
shallow.
One way to decrease the mismatch is to lower the refractive index of silica by
fluorine doping, which requires that the microsphere be built using expensive fluorinated
fiber. Even though this method was demonstrated for a polystyrene (PS) coated silica
microsphere, it is difficult to use for microspheres with a higher refractive index coating.
For zirconia (ZrO2) coating, the high refractive index (~1.9) cannot be compensated for
easily, and therefore continuous fiber coupling gives a large propagation constant
mismatch.
The pump-probe approach, however, does not require interference condition at the
coupling region to reveal a dip as detectable signal. Thus, even if a small amount of light
is coupled into the microsphere, the probe fiber can still pick up WGM easily, and the
zero background signals can be amplified if necessary.
Figure 11-14 : Pump-probe coupling to the same ZrO2 coated microsphere. Note the easily detectable
peaks, and large values of Q.
Ph.D. Thesis 2009 Biomedical Engineering
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This peak spectrum is obtained using the same ZrO2 coated microsphere as the one used
for Figure 11-13. Comparing the two figures, one can see that the peaks are easy to
identify for the pump-probe coupling. In addition, the Q values are not affected using the
pump probe coupling method.
11.13 Overall
The pump probe coupling method takes more effort to produce, but it allows microfluidic
miniaturization without a need for lithography. Its most useful application may be for
resonator coupling that has mismatch in refractive index.
Ph.D. Thesis 2009 Biomedical Engineering
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12 List of Abbreviations DAQ – Data acquisition
DFB – distributed feedback (laser)
DIO – Digital Input/Output
DPP – Dual Pump-Probe
EFL – Effective Fiber Length
(length of the tapered fiber which has its evanescent field exposed)
MC – Microcontroller
TTL – Transistor Transistor logic
PC – Personal Computer
PS – Polystyrene
PWM – Pulse width modulation
RSP – reactive sensing principle
SNR – Signal to Noise Ratio
TIR – Total Internal Reflection
WGM – Whispering Galley Mode
ZrO2 – Zirconia
Ph.D. Thesis 2009 Biomedical Engineering
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13 References All the scientific references are included in the individual publications attached. The
references here are relevant to the engineering of the experimental setup.
1 P.W. Ewald (2002) In The Next Fifty Years, ed. Brockman J (Vintage Books, New
York), pp 289–301. 2 S. Arnold, M. Khoshsima, I. Teraoka, S. Holler, F. Vollmer, Shift of Whispering
Gallery Modes in Microspheres by Protein Adsorption, Opt. Lett., 28, 272-274 (2003) 3 F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, S. Arnold, Protein
Detection by Optical Shift of a Resonant Microcavity, Appl.Phys.Lett., 80, 4057(2002) 4 F. Vollmer, S. Arnold, D. Braun, I. Teraoka, A. Libchaber, Multiplexed DNA
Quantification by Spectroscopic Shift of Two Microsphere Cavities, Bio. Phys. J., 85,
1974-1979, 2003 5 S. Arnold, R. Ramjit, D. Keng, V. Kolchenko and I. Teraoka, MicroParticle
photophysics illuminates viral bio-sensing, Faraday Discussions, 137, 65-83 (2008) 6 F. Vollmer, S. Arnold, and D. Keng, Single virus detection from the reactive shift of a
whispering-gallery mode, PNAS, 105, 20701-20704 (2008). 7 S. Arnold, D. Keng, S. I. Shopova, S. Holler, W. Zurawsky, and F. Vollmer, Whispering
Gallery Mode Carousel – a photonic mechanism for enhanced nanoparticle detection in
biosensing, Optics Express, 17, 6230-6238 (2009) 8 G. Guan, S. Arnold and M. V. Otugen, Temperature measurements using a microoptical
sensor based on whispering gallery modes, AIAA J., 44, 2385 (2006) 9 T. Ioppolo, and M. V. Otugen, Pressure Tuning of Whispering Gallery Mode
Resonators, J. Opt. Soc. Am. B, 24, 2721-2726 (2007) 10 F. Vollmer, and S. Arnold, Whispering-gallery-mode biosensing: label-free detection
down to single molecules, Nature Methods, 5, 591 -596 (2008) 11 T. P. Burg, M. Godin, S. M. Knudsen, W. Shen, G. Carlson, J. S. Foster, K. Babcock,
and S. R. Manalis, Weighing of biomolecules, single cells and single nanoparticles in
fluid, Nature, 446, 1066-1069 (2007)
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12 Y. Roichman, B. Sun, Y. Roichman, J. Amato-Grill, and D. G. Grier, “Optical forces
arising from phase gradients,” Phys. Rev. Lett., 100, 013602 (2008) 13 CYTOP specification sheet 14 NEL electrics DFB specification sheet 15 Corning SMF28e fiber specification sheet 16 J. P. Laine, B. E. Little, H. A. Haus, Etch-eroded fiber coupler for whispering-gallery-
1429 – 1430 (1999) 17 J. C. Knight, G. Cheung, F. Jacques, and T. A. Birks, "Phase-matched excitation of
whispering-gallery mode resonances by a fiber taper," Opt. Lett., 22, 1129-1131 (1997). 18 L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Z. Maxwell, and E.
Mazur, Subwavelength-diameter silica wires for low-loss optical wave guiding, Nature,
426, 816-819 (2003) 19 O. Gaathon, J. Culic-Viskota, M. Mihnev, I. Teraoka, and S. Arnold, Enhancing
sensitivity of a whispering gallery mode biosensor by subwavelength confinement,
Applied Physics Letters, 89, 223901 (2006) 20 J. C. Knight, G. Cheung, F. Jacques, and T. A. Birks, Phase-matched excitation of
whispering-gallery-mode resonances by a fiber taper, Opt. Lett., 22, 1129 (1997) 21 L. Collot, V. Lefèvre-Seguin, M. Brune, J. M. Raimond and S. Haroche, Very High-Q
Whispering-Gallery Mode Resonances Observed on Fused Silica Microspheres,
Europhys. Lett., 23, 327-334 (1993) 22 Y. Xia and G. M. Whitesides, Soft lithography, Annu. Rev. Mater. Sci., 28, 153–84
(1998) 23 D. W. Pohl, W. Denk, M. Lanz, Optical stethoscopy: image recording with resolution
λ/20, Applied Physics Letters, 44, 651 (1984). 24 P. K. Wong, T. H. Wang, and C. M. Ho, Optical fiber tip fabricated by surface tension
controlled etching, Solid-State Sensor, Actuator and Microsystems Workshop, 94-97
(2002)
Ph.D. Thesis 2009 Biomedical Engineering
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The following attachments are my refereed publications associated with this thesis.
Whispering gallery mode carousel – a photonic mechanism for enhanced nanoparticle detection
in biosensing
S. Arnold1*
, D. Keng1, S. I. Shopova
1, S. Holler
2, W. Zurawsky
1, and F. Vollmer
3
1MicroParticle PhotoPhysics Lab, Polytechnic Institute of NYU, Brooklyn, New York 11201, USA 2Novawave Technologies, Redwood Shores, California 94065
3The Rowland Institute, Harvard University, Cambridge, Massachusetts 02142, USA *Corresponding author: [email protected]
Abstract: Individual nanoparticles in aqueous solution are observed to be attracted to and orbit within the evanescent sensing ring of a Whispering Gallery Mode micro-sensor with only microwatts of driving power. This Carousel trap, caused by attractive optical gradient forces, interfacial interactions, and the circulating momentum flux, considerably enhances the rate of transport to the sensing region, thereby overcoming limitations posed by diffusion on such small area detectors. Resonance frequency fluctuations, caused by the radial Brownian motion of the nanoparticle, reveal the radial trapping potential and the nanoparticle size. Since the attractive forces draw particles to the highest evanescent intensity at the surface, binding steps are found to be uniform.
1. A. Ashkin and J. M. Dziedzic, “Optical Trapping and Manipulation of Viruses and Bacteria,” Science 235, 1517-1520 (1987).
2. F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nature Methods 5, 591-596 (2008).
3. A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317, 783-787 (2007).
4. T. M. Squires, R. J. Messinger, and S. R. Manalis, “Making it stick: convection, reaction and diffusion in surface-based biosensors,” Nature Biotechnol. 26, 417-426 (2008).
5. J. C. Knight, G. Chung, F. Jacques, and T. A. Birks, “Phase-matched excitation of whispering-gallery-mode resonances by a fiber taper,” Opt. Lett. 22, 1129-1131(1997).
6. L. Yang, T. Carmon, B. Min, S. M. Spillane, and K. J. Vahala, “Erbium-doped and Raman microlasers on a silicon chip fabricated by the sol-gel process,” Appl. Phys. Lett. 86, 091114 (2005).
7. S. Arnold, M. Khoshsima, I. Teraoka, S. Holler, and F. Vollmer, “Shift of whispering-gallery modes in microspheres by protein adsorption,” Opt. Lett. 28, 272-274 (2003).
8. L ≈ (λ/4π)(ns2-nm
2)-1/2, D = 2nm2 (2ns)
1/2(nnp2 – nm
2)/(ns2 – nm
2)(nnp2 + 2nm
2), where ns, nm, and nnp are the refractive indices of the microsphere (1.45), aqueous medium (1.33), and nanoparticle (1.5 for virus and 1.59 for polystyrene; D = 1.50 and 2.26 respectively).
9. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a Single-Beam Gradient Force Optical Trap for Dielectric Particles,” Opt. Lett. 11, 288-290 (1986).
10. Y. Roichman, B. Sun, Y. Roichman, J. Amato-Grill, and D. G. Grier, “Optical forces arising from phase gradients,” Phys. Rev. Lett. 100, 013602 (2008).
11. J. N. Izraelachvili, Intermolecular And Surfaces Forces. 173-191 (Academic Press, Inc. , San Diego, CA, 1987).
12. I. Teraoka and S. Arnold, “Theory of resonance shifts in TE and TM whispering gallery modes by nonradial perturbations for sensing applications,” J. Opt. Soc. Am. B 23, 1381-1389 (2006).
13. F. Vollmer, S. Arnold, and D. Keng, “Single Virus Detection from the Reactive Shift of a Whispering-Gallery Mode,” Proc. Natl. Acad. Sci. USA 105, 20701-20704 (2008).
14. The translation from a size to a mass spectrum requires knowledge of mass density.
(C) 2009 OSA 13 April 2009 / Vol. 17, No. 8 / OPTICS EXPRESS 6230#107949 - $15.00 USD Received 25 Feb 2009; revised 31 Mar 2009; accepted 31 Mar 2009; published 1 Apr 2009
15. H. J. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of
nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457, 71-75 (2009)
1. Introduction
Light forces interacting with mechanical systems provide a unique tool for studying small biological objects [1]. In the case of a whispering-gallery-mode (WGM) bio-sensor [2] where the intensity within the evanescent volume is built up resonantly a light-force may answer a puzzling question. Measured binding rates of bioparticles in aqueous solution using a toroidal WGM bio-sensor [3] at ultra-low concentrations appear to be about one hundred times higher than calculated based on diffusive and convective transport theory [4]. Traditionally Brownian motion of ultra-low concentration analytes crossing the boundary layer has been considered as a major hurdle for the practicality of miniature bio-sensors [4]. There is no comprehensive model to explain the physical mechanism of enhanced binding rates in the case of WGM bio-sensors. Here we report an observation and analysis of an optical mechanism that enhances the transport rate to the sensing volume of a microspherical silica resonator by more than 50x. Polystyrene nanoparticles are drawn toward this volume by evanescent optical gradient forces generated with just a few microwatts driving the resonator. At low ionic strength an addition electrostatic force repels the nanoparticle from the surface, contributing to a radial trap. Here the particle finds itself in the tangential momentum flux of the WGM and is driven to orbit by scattering forces. The radial trapping potential is elucidated from fluctuations in the micro-cavity’s resonance frequency, allowing the use of the Carousel as a surface-potential nanoprobe. The maximum fluctuation enables the size and mass of the trapped nanoparticle to be determined without binding, suggesting that the WGM Carousel mechanism can be used for size/mass spectrometry in solution. At a considerably high ionic strength the electrostatic field is screened to a much shorter depth, and the particle is drawn closer to the surface where it is caught by a van der Waal interaction and binds. Resonance shifts due to these binding events are found to be steps having uniform heights.
2. The Whispering Gallery Mode Carousel Phenomenon
Nanoparticles suspended in an aqueous environment normally appear to be in Brownian motion. However, we observe in the vicinity of a bare silica microsphere (oblate microspheroid, eccentricity < 5%, equatorial radius R ≈ 50 µm) excited into a circulating WGM (quality factor Q ~ 10
6), nanoparticles as small as 140 nm radius (a) are trapped for
hundreds of seconds in orbit within the sensing volume with driving light power P ≈ 50 µW. As shown in Fig. 1(a), these nanoparticles appear to circumnavigate in the direction that light takes within the WGM. The nanoparticle concentration was ≈ 1 fM in D2O. D2O (Aldrich, 99.9%) was used to minimize absorption loss in the infrared. The particle recorded in the video was seen to orbit for over two revolutions before escaping, Fig. 2.
A tapered fiber which coupled power into the microsphere was positioned a few microns to one side of the equator. At resonance, a dip was observed in the power transmitted through
the fiber at wavelength λr as the laser was tuned. The power P driving the WGM was estimated from this dip depth [5, 6]. In addition to the deterministic propulsion, the trapped particle is also under the influence of Brownian motion, revealed as a blinking of the elastic
scattering signal from the particle, as well as by the delimited fluctuations in λr (Fig. 1(b)). In what follows we will show that the physical interpretation of these fluctuations reveals the trapping potential and the size of the nanoparticle. This potential is responsible for increased transport of target nanoparticles to the sensing volume.
Fractional fluctuations in the resonance wavelength from the background level ∆λr/λr are clearly due to perturbations in the WGM as the result of nanoparticle’s interaction with the microcavity, and are equal at each instant to the ratio of the energy polarizing the particle Wp to the energy in the cavity Wc (reactive sensing principle, RSP) [7],
∆λr/λr = Wp /Wc (1)
#107949 - $15.00 USD Received 25 Feb 2009; revised 31 Mar 2009; accepted 31 Mar 2009; published 1 Apr 2009
Fig. 1. WGM-Carousel-Trap. (a) WGM excited in a microsphere (radius R = 53 µm) with Q =
1.2×106 by a 1060nm tunable laser using fiber-evanescent-coupling. The resonance wavelength is tracked from a dip in the transmitted light (PD). An elastic scattering image shows a
polystyrene particle (radius a = 375 nm) trapped and circumnavigating at 2.6 µm/s using a
drive power of 32 µW. (b) A particle is sensed through resonance wavelength fluctuations ∆λr that identify its size/mass. These fluctuations are recorded from before the particle enters the Carousel-trap until after it escapes ≈ 6 min later.
Fig. 2 (Media 1) This is a sped-up video (16× real time) of a single nanoparticle (a = 375 nm) being trapped and propelled by the WGM momentum flux. The fiber is coupled to the microsphere (R = 48 µm) by contact slightly off the equator on the backside. The WGM has Q = 1.5×106, and is driven with a power P = 25 µW. Light travels in the fiber from right to left (WGM scatter can be seen on the left edge of the microsphere). The trapped particle is observed through elastic scattering as a bright spot in front and in back of the microsphere. The ring pattern around the bright spot is caused by diffraction by the microscope objective. The nanoparticle is trapped, and propelled for just over two revolutions with a period of 140s before escaping. The particle appears to move faster on the backside due the transverse magnification in the microsphere image.
The shift ∆λr is therefore independent of the power driving the resonator but is proportional in a dipole approximation to the ratio of the intensity at the nanoparticle’s center r
c to the energy
in the mode; ∆λ
r(r
c) ∝ E
0
2 (rc) ε(r)E
0
2 (r ) , where 0
E is the electric field amplitude and
ε(r) is the modal permitivity. For the lowest order angular wave excited in our experiments
the intensity function is symmetrical about the equator with a Gaussian-like shape, and falls
20µµµµm
#107949 - $15.00 USD Received 25 Feb 2009; revised 31 Mar 2009; accepted 31 Mar 2009; published 1 Apr 2009
off at “latitudes” on either side with a characteristic width w ≈ 6 µm. In contrast, in the radial direction the intensity falls off as the square of a spherical Hankel function which is well approximated by a decaying exponentially with a much shorter “evanescent length” L ≈ 150 nm [8]. Images of the particle’s orbit show it travelling along the equator with a root mean
square transverse displacement to either side of < 1.5 µm. The time to diffuse over this distance for our typical nanoparticle is several seconds, whereas the observed fluctuations in
∆λr occur much faster: over a time scale associated with diffusion through a length ~ 100 nm. Consequently, these fluctuations are due to changes in the interfacial separation h between the nanoparticle’s surface and the surface of the microsphere, with the maximum fluctuation
occurring at h ≈ 0 (i.e. green line in Fig. 1(b)). Translating other wavelength shift levels into h
values is critical to our analysis. Fortunately, this translation is easily implemented. Based on the RSP
[7] the wavelength shift for the nanoparticle’s center at h+a to that on the surface is
∆λr(h + a)
∆λr(a)
= exp[- (h + a) L ]
exp[- a L ]= exp[- h L ] . (2)
Equation (2) enables wavelength shift statistics to be transformed into separation statistics. The results are particularly revealing.
