-
Observation of strongly enhanced ultrashort pulses in 3-D
metallic funnel-waveguide
Dong-Hyub Lee,1 Joonhee Choi,1 Seungchul Kim,2 In-Yong Park,3
Seunghwoi Han,1 Hyunwoong Kim,1 and Seung-Woo Kim1,*
1Ultrafast Optics for Ultraprecision Group, Korea Advanced
Institute of Science and Technology (KAIST), Daejeon 305-701, South
Korea
2Max Planck Center for Attosecond Science (MPC-AS), Pohang,
Kyungbuk 790-784, South Korea 3Division of Industrial Metrology,
Korea Research Institute of Standards and Science (KRISS), Daejeon
305-340,
South Korea *[email protected]
Abstract: For strong field enhancement of ultrashort light
pulses, a 3-D metallic funnel-waveguide is analyzed using the
finite-difference time-domain (FDTD) method. Then the maximum
intensity enhancement actually developed by the funnel-waveguide
upon the injection of femtosecond laser pulses is observed using
two-photon luminescence (TPL) microscopy. In addition, the
ultrafast dephasing profile of the localized field at the hot spot
of the funnel-waveguide is verified through the interferometric
autocorrelation of the TPL signal. Finally it is concluded the
funnel-waveguide is an effective 3-D nanostructure that is capable
of boosting the peak pulse intensity of stronger than 80 TWcm−2 by
an enhancement factor of 20 dB without significant degradation of
the ultrafast spatiotemporal characteristics of the original
pulses. ©2014 Optical Society of America OCIS codes: (190.7110)
Ultrafast nonlinear optics; (190.4180) Multiphoton processes;
(320.7120) Ultrafast phenomena.
References and links 1. M. I. Stockman, “Nanoplasmonics: past,
present, and glimpse into future,” Opt. Express 19(22),
22029–22106
(2011). 2. B. Sharma, R. R. Frontiera, A.-I. Henry, E. Ringe,
and R. P. Van Duyne, “SERS: Materials, applications, and the
future,” Mater. Today 15(1–2), 16–25 (2012). 3. E. M. Kim, S. S.
Elovikov, T. V. Murzina, A. A. Nikulin, O. A. Aktsipetrov, M. A.
Bader, and G. Marowsky,
“Surface-enhanced optical third-harmonic generation in Ag island
films,” Phys. Rev. Lett. 95(22), 227402 (2005).
4. S. I. Bozhevolnyi, J. Beermann, and V. Coello, “Direct
observation of localized second-harmonic enhancement in random
metal nanostructures,” Phys. Rev. Lett. 90(19), 197403 (2003).
5. P. Biagioni, D. Brida, J. S. Huang, J. Kern, L. Duò, B.
Hecht, M. Finazzi, and G. Cerullo, “Dynamics of four-Photon
Photoluminescence in Gold Nanoantennas,” Nano Lett. 12(6),
2941–2947 (2012).
6. H. Choo, M.-K. Kim, M. Staffaroni, T. J. Seok, J. Bokor, S.
Cabrini, P. J. Schuck, M. C. Wu, and E. Yablonovitch, “Nanofocusing
in a metal–insulator–metal gap plasmon waveguide with a
three-dimensional linear taper,” Nat. Photonics 6(12), 838–844
(2012).
7. J. Lehmann, M. Merschdorf, W. Pfeiffer, A. Thon, S. Voll, and
G. Gerber, “Surface plasmon dynamics in silver nanoparticles
studied by femtosecond time-resolved photoemission,” Phys. Rev.
Lett. 85(14), 2921–2924 (2000).
8. M. Merschdorf, C. Kennerknecht, and W. Pfeiffer, “Collective
and single-particle dynamics in time-resolved two-photon
photoemission,” Phys. Rev. B 70(19), 193401 (2004).
9. P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and
W. E. Moerner, “Improving the mismatch between light and nanoscale
objects with gold bowtie nanoantennas,” Phys. Rev. Lett. 94(1),
017402 (2005).
10. J. Choi, S. Kim, I.-Y. Park, D.-H. Lee, S. Han, and S.-W.
Kim, “Generation of isolated attosecond pulses using a plasmonic
funnel-waveguide,” New J. Phys. 14(10), 103038 (2012).
