Plasmon excitation by the Gaussian-like core mode of a ...Plasmon excitation by the Gaussian-like core mode of a photonic crystal waveguide or a fiber ... Typically, these sensors

Plasmon excitation by the Gaussian-like core mode of

a photonic crystal waveguide or a fiber

Maksim Skorobogatiy and Andrey [email protected]

Ecole Polytechnique de Montreal, Genie Physique, C.P. 6079, succ. Centre-VilleMontreal, Quebec H3C3A7, Canada

Abstract: Resonant excitation of a plasmon by the Gaussian-like leaky core mode of a metalcovered 1D photonic crystal waveguide or fiber is presented. Application in sensing and com-parison with the existing waveguide-based schemes is discussed.c© 2006 Optical Society of AmericaOCIS codes: (130.6010) Sensors, (240.6680) Surface plasmons, (230.1480) Bragg reflectors.

1. Introduction

Propagating at the metal/dielectric interface, surface plasmons are extremely sensitive to changes in therefractive index of the dielectric. This feature constitutes the core of many Surface Plasmon Resonance(SPR) sensors. Typically, these sensors are implemented in the Kretschmann-Raether prism geometry todirect p-polarized light through a glass prism and reflect it from a thin metal (Au, Ag) film deposited onthe prism facet [1]. The presence of a prism allows phase matching of an incident electromagnetic wavewith a plasmonic wave at the metal/ambient dielectric interface at a specific combination of the angle ofincidence and wavelength. Mathematically, phase matching condition is expressed as an equality between aplasmon wavevector and a projection of a wavevector of an incident wave along the interface. Since plasmonexcitation condition depends resonantly on the value of the refractive index of an ambient medium within200-300nm from the interface, the method enables, for example, detection, with unprecedented sensitivity, ofbiological binding events on the metal surface [2, 3]. The course of a biological reaction can then be followedby monitoring angular [2, 3], spectral [4] or phase [5] characteristics of the reflected light.

To miniaturize SPR biosensors, several waveguide and fiber based implementations have been introduced[4, 6]. In these sensors, one launches the light into a waveguide core and then uses coupling of a guided modewith a plasmonic mode to probe for the changes in the ambient environment. To excite efficiently a surfaceplasmon the phase matching condition between the plasmon and waveguide modes has to be satisfied, whichmathematically amounts to the equality between their modal propagation constants. Ideally, one would usea single mode waveguide (SMW) with all the power travelling in a single Gaussian-like core mode operatingnear the point of resonant excitation of a plasmon. Near such a point most of the energy launched into thewaveguide core could be efficiently transferred into a plasmon mode. Wilkinson [6] used such an approachto provide several compact designs of SPR biosensors based on planar waveguides. However, for such singlemode, low index-contrast waveguides the SPR coupling is realized at essentially grazing angles of modalincidence on the metal layer (for example, for the waveguides[6] angle of modal incidence exceeds 85o).As follows from the basic SPR theory [7], coupling at such grazing incidence angles leads to an inevitabledecrease of sensitivity of an SPR method.

In principle, to increase angle of modal incidence on the interface high index contrast waveguides could beemployed. However, quick inspection of a corresponding band diagram (Fig. 1(a)) shows that phase matchingbetween plasmon mode and a fundamental waveguide mode is not easy to realize. This is related to the factthat effective refractive index of such a mode is close to the refractive index of a core material, whichis typically larger than 1.45 due to the materials limitations. Refractive index of a plasmon is close to therefractive index of the ambient medium which is typically air n = 1 or water n = 1.3. Thus, large discrepancyin the effective refractive indexes makes it hard to achieve phase matching between the two modes, with anexception of higher frequencies (λ <650nm) where plasmon dispersion relation deviated substantially fromthat of an analyte material.

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Another solution to the phase matching and incidence angle problem is coupling to a plasmon via the highorder modes of a multimoded waveguide[8] (MMW). As seen from the plot of their dispersion relations(Fig. 1(b)), such modes can have significantly lower effective refractive indexes than a waveguide core index.In such a set-up light has to be launched into a waveguide as to excite high order modes some of which willbe phase matched with a plasmon mode. As only a fraction of higher order modes are phase matched to aplasmon, then only a fraction of total launched power will be coupled to plasmon.

In what follows, we demonstrate efficient SPR excitation with a Gaussian-like core mode of a PC waveguide.We show that such configuration makes the plasmon excitation possible at steeper angles of modal incidence,and lower frequencies, improving the sensitivity and enlarging the probe depth of a sensor.