3. Trapping potential well
Figure 3(a) shows the separation histogram taken on a nanoparticle (a = 140 nm) that circumnavigated a microsphere for just over two orbits. A pronounced maximum is seen at
h ≅ 35 nm from the sensing surface. The peak is indicative of a surface repulsion that
becomes more evident by translating these separation statistics into a potential curve using equilibrium statistical mechanics.
Under the assumption of thermal equilibrium the Boltzmann distribution relates the
potential U(h) to the probability density p(h); U (h) = −k
BT ln[ p(h) p(h
ref)] , where href is a
reference separation for which U (href) = 0. Figure 3(b) shows the result. The particle is clearly trapped in a radial potential well with its minimum 35 nm from the surface as it is driven to orbit by the WGM’s tangential momentum flux. These potential points were fit by a sum of
two exponentials: a short-range repulsive interaction ( )/ 6.2exp - / 17.6 nmBsU k T h= , and a
long-range attractive interaction ( )/ -8.0exp - / 142.7 nmBpU k T h= . The latter supports our
hypothesis that the particle’s motion is principally radial since its characteristic length of 143 nm is close to the evanescent length in the radial direction (146 nm). The attractive force arising from this potential is similar to the gradient force in optical tweezer experiments, for which the potential in the equatorial plane is expected to be the negative of the polarization
energy, U p (h) ≈ − (αex 4) E0
2(a) exp(−h / L) where αex is the nanoparticle’s polarizability [9].
Indeed, a series of experiments show that the value of this “polarization potential” at the surface Up(0) is proportional to the power P entering the mode. The gradient force is aided in keeping the particle on an equatorial track by a transverse phase-gradient contribution [10]. The positive potential Us is independent of power, and appears to be due to repulsion between ionized silanol groups on the bare silica surface (pH = 7), and the negatively charged polystyrene nanoparticle (the particles used were slightly sulfonated). The characteristic
length of Us is close to the Debye length λD arrived at from the measured conductivity of our
medium [11], λD ≈ 20 nm, assuming monovalent ions. By varying the ionic conductivity of the solution one can effectively change the range of Us. In contrast, Up is independent of ionic conductivity and reaches much deeper into the solution. In effect the combined potential forms a “sink-hole” that draws particles toward the optimal region in the sensing volume.
#107949 - $15.00 USD Received 25 Feb 2009; revised 31 Mar 2009; accepted 31 Mar 2009; published 1 Apr 2009
Fig. 3. Separation histogram and trapping potential. (a) separation histogram collected from a single tapping event of a polystyrene (PS) particle (from mean radius <a> =140 nm hydrosol).
The WGM with Q = 7.3×105 was excited with P = 233 µW at λ ≈1060 nm in a microsphere
with R = 44 µm. The statistics were comprised of 1000 points. (b) Potential plot arrived at from the histogram in (a). These points are fit to a sum of two potentials (in red).
It is important to point out that not all forces in the optical problem may be considered conservative. [10] Our description of a potential associated with the separation statistics is strictly meant to apply to conservative forces in the equatorial plane.
The value of the polarization potential at zero separation, Up(0), may be calculated directly
in terms of the maximum wavelength shift (∆λr)max = ∆λr(a), the power P driving the mode, and its resonant Q by using the RSP, Eq. (1). [7] The polarization energy at zero separation Wp(0) = - Up(0) and the energy in the cavity Wc is the driving power P times the photon
lifetime Q/ωr. Consequently, the potential at zero separation is
U
p(0) = − ∆λ
r( )max
P Q / 2πc( ), (3)
where c is the speed of light. Whereas (∆λr)max is independent of P or Q, the attractive potential grows as their product. If we suppose Us is very short range, then the minimum
power to perceive trapping, Pmin , can be estimated by setting (0)p BU k T≈ ;
P
min≈ k
BT (2πc) / [Q (∆λ
r)
max] . (4)
Since all of the parameters on the right in Eq. (4) are measurable, the thermal escape hypothesis is testable by measuring Pmin.
A series of five experiments were performed in order to detect the minimum power to keep a particle in orbit. In each the power driving a WGM was lowered as an orbiting particle’s velocity was measured from a video recording. Figure 4 shows the results of one of
these experiments for which the power was lowered from 42 µW over a period of 1200 s. The
particle was lost as the power reached 7.3 µW. At this power the normalized potential from
Eq. (3) (0) 1p BU k T ≈ , consistent with thermal escape (as indicated by the top horizontal
#107949 - $15.00 USD Received 25 Feb 2009; revised 31 Mar 2009; accepted 31 Mar 2009; published 1 Apr 2009
scale in the Fig. 4). The recorded velocities in the Fig. 4 do not appear to be heading toward an intercept at the origin as might be expected. The reason lies in the fact that although the momentum flux at a given height decreases in proportion to drive power, the flux seen by the particle falls more rapidly, since the particle moves outward as the drive power decreases. The other four experiments showed similar results. The picture that evolves is of a particle attracted to the orbit and rapidly fluctuating radially above the equator by Brownian forces. This trapping mechanism also leads to enhanced detection rates in the WGM biosensor.
Fig. 4. Particle velocity as a function of drive power P. A nanoparticle of radius a = 375 nm
was trapped in a Carousel of a microsphere with R = 45 µm and Q = 1.5×106. The power was
gradually reduced over a period of 1200 s. Upon reaching 7.3 µW the particle escapes within 10 s, as seen by imaging and through the cessation of wavelength fluctuations. The upper horizontal scale is calculated from Eq. (3).
Carousel trapping is expected to enhance binding rate detection in the following manner: The enhanced transport increases accumulation of particles in the sensing volume, and forced re-visitations by a particle to the surface increases the probability for finding a binding site. To measure the enhancement of the transport rates we compared the case of pure diffusion driven particles by operating at an arbitrarily low polarization potential |Up(0)|d ≈ 0.01 kBT to the case where the polarization potential was near the threshold for escape, |Up(0)|e ≈ 1kBT. These experiments were carried out for particles with a = 250 nm and for a concentration of 6 fM. In each case we counted the number of visitations to the sensing volume by registering
the number of wavelength shift pulses exceeding 0.25(∆λr)max. For |Up(0)|d we detected only one visitation to the sensing volume in 1 hour. However for |Up(0)|e, 49 visitations ~ 1 s in duration were detected in 1 hour. As the potential was increased to |Up(0)| > 5kBT, particles were strongly trapped in the Carousel, and accumulation of multiple particles over time became unavoidable. With |Up(0)| above 2kBT trapping of a single particle for several minutes became highly probable, which allowed us to observe the delimited fluctuation. This limit,
where the particle temporarily “touches” the surface, (∆λr)max provides a means for the determination of the particle size/mass.
The maximum wavelength shift signal (∆λr)max registered for a given laser-resonator combination appears to depend only on the size and dielectric properties of the orbiting nanoparticle. This signal occurs when the particle encounters the greatest evanescent field. As the drive power is raised more of these events occur, but the largest have the same limiting value. Theory was constructed early on that related this wavelength shift to the particle’s polarizability and size by using the RSP [7, 12], but its confirmation has only come recently
#107949 - $15.00 USD Received 25 Feb 2009; revised 31 Mar 2009; accepted 31 Mar 2009; published 1 Apr 2009
with the observation and measurement of single wavelength shift steps in non-specific binding experiments [13]. However, these steps were random in size, associated with particles adsorbing at different latitudes on the sphere’s surface where the sensing response can vary over orders of magnitude. In the Carousel mechanism, the particles are attracted to the equator, and therefore produce uniform response in the delimited fluctuation. This allows a nanoparticle to be sized without the need for binding. The RSP
[7] provides an illuminating
equation for describing the wavelength shift [13]
( )1/ 2
3
5 / 2 max
r
r
a LD a
Re
λλ −∆ ≃ (5)
where D is a dimensionless dielectric factor equal to 2.26 for polystyrene in water. [8] Table 1
shows a comparison of particles sizes determined from (∆λr)max, for separate experiments on single polystyrene nanoparticles caught in Carousel traps by inverting Eq. (5), with the mean size reported for a statistical number of particles by the manufacturer.
Table 1. Nanoparticle Sizing by WGM Carousel. Size determined for each of four Carousel trapped nanoparticles
from their delimited wavelength shift (∆λr)max using Eq. (5) (far right) as compared with the mean size given by the manufacturer for the associated hydrosol <a>.
<a> (nm)
σ = 5% λ (nm)
Nominal R ± 1.5
(µm)
(∆λr)max ± 0.02 (pm)
a (nm) from RSP
140 ± 7 1059 43 0.25 158 ± 12
245 ± 12 1059 51 0.32 228 ± 19
245 ± 12 1312 56 0.42 247 ± 17
375 ± 19 1312 56 0.67 350 ± 21
Although the experiments were for resonators of different sizes and driven by different lasers, the nanoparticle size obtained by inverting Eq. (5) agreed with the manufacturer’s mean size <a> within the uncertainties in the experiment and the standard deviation in the manufactured hydrosols. This clearly opens the door for a nanoparticle size/mass spectrometer
in solution [14]. With a microsphere for which R = 40 µm and Q ≈ 107
individual bioparticles
having a mass of HIV (600 attograms, a ≈ 50 nm) should be easily sizable with P ≈ 50 µW at
λ ≈ 780 nm. For a power of 2 mW using the same resonator a smaller virus with a = 15 nm (mass ≈ 15 attograms, e.g. Poliovirus) is within reach.
Finally we return to the subject of binding. A particle caught in a Carousel orbit is in a pre-binding state which is easily converted to a binding state by reducing the range of the electrostatic repulsion and thereby allowing the optical force to pull a nanoparticle to the surface where the intrinsic van der Waal attraction can take hold. Decreasing the range of the electrostatic repulsion is accomplished by increasing the conductivity of the solution. Figure 5 shows two separate experiments on individual particles caught in Carousels for which the solution conductivities differed by an order of magnitude. The experiment at higher conductivity clearly shows the separation between the nanoparticle and the surface to be substantially reduced. An analysis of these separation statistics gave a repulsive potential for the low conductivity case corresponding to 0.5mM NaCl of
( )/ 6.2exp - / 17.6 nmBsU k T h= , whereas in the higher conductivity case corresponding to
5 mM NaCl ( )/ 4.9exp - / 6.1 nmBsU k T h= . The reduction in the range of the repulsive
potential by a factor of 2.9 is close to the expected reduction in the Debye length. The later is known to be inversely proportional to the square root of the salt ionic strength, (reduction in range by 3.2). [11]
#107949 - $15.00 USD Received 25 Feb 2009; revised 31 Mar 2009; accepted 31 Mar 2009; published 1 Apr 2009
Fig. 5. Particle separation histograms for two different NaCl concentrations (0.5 mM and 5 mM). Note that the particle is closer to the surface for higher salt concentration, indicated by the peak position of the statistics.
By adding 20 mM of NaCl to our D2O solution its conductivity was increased 40×. Nanoparticles (a = 375 nm) were trapped in the Carousel and bound to the surface. Figure 6(a)
shows the first three binding events registered as uniform steps in ∆λr. Although spatially random particle adsorption leads to a distribution of step heights which vary by more than an order of magnitude [13], the constancy of the step heights in Fig. 6(a) shows that the equator can be spatially isolated for binding. Such characteristics were also demonstrated with smaller nanoparticles (a = 140 nm). Figure 6(b) shows an experiment in which several of these particles bind to the Carousel surface from a 10 fM solution over a period of 20 minutes. In this case, there were two parallel paths, corresponding to a mode for which quantum number
1m l= − , indicating that the Carousel effect exists for higher order angular modes as well.
Fig. 6. (a) First three binding steps of nanoparticles (a = 375 nm) on a microsphere with R = 45
µm and P = 150 µW, Q = 2×105, Note the uniformity in step height. Red dash separation is set to 0.45 pm. (b) Image of a = 140 nm particles trapped and bound in the Carousel orbit, R = 39
µm.
4. Conclusions
In conclusion, the WGM Carousel mechanism provides underlying physics which answers the question posed in Ref. 4. We clearly see that detection rates are not limited by diffusion, and
20µµµµm 20µµµµm
#107949 - $15.00 USD Received 25 Feb 2009; revised 31 Mar 2009; accepted 31 Mar 2009; published 1 Apr 2009
can be increased by ~ 100×. In addition we discover that the new light-force mechanism provides a sensitive means for sizing individual particles and detecting their interactions with the sensor’s surface. The effects produced by Carousel trapping should be difficult to avoid for viral sized nanopartices such as HIV or Influenza A, since the power needed to form the
Carousel is < 200 µW. This power is orders of magnitude smaller than the trapping power reported with linear optical waveguides (~ 250 mW) [15]. Analytical and experimental studies show that our low trapping power is due to resonant build up within the spherical microcavity structure. In addition, by controlling the ionic strength and the trapping optical power, the particles are shown to bind preferentially within the Carousel. All of this provides optical WGM sensors with a distinct advantage not afforded to non-optical devices since the attractive potential reaches out into a solution and draws nanoparticles to the optimal sensing region unabated by ionic screening. In addition, proteins are also expected to interact with the Carousel, and light-force assisted functionalization of the resonator’s equator is possible.
Acknowledgments
S. A. thanks D. G. Grier of NYU for useful discussions. This work was principally supported by the National Science Foundation - Division of Bioengineering and Environmental Systems Grant No: 0522668. D.K. thanks an NYU-POLY seed grant for partial support. F.V. was supported by a Rowland Junior Fellowship.
#107949 - $15.00 USD Received 25 Feb 2009; revised 31 Mar 2009; accepted 31 Mar 2009; published 1 Apr 2009
Single virus detection from the reactive shiftof a whispering-gallery modeF. Vollmera,1, S. Arnoldb,1, and D. Kengb
aThe Rowland Institute, Harvard University, Cambridge, MA 02142; and bMicroParticle PhotoPhysics Lab, Polytechnic Institute of New York University,Brooklyn, NY 11201
Edited by Robert H. Austin, Princeton University, Princeton, NJ, and approved November 10, 2008 (received for review September 9, 2008)
We report the label-free, real-time optical detection of Influenza Avirus particles. Binding of single virions is observed from discretechanges in the resonance frequency/wavelength of a whispering-gallery mode excited in a microspherical cavity. We find that themagnitude of the discrete wavelength-shift signal can be suffi-ciently enhanced by reducing the microsphere size. A reactivesensing mechanism with inverse dependence on mode volume isconfirmed in experiments with virus-sized polystyrene nanopar-ticles. By comparing the electromagnetic theory for this reactiveeffect with experiments, the size and mass (5.2 1016 g) of abound virion are determined directly from the optimal resonanceshift.
biosensor influenza optical resonance
V irus particles are a major cause for human disease, and theirearly detection is of added urgency since modern day travel
has enabled these disease agents to be spread through popula-tions across the globe (1). Fast and early detection on site of anoutbreak requires biosensors where ideally individual viral par-ticles produce a quantitative signal. Here, we report the obser-vation of discrete changes in frequency of whispering gallerymodes (WGMs) as Influenza A virions bind to a microspherecavity. A ‘‘reactive’’ perturbation of the resonant photon state isconfirmed in measurements with similar-sized polystyrene (PS)particles near a wavelength of 1,310 nm: The frequency/wavelength shift signal follows a strong dependence on cavitycurvature near the predicted R5/2 scaling (2), providing amechanism for increasing signal by limiting modal volume. Byreducing the microsphere radius to just 40 m and operatingat a more favorable wavelength near 760 nm where reducedwater absorption is expected to enhance sensitivity (3), bindingsteps of individual Influenza A (InfA) virions are seen that easilyexceed the experimental noise level. Analytic equations arederived that relate discrete changes in resonance wavelength tothe size and mass of adsorbed virions. Although field effecttechniques using nanofibers (4) and interferometric approachesbased on light scattering (5) have demonstrated single virionsensing in the past, reactive WGM sensing adds new dimensionsto what can be learned: The measured wavelength shift enablesone to quantitatively identify the virion size and mass.
Experimental ApproachWGM resonances are perturbed toward longer wavelength asparticles with polarizability in excess to that of water adsorb toa microsphere cavity. Individual binding events have beentheorized to produce discrete steps in a time-trace of thewavelength shift signal (2). To probe for single binding events weimmerse a silica microsphere in a suspension of polystyreneparticles (PS) with radius a 250 nm (Fig. 1). The PS particlesare diluted in PBS to final concentrations 10–50 fM. A tunabledistributed feedback laser (DFB) (1,311 nm nominal wave-length) excites WGMs by evanescent coupling from a taperedoptical fiber. A WGM mode is detected as a Lorentzian-shapedtrough in a spectrum acquired by a photodetector that measurestransmission through the fiber as the wavelength of the laser is
tuned (6). Fig. 1 Inset shows the typical transmission spectrumfor a WGM excited in silica microsphere (here radius R 50m) immersed in aqueous solution. The linewidth 5 pm, asdetermined from the full width at half-maximum, corresponds toa Q factor Q / 2.6 105, primarily limited by overtonevibrational absorption of water in the near infrared. Micro-spheres are fabricated from tapered optical fiber tips that aremelted in a focused 10-W CO2 laser (7). Immediately afterfabrication, the microsphere-on-a-stem is mounted on the sam-ple cell and immersed in PBS solution. A small box encloses thesample cell to limit air f low and stabilize the ambient humiditylevel. A transmission spectrum is acquired every 20 ms, and theresonance wavelength is determined from a parabolic minimumfit to the Lorentzian-line, typically with precision 1% of thelinewidth. The dip-trace is displayed as fractional shift in wave-length /.