11. S. Kim, J. Jin, Y. J. Kim, I. Y. Park, Y. Kim, and S. W.
Kim, “High-harmonic generation by resonant plasmon field
enhancement,” Nature 453(7196), 757–760 (2008).
12. I. Y. Park, J. Choi, D. H. Lee, S. Han, S. Kim, and S. W.
Kim, “Generation of EUV radiation by plasmonic field enhancement
using nano‐structured bowties and funnel‐waveguides,” Ann. Phys.
525(1–2), 87–96 (2013).
13. I. Y. Park, S. Kim, J. Choi, D. H. Lee, Y. J. Kim, M. F.
Kling, M. I. Stockman, and S. W. Kim, “Plasmonic generation of
ultrashort extreme-ultraviolet light pulses,” Nat. Photonics 5(11),
678–682 (2011).
#212831 - $15.00 USD Received 28 May 2014; revised 2 Jul 2014;
accepted 2 Jul 2014; published 9 Jul 2014(C) 2014 OSA 14 July 2014
| Vol. 22, No. 14 | DOI:10.1364/OE.22.017360 | OPTICS EXPRESS
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-
14. N. Pfullmann, M. Noack, J. Cardoso de Andrade, S. Rausch, T.
Nagy, C. Reinhardt, V. Knittel, R. Bratschitsch, A. Leitenstorfer,
D. Akemeier, A. Hütten, M. Kovacev, and U. Morgner, “Nano-antennae
assisted emission of extreme ultraviolet radiation,” Ann. Phys.
526(3–4), 119–134 (2014).
15. M. Sivis, M. Duwe, B. Abel, and C. Ropers,
“Extreme-ultraviolet light generation in plasmonic nanostructures,”
Nat. Phys. 9(5), 304–309 (2013).
16. M. Lupetti, M. F. Kling, and A. Scrinzi,
“Plasmon-enhanced-attosecond-extreme ultraviolet source,” Phys.
Rev. Lett. 110(22), 223903 (2013).
17. J. Beermann, S. M. Novikov, T. Holmgaard, R. L. Eriksen, O.
Albrektsen, K. Pedersen, and S. I. Bozhevolnyi,
“Polarization-resolved two-photon luminescence microscopy of
V-groove arrays,” Opt. Express 20(1), 654–662 (2012).
18. H. Choi, D. F. P. Pile, S. Nam, G. Bartal, and X. Zhang,
“Compressing surface plasmons for nano-scale optical focusing,”
Opt. Express 17(9), 7519–7524 (2009).
19. D. K. Gramotnev, “Adiabatic nanofocusing of plasmons by
sharp metallic grooves: Geometrical optics approach,” J. Appl.
Phys. 98(10), 104302 (2005).
20. T. Hanke, G. Krauss, D. Träutlein, B. Wild, R. Bratschitsch,
and A. Leitenstorfer, “Efficient nonlinear light emission of single
gold optical antennas driven by few-cycle near-infrared pulses,”
Phys. Rev. Lett. 103(25), 257404 (2009).
21. P. Ginzburg, D. Arbel, and M. Orenstein, “Gap plasmon
polariton structure for very efficient microscale-to-nanoscale
interfacing,” Opt. Lett. 31(22), 3288–3290 (2006).
22. E. Verhagen, A. Polman, and L. K. Kuipers, “Nanofocusing in
laterally tapered plasmonic waveguides,” Opt. Express 16(1), 45–57
(2008).
23. C. Kern, M. Zürch, J. Petschulat, T. Pertsch, B. Kley, T.
Käsebier, U. Hübner, and C. Spielmann, “Comparison of femtosecond
laser-induced damage on unstructured vs. nano-structured
Au-targets,” Appl. Phys., A Mater. Sci. Process. 104(1), 15–21
(2011).
24. M. I. Stockman, “Nanofocusing of optical energy in tapered
plasmonic waveguides,” Phys. Rev. Lett. 93(13), 137404 (2004).
25. M. W. Vogel and D. K. Gramotnev, “Adiabatic nano-focusing of
plasmons by metallic tapered rods in the presence of dissipation,”
Phys. Lett. A 363(5–6), 507–511 (2007).
26. J. Beermann, S. M. Novikov, T. Søndergaard, A. E.
Boltasseva, and S. I. Bozhevolnyi, “Two-photon mapping of localized
field enhancements in thin nanostrip antennas,” Opt. Express
16(22), 17302–17309 (2008).