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Fig. 1. Band diagrams of a) a SMW mode (solid thin) and a plasmon (solid thick). Inset - coupler schematic;|Hy|2 of a plasmon (left) and a SMW mode (right). b) the MMW modes (solid thin) and a plasmon (solidthick). Inset - coupler schematic; |Hy|2 of a plasmon (left) and a high order MMW mode (right) at thephase matching point (black circle). c) Band diagrams of the core mode of a PC waveguide (solid thin)and plasmon (solid thick). Two waveguide designs are presented demonstrating that phase matching point(black circles) can be chosen at will. Inset - coupler schematic; |Hy | of a plasmon (left) and a Gaussian-likecore mode of a PC waveguide (right).

2. Plasmon excitation by a core mode of a Bragg waveguide

In what follows we consider plasmon excitation by a Gaussian-like TM polarized mode of an anti-guidingphotonic crystal waveguide (Fig. 1(c)) where light confinement in a lower refractive index core is achieved by asurrounding multilayer reflector. As incoming laser beam is typically Gaussian-like, power coupling efficiencyinto the core mode is high due to good spatial mode matching. Moreover, coupling to such waveguides can befurther simplified by choosing waveguide core size to be significantly larger than the wavelength of operation.This is possible as antiguiding waveguides operate in the effectively single mode regime regardless of the coresize. Leaky core mode can be easily phase matched with a plasmon mode by design, as effective refractiveindex of such a mode can be readily tuned to be well below the value of a core index. Another importantaspect of a proposed setup is a freedom of adjusting coupling strength between the core and plasmonic modes.As penetration of a leaky mode reduces exponentially fast into the multilayer reflector, coupling strengthbetween the plasmon and core modes can be controlled by changing the number of reflector layers betweenthe core and a metal film.

We would like to note that although in this paper we consider planar geometries, proposed plasmon excitationsetup can be equally well implemented in fiber geometries. For example, metallized Bragg fiber with a filledlower index core can be used to implement radial index distribution of Fig. 1(c). In fact, we have recentlysucceeded in developing fabrication technique for all-polymer Bragg fiber fabrication [10] and we are currentlyimplementing proposed plasmonic coupling setup using home drawn all-polymer Bragg fibers Fig. 2.

Photonic crystal waveguide under consideration consists of 27 alternating layers with indexes nh = 2.0,nl = 1.5. Core layer is number 12 with index nc = nl. Analyte (first cladding) is water ns = 1.332 bordering

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10 µm

PVDF

PC

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PVDF/PC

Fig. 2. Examples of home drawn all-polymer Bragg fibers with filled and hollow cores. Two material com-binations are presented, PVDF/PC and PMMA/PS.

a 50nm layer of gold. Substrate index is 1.5. Theory of the planar PC waveguides with infinite reflectors wherenc = nl, predicts that for a design wavelength λd effective refractive index of the fundamental TE and TMmodes of a PC waveguide can be designed at will 0 ≤ neff < nl by choosing the reflector layer thicknesses

as dl

√n2

l − n2eff = dh

√n2

h − n2eff = λd/4, and a core layer thickness as dc = 2dl. Moreover, for this choice

of nc field distribution in the core is Gaussian-like both for TE and TM modes [9]. By choosing effectiverefractive index of a core mode to be that of a plasmon a desired phase matching condition is achieved.For a waveguide with a finite reflector same design principle holds approximately. Thus, for a wavelengthof operation λ = 640nm phase matching is achieved when PC waveguide above is designed for neff = 1.46with λd = 635nm.

Near the phase matching point, fields of a core guided mode contain strong plasmon contribution (inset ofFig. 3(a)). As plasmon exhibits very high propagation loss, the loss of a core mode (lines with circles inFig. 3(a)) will also exhibit sharp increase near the phase matching point. For comparison, dashed line atthe bottom of Fig. 3(a) presents the loss of a core guided mode in the absence of a metallic layer on top ofa multilayer. When analyte refractive index is varied plasmon dispersion relation changes leading to a shiftin the position of the phase matching point with a core guided mode. Thus, at a given frequency, loss of acore guided mode will vary dramatically with changes in the ambient refractive index. Field distribution ina plasmon mode propagating on the top of a PC multilayer shows some penetration into the multilayer andlosses almost independent of the analyte refractive index (line with crosses in Fig. 3(a)), for comparison,dashed line at the top of Fig. 3(a) corresponds to the plasmon losses in the absence of a multilayer.