Fig. 2A shows a trace of / for a 250 nm PS particlesinteracting with a microsphere with R 45 m. Steps of variousheights are clearly visible against the background cavity noiseindicating adsorption of individual PS particles. We believe thatthe spikes such as those shown in Fig. 2B are associated withunsuccessful adsorption attempts. Fig. 2C shows the step statis-tics. A maximum step height can be distinguished. With theability to detect discrete steps and identify optimal step heightwithin a dip trace for a given nanoparticle radius, we can nowdirect our attention toward measuring the dependence of theoptimal shift signal on the microsphere curvature. We experi-ment with different-sized microspheres (R 44–105 m) andplot maximum step heights versus curvature (i.e., 1/R, Fig. 3).Interestingly, we find a strong dependence of the fractionalwavelength shift on the cavity radius, scaling as R2.67. This is ingood agreement with electromagnetic theory associated withreactive WGM sensing, for which steps have been predicted forsingle protein binding, with maximum step heights in proportionto R2.5 (2). The largest step heights are predicted for proteinparticles binding to the equator, whereas a 1/R dependence (2)is expected for a shift due to a random surface density. (6) Thesmall discrepancy in the exponent (2.67 vs. 2.5) in our PSparticle experiments may be explained by an increase in theevanescent interaction caused by a slight lengthening in theevanescent field depth L as the microsphere size is decreased,and is associated with large particles adsorbed for which a/L 1. For particles that are small compared with the evanescent fielddepth, such as protein or InfA virus, our optimal wavelengthshifts are consistent with the reactive theory, but the weak signal
Author contributions: F.V. and S.A. designed research; F.V. performed research; F.V.contributed new reagents/analytic tools; F.V., S.A., and D.K. analyzed data; and F.V. andS.A. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
Freely available online through the PNAS open access option.
www.pnas.orgcgidoi10.1073pnas.0808988106 PNAS December 30, 2008 vol. 105 no. 52 20701–20704
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associated with these smaller particles prohibits us from acquir-ing data over a wide range of microsphere sizes.
Having identified a means for increasing the shift magnitudeby reducing microcavity size, we set out to optimize the micro-sphere system for the detection of single InfA virions. InfAvirions have an average radius a 50 nm (8) and a refractiveindex below that of PS. Although our microcavity fabricationmethod would allow us to take further advantage of the largecurvature enhancement of the wavelength shift signal by formingsmaller cavities, the success of this approach is limited: furtherreduction of cavity size also increases cavity leakage so that anygain in sensitivity due to shift enhancement is offset by abroadening of the resonance linewidth. Instead, we find thatfurther increase in sensitivity is possible if we scale down thewavelength and the cavity. A wavelength 1,311 nm is alsofavorable due to less absorption in water. Following this ap-proach, we use DFB laser with 763 nm and excite a WGMwith Q 6.4 105 in R 39-m microspheres. We inject InfAvirions at concentration of 10 fM directly into a PBS filledsample cell, since the virions are known to adsorb to silica (9).The dip-trace of the resonance wavelength InfA/ in Fig. 4
reveals clear steps associated with binding of single viral particlesand one unbinding event. The signal-to-noise ratio (InfA/noise 3) can be further improved upon by signal processingschemes such as Median filtering; the solid line in Fig. 4 showsa median filter of rank 3. A similar median filter has been appliedin the green curve in Fig. 2 A.
High-sensitivity measurements of individual virus particles aremade possible by reducing modal volume, a principle that shouldalso apply to other WGM cavity geometries (10) and othernon-WGM microcavities (e.g., photonic crystals with ‘‘defects’’)(11). Below, we show that the steps heights already recorded forthe microsphere geometry can be described analytically by usingthe reactive theory, and that the viral size and mass may beidentified.
Reactive Sensing MechanismReactive sensing relies on the fact that work is done by theevanescent field of a microcavity as a polarizable nanoparticlemoves from a distant position to the microcavity surface. As aresult, the energy of light in the resonator is reduced. With thenumber of cavity photons conserved, the frequency of each
Fig. 1. Excitation of an equatorial WGM of a microsphere by evanescent coupling to a guided wave in a tapered optical fiber. Resonance positions are detectedas dips in the transmitted light T at particular laser wavelengths.
Fig. 2. Nanoparticle wavelength shift. (A) Dip-trace for a 250 nm PS particles interacting with a microsphere with R 45 mm. (B) A 15 second zoom-in. (C)Wavelength step statistics.
20702 www.pnas.orgcgidoi10.1073pnas.0808988106 Vollmer et al.
resonant photon is shifted by r in accordance with refs. 2and 3.
–hr ex
2Erv, t2 , [1]
where E(rv, t)2 is the time average of the square of the field atthe nanoparticle’s position rv due to a single photon resonantstate. We have assumed that the particle is small in relation tothe wavelength, and has an isotropic excess polarizability ex
including local field effects. Under these conditions, Eq. 1 shouldwork for any microcavity geometry. By dividing the shift infrequency by the single photon energy –hr on the left and by thevolume integral of the associated electromagnetic energy densityon the right, we arrive at a simple expression for the fractionalfrequency shift (2),
r
r
ex/0 E0rv 2
2 rr E0r 2dV
, [2]
where E0 is the electric field amplitude, and r(r) is the dielectricconstant throughout the cavity. Although the field in Eq. 1 isassociated with a single photon, this restriction does not apply toEq. 2, since both the numerator and denominator are separatelyproportional to the number of photons; the reactive effect isindependent of intensity. In addition, the volume integration inthe denominator suggests that the reactive effect should varyinversely with volume. This insight although approximate, isnone-the-less almost correct. In what follows we describe ourtheoretical results for the resonance shift of a microsphericalcavity. From this point onward we will express the resonanceshift as a shift in free space wavelength in accord with theexperimental data (i.e., r/r r/r).
Evaluation of Eq. 2 for a microspherical cavity is mostelegantly carried out for the lowest order WGM launchedaround the equator of a glass sphere of radius R.2 Such a modespreads symmetrically to either side of the equator with aGaussian-like profile, causing nanoparticles adsorbing above orbelow the equator to have a diminished shift relative to theequatorial shift. The maximum shift (i.e., equatorial) for ananoparticle of radius av adsorbing on the equator is found to be
r
r
max
Dav
3
R5/2 r1/2 eav/L, [3]
where L is the characteristic length of the evanescent field, andD is dimensionless dielectric factor* associated with both themicrosphere and nanoparticle. The wavelength shift enhance-ment that results from the reduction in microsphere size is clearlyseen in Eq. 3 to be proportional to R5/2, in good agreement withexperiment (Fig. 3). The exponential factor on the right resultsfrom the variation of the evanescent field over the radius of thenanoparticle. One can invert this transcendental equation toobtain the radius av of the adsorbed particle;
av a0
1 a0
3L
, [4]
where a0 is
a0 R5/6r
1/6
D1/3 r
r
max
1/3
. [5]
Numerical studies indicate that Eq. 4 deviates from the exactsolution to Eq. 3 by 1% for av 90 nm, and R 30 m.
DiscussionEq. 3 provides a clear statement with respect to the dependenceof the wavelength shift on microsphere curvature, and ourpolystyrene experiments agree well with respect to the exponent.Further evidence for the reactive mechanism results by compar-ing the nominal radii of the particles used in our experimentswith the radii arrived from the maximum measured wavelengthshifts (using Eq. 4). These results are summarized in the table.We note that our measurements agree well with Eq. 4 for a 250 nm. We also would like to point out that the estimate ofradius is a lower limit since only few particles bind directly on theequator. The mass mv of the InfA virion can now be evaluatedfrom its volume times its density to be 5.2 1016 g, inagreement with results for InfA’s molecular weight found fromthe sedimentation in density gradients based on a statisticalnumber of viruses (3 108 g/mol) (12).
*L (/4) (ns2 nm
2 )1/2 and D 2nm2 (2ns)1/2(nnp
2 nm2 )/(ns
2 nm2 )(nnp
2 2nm2 ), where ns, nm,
and nnp are the refractive indices of the microsphere (1.45), aqueous medium (1.33), andnano-particle (1.5 for virus and 1.59 for polystyrene).
Fig. 3. Maximum step height vs. microsphere curvature for polystyreneparticles with radius a 250 nm.
Fig. 4. Shift signal for InfA. The data were acquired for a microsphere withR 39 mm, and a DFB laser having a nominal wavelength of 763 nm.
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ConclusionsWe have shown that adsorption of individual nanoparticlesproduce discrete changes in resonance frequency/wavelength ofa WGM. We confirm the reactive sensing mechanism (Eq. 1 and2) and use its signal enhancement by reducing the size ofmicrospherical cavities. Detection of individual InfA virions inaqueous buffer is then demonstrated directly from steps in thewavelength shift signal. Both the virus size and mass are iden-tified from maximum step height associated with binding nearthe equator. This work may be considered a forerunner forreactive biosensing with microcavities of ultrasmall modal vol-ume such as ‘‘defects’’ within photonic crystals (11), since the Eq.1 and 2 should still apply.
The number of attempts needed to bind is a direct reflectionof the affinity of the bioparticle to a surface. No effort has beenmade in this first demonstration to extract ligand-receptoraffinities, however, such experiments will be soon to follow. Inaddition the tumbling of a nearly spherical virus is not expectedto lead to significant time dependent variations in the wavelengthshift signal, however, rod like virus will couple through a tensor(3) interaction to the electromagnetic field and should lead tosignificant time variations, allowing one to gain more detailsconcerning affinities associated with orientation. Fortunately,our approach has considerable bandwidth since a WGM cansense temporal variations down to the photon life Q/, whichis 1010 s for the Q values reported in the current work.Furthermore, the genus of a virus may be determined frommeasurements that are sensitive to a virion’s shape in additionto its size and mass. Considering the quantitative nature of thephysical interaction, and its large available bandwidth, the futureof single particle reactive WGM experiments is expected to beexpansive. The approach based on microspheres has advantagesover other cavity geometries and label-free sensing mechanismswhere a closed-form analysis of the wavelength shift signal maynot be possible (13).
MethodsPurified and formalin-inactivated human InfA virus A/PR/8/34 is purchased in4-(2-hydroxyethyl)-1-piperazineethanesulfonic acid (Hepes) buffer fromCharles River Laboratories. The virus sample is passed through a 0.2 m nylonfilter to remove aggregates and then concentrated in a speed vac. WGMsample cells (Fig. 1) are assembled from o-rings (McMaster–Carr, 12.5 mmdiameter) glued to a 48 65 mm no. 1 coverslip (Gold Seal). A microsphere-on-a-stem is then glued to the o-ring so that the sphere resides in the centerof the cell without touching the coverslip. The sample cell is mounted on aninverted microscope and visually inspected. The midsection of a taperedoptical fiber, which is held between the posts of a u-shaped metal holder, ispositioned in contact with the equator of the sphere (Fig. 1), using micrometerscrews. Alignment is adjusted by optimizing the coupling to WGM modes byslightly moving the point-of-contact between taper and sphere within theequatorial region. To check for viral aggregates and estimate concentration,an aliquot of the purified virion solution is stained with DiIC membrane dye(Invitrogen) and fluorescently imaged using a cooled charge-coupled device(CCD) camera (Cooke). Similarly, fluorescent carboxylated polystyrene parti-cles (Invitrogen) are checked for aggregates before use. Microspheres ofcontrollable size are fabricated from tapered optical fiber (Corning; SMF-28).The taper is held on a stage above a reflecting Aluminum surface and meltedin the focal spot of a focused 10-W CO2 laser (Synrad). The process is inspectedon a CCD camera while progressively more silica can be melted by pushingmore fiber into the beam where surface tension immediately forms a sphere.Tapered SMF-28 fiber for evanescent coupling to microspheres is fabricated bypulling of the fiber on a motorized stage while softening its midsection in abutane/nitrous-oxide flame (Microtorch; Azure Moon Trading Corp.). Thetaper is typically 5 cm in length with a thinnest diameter 2 m for couplingat 760 nm wavelength. DFB lasers are purchased from Thorlabs (1,311 nmwavelength) and Eagleyard (763 nm wavelength) and optically isolated (iso-lators purchased from Thorlabs and OFR). A free-space coupler (Thorlabs)equipped with a 20x objective is used to couple to the SMF-28 fiber. ILXLightwave controllers are used to tune the laser diode by sweeping the currentwith a sawtooth-shaped function.
ACKNOWLEDGMENTS. This work was supported by a Rowland Junior Fellow-ship (to F.V.) and National Science Foundation Division of Bioengineering andEnvironmental Systems Grant 0522668 (S.A.).
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7. Collot L, Lefevre-Seguin V, Brune M, Raimond JM, Haroche S (1993) Very high-Q whispering-gallery mode resonances observed on fused silica microspheres. Europhys Lett 25:327–334.
8. Lamb RA, Krug RM (2001) In Fundamental Virology, eds Knipe DM, Howley PM(Lippincott Williams & Wilkins, Philadelphia), pp 725–728.
9. Bresler SE, et al. (1975) Purification of influenza-viruses on wide-pore glass columns.Acta Virologica 19:190–196.
10. Vollmer F, Arnold S (2008) Whispering-gallery mode Biosensing: Label-free detectiondown to single molecules. Nat Methods 5:591–596.
11. Song BS, Noda S, Asano T, Akahane Y (2005) Ultra-high-Q photonic double-heterostructure nanocavity. Nat Mater 4:207–210.
12. Reimer CB, Baker RS, Newlin TE, Havens ML (1966) Influenza virus purification with thezonal ultracentrifuge. Science 3:1379–1381.
13. Armani AM, Kulkarni RP, Fraser SE, Flagan RC, Vahala KJ (2007) Label-free, single-molecule detection with optical microcavities. Science 317:783–787.
Table 1. Measurement of size and mass for different particles
20704 www.pnas.orgcgidoi10.1073pnas.0808988106 Vollmer et al.
MicroParticle photophysics illuminates viral
bio-sensing
S. Arnold,* R. Ramjit, D. Keng, V. Kolchenko and I. Teraoka
Received 26th February 2007, Accepted 11th April 2007First published as an Advance Article on the web 17th July 2007DOI: 10.1039/b702920a
The authors present an approach for specific and rapid unlabeled detection
of a virus by using a microsphere-based whispering gallery mode sensor that
transduces the interaction of a whole virus with an anchored antibody.
They show theoretically that this sensor can detect a single virion below the
mass of HIV. A micro-fluidic device is presented that enables the
discrimination between viruses of similar size and shape.
Introduction
None of civilization’s socio-political catastrophes (e.g. world wars) have caused anequivalent destructive effect on the world’s population as biological pandemics.1
Exponentially growing pathogens are difficult to contain and eliminate unless theycan be detected early on. Some years ago, one of us (S.A.) reflected on this problemas a friend was dying from a viral infection. His friend’s diagnosis came too late;real-time methods for testing for the virus were not available. A decision was madeto direct the MicroParticle PhotoPhysics Lab toward finding a solution. This paperrepresents its first expose.Our approach is to sense bio-particles using the high sensitivity afforded
by the perturbation that an adsorbed molecule has on high Q (4107) opticalresonances of a microparticle.2 In particular, bio-particle adsorption will be sensedfrom the associated shift in resonance frequency.3,4 We are interested in the opticalspectroscopy of microparticles, but not in the spectroscopy of the nanoscopic bio-particles (e.g. protein, DNA, virus). Although optical spectroscopy can be particu-larly useful for small molecules, bio-particles such as protein are difficult todistinguish by optical spectroscopy, since they are considerably larger and sharecommon vibrational and electronic states, as a consequence of being made up of thesame 20 amino acids. The same can be said for distinguishing between strands ofDNA, since they have four nucleotides in common. Biology is a great teacher in thisrespect. Through all the eons of evolution, biology has not taken a spectroscopicapproach; there is no light in our bodies. Instead nature evolves bio-nano-probesthat specifically grab onto protein, DNA and foreign invaders throughphysio-chemical interactions. Our approach is to use these bio-nano-probes assurface-bound recognition elements and the microparticle to transduce (report)the interaction.We are not interested in labeling the bio-particle with markers (e.g. fluorescent
tags). Labels can structurally and functionally interfere with the assay, may not bespecific and block our goal of real-time detection by involving an additional step.5
Faraday Discuss., 2008, 137, 65–83 | 65This journal is c The Royal Society of Chemistry 2007
There are other unlabeled biosensors such as the Surface Plasmon Resonance (SPR)device, however it has limited sensitivity, which has not substantially improved fromits inception.6,7 Our ultimate goal is to demonstrate the unlabeled sensing of a singlebio-particle.We are also not interested in identifying a virus from a multi-step analysis of
geonomic information within its protein coat. Instead, we will seek to identify thewhole virus by tranducing the immobilization that takes place when a coat proteinon its surface interacts with a complementary antibody anchored to the micro-particle surface.