27. I.-Y. Park, S. Kim, J. Choi, D.-H. Lee, and S.-W. Kim,
“Plasmonic field enhancement for generating ultrashort
extreme-ultraviolet light pulses,” Proc. SPIE 8096, 80960S
(2011).
28. M. Li, S. Menon, J. P. Nibarger, and G. N. Gibson,
“Ultrafast electron dynamics in femtosecond optical breakdown of
dielectrics,” Phys. Rev. Lett. 82(11), 2394–2397 (1999).
1. Introduction
Local field enhancement occurring in nanometer-scale structures
[1] has widely been investigated for diverse applications such as
surface-enhanced Raman scattering [2], multi-photon interaction for
harmonic generation [3,4] and photoemission or photoluminescence
[5–9]. Recently attention is being paid to strong field enhancement
of ultrashort light pulses for generation of extreme ultraviolet
light in interaction with noble gases [10–16]. This highly
nonlinear optical frequency upconversion requires achieving high
peak pulse intensities of stronger than 10 TWcm−2 from moderate
pulses of ~0.1 TWcm−2 intensity. Such strong field enhancement may
be accomplished with V-groove nanostructures [17–19] exploiting the
adiabatic slowdown of surface plasmon polaritons, or by adopting
nanoantennas [9,20] and tapered slab waveguides [21,22] designed to
induce narrowly localized resonance of surface plasmons. Most
nanostructures readily fabricated on thin metal films are
susceptible to thermal damage [12,23] caused by intense ultrashort
pulses. On the other hand, bulk-type nanostructures such as
nano-tips [24,25] are capable of providing more robustness to
thermal damage, but the resulting hot spot volume tends to reduce
due to lower power coupling efficiency to the incident laser
field.
In this investigation, we conduct an elaborate evaluation on a
3-D waveguide that was previously designed by the authors for
strong field enhancement of femtosecond laser pulses for generation
of extreme ultraviolet light [12,13]. The waveguide is fabricated
on a thick silver film using the focused ion beam (FIB) process in
the form of a single tapered hollow core of funnel shape, through
which the incident laser pulse is coupled without significant power
loss for strong field enhancement along with high thermal immunity.
Here, the dynamic evolution of the field enhancement occurring
within the funnel-waveguide is analyzed through finite-difference
time-domain (FDTD) simulation. Then, two-photon luminescence (TPL)
microscopy [6,9,17,26] is adopted to probe the strong field
enhancement
#212831 - $15.00 USD Received 28 May 2014; revised 2 Jul 2014;
accepted 2 Jul 2014; published 9 Jul 2014(C) 2014 OSA 14 July 2014
| Vol. 22, No. 14 | DOI:10.1364/OE.22.017360 | OPTICS EXPRESS
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actually developed within the hot spot volume of the
funnel-waveguide. In addition, the ultrafast spatiotemporal
characteristic of the enhanced field is measured using the
interferometric autocorrelation (IAC) of the TPL signal. This
investigation validates that the funnel-waveguide is an effective
3-D nanostructure capable of boosting the peak pulse intensity of
stronger than 80 TWcm−2 by an enhancement factor of 20 dB without
significant degradation of the ultrafast temporal characteristics
of the original pulses.
2. Strong field enhancement in funnel-waveguide
Figure 1 shows the funnel-waveguide prepared to be tested by TPL
microscopy in this investigation. The waveguide is designed so as
to compress the incident femtosecond pulse along the tapered hollow
core. The cross-section of the hollow core is of elliptical shape
and its elliptic ratio of the minor-axis diameter to the major-axis
diameter remains constant along the way from the inlet aperture to
the exit aperture. The waveguide is fabricated by adopting the
focused ion beam (FIB) milling process on a thick Ag layer
deposited inside the probing tip of a micro-cantilever commercially
available for near-field scanning optical microscopy (NSOM)
[13,27]. Details on the fabrication procedure are found in Ref
[27]. The geometry of the waveguide is characterized by the four
parameters; the minor-axis diameter of the exit aperture (d), the
minor-axis diameter of the inlet aperture (b), the elliptic ratio
of the cross-section (r = b/a) with a being the major-axis diameter
of the inlet aperture, and the waveguide length (h). The
geometrical parameters are optimized so as to yield a large hot
spot in which the intensity enhancement exceeds 20 dB. Through a
series of FDTD simulations (Lumerical solutions, ver. 8.0), the
parameters are selected as d = 70 nm, b = 2.2 μm, r = 0.5 and h = 9
μm. The resulting hot spot has a volume of 250 nm × 250 nm × 500 nm
in three dimensions with the maximum intensity enhancement factor
being ~400 at the center of the hot-spot volume. This waveguide is
found almost identical to the previous design explained in Ref
[13], except the exit aperture diameter (d) being reduced to 70 nm
from the previous value of 100 nm.