To verify mode analysis predictions field propagation was performed. A TM polarized 2D Gaussian beam (Hfield along Y direction) was launched into a waveguide core from air (inset in Fig. 3(b)). At the air-multilayerinterface incoming Gaussian was expanded into the fields of all the guided and leaky, and some evanescentmultilayer modes (60 altogether), plus the field of a reflected Gaussian by imposing continuity of the Z andY field components at the interface. Optimal coupling of 71% of an incoming power into the Gaussian-likecore mode was achieved with a Gaussian beam of waist 0.8dc centered in the middle of a waveguide core.Reflection from the air-multilayer interface was less than 3%.

In Fig. 3(c) distribution of an X component of the energy flux Sx in a propagating beam is shown for variousvalues of an ambient refractive index. From the figure it is clear that beam propagation loss is very sensitiveto the changes in the ambient refractive index. To quantify sensitivity of our design in Fig. 3(b) we presentSx distribution across a waveguide crossection after 1cm of beam propagation. From this figure we calculatethat change in the integrated energy flux as a function of the ambient index deviation from 1.332 of a purewater can be approximated as ∆P/P1.332 ' 60|na−1.332|; thus, an absolute variation of 0.001 in the ambientrefractive index would lead to a ∼ 6% variation in the transmitted power which is readily detectable. Similarcalculations can be carried out assuming that refractive index of water stays unchanged, while on the top

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Fig. 3. a) Solid lines with circles - loss of a waveguide mode near the phase matching point with a plasmon fordifferent values of an ambient refractive index. Inset: |Hy | field distribution in the waveguide and plasmonicmodes. Sx energy flux in a multilayer waveguide for various values of the ambient refractive index. b)distribution across waveguide crossection after 1cm of propagation c) distribution over 2cm of propagation.

of a metal layer one deposits a very thin layer of thickness dbio of a biological material with refractive index1.42. In this case sensitivity of the same design will be ∆P/P1.332 ' 0.05dbio/1nm; thus, adding 1nm of abio-layer would change the transmitted intensity by ∼ 5%.

3. Conclusion

In conclusion, we have presented a novel approach to design of a waveguide based SPR sensor, whereGaussian-like mode of an effectively single mode PC waveguide can be phase matched at any desirablewavelength to a surface plasmon propagating on the top of such a waveguide. Moreover, in resonance, modalincidence angle onto a metallic layer is not grazing resulting in enhanced sensitivity. Coupling strengthbetween the waveguide core and plasmon modes can be varied by changing the number of intermediatereflector layers, thus enabling design of an overall sensor length.

4. References[1] E. Kretschmann and H. Raether, Naturforschung A 23, 2135 (1968)[2] B. Liedberg, C. Nylander, and I. Lundstrum, ”Surface-plasmon resonance for gas-detection and biosensing,” Sens. Actuat.

B 4, 299 (1983)[3] J.L. Melendez, R. Carr, D.U. Bartholomew, K.A. Kukanskis, J. Elkind, S.S. Yee, C.E. Furlong, and R.G. Woodbury, ”A

commercial solution for surface plasmon sensing,” Sens. Actuat. B 35, 212 (1996)[4] L. Zhang and D. Uttamchan, Electron. Lett. 23, 1469 (1988)[5] A.N. Grigorenko, P. Nikitin, and A.V. Kabashin, ”Phase jumps and interferometric surface plasmon resonance imaging,”

Appl. Phys. Lett. 75, 3917 (1999)[6] R. Harris and J.S. Wilkinson, ”Wave-guide surface plasmon resonance sensors,” Sens. Actuat. B 29, 261 (1995)[7] V.M. Agranovich, D.L. Mills, eds., Surface Polaritons (North-Holland, Amsterdam 1982)[8] B.D. Gupta and A.K. Sharma, ”Sensitivity evaluation of a multi-layered surface plasmon resonance-based fiber optic

sensor: a theoretical study,” Sens. Actuat. B 107, 40 (2005)[9] M. Skorobogatiy, ”Efficient anti-guiding of TE and TM polarizations in low index core waveguides without the need of

omnidirectional reflector,” Opt. Lett. 30, 2991 (2005)[10] Y. Gao, N. Guo, B. Gauvreau, M. Rajabian, O. Skorobogata, E. Pone, O. Zabeida, L. Martinu, C. Dubois, and M.

Skorobogatiy, ”Consecutive Solvent Evaporation and Co-Rolling Techniques for Polymer Multilayer Hollow Fiber PreformFabrication,” accepted for publication in the Journal of Materials Research, 2006.

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