Resonant sensors-general considerations
Each and every oscillator, whether a mass on a spring, a violin string, the thorax of acricket or a Fabry–Perot cavity has the common property of resonance. If they aredriven by a harmonic source, the square of the oscillator’s amplitude |A|2
(i.e., energy) will demonstrate a Lorentzian-shaped frequency response with max-imum at or and linewidth g (Fig. 1). At the same time they can be sensitive toperturbations. Allowing dust to fall on a violin string causes its tone to be reduced by|Do|. One can imagine putting bio-nano-probes on the violin string in order to detectspecific dust (e.g. anthrax spore). However, one is apt to find in a world awash withnoise that the frequency shift may not be sufficient for real time detection. Theprincipal difficulty is in measuring a frequency shift much smaller than the linewidth(Fig. 1).We will characterize this competition by a ‘‘measurement acuity factor’’,
F = |Do|min/g where |Do|min is the smallest measurable frequency shift. Clearly,smaller F is better, but more difficult to achieve. One thing is certain: for a given Fthe minimum frequency shift that can be measured is proportional to the line width,so that the fractional minimum shift |Do|min/or = Fg/or. Whereas F and or arecontrolled principally by the non-dissipative physics of the oscillator and thebandwidth of the detection system, g is principally controlled by dissipation. Toreduce the minimum measurable shift, one can reduce dissipation. By convention wewill represent the linewidth-to-frequency ratio by 1/Q, where Q is the so-calledQuality factor; g/or = 1/Q. With this definition
|Do|min/or = F/Q. (1)
The larger Q, the smaller the dissipation and the smaller the dust particle that can bedetected. Since a mechanical system like a violin string agitates the fluid around it, itis a far from an ideal sensor; dissipation is assured. By the same token, aFabry–Perot cavity with metalized mirrors has dissipation due to Ohmic losses onreflection. The least dissipative reflection in this regard is Total Internal Reflection(TIR), in which light propagating in a medium with refractive index n1 is reflected ata sufficient angle y from a medium with a lower refractive index n2. TIR is, inprinciple, without loss. Light that bounces off the interior surface of a sphere
Fig. 1 The frequency response of an oscillator before and after a perturbation.
66 | Faraday Discuss., 2008, 137, 65–83 This journal is c The Royal Society of Chemistry 2007
while executing a polygonal orbit has this appeal. Such an orbit [Fig. 2, withy 4 sin1(n2/n1)] is known as a Whispering Gallery Mode (WGM).The WGM in Fig. 2 has no apparent loss. This implies an infinite Q. However, it is
well known that Q has limits. The largest Q for a WGMmode currently measured ina silica microsphere is B1010.8 Clearly, Fig. 2 is misleading, light does not havestationary states in a dielectric. Photons orbiting in the polygon are only partiallytrapped. They can ‘‘tunnel’’ into free space modes. Before providing a morecomplete description of a WGM, we will attempt to obtain a heuristic estimatefor the shift of its resonant frequency due to a perturbing layer.
WGM layer perturbation: heuristic approach
There is always a wave-particle duality associated with the photon as there is for theelectron. Instead of the description in Fig. 2 of a particle bouncing against theinterior of the microsphere, we now turn to a wave description for estimating thesensitivity of the microsphere resonance frequency to adsorption. Fig. 3(a) showsthis point of view. It represents the mode by a wave that circumnavigates near thesurface of a sphere of radius R and returns in phase.This picture, which is analogous to a Bohr–de Broglie atom, may be appropriately
called a Photonic Atom.9 By this analogy, the angular momentum of the photon ischaracterized by a quantum number l that is equal to the number of wavelengths inthe orbit. In what follows, this wave description will be used to obtain an estimatefor the minimum thickness of an adsorbed layer that is required to produce ameasurable shift of the mode’s frequency. Later, this quantum analog will beexpanded to determine the fields and probability densities associated with thesephotonic modes.Let us suppose that a material having the same dielectric constant as the
microsphere adsorbs on the sphere’s surface to a thickness t (Fig. 3(b)). This layercauses all lengths in Fig. 3(b) to be scaled up, while l for the given mode remainsinvariant. As a result the wavelength increases so that its fractional increase is the
Fig. 2 WGM within a dielectric microsphere.
Fig. 3 (a) Photonic AtomMode; (b) Anticipated wavelength change caused by the addition ofa spherically-symmetric layer.
Faraday Discuss., 2008, 137, 65–83 | 67This journal is c The Royal Society of Chemistry 2007
same as the fractional increase in radius; Dl/l = t/R. Since frequency andwavelength are inversely related,
|Do|/or= t/R. (2)
The smallest measurable thickness is found by combining eqn (1) and (2),
tmin = F R/Q. (3)
For a conservative estimate for tmin, we take the measurement acuity F = 1,R = 100 mm and Q = 106, for which our minimum thickness is 0.1 nm (the sizeof a hydrogen atom). With a greater effort we have found experimentally that F canbe reduced to 1/50, corresponding, for our example, to a minimum detectablethickness t = 0.002 nm. This thickness is approximately one hundredth the size of ahydrogen atom! Although too small to be physical, it certainly shows the promise ofthe microsphere as an adsorption sensor.Our analysis thus far is strictly heuristic. Although it only applies to a
spherically-symmetric layer adsorbed on a homogeneous sphere and does not allowthe layer to have a different refractive index from the microsphere, it provides a greatdeal of guidance. Perhaps the most important rule, for our homogeneous sphericalsubstrate, is that the smallest amount of adsorbate is detected by minimizing theratio R/Q.Before we can address the problem of single bio-particle sensitivity, we must first
discuss a theory for the effect of local dielectric perturbations on microsphereresonances.This requires an understanding for the fields associated with the resonances. We
will approach this subject through a quantum analog using a pseudo-potentialapproach. Following the discussion of the theory for perturbation of microsphereresonances by bio-particles, we will present our virus experiments and show specificreal time detection of a virus from the frequency shift of a microcavity resonance, forthe first time.
WGM field: A quantum analog approach
Ultra-high Q WGM resonances were first seen in the microparticle area in opticallevitation measurements in air.10 Their interpretation came throughMie theory, which includes both incident and scattered fields.11 An easierapproach, pioneered by Nussenzvieg,12 utilizes a quantum analog and may be bestdescribed as a Photonic Atom (PA) model.9 Here, we briefly describe the model forcompleteness. For anyone who has studied the quantum mechanics of hydrogen thisapproach should be familiar. More importantly, it is concise and particularlyphysical.In the PA particle description, the photon is seen as a particle that orbits by
bouncing off the interior wall of the dielectric microsphere (Fig. 4a). This ‘‘quantumbilliard’’13 possesses quantized orbital angular momentum l just as the electron in aBohr atom.The PA wave description of a Transverse Electric (TE) mode is constructed by
inserting an electric field of the form
E = AL [cr (r) Yl,m/r] (4)
into the electromagnetic vector Helmholtz equation, where L is a dimensionlessangular momentum operator, L= ir r, Yl,m is a spherical harmonic and A is aconstant. As a result the radial wavefunction cr is found to follow a one dimensionalSchrodinger equation
d2cr
dr2þ ðEeff Veff Þcr ¼ 0; ð5Þ
68 | Faraday Discuss., 2008, 137, 65–83 This journal is c The Royal Society of Chemistry 2007
where the effective energy Eeff = k02, the square of the free space wave vector and the
effective potential
Veff = k02[1 n(r)2] + l(l + 1)/r2. (6)
The first term in this potential describes dielectric confinement for a radiallyvariable refractive index n(r), while the second represents centrifugal repulsion.Fig. 4 connects up the particle (4a) and wave (4b) points of view for a homogeneoussphere.The analog particle with effective energy k0
2 is caught in a potential ‘‘pocket’’ inVeff as it oscillates radially between the classical turning points at rmin and R.However, since the particle is a quantum analog it can tunnel through the barrierextending from R to r2. Within the barrier the probability density falls. Thisnearly-exponential fall between r = R and r = r2 is known in electromagnetictheory as the region of the evanescent field (the analog probability density isproportional to the square modulus of the electromagnetic field, E* E). Anyprobability density left at the end of the barrier leads to energy loss in the form ofan outward radiating spherical wave. Consequently, unlike the electron in thehydrogen atom, confinement in a dielectric Photonic Atom cannot be complete;the intrinsic Quality factor is finite.The probability density illustrated for the mode in Fig. 4b has one peak in the
potential pocket and is known as a first order mode (n = 1). At higher energies,modes may form with more interior peaks, corresponding to higher order numbers.In all, four attributes are required to describe a mode: radial order number n, angularmomentum quantum number l, z-component of angular momentum m and polar-ization P (TE or TM). As in hydrogen,m can have integer values betweenl and l. Ageneralized mode will be labeled as Pv
l,m. For a sphere having a uniform refractiveindex, the radial wavefunctions cr in the interior and beyond are so called Riccati–Bessel functions;
cr = r jl(nsk0r) for r r R, (7)
cr = [jl(nsk0R)/hl(nmk0R)] rhl(nmk0r) for r Z R, (8)
where jl and hl are spherical Bessel and spherical Hankel functions and ns and nmare the refractive indices in the microsphere and the surroundingmedium. Mode energies are found, as in quantum mechanics, by matchingthe logarithmic derivatives of the Cr functions on either side of the interfacialboundary.
Fig. 4 The inter-relationship between the WGM model and the Photonic Atom Model for amicrosphere having a uniform refractive index.
Faraday Discuss., 2008, 137, 65–83 | 69This journal is c The Royal Society of Chemistry 2007
Local dielectric perturbations of WGMs
Molecules that approach the surface of a microsphere interact with a WGM as theyenter the evanescent field. This oscillating field polarizes molecules, and as aconsequence causes a frequency shift of the mode.Fields due to photons are polarized due to the photon’s spin. If a microsphere is in
a single photon resonant state of energy ho, it will have an associated semi-classicalfield E(r, t) = Re[E0(r)e
iot]. With a bio-particle outside the sphere at position rj, aninteraction will occur; the bio-particle will be polarized and develop an oscillatingdipole moment in excess of the displaced solvent, Dp(t) = Re[Dp0e
iot]. The time-averaged energy required to polarize the bio-particle serves as the perturbation thatshifts the photon energy of the resonant state by
hDo ¼ 1
2hDpðtÞ E0ðrj; tÞit ¼
1
4Re½E0ðrjÞ Da# j E0ðrjÞ ð9Þ
where Da#
is the bio-particle’s excess polarizability tensor. By dividing this energy
shift by the energy of the mode
hor ¼ ð1=2ÞZ
eðrÞE0ðrÞ E0ðrÞdV ð10Þ
we arrive at a useful expression for the shift associated with a single bio-particleinteraction,
Door
j
¼ Re½E0ðrjÞ Da#j
E0ðrjÞ2ReðrÞE0ðrÞ E0ðrÞdV
ð11Þ
where e(r) is the dielectric function within the microparticle and in its surroundings(absent the bio-particle). Eqn (11) provides a much more general result than hadbeen presented previously.14 By simply switching from a real to imaginary operatorin eqn (11), one may also obtain an expression for the change in the linewidth Dg ofthe resonant mode due to molecular absorption,
Dgor
j
¼Im½E0ðrjÞ Da#j
E0ðrjÞ2ReðrÞE0ðrÞ E0ðrÞdV
ð12Þ
For our experiments, D can be assumed to have no imaginary part, since experimentswill be carried out at low enough energies to avoid absorption by protein or DNA.In this way, our measurements can be used to obtain added information about thesebio-particles.So long as one uses photon energies well below excited electronic states, water-
soluble proteins have dielectric properties that deviate less than 1% from one toanother. In addition, they also share very similar mass densities. On this basis thetrace of the polarizability tensor is proportional to the volume of the protein,15 andto the mass. This allows the Whispering Gallery Mode Biosensor (WGMB) to enjoya distinct advantage. The resonance shift contributed by a protein containsmolecular weight and size information. This is distinct from sensing schemes thatuse labels or detection involving protein charge.16,17 Another distinct advantage iscontained within the form of the interaction.Since the shift is proportional to E0ðrjÞ Da#j
E0ðrjÞ, a non-spherical proteinmolecule when adsorbed on a surface will show a different shift for a field polarizedperpendicular to the interface (TM polarization) than for the parallel case(TE polarization). This approach has recently been used for determining theorientation of the protein Bovine Serum Albumin (BSA) on a silica microspherein biological buffer.18
Many viruses that infect our cells are nearly spherical. For example HIV, HPVand HSV are icosahedral. This is fortunate since the excess polarizability tensor for
70 | Faraday Discuss., 2008, 137, 65–83 This journal is c The Royal Society of Chemistry 2007
such a shape is essentially diagonal with identical elements (i.e. isotropic) and thebasic interaction between the field and the bio-particle at rj in eqn (11) may bewritten as
E0ðrjÞ Da#j E0ðrjÞ ¼ DajE0ðrjÞ E0ðrjÞ ð13Þ
On this basis, the shift due to a single bio-particle perturbation is
Door
j
¼ DajE0ðrjÞ E0ðrjÞ
2ReðrÞE0ðrÞ E0ðrÞdV
: ð14Þ
The shift caused by a large number of bio-particles is most easily computed byassuming that the field at a particular bio-particle is not influenced by thecontributions from its neighbors,19 so that eqn (14) can be summed over a numberdensity r(r),
Door
¼
RrðrÞDaðrÞE0ðrÞ E0ðrÞdV2ReðrÞE0ðrÞ E0ðrÞdV
: ð15Þ
By taking a more condensed view (i.e., r(r)c l3), the factor r(r) D a(r) E0(r)withinthe integrand in eqn (15) may be replaced by De (r) Ein (r), where De (r) and Ein (r) arethe excess permittivity and the ‘‘true’’ local field at r respectively. With thisMaxwellian approach, a truly continuum equation for the frequency shift perturba-tion evolves
Door
¼
RDeðrÞEinðrÞ E0ðrÞdV
2ReðrÞE0ðrÞ E0ðrÞdV
ð16Þ
This is a familiar result obtained from traditional perturbation theory for dielectricparticles within metallic cavities20 and near dielectric cavities.21 Our approach ofstarting from a molecular property is somewhat non-traditional, however, it leavesus with several useful results for perturbations that are discrete (eqn (11)) orcontinuous (eqn (15)).Eqn (15) may be applied to analyte molecules nearby in solution as well as those
adsorbed. The former, which is normally referred to as refractive index sensing, is oflittle interest to our current investigation.There are alternative ways to utilize the above theory in dealing with adsorbed
virus. If the adsorbed virus particle is much smaller than the evanescent field lengththen the field in its vicinity may be considered to be uniform, and one may expecteqn (14) to apply with |rj| = R. However, if the virus particle is comparable to orlarger than the evanescent field length then one must consider it to be in a non-uniform field. A model for its excess dielectric form may then be input for De (r) ineqn (16) and the numerator evaluated.Although the numerators in eqn (11), (14), (15) and (16) depend on the specific virus
being adsorbed and the evanescent field characteristics, the mode energy integral withinthe denominators in all of these equations are the same and may be simply estimated.In what follows, we will evaluate the shift due to a single bio-particle with radius a ladsorbed on a sphere resonating in an equatorial TE mode; TEv
l,l. This mode is ofparticular interest since it is possible to excite it selectively using an optical fiber.For a high Q resonance, the mode energy is dominated by the interior energy.22
Consequently, we will approximate the denominator of eqn (14) by limitingthe integration only to the interior. From eqn (4) and (7), the field in the interiorwithin an equatorial mode E0 = Ain jl (ns k0r) L Yll, and consequently eqn (14)becomes
Door
j
Daj½jlðnsk0RÞ2jLYll j2
2esR
jlðnsk0rÞ½ 2r2drR
LYll
2 sinðyÞdydf ð17Þ
Faraday Discuss., 2008, 137, 65–83 | 71This journal is c The Royal Society of Chemistry 2007
for l c 1, |LYll|2p |Yll|
2.23 In addition, the spherical harmonic is normalized withrespect to solid angle,
HYllj j2dO ¼ 1, which reduces eqn (17) to
Door
j
Daj½jlðnsk0RÞ2jYll j2
2esR
jlðnsk0rÞ½ 2r2dr: ð18Þ
On resonance, the integral in the denominator of eqn (18) may be asymptotically(2pR/l c 1) related to the surface value of jl
2 through
Z R
0
½jlðnsk0rÞ2r2dr ffiR3
2½jlðnsk0RÞ2
n2s n2mn2s
: ð19Þ
where nm is the relative permittivity of the surrounding medium.24 By combiningeqn (19) with eqn (18), the shift due to a single bio-particle appears,
Door
j
DajjYllðrjÞj2
e0R3ðn2s n2mÞ: ð20Þ
Where e0 is the permittivity of free space (e0 = es/ns2), and the unit position vector rj
is used to denote the angular orientation at which the spherical harmonic isevaluated. This result does not depend on the resonance order, but possesses astrong dependence on polar angle and microsphere radius. In particular, thespherical harmonic in eqn (20) has a square modulus that peaks at (y = 901),producing a ‘‘band’’ of sensitivity around the equator (Fig. 5). With eqn (20) inhand, it is now possible to estimate the Limit Of Detection (LOD).We will first concentrate on this equatorial region, since particles adhering to this
region produce the largest possible shift. For a small number of virus particles N, wewill assume that each particle produces an equivalent shift. To estimate the smallestdetectable number NLOD we allow the accumulated shift |Do| using eqn (20) to beequal to |Do|min in eqn (1);
NLOD R3ðn2s n2mÞF
ðDa=e0ÞjYllðp=2Þj2Q: ð21Þ
NLOD is controlled by a number of factors. Since purified silica is readily available(i.e., optical fiber) and easily shaped, we choose silica for the microsphere. Weassume the virus to be blood borne, so the medium will be essentially aqueous. F isfixed by the measurement system and fluctuation theory, however, we find that a10 Hz bandwidth can be achieved with F = 1/50, and we will use this number in
Fig. 5 Depiction of the intensity associated with an equatorial mode (l = m).