Inlet aperture
Exit aperture
(b)(a)Exit aperture
Inlet aperture
Fig. 1. Schematic drawing and scanning electron microscope (SEM)
image of the funnel-waveguide. (a) Cutaway drawing of the
funnel-waveguide made of a single tapered hollow core of 9 μm depth
and 0.5 elliptic ratio cross-section. (b) SEM image of the
funnel-waveguide fabricated on a micro cantilever. Inset images are
the top view of the inlet aperture (2.2 μm, minor axis diameter)
and the bottom view of the exit aperture (70 nm, minor axis
diameter).
First of all, we calculated the temporal evolution of the field
enhancement developed in the designed funnel-waveguide, of which
the result is summarized in Fig. 2. In this FDTD calculation, for
simulation of the real experimental situation, the incident light
was assumed as a femtosecond laser pulse of an 800-nm center
wavelength with 12-fs FT-limited pulse duration. The polarization
direction of the incident pulse was aligned parallel to the
minor-axis of the elliptical cross-section (Fig. 2(a)). The
calculation result shows that the propagation of the incident pulse
along the waveguide is represented by the fundamental mode that is
symmetrical about the minor-axis of the elliptical cross-section.
The effective refractive index (neff) of the fundamental mode was
also calculated, of which the real part
#212831 - $15.00 USD Received 28 May 2014; revised 2 Jul 2014;
accepted 2 Jul 2014; published 9 Jul 2014(C) 2014 OSA 14 July 2014
| Vol. 22, No. 14 | DOI:10.1364/OE.22.017360 | OPTICS EXPRESS
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Re(neff) and imaginary part Im(neff) vary along the z-axis of
the waveguide (Fig. 2(b)). It is noted that Re(neff) is larger than
unity when the incident pulse enters the inlet aperture (z = 9 μm).
This indicates that the fundamental mode is a plasmonic mode
coupled with surface plasmon polaritons (SPPs). As the fundamental
mode propagates further into the waveguide, Re(neff) gradually
decreases and eventually crosses the unity line at z = ~3 μm, which
implies that the fundamental mode converts to a photonic mode
before reaching the exit aperture. The conversion is explained due
to the fact that the plasmonic coupling weakens near the exit
aperture because the neutralization of electrons through the
circumferential silver wall begins to arise in the narrowed
polarization gap. Further, as the photonic-converted fundamental
mode comes near the exit aperture, Re(neff) reduces drastically
while Im(neff) rises up at z = ~1 μm. The increase of Im(neff)
infers that the propagation length reduces with increasing energy
loss. Eventually, the photonic mode reflects backwards before
reaching the exit aperture by the mode cut-off occurring where the
cross-section shrinks to a major-axis diameter of less than half
the wavelength of the incident laser.
Our FDTD simulation also reveals that the overall behavior of
field enhancement within the funnel-waveguide is critically
affected by the center wavelength of the excitation laser. For
instance, if the center wavelength changes from the current value
of 800 nm to a long 1,300 nm wavelength, the design parameters of
the funnel-waveguide have to be considerably altered to achieve a
similar level of field enhancement. On the other hand, the pulse
duration yields no significant effect if it is longer than ~5 fs
(see Fig. 5(d)).
A temporal sequence of three snap shots of enhanced intensity
distribution is shown in Fig. 2 to illustrate how the fundamental
mode of the incident pulse develops as it propagates through the
waveguide. In the early period near the inlet aperture, the field
enhancement is confined only to the silver wall (Fig. 2(c)). As the
incident pulse moves inward further, the plasmonic enhancement
extends towards the center of the hollow core (Fig. 2(d)). Finally,
near the exit aperture where the fundamental mode turns to a
photonic mode and subsequently converges to a hot spot at z = ~0.55
μm, the intensity distribution becomes nearly uniform without
significant non-homogeneity across the entire area of the
cross-section (Fig. 2(e)). Another fact is that when the
fundamental mode is reflected backwards by the mode cut-off, its
leading edge is folded with the tailing edge that comes into the
hot spot. The result is the constructive interference that
increases the enhanced intensity by a factor of 4. In consequence,
the intensity enhancement factor in the hot spot reaches 400 with a
large 20-dB volume of ~3 × 107 nm3.