72 | Faraday Discuss., 2008, 137, 65–83 This journal is c The Royal Society of Chemistry 2007
subsequent calculations. Microsphere size plays a critical role. It explicitly affects theR3 factor in the numerator and implicitly affects the |Yll (p/2)|
2Q factor in thedenominator. At a fixed wavelength, the spherical harmonic factor increases withl and therefore increases with R. For large l, |Yll (p/2)|
2 B R1/2, so R3/|Yll (p/2)|2 B
R5/2. As for Q, the story is more complicated. Q is a measure of the rate at which amode’s energy decays (i.e. g = o/Q). The paths for decay are numerous, includingintrinsic loss rates due to tunneling (o/Qint), absorption (o/Qabs), Raman scattering(o/QRaman) and Rayleigh scattering (o/QRaleigh, including surface roughness); (o/Q)= o/Qint + o/Qabs + o/QRaman + o/QRaleigh. Surface scattering is expected tolimit the ultimate Q for a large silica sphere in vacuum (B1012).25 For ourexperiments in aqueous buffer solution, Q for spheres with radii from 20 mm to200 mm is limited to values orders of magnitude below the ultimate vacuum value,due to loss of dielectric contrast (i.e., increased tunneling) and aqueous absorption;
1
Q 1
Qintþ 1
Qabs: ð22Þ
As R increases above 20 mm, both tunneling and absorption decrease, causing 1/Q todecrease faster than R5/2. As a result, NLOD decreases with increasing R. Buttunneling decreases much more rapidly than absorption, causing it to have aminority influence as the size further increases. This causes NLOD to begin toincrease. Fig. 6 shows a theoretical plot for NLOD for HIV virus particles as afunction of the silica sphere radius for two wavelength regions, 1300 nm and 780 nm.The substantially smaller NLOD values in the 780 nm region are due to considerablysmaller absorption by water at this wavelength. At either wavelength, we predictvery high sensitivity, with NLOD dipping below one tenth at 780 nm for a micro-sphere approximately 40 mm in radius.Fig. 6 was constructed from an estimate of the HIV polarizability. Although the
excess polarizability of HIV has not been measured, it is not difficult to estimate Dafrom the virus’ mass. Viruses are principally composed of protein and protein havethe convenient property of raising the refractive index of an aqueous solution bynearly the same amount for the same mass concentration; the differential refractiveindex of protein in an aqueous buffer dn/dc E 0.18 cm3 g1 (visible).26 Tobacco
Fig. 6 Smallest theoretical detectable number of HIV virus particles adsorbed on theequatorial rim of a homogeneous silica WGMB as a function of microsphere radius R forF = 1/50 and wavelength near 1300 nm or 780 nm.
Faraday Discuss., 2008, 137, 65–83 | 73This journal is c The Royal Society of Chemistry 2007
Mosaic Virus (TMV) is one of the few examples for which dn/dc has been measuredand the correspondence with protein verified (l= 488 nm).27 Although dispersion isprojected to lower dn/dc by 0.006 between 780 nm and 1300 nm,28 we have neglectedthis difference and used the visible value for our calculations. The excess polariz-ability is related to dn/dc and the molecular mass m through
Dae0¼ 2nm
dn
dcm: ð23Þ
HIV is a fusion virus with a lipid bilayer surrounding its capsid. From the densityand average size of the viral particle (110 nm), we estimate its mass to be 8 1016 gm and Da/e0, from eqn (23), to be 4 104 mm3.Although we will capture virus particles from a fluid flow, we are currently not at
the point of having them deposit only at the micro-sphere equator. Instead, theentire spherical surface will be functionalized. Here, the more relevant question is thetheoretical limit of detection associated with surface mass density, sm,Lod, which isderived by adding individual frequency shifts (eqn 20) from bio-particles placed atrandom positions on the surface and setting this overall shift to the minimummeasurable shift (eqn (1)). Before calculating sm,Lod we will first obtain the shift dueto a uniform layer of bio-particles.The frequency shift due to a random layer of bioparticles is found by summing
eqn (20) over random position coordinates on the microsphere surface. This discretesum may be made continuous by defining a number of adsorbates per unit solidangle dN/dO = s4pR2/4p and integrating over solid angle,
Doj jor¼ Da s
e0ðn2s n2mÞR: ð24Þ
The result has the same 1/R dependence that we heuristically obtained in eqn (2).The two equations may be further related by describing the bioparticles as having arefractive index nbp and forming a layer of thickness t in which the protein volumefraction is f. With an effective medium approach Da s/e0 = f(nbp
2 nm2)t, and
consequently
Doj jor¼
f ðn2bp n2mÞðn2s n2mÞ
t
R: ð25Þ
A uniform silica layer on silica corresponds to f= 1 and nbp = ns for which eqn (25)agrees with eqn (2). We can now calculate the limit of detection for surface massdensity by setting s= sm,Lod/m and in eqn (24). The results for 760 nm and 1300 nmare shown in Fig. 7.It should be noted that we have indicated the typical baseline sensitivity levels for
other label-free sensing techniques in Fig. 7. Interestingly, the sensitivity for theWGMB at 1300 nm for a relatively large microsphere (200 mm) is potentially betterthan the typical baseline sensitivity for the Quartz Crystal Microbalance (QCM),SPR,7 or Micro-Cantilevers (MC),29 and the minimum on the 780 nm curve beats thebest of these by more than two orders of magnitude.In what follows, we will describe our experimental approach and present our
results on specific virus sensing.
Experimental approach
There are two essential parts to our sensor design: the WGM resonator and thedriver that stimulates it.The WGM resonator is formed from silica by rotating the end of a bare
telecommunication fiber in an oxygen–propane micro-flame. The end of the glasssoftens and flows into a spheroidal shape. Our spheroids are oblate with aneccentricity B6% and equatorial radii between 75 and 200 mm.
74 | Faraday Discuss., 2008, 137, 65–83 This journal is c The Royal Society of Chemistry 2007
The use of spheroids may come as a surprise, since the theory in the last sectionwas developed for spheres. However, our theory applies equally well to modes withorbits near the equator of a spheroid so long as the perturbation does not change theeccentricity.The resonator is driven by evanescently coupling it at its equator to a tapered
optical fiber wave guide. Excitation of a micro-spheroid mode is signalled by a dip inthe transmission through the fiber.30 The fiber is flame tapered adiabatically from adiameter of 125 mm to a skirt width of B2 mm using an asymmetric pulling device,31
and directed perpendicular to the spheroid’s axis of symmetry (z, Fig. 8a). In thisconfiguration, energy is most efficiently coupled into the equatorial mode (m = 1).Other modes with orbits tilted from the equatorial plane have |m| values less than l,and as a consequence of the spheroidal shape differ in circumference and resonancefrequency (Fig. 8b).
Fig. 7 Smallest theoretical detectable uniform mass density on a silica WGMB as a function ofmicrosphere radius R for F = 1/50 and wavelength near 1300 nm or 780 nm.
Fig. 8 (a) The optical configuration. (b) A recorded transmission spectrum in water for a silicaspheroid having a 200 mm equatorial radius. Adjacent resonances differ by |Dm| = 1.
Faraday Discuss., 2008, 137, 65–83 | 75This journal is c The Royal Society of Chemistry 2007
The fiber transmission spectrum taken in water in Fig. 8b has a complete rangecomparable to the resolution of a good fluorescence spectrometer (0.2 nm), however,for our experiments the resolution is much higher. It is ultimately controlled by thelinewidth of a Distributed Feedback Laser (DFB, o0.00001 nm) operating near1312 nm. This DFB laser is tuned directly from its power supply, by driving the laserwith a saw tooth current source. As the forward current increases, both the outputpower and wavelength of the laser increase. The lower fiber transmission spectrum inFig. 8b reflects this tuning approach with the resonant dips dropping from a sawtooth backbone. The upper curve is constructed by normalizing to constantintensity. Adjacent resonances differ by |Dm| = 1.The perturbation in the frequency/wavelength of a resonance in a spectrum such
as Fig. 8b is tracked by the movement of a resonance dip by the use of a five pointparabolic fit and frequency/wavelength positions are recorded every 200 ms as a ‘‘diptrace’’. For a resonance having a Q B106, the fluctuations in the base line of the diptrace have an rms value as small as 0.00002 nm for a time period of 5 s.Two fluidic configurations were chosen. For non-specific binding experiments the
sphere and fiber are immersed in a 1 cm3 volume containing a stirred aqueous buffersolution. For specific binding experiments it is necessary to look at both adsorptionand desorption rates. For this purpose, a much smaller micro-fluidic cell with amotorized fluid exchange system was developed. This device will be described inmore detail along with our specific binding experiments.We will next focus on surface preparation for non-specific adsorption experiments
and attempt to detect virus particles in this way. Following this, we will turn to thepreparation of a surface for specific adsorption and demonstrate specific detectionthough the discrimination between similar viruses.
Surface modificatoin: non-specific sensing
Our interest is in functionalizing a silica surface for either non-specific or specificsensing. In all cases reported in this paper, we start by cleaning the surface in anoxygen plasma. In the presence of background humidity, silanol groups (Si–OH)form at the surface. Our surfaces will be functionalized by reacting the protrudinghydroxyl groups covalently with the methoxy/ethoxy components of linking com-pounds known as silanes.The silane compound chosen for non-specific sensing is one that leaves the silica
surface with an opposite charge to the net charge on the adsorbate. Most proteinsacquire a negative charge at a biological pH (B7.4). To produce a positively chargedsurface we react the protruding hydroxyl groups with 3-aminopropyltriethoxysilane(APTES), since its amino terminus is protanated to NH3
+ as a consequence of thepKa of NH2 (B8). APTES is deposited from the vapor phase in a partial vacuum.32
After bringing the vacuum chamber to atmospheric pressure, the microspheres aretransferred to an oven at 120 1C, where the silane rug is cured (i.e. cross-linked). Thechemical progression is shown in Fig. 9.
Non-specific sensing of virus
For a preliminary test of our sensor, we non-specifically adsorbed BSA on itssurface. At sufficient concentration (4100 nM) it produced a Langmuir-likesaturation with a frequency shift consistent with eqn (24), based on the molecularweight of BSA (66.4 103 Da) and a maximum surface density built up by randomsequential adsorption.33 Although BSA is relatively small in comparison with a virusparticle, similar experiments using carboxylated polystyrene beads with diameters of100 nm (mass B3.5 108 Da) gave good agreement with eqn (24).For virus adsorption, we chose a virus that kills E. coli but is friendly to humans as
a model system for both non-specific and specific sensing. The RNA virus known asMS2 is icosahedral in shape, as is HIV, although it has a far smaller size with a
76 | Faraday Discuss., 2008, 137, 65–83 This journal is c The Royal Society of Chemistry 2007
diameter of only 23.6 nm and a mass of 3.6 106 Da. MS2 phage has a pI of 3.9,34
making it suitable at pH 7.4 to take on a negative charge.Virus stock was obtained from American Type Culture Collection (ATCC,
Manassas, VA). MS2 phage was propagated in E. coli K91 host and incubated onLB plates (courtesy of N.L. Goddard, Harvard University). After filtration, the viruswas resuspended in PBS and stored at 4 1C.Our experiment is begun by injecting 30 mL of MS2 solution [3 109 pfu (plaque
forming units)] into 1 mL of PBS buffer (pH = 7.4) in the sample cell of our non-specific sensing system. As a micro-stirring bar homogenizes the solution to aconcentration of 5 pM, all resonance dips shift toward longer wavelengths. Thedip trace represented in Fig. 10 by plotting the normalized shift RDl/l, shows theadsorption of virus in real time and is indicative of monolayer formation. We cantrack the density of adsorbed virus by inverting eqn (24),
s ¼ RDllðn2s n2mÞDa=e0
: ð26Þ
With appropriate values for the refractive indices of silica (ns = 1.452) and the buffer(ns = 1.32), and by calculating Da/e0 from eqn (23) (3.7 1018 cm3), we find thatthe surface density associated with the equilibrium shift in Fig. 10 is se = 2.6 1010
cm2. This layer is far from compact. In our previous experiments with protein,surface densities approached the maximum density for random sequential adsorp-tion, srsa,max.
33 This density is 55% of the inverse ‘‘foot print’’ area (srsa,max = 0.55sfp = 0.55 /(pa2) = 1.2 1011 cm2). The reason for the small surface density atequilibrium in Fig. 11 lies in the balance between adsorption and desorption rates.Although there was not enough incubated virus to make runs at higher concentra-tions, measurements made at lower concentration reveal that the equilibriumwavelength shift is in proportion to concentration [v] up to 5 pM (insert, Fig. 10).This may be understood from Langmuir’s isotherm. Here, the fraction of maximumsurface coverage at equilibrium ye = ka [v]/(ka [v] + kd), where ka is the adsorptionrate constant and kd is the desorption rate. For our equilibrium shift to beproportional to [v], ka[v] must be considerably less than kd, so that the Langmuirisotherm has the approximate form ye = ka[v]/kd. By making the reasonable
Fig. 9 Amino-silanization using APTES on cleaned microsphere support.
Faraday Discuss., 2008, 137, 65–83 | 77This journal is c The Royal Society of Chemistry 2007
assumption that ye C se/srsa,max, we estimate an upper limit for the equilibriumconstant Ke = ka/kd B1011 M1.So far, we have shown that we can detect the binding of virus particles to a
microsphere from the shift in wavelength of a whispering gallery mode and extractthe associated equilibrium constant. Our ultimate goal, specific sensing, will requirethe ability to follow the desorption process. This requires a microfluidic system andthe design of a surface that can be specific to MS2.Before discussing our microfluidic system, it should be pointed out that the mass
density sensitivity associated with the rms baseline signal in Fig. 10 is consistent withour calculation of sm,LOD in Fig. 7 for R = 200 mm; 0.2 ng cm2.
Micro-fluidic system for specific sensing
Specific sensing will be tested through the difference in desorption rates associatedwith different virus on a surface functionalized with antibody. This can reasonablybe done by utilizing a microfluidic flow system that incorporates the microsphereand a tapered optical fiber.Our specific sensing system is shown in Fig. 11. It consists of a tapered fiber bound
by UV adhesive to a glass slide as a foundation. Below this foundation is athermoelectric stage and above it is a polymer cap with multiple entry points. Thistransparent cap, formed by moulding poly-dimethyl siloxane (PDMS) in amicromachined master, is accesible to fluids, the microsphere, laser excitation andan optical detection port. The cross section of the microfluidic channel is 1.5 mm 2.5 mm and has a total volume of 100 mL.A fluidic system was designed to handle the various solutions used in our
experiments. This system was supplied by two syringe pumps that are directed bya custom LabVIEW driver program. Each pump is fitted with a 25 mL syringehaving 24000 steps of total travel (1 mL per step). The step rate is controlled by thedriver that delivers liquid over a range from 1 step per 20 d to 100 steps per 1 s. Atypical experiment is run at 38 mL min1. One pump is dedicated to the buffer usedfor washing in between each sample injection. The other is the sample pump thatpushes the contents of a 700 mL teflon sample loop into the fluidic channel. The loop
Fig. 10 Dip trace for non-specific MS2 adsorption for a 5 pM concentration. The insert showsthe equilibrium shift isotherm below 5 pM.
78 | Faraday Discuss., 2008, 137, 65–83 This journal is c The Royal Society of Chemistry 2007
is washed with buffer between each sample injection, ensuring that the syringe is freeof cross-sample contamination.
Surface modification: specific virus detection
Anti-MS2 (in PBS, pH 7.4, Tetracore) antibodies were covalently linked to themicrosphere using amine–carboxyl coupling chemistry (Fig. 12). Briefly, sphereswere cleaned by oxygen plasma for 4 min. Immediately after, spheres were immersedin 2% 3-(Triethoxysilyl)propylsuccinic anhydride in ethanol/acetic acid for 2 minthen rinsed with ethanol to yield anhydride groups on the silica. Spheres were driedat 115 1C for 20 min. After this, a sphere was coupled to fiber inside the flowcell andslightly basic buffer (pH 8.3) was introduced into the cell, which hydrolyzes theanhydride to create a carboxyl rug across the sphere’s surface (Fig. 13).The sphere was allowed to incubate in the flow cell for 45 min. The rest of the
assembly is followed by the dip trace in Fig. 13. Next, activation of carboxyl groupsby EDC/NHS provided for a semi-stable amine, highly-reactive ester surface. 200 mLof 0.4 M 1-ethyl-3-(3-dimethylaminopropyl)-carbodiimide (EDC) was mixed with
Fig. 11 Microfluidic system for sensing.
Fig. 12 Specific surface chemistry.
Faraday Discuss., 2008, 137, 65–83 | 79This journal is c The Royal Society of Chemistry 2007
200 mL 0.1 MN-hydroxysuccinimide (NHS) and injected into the flow channel. NHSesters react with amine groups on the antibody to form covalent links. Underconstant flow, the surface was allowed to react for 5 minutes. After rinsing with PBS,MS-2 antibodies were injected at a concentration of 620 nM and allowed to incubatefor 60 min with flow off. From the overall shift of 5 nm and the molecular weight ofthe antibody (155 000 Da), the surface density was estimated from eqn (26) to be1.1 1012 cm2, about 5 antibodies within an MS2 footprint. Unbound antibodieswere then washed away and the surface was blocked with 1 M ethanolamine (pH8.5). Remaining antibodies are covalently bound to the surface. After a thoroughrinse, surfaces were ready for specific virus detection. All steps involving flow wereperformed at a flow rate of 38 mL min1. The setup and microsphere surface are nowready for virus specificity detection.
Specific virus detection
In order to discriminate between different viruses, we designed a cycling scheme thatincluded another E. coli virus, Phix174, as a negative control. Phix174 is a DNAvirus of icosahedral shape and has a mass and diameter of 6.2 106 Da35 and28.4 nm, respectively. Its coat proteins contain epitopes different from the MS2virus, and therefore should not exhibit specific binding to our anchored anti-MS2.The experiment proceeds as follows. At a flow rate of 38 ml min1, 500 ml of MS2
phage at a final concentration of 5 pM was flowed through the microfluidic channeland then the pump was turned off. MS2 was allowed to bind to the surface for 5 min.We observed that all resonant dips shifted to longer wavelengths, indicatinginteraction between the modified surface and virus (top trace, Fig. 14). Just after,PBS was flowed into the channel for 10 minutes. We observed a resonance frequencyshift towards smaller wavelength, indicating that weakly-bound virus was present onour surface. However the signal did not return to the value of pre-injected MS2. Theresidual surface bound MS2 after this wash was calculated (eqn (26)) to be sv = 9 109 cm2. Once again, this surface density is far less than the maximum density forrandom sequential adsorption, even though there are an average of five antibodieswithin an MS2 footprint. Under the supposition that few antibodies are in a positionand orientation to be viable, a decision was made to lower the concentration and
Fig. 13 Dip trace following the preparation of a silica microsphere with antibody.
80 | Faraday Discuss., 2008, 137, 65–83 This journal is c The Royal Society of Chemistry 2007
repeat the experiment. This required an antibody-preserving regeneration step,which will be discussed later. The lower trace in Fig. 14 shows this second experimenton the same microsphere, at half the previous MS2 concentration. It should be notedthat although the buffer wash caused virus to be removed at the higher concentrationrun, at 2.5 pM there was no evidence of desorption. We conclude that oursupposition is correct; only a small fraction of the antibodies are viable for specificadsorption.The very useful regeneration step previously noted deserves some attention at this
point. It is accomplished by introducing 10 mM glycine into the flow channel(pH 2.0) and allowing the microsphere to bathe in this solution for 5 min. Theglycine solution competitively disrupts the electrostatic portion of theantibody–antigen interaction.36 During this time, the residual signal associated withspecifically bound virus is eliminated without eliminating the covalently boundantibody. To complete the regeneration step, PSB is flowed into the channel forB10 min. At this point, the microsphere is ready for reuse with another virus(e.g. the control Phix174).With the same microsphere in place, we next tested our sensor against Phix174
(Fig. 15). Phix174 was injected into the cell at 5 pM and allowed to bind as above.After injection, the frequency shifted toward longer wavelength, reachingequilibrium before the pump was turned off. About 100 seconds later PBS waspumped into the channel and the wavelength dropped toward the baseline, indicat-ing that Phix174 non-specifically binds to our surface. The MS2 trace from Fig. 14 isreproduced in Fig. 15 for comparison. This figure clearly shows that the WGMBtechnique can discriminate between the non-specific binding by Phix174 and specificbinding by MS2. The experiments were repeated several times with similar results.
Conclusions
By using perturbation ideas from microparticle photophysics, combined withbiochemical surface functionalization and microfluidics, we have found a meansfor specifically sensing a virus. The axial symmetry associated with a slightlyperturbed sphere allows for simple analytical equations that connect up wavelengthshifts with the polarizability and surface density of the adsorbed virus. By using
Fig. 14 MS2 virus experiment at 5 pM (upper) and after regeneration at 2.5 pM (lower).
Faraday Discuss., 2008, 137, 65–83 | 81This journal is c The Royal Society of Chemistry 2007
chemical regeneration, our microparticle-inspired real time sensing approach allowsus to follow virtually all aspects of the surface modification and viral sensing on thesame sphere in situ.Although our calculations looked in part at the question of single virion sensing,
our experiments concentrated on the demonstration of specific detection usinghigher surface densities. This is not a limitation of baseline noise. Rather, theproblem involves not being able currently to spatially localize adsorption solely tothe equator of the sphere. We are currently designing a photolythographic techniquethat will allow us to place antibodies only along the equator. Once implemented, ashorter wavelength DFB laser will be employed in order to test our single virioncalculations in Fig. 7. We expect the dip trace to contain a randomly-spacedstaircase. Based on the agreement between our surface saturation measurementsand theory (see the section titled ’’Non-specific sensing of virus’’), the height of eachstep should reveal the molecular weight of the adsorbate.We have merely scratched the surface in our use of the WGMB technique. Within
a flow cell there can be a multitude of resonant microcavities each functionalizedwith different antibodies for different viruses. One can do this while multiplexingboth the fiber and fluid channel. Other cross configurations will surely be imagined.
Acknowledgements
This research was supported by NSF through the Division of Bioengineering andEnvironmental Systems, Grant No. 0522668. We thank N. L. Goddard, HarvardUniversity, for incubating the MS2 virus used in our experiments.
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Fig. 15 Comparison between Phix174 and MS2 experiments on the same sphere.
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Faraday Discuss., 2008, 137, 65–83 | 83This journal is c The Royal Society of Chemistry 2007
Resonance fluctuations of a whispering gallery mode biosensorby particles undergoing Brownian motion
D. Keng, S. R. McAnanama, I. Teraoka, and S. Arnolda
MicroParticle PhotoPhysics Laboratory, Polytechnic University, Brooklyn, New York 11201
Received 31 July 2007; accepted 8 August 2007; published online 4 September 2007
There is an extant revolution in label-free biosensingbrought on by the use of whispering gallery mode WGMresonances. Nanoparticles in the vicinity of a resonator sen-sitively perturb its characteristics e.g., resonance wave-length. Already, resonance wavelength shift data have en-abled the label-free specific sensing of protein,1,2 DNA,3 andvirus,4 as well as the characterization of nanolayer growth5
and solvent refractive index changes.6,7 These sensing appli-cations have been implemented by simply measuring the dccomponent of the resonance wavelength shift signal. Herein,we show that the broadband “noise” on this signal providesphysical information not available from its dc component.Stochastic effects associated with molecules undergoingBrownian motion near the resonator surface are responsiblefor this noise. This observation allows this all-photonic sen-sor to enter a world that has been dominated by total internalreflection fluorescence correlation spectroscopy TIR-FCS,8
without the need for fluorescent labels. In what follows, wecharacterize the noise in resonance wavelength fluctuationsof a spherical microcavity bathed in a solution containingnanoparticles of viral size, and demonstrate that nanoparticlesizes may be estimated from the analysis of this noise.
Let us consider the situation depicted in Fig. 1a. Ananoparticle diameter d1–200 nm in an aqueous solu-tion just outside a spherical microresonator radius R50–500 m diffuses through the evanescent field of aWGM. The WGM is driven by coupling the microsphereevanescently to light guided through an optical fiber.9 Eachnanoparticle diffusing within the evanescent field near theequator of the microsphere influences the resonance wave-length as a result of polarization by the field.10 As the freespace wavelength of the laser driving the fiber is sweptacross the resonance, the WGM is revealed as a dip in thetransmitted intensity T through the fiber11 Fig. 1b. Theresonance wavelength at the center of this Lorentzian dip, r,fluctuates as a result of the interaction with this particle andothers in the surrounding solution. Temporal changes of theresonant wavelength are transduced and amplified by posi-tioning the laser wavelength at bias on one side at the maxi-
mum slope of the dip and recording the intensity, as shown inFig. 1b.
In previous studies, we followed the slow variation ofthe resonance dip position using a scanning approach torecord the fiber transmission spectrum.1 In this way, the dipposition was updated every 0.1 s. With the bias scheme inFig. 1, we can follow variations in the resonance wavelengthat a much faster pace, limited only by our data acquisitionsystem, which samples the transmitted intensity with 16 bitprecision at 200 kHz. The noise with Brownian particlespresent in the surrounding solution will be different in com-parison to the neat buffer, as shown in Figs. 1c and 1d.Since the noise is stochastic, it will be characterized by itsautocorrelation function ACF. Below, we describe someexperimental details.
The WGM biosensor consisted of a silica microsphere200 m radius coupled to a phase-matched silica optical
FIG. 1. Color online Measurement principle for transducing WGM reso-nance fluctuations: a Brownian particle passing through the evanescentfield of a WGM in a microsphere coupled to a fiber. b Resulting transmis-sion showing a fluctuating WGM resonance dip. c and d Recordedintensity traces at bias as a function of time t with d=37 nm and withoutBrownian particles, respectively.
fiber12 within a microfluidic cell molded from silicone, asshown in Fig. 2. A 1300 nm pigtailed distributed feedbacklaser was connected to the input end of the fiber, and itswavelength was controlled through the drive current.11
Noise associated with nanoparticles was first discernedwhile sensing bacterial virus. To understand the phenom-enon, we chose polystyrene particles having a carboxylatedsurface and mean diameters of 37, 103, and 219 nm Poly-sciences, Inc., as measured by dynamic light scatteringN4Plus, Coulter, as viral simulants.
After recording resonance fluctuations using a filteredphosphate buffered saline PBS solution pH=7.4 for 1 s,the ACF of the signal was computed. This procedure wasrepeated 50 times with each new ACF added to the previousones in order to form an average. Following this, particles ofa given size suspended in PBS were injected into the mi-crofluidic channel Fig. 2 using a digitally controlled sy-ringe pump, and the resonance wavelength was seen to shifttoward a longer wavelength, indicative of adsorption. Whenthe wavelength shift stabilized, the ACF of the signal wascalculated as in the case of the buffer. Then, the microfluidicchannel was washed with the buffer solution using a seconddigitally controlled pump Fig. 2. As the particles were re-moved from the solution surrounding the microsphere, theresonance wavelength changed only slightly, indicative ofstrong nonspecific binding. The rms value of the resonancewavelength fluctuations essentially returned to its value be-fore the particles were injected into the channel, indicatingthat the observed fluctuations were principally associatedwith particles diffusing in solution. Experiments for eachnew particle size utilized a new microsphere, but otherwisefollowed the same procedure.
The initial decay in the normalized ACF, c /c0, forthe three particle sizes is shown in Fig. 3 as a function ofdelay time for the first 1 ms. Each ACF is seen to falllinearly with time following the empirical equationc /c0=1− for 1 The inset shows that the decayrate is approximately proportional to the inverse diameterof the particles: /d, with =13.1103 nm/s.
The results in Fig. 3 may be understood from the Brown-ian motion of particles in the evanescent field near the sur-face of the microsphere. A given particle at position r causes
a resonance wavelength shift r as a reaction to beingpolarized by the evanescent field Er , t.10 The shift is pro-portional to the scalar product of the induced dipole and theelectric field, and is consequently proportional to the squaremodulus of the field Er2. The accumulated resonancewavelength shift from many particles is most easily ac-counted for by utilizing a number density r , t and per-forming a simple sum,
rt r,tEr2dV . 1
Before evaluating Eq. 1 it is useful to consider the charac-teristic lengths of our system. The “ribbon” of intensity nearthe equator Fig. 1 has three characteristic lengths: the cir-cumference 600 m, the width along a meridian 3m, and the evanescent intensity length L0.2 m. Con-sidering that the time to diffuse through a given length isproportional to its square, the short time behavior demon-strated in Fig. 3 should be overwhelmingly controlled by L.This allows us to pare down the integral in Eq. 1 to essen-tially one dimension,
FIG. 2. Color online Microfluidic system incorporating a microsphere resonator and a coupling fiber.
FIG. 3. Color online Normalized autocorrelation of resonance wavelengthfluctuations for several particle diameters d. Each follows c /c0=1− ,for 1 Inset: plot of vs 1/d.
103902-2 Keng et al. Appl. Phys. Lett. 91, 103902 2007
Downloaded 04 Jan 2008 to 128.122.149.42. Redistribution subject to AIP license or copyright; see http://apl.aip.org/apl/copyright.jsp
rt ,texp− /Ld , 2
where is the distance from the surface. The normalizedACF is then
cc0
=rr0
r02
= 0
d0
d,,0exp− + /L .
3
Fortunately, this integral has been worked out for a self-similar problem in TIR-FCS.8 It is the problem of fluores-cence fluctuations from particles diffusing in the evanescentfield at the back of a prism. The solution involves derivingthe density autocorrelation , ,0 from the diffu-sion equation under a prescribed boundary condition, andcarrying out the integration. For a reflecting boundary, con-sistent with having saturated the surface with particles hav-ing the same charge as those diffusing, the solution is13
cc0
= 1 − 2ReexpReerfcRe1/2 + 2Re
1/2
,
4
where Re=D /L2, with D being the diffusion coefficient. Forshort times 1/Re, c /c0=1−Re allowing us toidentify our experimental with Re. The approximate pro-portionality found between and 1/d would also be ex-pected based on bulk diffusion for which D follows theStokes-Einstein S-E relation D=kBT / 3 d, where kBTis the thermal energy and the solvent viscosity. Theassumption of S-E diffusion also allows us to calculate ,=kBT / 3 L2, from which we can estimate the evanes-cent field length without using optics; L= kBT / 3 1/2.Using our experimental value for =13.1103 nm/s, weextract L=193 nm. Optical calculations based on a micro-sphere of 200 m in radius with a refractive index for silicaof 1.452 and water of 1.32 for the first order radial mode14
gives L=188 nm, in good agreement with the estimate pro-duced by comparing fluctuation theory with experiment.
Although S-E diffusion is a good approximation for de-scribing our experimental results, it is wanting. This is best
seen by inverting our previous discussion and asking howaccurately we can determine nanoparticle diameters from thesimple S-E based equation,
d = kBT
3 L2 1
. 5
With L taken as before to be 188 nm, the diameters arrived atfrom Eq. 5 for our three standard diameters of 37, 103, and219 nm are 39, 111, and 309 nm, respectively. Here, we seegood agreement for the smallest size and a progressive de-viation as the nanoparticle size is increased. This is likelydue to hydrodynamic effects near the phase boundary.13 Dif-fusion is expected to slow as one approaches an interface,and this effect increases with particle size.15
This letter should leave little doubt concerning the roleof Brownian motion in the resonance wavelength fluctua-tions of a WGM. It may be considered a harbinger for usingthe WGM biosensor for studying the dynamics of nanopar-ticles near interfaces.
This research was supported by NSF through Division ofBioengineering and Environmental Systems Grant No.0522668. The authors thank Steve Holler of Novawave Tech-nologies Inc. and Ralph v. Baltz of Universität Karlsruhe forvaluable discussions.
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Detection of Protein Orientation on the Silica Microsphere Surface UsingTransverse Electric/Transverse Magnetic Whispering Gallery Modes
Mayumi Noto, David Keng, Iwao Teraoka, and Stephen ArnoldMicroparticle Photophysics Laboratory, Polytechnic University, Brooklyn, New York 11201
ABSTRACT The state of adsorbed protein molecules can be examined by comparing the shifts in a narrow line resonancewavelength of transverse electric (TE) and transverse magnetic (TM) whispering gallery modes (WGM) when the moleculesadsorb onto a transparent microsphere that houses WGM. In adsorption of bovine serum albumin (BSA) onto an aminopropyl-modified silica microsphere, the TM/TE shift ratio indicated highly anisotropic polarizability of BSA in the direction normal to thesurface, most likely ascribed to anchoring the heart-shaped protein molecule by one of its tips. The polarization-dependent res-onance shift was confirmed when the surrounding refractive index was uniformly changed by adding salt, which would simulateadsorption of large objects.
INTRODUCTION
The quantity and quality of protein adsorbed on a surface is
of a great concern (1–4). The amount of the surface-bound
protein can be evaluated by various methods (2–11). How-
ever, methods to find the state of the adsorbed molecules are
not well established, except that submolecular information
can be obtained using spectroscopic methods (8–10). There
are controversies about the state and orientation of adsorbed
molecules, even for often studied proteins such as serum
albumin (2,4,11). Their conformation may depend on the
surface—whether it is hydrophobic or ionic (positively or
negatively charged)—and on the pH of the immersing aque-
ous phase. This article proposes using resonance shifts of
photonic whispering gallery modes (WGM) as a method to
determine the state of adsorbed protein.