The transmittance of the funnel-waveguide is defined as the
ratio of P(z)/Pinc wherein Pinc is the incident pulse power while
P(z) denotes the pulse power actually propagating along the z-axis
from the inlet aperture. For calculation of P(z)/Pinc using the
FDTD method, as shown in Fig. 3(a), a straight hollow tube of an
elliptical cross-section (260 nm × 520 nm) which is slightly larger
than the cross-section of the hot spot was virtually attached to
the exit aperture so that the contribution of the mode-cutoff light
reflected from near the exit aperture can be eliminated in
determining P(z)/Pinc. In addition, a perfectly matched layer (PML)
was added to eliminate all the light reaching the exit aperture by
absorption. These two virtual modifications allowed us to determine
P(z)/Pinc precisely as shown in Fig. 3(b). The computed
transmittance P(z)/Pinc reveals that the power coupling efficiency
at the hot spot (z = 0.55 μm) turns out to be 53%. This result
implies that in consideration of the constructive interference
occurring between the leading and trailing edge of the fundamental
mode, the pulse power concentrated within the hot spot becomes
instantly more than twice the incident power, which is worked out
to be 4 × 53% of Pinc. It is necessary to note that at the inlet
aperture (z = 9 μm) where the incident pulse enters the waveguide,
the transmittance is only ~76%, not 100%, because 24% of the
incident light reverses its propagation due to the mode cut-off
before reaching the hot spot, escaping the waveguide structure
through the inlet aperture. The remaining 23% of the incident
light, i.e., 76% at the inlet minus 53% at the hot spot, is lost in
the form of absorption and scattering along the hollow core silver
surface of the waveguide.
#212831 - $15.00 USD Received 28 May 2014; revised 2 Jul 2014;
accepted 2 Jul 2014; published 9 Jul 2014(C) 2014 OSA 14 July 2014
| Vol. 22, No. 14 | DOI:10.1364/OE.22.017360 | OPTICS EXPRESS
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(c)
(d)
(e)
(a) (b)
zy
x
30 6 9
30 6 9
30 6 9
z (μm)
z (μm)
z (μm)
x(μ
m)
x(μ
m)
x(μ
m)
0
1.1
-1.1
0
0
3.3
0.0
0
400
20
0
|E|2
enha
ncem
ent
|E|2
enha
ncem
ent
|E|2
enha
ncem
ent
0 3 6 90.2
0.4
0.6
0.8
1.0
1.2
Im(n
eff )
Re(
n eff )
z (μm)
Re(neff)
10-4
10-3
10-2
10-1
100
Im(neff)
(c)(d)
(e)
Exit aperture Inlet aperture
1.1
-1.1
1.1
-1.1
Fig. 2. FDTD calculations for evolution of the field enhancement
within the funnel-waveguide. (a) Cross-sectional view of the
funnel-waveguide being cut along the minor axis. Polarization
direction of the incident laser with respect to the
funnel-waveguide is also shown. (b) The effective refractive index
inside the funnel-waveguide obtained along the z-axis for λ = 800
nm. (c)-(e) FDTD simulation snapshots of the spatial intensity
distribution inside the funnel when the incident field is
propagating at the positions indicated in (b).
#212831 - $15.00 USD Received 28 May 2014; revised 2 Jul 2014;
accepted 2 Jul 2014; published 9 Jul 2014(C) 2014 OSA 14 July 2014
| Vol. 22, No. 14 | DOI:10.1364/OE.22.017360 | OPTICS EXPRESS
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Fig. 3. FDTD calculation of the power coupling efficiency at the
hot spot of the funnel-waveguide. (a) A straight hollow tube of
elliptical cross-section (260 nm x 520 nm) is virtually attached at
the exit aperture to eliminate the mode-cutoff reflected light from
near the exit aperture. (b) Transmittance curve calculated along
the z-axis.
For experimental verification of the strong field enhancement
using TPL microscopy, the waveguide is illuminated through the
inlet aperture with femtosecond laser pulses. Then, by nonlinear
two-photon absorption, frequency-upconverted TPL radiation is
generated from the inner silver surface of the hollow core. The TPL
signal escaping from the hollow core through the inlet aperture is
observed while the waveguide is scanned in steps along the
transverse direction as illustrated in Fig. 4(a). The excitation
laser pulses are emitted from a Ti:sapphire oscillator
(Femtolasers, Femtosource sPro) at a 75-MHz repetition rate with a
100-nm spectral bandwidth about an 800-nm center wavelength. The
near infrared (NIR) laser pulses are tightly focused onto the inlet
aperture using a focusing lens (8 mm focal length). The group delay
dispersion (GDD) is pre-compensated to ~800 fs2 using a pair of
chirped mirrors. The pulse duration is maintained at a nearly
Fourier-transform-limited (FT-limited) level of 12 fs by use of a
wedge pair. The TPL signal is then directed via a dichroic mirror
to a photo-multiplier tube (PMT, Hamamatsu, H10721) of 300 - 500 nm
detection wavelengths. A spectral filter of a 400 ± 40 nm
wavelength transmission band is inserted before the PMT to suppress
the noise coming from surroundings as well as the excitation beam.
The micro-cantilever structure housing the waveguide is mounted on
a 3-axis motorized stage for precise alignment with the aid of a
CCD camera installed with a flipping beam splitter.
Figure 4 presents our experiments to monitor the TPL signal by
moving the funnel-waveguide in steps along the major-axis direction
of the elliptical hollow core in steps of 20 nm. The measured TPL
signal was normalized with respect to the reference signal that was
obtained from the smooth flat silver surface on the
micro-cantilever that houses the funnel-waveguide. The incident
average power of the driving laser pulses was set to 15 mW and
focused on the inlet aperture with a peak intensity of ~0.05
TW/cm2. As expected, the TPL
#212831 - $15.00 USD Received 28 May 2014; revised 2 Jul 2014;
accepted 2 Jul 2014; published 9 Jul 2014(C) 2014 OSA 14 July 2014
| Vol. 22, No. 14 | DOI:10.1364/OE.22.017360 | OPTICS EXPRESS
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signal is found polarization-dependent with its maximum reaching
80 (red solid line) when the incident polarization is in parallel
with the minor-axis of the inlet aperture. The TPL signal intensity
is proportional to the fourth power of field enhancement. Thus, the
TPL signal is mainly generated by the high intensity field of the
hot spot with insignificant contributions from the remaining
surface inside the waveguide. From the measured TPL signal, the
intensity enhancement factor α is estimated as [6,9,26]
2
22
hot ref ref
ref hot hot
TPL A P
TPL A Pα = (1)
where the subscripts hot and ref denote the hot spot and the
reference flat surface, respectively. In addition,
represents the average excitation power and A is the effective
surface area where the TPL signal originates. In determining the
value of α from Eq. (1), the ratio of TPLhot/TPLref is obtained
from the measured data of Fig. 4(b) as ~80. Besides, and are taken
from the experimental conditions as 15 mW. The excitation laser is
assumed to have a circular spot of ~6.5 μm diameter being
illuminated through a 1-mm diameter aperture located before the
focusing lens. Aref is determined to be ~33.2 μm2 from the focal
spot area. And, Ahot is calculated as the effective area of the TPL
signal, which is defined as [9]
4 4max/hot hotsurface
A E da E= ⋅ (2)
where Ehot is the electric field on the inner surface of the
hot-spot volume and Emax is the maximum electric field.
Specifically, within the hot spot volume the amplitude of enhanced
field is location-dependent, and so is the TPL signal. Thus, from
the FDTD calculation presented in Fig. 2(e), Ahot is obtained as ~1
× 105 nm2. Finally, putting all the computed and measured values of
the parameters into Eq. (1) permits determining the value of α to
be 165. This measured value is found to be less than the FDTD
estimation of ~400 in Fig. 2(e). However, the actual value of α
within the hot spot is speculated to be larger than the measured
value because the absorption loss of the TPL signal by the inner
silver surface of the waveguide, which inevitably occurred during
the backward propagation of the TPL signal from the hot spot to the
inlet aperture, was not precisely considered due to practical
difficulties of estimation. The polarization-dependence of the
enhanced field was well verified by the observation that the
measured enhancement factor reduces to ~10 when the polarization of
the excitation laser is rotated to the direction of the major-axis
of the elliptical hollow core.