A transparent microsphere can accommodate WGM in the
vicinity of the sphere surface. The light propagates near the
curved surface by total internal reflection. Resonance is
achieved when the light path closes upon itself in phase after
one cycle. If the diameter of the sphere is sufficiently large
compared with the wavelength, the resonance can have a nar-
row width. The Q value of a silica microsphere in water at a
1.3-mm wavelength can be as large as 2 3 106 (12). A much
greater Q value, exceeding 108, is reported for a toroidal reso-
nator at 680 nm (13).
In each reflection along the circular path of WGM, the
light seeps into the surroundings as an evanescent wave. The
wavelength of the sharp resonance is sensitive to small changes
in dielectric property in the immediate neighborhood of the
transparent microsphere (14). The changes include adsorp-
tion of molecules onto the microsphere and a change of re-
fractive index (RI) in the surrounding medium. The shift of
the wavelength upon adsorption of biomolecules onto the
microsphere has been heralded as the most sensitive detector
ever made possible without the necessity for fluorescent label-
ing (12,15–18). Detection of a single protein molecule is
considered within reach (15). Recent prediction (19) and dem-
onstration (20) of enhanced sensitivity by a high RI coating
has paved the way for the difficult detection. The sensor’s
capability is not limited to estimating the surface density of
adsorbed molecules. Independent detection of the resonance
shifts for two polarization modes—transverse electric (TE) and
transverse magnetic (TM)—is expected to allow us to esti-
mate the orientation of adsorbed anisotropic molecules (21).
Each WGM is specified by l, m, n, and polarization (22). lrepresents the number of waves in a circular orbit, m (¼ l,l 1 1, . . . , l) is the azimuthal index, and n is equal to the
number of peaks in the radial function of the electric field
intensity, thus specifying the radial mode. The polarization is
either TE or TM. The wavelength at resonance is determined
by l, n, and polarization. In a perfect spherical resonator,
modes of different m are degenerate. The shift of resonance
wavelength in response to the environmental changes depends
also on l, n, and polarization (23). It was recently demonstrated
that the observed shifts of TE modes due to RI changes in the
surroundings were in agreement with the shifts calculated
using the indices evaluated for the microsphere used (24).
More than a decade ago, Folan distinguished TE and TM
shifts of WGM in a small polystyrene sphere levitated elec-
trodynamically in air (25). Folan examined the change in the
scattering spectrum as water condensed onto the polymer
sphere for the two polarizations, but the difference between
the two shifts was insignificant within experimental error.
In this report, we use side coupling of a core-exposed single-
mode fiber to induce both TE and TM polarizations in a silica
microsphere and measure the wavelength shifts when proteins
are added to the surrounding fluid to adsorb onto the sphere
surface. We find that the shifts are different for TE and TM
and the ratio of the two shifts provides information on the state
of adsorbed protein. We confirmed the polarization-sensitive
Submitted December 15, 2006, and accepted for publication February 15,
2007.
Address reprint requests to Iwao Teraoka, E-mail: [email protected].
Mayumi Noto’s present address is Nantero Inc., Woburn, MA 01801.
The other parts of the measurement system are similar to those described
earlier (18). For this study, the laser wavelength, l, was scanned at 10 Hz by
changing the laser drive current, i, linearly with time. A sawtooth function
generator was used for that purpose. The scan range was ;0.2 nm. The
relationship between l and i was evaluated using an interferometer (Agilent,
Santa Clara, CA; HP3325A). In each scan, the laser intensity and wave-
length increase almost linearly with time, and the two increases are nearly
parallel to each other. When a microsphere is placed in contact with the core-
exposed section of the fiber, destructive interference by the WGM causes
dips in the light intensity at the photodetector. Each dip represents a WGM
of a unique set of indices (l, m, n, polarization).
RESULTS AND DISCUSSION
TE and TM spectra
In each experiment, the position of a microsphere relative to
the fiber was adjusted to produce dips of reasonable depths in
the wavelength scan of the light intensity through the fiber.
Examples of the TE and TM spectra of the photodiode signal
when the DFB laser was scanned by a current sweep, dis-
played in Fig. 3, are similar. Each spectrum has a period of
;0.042 nm, ascribed to splitting of the degenerate azimuthal
modes (m) by a spheroidal shape of the microsphere; Lai
et al. predicted polarization-independent splitting by distor-
tion of the meridional cross section of the microspheroid (35).
There is a major dip and several minor dips in each period.
The major dips are for n ¼ 1. Our scan range of ;0.2 nm
sees just a part of a cluster of the dips having the same l but
different values of m. The minor dips are ascribed to higher
order radial modes (n ¼ 2, 3; l may be different) and a tail
portion of adjacent clusters with n ¼ 1 (l is different by 1).
Adsorption of BSA
One of the microspheres (radius a ¼ 167–203 mm) whose
surface was modified with aminopropylsilane was immersed
in a 980 mL solution of PBS at pH 7.4 that was constantly
stirred and held at 25C. For each adsorption study, a fresh
microsphere was used. Resonance dips in the fiber trans-
mission spectrum were traced as a 20 mL solution containing
BSA (pI ¼ 4.8) was added. The final concentration, 1 mmol/
L, is sufficiently low to make the resonance shift due to the
surroundings’ RI change negligible compared with the shift
due to adsorption but sufficiently high to cause the highest
possible surface coverage for this pH and surface (18). We
expect that the surface coverage is similar for all the mi-
crospheres. Fig. 4 shows typical changes of the TE and TM
spectra. A part of the scan range is zoomed for clarity. The
pair of experiments in Fig. 4 was selected so that the micro-
sphere used for TM is slightly larger than the one used for
TE. The intensity spectrum undergoes a red shift without
changing the overall pattern. In either TE or TM mode, deep
and shallow dips shift nearly equally. The TM shifts are
greater than the TE shifts, although the sphere radius, a, is
greater for TM; the shift is reciprocally proportional to a.
We did two measurements for TE and three for TM using
spheres of different radii. To eliminate the radius dependence
of the fractional shift, we compare the reduced fractional shift,
FIGURE 2 Optical part of microsphere WGM resonance shift measure-
ment system that allows change of the polarization. A zoomed view of the
fiber-microsphere coupling is also shown.
FIGURE 3 Light intensity through the fiber in the wavelength scan for TE
and TM modes. The microsphere of 195-mm radius was immersed in water.
FIGURE 4 Light intensity spectrum before and after injection of BSA.
The radii of the microspheres used for TE and TM modes are 167 mm and
186 mm, respectively. The arrows indicate the shifts for some dips.
Protein Orientation on Silica Surface 4469
Biophysical Journal 92(12) 4466–4472
k0aDl/l0, where k0 ¼ 2p/l0 (k0a is called a size parameter).
From Eq. 2, we find that k0aDl/l0 is proportional to the pro-
duct of the number density of BSA on the surface and the
polarizability. A similar relationship exists for the TM modes.
In our TE mode experiments, 103k0aDl/l0 is 7.7 6 0.1
(mean 6 SD), regardless of whether the dip is deep or
shallow. For the TM modes, the reduced shift is 10.3 6 0.2.
The shift’s independence of the radial mode agrees with the
theoretical prediction for adsorption of small particles (21).
The ratio of the TM shift to the TE shift is 1.34, which is
close to the ratios for standing rods and standing disks in
Table 1. It is known that the BSA molecule is heart-shaped at
pH¼ 7.4 (36). The result of our TE-TM shift study indicates
adsorption of the heart-shaped molecule by one of its tips. At
pH ¼ 7.4, the protein surface has a high density of N1H3
and COO (4), and the microsphere surface is dense with
N1H3. It is not surprising that the protein anchors to the
aminopropyl surface by facing one of the sections covered
predominantly with COO to the sphere surface. A study of
protease digestion of BSA adsorbed on an unmodified silica
surface at the same pH indicates a similar geometry (4), al-
though sections predominantly covered with N1H3 would
face to SiO on the silica surface in the latter experiment.
The volume of a BSA molecule, Vp, is estimated from the
molecular mass (1.10 3 1019 g) and the specific volume of
BSA, 0.734 g/cm3 (37), as 81.0 nm3. To estimate the surface
coverage of BSA from our experimental data, we use below
a picture of a standing disk with radius R and height H. First,
we note that the above Vp can be equated to a disk of R¼ 4.1
nm, H ¼ 1.5 nm, where the aspect ratio is close to the one
proposed (38) in a phosphorescence study as consistent with
x-ray crystallographic data (36). Then, from Table 1, we
obtain att/e0 as 46.1 nm3, where er2 ¼ 1.322 and erp ¼ 1.552
were used. The surface density of the BSA molecules can be
estimated using the formula
Np
4pa2 ¼ k0a
DlTE
l0
3er1 er2
k0a=e0
: (5)
Since k0 ¼ 2p/l0 ¼ 4.796 mm1, er1 ¼ 1.4522, and
k0a(Dl/l0)TE ¼ 7.7 3 103 in our measurement, Np=ð4pa2Þis estimated as 1.3 3 104 mm3. Therefore, the area fraction
F of the projection of the rectangular cross section 2RH onto
the surface is estimated as F ¼ ½Np=ð4pa2Þ2RH ¼ 0:15.
The latter value is ,1/3 of the highest possible value of F by
spheres, 0.55 (30,32–34).
We could assume another geometry for the BSA mole-
cule, for instance, a standing rod. The molecular dimension
of the rod that gives Vp ¼ 81.0 nm3 is R ¼ 1.9 nm and H ¼7.1 nm, for example. Then, att/e0¼ 44.9 nm3, virtually iden-
tical to the one we obtained for the disk model.
As discussed earlier, F ¼ 0.15 is too low for the dipoles
induced in nearby particles to affect the estimate of F or the
TM/TE shift ratio. Therefore, we do not need to change our
discussion for the surface density and orientation of the ad-
sorbed BSA molecules.
Refractive index change of the surroundings
We tested our polarization-sensitive WGM sensor for a
uniform change of relative permittivity, Dn22, in the sur-
roundings. The change mimics adsorption of particles with a
linear dimension greater than the penetration depth of the
evanescent field. The shift will be greater for the mode with a
greater n, since its evanescent field penetrates deeper into the
surroundings. Numerical calculation of the resonance con-
ditions (23) gives the reduced response, k0aDl/(l0Dn22), of
the TE mode in a microsphere with a ¼ 174 mm at l0 ¼1.312 mm as 2.507 and 2.755 for n ¼ 1 and 2, respectively.
The reduced response of the TM mode will be 2.950 and
3.252 for n ¼ 1 and 2, respectively. The reduced response is
insensitive to a: At a ¼ 196 mm, the response for n ¼ 1 is
;0.9% less than it is at a ¼ 174 mm.
In adding NaCl to the surroundings three times, the shifts
exhibited a complicated pattern, as each radial mode had a
different shift. Two parts of Fig. 5 show 103k0aDl/l0 for TE
and TM modes as a function of NaCl concentration c in PBS
buffer surrounding a plain silica microsphere (a ¼ 174–196
mm). The data were compiled from the shifts of different dips
in a few measurements. Attention was paid not to include
broad dips that apparently consisted of two or more dips at
any stage of NaCl addition; the shape of these dips changed
as more NaCl was introduced.
In Fig. 5, the shift for each dip in successive NaCl addition
follows a straight line through the origin. The slope of the
line is slightly different for each dip. The variations are
ascribed to uncertainties in c and a and fluctuations in the
resonance position. For the TE mode (Fig. 5 a), most of the
data run along the lower solid line, ascribed to the n ¼1 modes. The line gives 103k0aDl/(l0Dc)¼ 0.990 L/g. With
k0aDl/l0¼ 2.507 3 2n2Dn2, we obtain dn/dc¼ 0.150 mL/g,
FIGURE 5 Fractional wavelength shift times the size parameter for (a) TE
and (b) TM modes when a 20 mL, 0.0163 g/mL solution of NaCl is incre-
mentally added to a buffer surrounding a silica microsphere. The lines are
the best fit for two groups of data.
4470 Noto et al.
Biophysical Journal 92(12) 4466–4472
slightly less than 0.171 mL/g, the value reported for l ¼ 589
nm at 25C (39). We believe that the difference is mostly due
to RI dispersion. Likewise, most of the data run along the
lower solid line in the plot for TM modes (Fig. 5 b). The ratio
of the TM slope to the TE slope is 1.19, close to the theo-
retical value of 1.18.
In both of TE and TM plots, two sets of data are away
from those for n ¼ 1. They are ascribed to the n ¼ 2 modes.
The ratio of k0aDl/(l0Dc) for these sets to that for n ¼ 1 is
1.11 in TE and TM. The ratio compares favorably with the
theoretical values.
CONCLUSIONS
We have demonstrated a simple method to excite TE and TM
modes separately in a microsphere and observe the shifts of
resonance lines when protein molecules adsorb at high
densities. Studies of protein adsorption on different surface
chemistries in different pH at different surface coverages will
help us understand the state of protein on the surface. In
particular, studies at low coverages will be important, as the
TM/TE shift ratio allows us to estimate the polarizability
anisotropy ratio of isolated molecules. The studies will be
facilitated by simultaneous observation of the TE and TM
shifts for a common microsphere which can be accomplished
by feeding the light linearly polarized at ;45 from the TE
direction, splitting the light by the polarizations right before
the photodetector, and measuring the fiber transmission
spectra using two photodiodes. The high sensitivity of the
WGM sensor will allow such measurements at extremely
low coverages of small molecules.
We thank L. Folan for helpful discussion.
This work was supported by the National Science Foundation through
BES0522668.
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APPLIED PHYSICS LETTERS 87, 223901 2005
Molecular weight dependence of a whispering gallery mode biosensorM. Noto, M. Khoshsima, D. Keng, I. Teraoka, V. Kolchenko, and S. Arnolda
Microparticle Photophysics Lab(MP3L), Polytechnic University, Brooklyn, New York 11201
Received 6 July 2005; accepted 19 October 2005; published online 23 November 2005
Label-free detection of biomolecules has become an ac-tive area of research. New sensing methods have been soughtto enhance the sensitivity and facilitate miniaturization ofdevices. Recent notable approaches are the direct electricaldetection of biomolecules using field-effect transistorsFET.1–4 Single viral particle detection has been demon-strated with a silicon nanowire FET.2 Although FET sensorsallow scalable detection of biomolecules in real time, thesignal transduction relies on charges carried on analyte mol-ecules. The sensor signal alone does not provide the infor-mation on properties such as molecular weight M.
The use of a high-Q optical resonator for biomoleculardetection has been demonstrated for protein adsorption anddeoxyribonucleic acid hybridization with unprecedentedsensitivity.5,6 Based on first-order perturbation theory, wefind that a resonance frequency shift is proportional to theexcess polarizability of an analyte molecule and its surfacedensity.7 Since polarizability scales with the volume of amolecule,8 a resonance frequency shift is expected to containmolecular size information i.e., molecular weight.
In what follows, we investigate the M dependence of aresonance frequency shift. We test five protein samples from5000 to 700 000 g/mol, and measure the shift for proteinmonolayer formation on the microparticle surface. We thenprovide a quantitative analysis of a protein layer to addressthe M dependence.
Our biosenser consists of a distributed feedback laserwith a nominal wavelength of 760 nm Princeton Light-wave as the light source, a sample cell, and a Si detector818SL, Newport to monitor the transmitted light intensityFig. 1. The setup is similar to the one reported earlier,6 butwe modified the sample cell and improved on the tempera-ture control and the solution mixing. The new sample cell isfashioned from a disposable polystyrene cuvette cut to 1.5cm height. A single-mode optical fiber 780 HP, Nufern ispassed through the cuvette and secured with epoxy resin. Thesample cell is placed on a modified laser mount, whose tem-perature is maintained at 25 °C by a laser controller LDC-3742B, ILX Lightwave.
To stimulate a resonance in a microparticle also knownas whispering gallery mode WGM, a section of the optical
0003-6951/2005/8722/223901/3/$22.50 87, 22390Downloaded 11 Dec 2005 to 128.122.88.167. Redistribution subject to
fiber is acid eroded to a final diameter 4 m in the samplecell, thus exposing the evanescent filed. We fabricate a silicamicroparticle equatorial radius R200 m of an oblateshape with the eccentricity of 0.05 by melting a single-mode optical fiber in a butane/nitrous oxide flame. The mi-croparticle is positioned to make contact with the etched sec-tion of the fiber. Optical resonances in the microparticle aredetected as dips in the transmitted light intensity when thewavelength is scanned repeatedly at 2 Hz between 24 and 32mA using a saw-tooth-shaped function 3325 A, HewlettPackard. The output wavelength has a drive current imA dependence of nm=761.0185+0.0043i+1.010−5i2. The LABVIEW program records the transmissionspectrum and tracks a resonant dip by detecting its positionwith a parabolic minimum fit. A typical quality factor of aresonance in water is 4106.
We selected five water-soluble proteins with M rangingfrom 5000 to 700 000 g/mol: Insulin I5500, Sigma, M=5800, -lactalbumin LA, L6010, Sigma, M =14 300, bo-
FIG. 1. a Experimental setup. b Close-up view of the optical fiber and
223901-2 Noto et al. Appl. Phys. Lett. 87, 223901 2005
vine serum albumin BSA A2153, Sigma, M =66 000,-globulin 191 478, ICN Biomedical, M =152 000, andthyroglobulin T1001, Sigma, M =670 000. All protein stocksolutions were prepared by dissolving protein in 10 mMphosphate buffered saline PBS pH 7.4 except -globulin,which was dissolved in 50 mM PBS at pH 6.
Microparticle surfaces are chemically modified to en-hance protein adsorption onto the surfaces. Amine surface9 isused for all the proteins except -globulin. Carboxylsurface10 is used for the latter.
To measure a resonance shift at monolayer saturation foreach protein sample, we first carry out adsorption isothermexperiments to find the protein concentration necessary formonolayer formation on the microparticle surface.
The sample cell is filled with 980 l PBS, and a freshlymodified microparticle is mounted on the xyz stage and al-lowed to thermally equilibrate with the sample cell solution.20 l of a protein stock solution is injected and the adsorp-tion is monitored by following the resonance dip position.The measurement is carried out under constant mixing and isterminated when the dip position no longer changes. LA,BSA, and thyroglobulin achieve monolayer saturation at0.2 M Fig. 2, whereas insulin and -globulin require 0.5nM and 4.3 M, respectively. The adsorption isotherm fol-lows a Langumir-type pattern, indicating that protein layer isno more than one layer.
Using the monolayer concentrations determined from theisotherm experiments, a wavelength shift is measured threetimes for each protein sample. A fractional wavelength shift /R at monolayer saturation is plotted at logarithmicscale in Fig. 3. The slope is 0.31±0.02. The inset confirmsthat the fractional shift is proportional to M1/3 and the errorbars indicate the spread of data from the three measurements.The linear fit of the M1/3 graph has the slope 0.060±0.003.
Having confirmed the M dependency of /, we pro-ceed with quantitative analysis of protein layers. We start ouranalysis by obtaining the analytic expression for a resonanceshift for a protein layer formation. A layer perturbation cor-responds to adding the dielectric excess nl
2−nm2 of thickness t
to the microparticle surface, where nl and nm are the refrac-tive indices of the layer and the medium, respectively. Fromthe first-order perturbation theory, the fractional wavelength
FIG. 2. Adsorption isotherm of LA, BSA, and thyroglobulin.The dotted lines are a guide for the eyes.
shift isDownloaded 11 Dec 2005 to 128.122.88.167. Redistribution subject to
=
nl2 − nm
2 ns
2 − nm2
t
RL
t1 − exp− t/L , 1
where L is the evanescent field length given by L= /4nef f
2 −nm2 −1/2 , ns is the refractive index of the micropar-
ticle, and neff is the effective index for propagation within theWGM.11 In the limit of a thin layer t /L1, Eq. 1 can beapproximated and we take an effective medium approach toaccount for inhomogeneity of the layer. We obtain
=
fnp2 − nm
2 ns
2 − nm2
t
R, 2
where f is the volume fraction of protein and np is proteinrefractive index.
LA, -lactalbumin, is known to assume a sphericalshape and its adsorption kinetics is successfully modeled bytreating LA as a sphere.12 We treat LA as a model protein.The volume of a protein molecule can be written asMNAp−1, where NA is Avogadro’s number and p is massdensity. Relating this expression to the volume of a sphere,4 /3r3, we find the radius r in terms of M :r= 3M /4NAp1/3. The thickness of a layer packed withspheres is 2r, and Eq. 2 becomes
=
fnp2 − nm
2 ns
2 − nm2
2
R 3
41/3 M
NAp1/3
. 3
Molecular weight dependence is evident in Eq. 3. We com-pare Eq. 3 to our empirical result /R=0.060M1/3.Using p1.37 g/cm3, which is practically constant formost proteins,13 np=1.50,14 nm=1.33, and ns=1.46, we findthe f value for the LA layer is 0.34.
Random packing of spheres onto a planar surfaceachieves lower surface coverage than hexagonal close pack-ing. The simulation study by Torquato15 estimates that themaximum fractional area coverage for the random packing is0.55. Thus, the volume fraction is 0.367. Our LA layer isclose to the theoretical limit.
Although all of our candidate proteins are termed12
FIG. 3. Resonance wavelength shifts against M at logarithmic scale.Insulin, LA, BSA, -globulin, and thyroglobulin. Theline was drawn manually to fit the data points. Inset: Linear plot of /*R against M1/3.
“globular”, LA has been characterized as being spherical. AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp
223901-3 Noto et al. Appl. Phys. Lett. 87, 223901 2005
The others vary in shape. It appears from Fig. 3 that theWGM sensor is relatively insensitive to the shape morphol-ogy. The WGM sensor started out as a means for biomolecu-lar detection, yet it now appears that one can make estimatesof protein size.
Research at Polytechnic was supported by a NSF grantNo. BES-0522668. The authors thank Frank Vollmer andSteve Holler for valuable discussions.
1W. U. Wang, C. Chen, K. Lin, Y. Fang, and C. M. Lieber, Proc. Natl.Acad. Sci. U.S.A. 102, 3208 2005.
2F. Patolsky, G. Zheng, O. Hayden, M. Lakadamyali, X. Zhuang, and C. M.Lieber, Proc. Natl. Acad. Sci. U.S.A. 101, 14017 2004.
3J. Fritz, E. B. Cooper, S. Gaudet, P. K. Sorger, and S. R. Manalis, Proc.Natl. Acad. Sci. U.S.A. 99, 14142 2002.
4R. J. Chen, S. Bangsaruntip, K. A. Drouvalakis, N. W. S. Kam, M. Shim,Y. Li, W. Kim, P. J. Utz, and H. Dai, Proc. Natl. Acad. Sci. U.S.A. 100,
4984 2003.
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5F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, and S.Arnold, Appl. Phys. Lett. 80, 4057 2002.
6F. Vollmer, S. Arnold, D. Braun, I. Teraoka, and A. Libchaber, Biophys. J.85, 1974 2003.
7S. Arnold, M. Khoshsima, I. Teraoka, S. Holler, and F. Vollmer, Opt. Lett.28, 272 2003.
8F. Fröhlich, Theory of Dielectrics Oxford University Press, London,1958, p. 28.
9N. Zammatteo, L. Jeanmart, S. Hamels, S. Courtois, P. Louette, L. Hevesi,and J. Remacle, Anal. Biochem. 280, 143 2003.
10Amine-modified microparticles are treated with 0.1 M succinic anhydridein N,N-dimethyl formamide for 15 min, rinsed with the solvent and etha-nol, and dried in the oven for at least 10 min at 70 °C.
11M. Noto, F. Vollmer, D. Keng, I. Teraoka, and S. Arnold, Opt. Lett. 30, 12005.
12A. P. Minton, Biophys. J. 76, 176 1999.13C. R. Cantor and P. R. Schimmel, Biophysical Chemistry Part II W.H.
Freeman and Company, New York, 1980, p. 554.14P. A. Cuypers, W. T. Hermans, and H. C. Hemker, Biochemistry 84, 56
1978.15
S. Torquato, Phys. Rev. Lett. 74, 2156 1995.
AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp
It is common in optics to create nanoscopic dielectriclayers from inorganic insulators, semiconductors, andmetals; however, as biophotonics1 looms more strongly,soft condensed biofunctional layers formed at anaqueous–solid interface and made of DNA, protein,lipids, and hydrogels are gaining strong appeal. Thisappeal is being driven by the need for biosensorsfor clinical and military use and for investigationof biomolecular interactions as they relate to drugdiscovery. Although techniques outside of optics,such as neutron ref lection, have been used to gaugethe thickness of these layers, new methods to monitorthe formation of such layers and to characterize themin a noninvasive manner are greatly needed. Weshow in what follows that wavelength-multiplexingexperiments on microspherical optical cavities canfollow the growth, gauge the thickness, and determinethe optical dielectric constant for adsorbed layers.
Our experimental approach is driven by the pre-dicted theoretical effect that a nanoscopic layer has onthe shifts of whispering-gallery modes (WGMs) in amicrosphere. In particular, the ratio of the shifts be-tween resonances stimulated at separated wavelengthscan be used to determine the thickness of a layer. Inaddition, the dielectric constant of the layer can beevaluated by use of this thickness and the shift at ei-ther wavelength. The theoretical approach we employhere is distinct from recent work2 on individual dipoleperturbations, in which the sensitivity of such a sys-tem for the detection of single biomolecular adsorptionevents was estimated. Although the latter theory hasbeen successfully applied to sensitivity issues associ-ated with the identification of mismatches in DNA,3
for the current work our interest is in the perturba-tions by a dielectric layer.
In what follows we first outline our perturbationtheory. Our approach will be to turn the microsphereperturbation problem into a quantum analog4 and per-turb the analog potential by adding a layer. Thenwe present experiments that test this theory. Finallywe attempt to determine the thickness and refractive-index perturbation for a thin hydrogel layer.
Although the full theory will appear elsewhere,5
here we outline its basic components. Our approach
0146-9592/05/050510-03$15.00/0
resembles first-order perturbation theory in quantummechanics. We concentrate on TE modes. Represent-ing the electric f ield in terms of a scalar functionE LC, where L is a dimensionless angular momen-tum operator, allows us to easily reduce the problemof solving the vector wave equation to the solution ofa Schrödinger-like equation for the radial part of C,Cr.6 The effective energy Eeff for this quantum ana-log is the square of the free-space wave vector Eeff k2
0 ,and the effective potential Veff k2
01 2 n2 1
ll 1 1r2, where n is the radial refractive-indexprofile and l is the angular momentum quantumnumber of a particular mode. A layer perturbationcorresponds to changing n2 from the surface out to athickness t by dn2. The f irst-order perturbation is
dEeff crjdVeffjcr , (1)
where cr is constructed from appropriate quasi-normalized functions.7 After substituting for themajor components in expression (1) we find that thefractional perturbation in effective energy is
dk20
k20
2
Ω2tR
∑dn2
n2s 2 n2
m
∏æ ΩLt
1 2 exp2tLæ
, (2)
where ns and nm are the refractive indices of the sphere(silica, 1.47) and its environment (water, 1.33), respec-tively; R is the sphere radius; and L is the evanes-cent f ield length, with L l4p n2
eff 2 n2m212. The
fractional wavelength shift dll is related to dk20k2
0through dll 212 dk2
0k20, where neff is the ef-
fective index for propagation within the WGM. Sinceour sphere has an 200-mm radius and is much largerthan either of the laser wavelengths, neff varies by only1% between radial modes8 and will be approximatedby its grazing incidence value ns. Equation (2) mayseem awkward; however, it has a particularly simplestructure when one considers that the principal wave-length dependence is contained within the evanescentfield length in the rightmost factor on the right-handside. By a judicious choice of the wavelength regionsto be used, the leftmost factor on the right-hand side
can be considered relatively constant. Consequently,by taking a ratio of the fractional shift at one wave-length l1 to that at a longer wavelength l2, we arrive ata particularly simple expression that provides the de-sign principle for our surface analysis approach. Thisratio S is
S
µdl
l
∂1µ
dl
l
∂2
L11 2 exp2tL1L21 2 exp2tL2
. (3)
For an ultrathin layer (i.e., tL1, tL2 ,, 1), Sapproaches 1, whereas for a thick layer (i.e.,tL1, tL2 .. 1), S approaches L1L2, which with nefftaken constant is just l1l2. For our experimentsthis ratio is 760 nm1310 nm 0.58. For ourchosen wavelengths, S falls off in an approximateexponential fashion in between the two extreme caseswith a characteristic length of tc 192 mm [i.e.,S L1L2 1 1 2 L1L2exp2ttc]. MeasuringS therefore allows us to estimate t. With t in hand,Eq. (2) gives dn2.
We performed wavelength-multiplexing experimentswhile forming nanolayers on a silica microsphere sur-face. Light from two current-tunable distributed-feedback lasers with nominal wavelengths of 760 and1310 nm was coupled to a single-mode fiber (Nufern780-HP) (Fig. 1). A portion of the f iber was acideroded down to a 3-mm diameter to facilitate couplingto the WGMs of a silica microsphere.9 The micro-sphere and fiber were contained within a temperature-controlled 1-ml cuvette containing buffer solution anda magnetic stirrer. Beyond this cuvette the fiberwas led to an InGaAs detector. By scanning bothlasers with a synchronous ramp, we observed thatthe light from each independently stimulates WGMsin the microsphere and yields a distinct transmissionspectrum with a superposition of resonant dips fromeach. By observing which resonances disappear aseither laser is shut off, the resonances are easilyassociated with the 760- and 1310-nm region. In thisway, resonances can be identified and tracked.
As a test of our perturbation theory we constructedtwo experiments at the extreme limits. First we builta monolayer of bovine serum albumin (BSA) 3 nmthick.10,11 The microsphere surface was treated with3-aminopropyltrimethoxysilane, and BSA with afinal concentration of 1 mM was injected into 10-mMphosphate-buffered saline (pH of 7.4). The shiftsof resonances at two wavelengths, l1 760 nm andl2 1310 nm, are shown in Fig. 2(a). The BSAreached Langmuir-like saturation (i.e., monolayerformation10) at dll 1 3 1025. The two resonancesfrom each wavelength region shifted almost the sameamount. As a second test case we injected NaCl intothe water surrounding a sphere. We sequentiallyincreased the salt concentration by 0.1-M incrementsstarting with de-ionized water. Figure 2(b) shows thetime trace of the resonance shifts in dll from eachwavelength region. In this case the fractional shiftat 760 nm is considerably less than that at 1310 nm.Figure 3 summarizes the experimental results and
the layer theory prediction. For a BSA monolayer,tL ,, 1, and S in Eq. (3) should approach 1. The ex-periment yields a slope of 1.04. For the NaCl experi-ment, tL .. 1, and S should approach the ratio ofthe wavelengths, 0.58. The experimental result was0.54. Our limiting tests are in reasonable agreementwith theory. We are now in a position to demonstratethe usefulness of our approach by attempting toevaluate the optical properties of biophysically rele-vant hydrogel.
Poly-L-lysine (PLL) is a hydrogel that takes on ex-tremely positive charge in water and is consequentlyfavored as a means for adsorbing biomolecules witha negative charge. However, the physical properties
Fig. 2. (a) Resonance shifts at two wavelengths [l1 760 nm (thin curve) and l2 1310 nm (thick curve)]owing to BSA adsorption. (b) Resonance shifts at thesame wavelengths owing to two sequential injections ofNaCl by 0.1-M increments.
Fig. 3. Plot of dll760 nm versus dll1310 nm for BSAlayer formation (dots) and for six incremental 0.1-M in-jections of NaCl (squares). Points represent experimentalvalues and lines represent the layer perturbation theory.
of PLL are difficult to measure since it deposits ina thin layer with extremely low contrast in a waterenvironment. We used a PLL solution from Sigma(P8920, 0.1% wt.vol. in water, average molecularweight of 225,000 gmol) that is commonly used inbiology to treat glass slides. To generate a layer,40 ml of the PLL solution was injected into 900 mlof phosphate-buffered saline surrounding the micro-sphere. We observed a shift toward longer wave-lengths that saturated in the usual Langmuir fashionfor monolayer formation. However, the fractionalshift at a saturation of 2 3 1026 was well belowanything we had seen previously. Slope S based onthe average of a number of experiments was 0.82.This slope fed back into Eq. (3) gives a thickness of110 nm, which is reasonable considering the molecu-lar structure of the polymer. After substitutingthis thickness into Eq. (2), we determined the waterexcess increment in the optical dielectric constant tobe dn2 0.0033. Consequently, dn 0.0012, whichis indeed small.
We have provided support for our simple layer per-turbation theory, and as a result the WGM resonatorgoes beyond its original promise as a biosensor. Byanalyzing wavelength-multiplexed experiments withthis theory, we can not only monitor the growth ofnanolayers, but we can also determine the opticaldielectric constant for the resulting f ilm. All thishas been done at one polarization (TE) that can beconveniently arranged by matching the polarizationcharacteristics of the lasers and by reducing the lengthof optical f ibers. Surprisingly, so long as both laserslaunch the same polarization into their respectivemodes (i.e., TE or TM), Eq. (3) should be identical foreither polarization. This interesting result can beshown by use of the more electromagnetically detailedwork of Teraoka et al.12
Wavelength-multiplexing experiments have createda new window of opportunity for the WGM resonator.For the first time to our knowledge, a WGM resonatorwas applied to study a commonly used biofunctionallayer. It will be interesting to measure the changein S as a self-assembled monolayer forms on a sur-face. As the layer density increases, the morphologyof the molecules in the layer may change. This phasetransition will lead to a change in the layer thickness,and a real-time measurement of S should reveal thistransition.
Our method can be extended to individual particles.However, the spherically symmetrical theory thatgenerated Eq. (2) cannot be used. Instead a Green’sfunction approach must be applied. This alternatedirection is in the works. The result shows promisefor looking at heterogeneous structures such as ad-sorbed bacteria.
M. Noto and F. Vollmer are grateful for their gradu-ate and postdoctoral support while at Polytech-nic University from the National Science Foundation(BES-0119273). S. Arnold’s e-mail address is [email protected].
*Present address, Rowland Institute, Harvard Uni-versity, Cambridge, Massachusetts 02142.
References
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6. S. Arnold and S. Holler, in Cavity-Enhanced Spectro-scopies, R. D. van Zee and J. P. Looney, eds. (Academic,San Diego, Calif., 2002), pp. 227–253.
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