Figure 4(c) shows how the TPL signal varied as the incident
power of the excitation laser was increased from 0 to 140 mW and
subsequently decreased back to 0. The TPL signal measured from the
inlet aperture yielded a quadratic dependence on the incident
power. This observation supports that the measured signal is
generated by two-photon absorption. Further, the quadratic
dependence was consistently held even when the incident power was
increased up to 140 mW, and no significant hysteresis was observed
during the two cycles of incident power sweeping shown in the
figure. More importantly, no sign of thermal damage due to melting
or ablation was detected [9, 28]. The incident power of 140 mW is
equivalent to a peak intensity of 0.5 TW/cm2 when focused on the
inlet aperture. This infers that the funnel-waveguide is capable of
producing intensities of stronger than 80 TW/cm2 in consideration
of the intensity enhancement factor obtained from the TPL
experiment ( × 165). This experimental observation concludes that
the funnel-waveguide offers strong thermal immunity in comparison
to the nanostructures fabricated on thin metal layers [12, 14,
23].
#212831 - $15.00 USD Received 28 May 2014; revised 2 Jul 2014;
accepted 2 Jul 2014; published 9 Jul 2014(C) 2014 OSA 14 July 2014
| Vol. 22, No. 14 | DOI:10.1364/OE.22.017360 | OPTICS EXPRESS
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-10 -5 0 5 100
20
40
60
80
TPL h
ot /
TPL r
ef
y (μm)
x-pol. y-pol.
Inlet aperturey
x Scan direction
1 10 10010-1
100
101
102
103
104 Increasing Pin (1) Decreasing Pin (1) Increasing Pin (2)
Decreasing Pin (2)
PM
T cu
rrent
(nA
)Incident power, Pin (mW)
0.01 0.1Peak intensity (TW/cm2)
Slope=2
(b) (c)
(a) Focusinglens
Femtosecondlaser
Dispersioncontrol
FlippingBS
Cantilever
Dichroicmirror
Mov
ing
PMT CCD
Fig. 4. Experimental setup for TPL microscopy and results. (a)
System layout to implement TPL microscopy in reflection mode. The
autocorrelation trace of the TPL signal is also measured by
incorporating a Michelson-type interferometer after the femtosecond
laser source (not shown). (b) TPL signal measured by varying the
polarization direction of the driving laser field. The incident
femtosecond light was scanned along the major-axis of the
elliptical cross-section of the waveguide. The TPL signals were
normalized to their respective reference values taken from the
smooth silver surface. The inset SEM image shows the inlet aperture
of the funnel-waveguide, indicating the polarization directions for
the two measured TPL signals. (c) Quadratic dependence of the
measured TPL signal on the incident power that was increased and
then reversely decreased in two cycles.
3. Ultrafast pulse generation in funnel-waveguide
Characterizing the enhanced field inside the funnel-waveguide
requires not only the spatial distribution of the localized hot
spot volume but also the temporal shape of the enhanced field
within the hot spot. Accordingly, the ultrafast dynamic nature of
the enhanced field was examined by experiments together with FDTD
calculations. Considering that the incident laser offers a
FT-limited pulse duration (ti) of 12 fs at an 800-nm center
wavelength, the FDTD calculation shown in Fig. 5(a) indicates that
the enhanced field at the hot spot undergoes no significant
temporal pulse broadening. The enhanced pulse duration (te) lies in
the range of 12.5 – 13 fs near the hot spot (z = ~0.55 μm). In the
region away from the maximum field point (z > 0.6 μm), the pulse
duration is found increasing rapidly. However, the pulse duration
increase is not caused by a prolonged dephasing time but by the
overlapping effect of the leading edge of the reflected wave by the
mode cut-off with the trailing edge of the forward-moving pulse.
The dotted line (blue) indicates the variation of the center
wavelength of the propagating pulse that becomes shorter as the
pulse propagates towards the exit aperture. The reason is that the
mode cut-off wavelength is proportional to the diameter of the
tapered hollow core so that longer wavelengths reflect backwards
before shorter wavelengths. This spatial wavelength separation
reduces the spectral bandwidth of the enhanced field, widening the
pulse duration at the hot spot. The center wavelength at the
maximum field intensity location (z = 0.55 μm from the exit
aperture) is calculated to be 800 nm, which is the same as that of
the incident light pulse. The pulse duration of the enhanced field
at the hot spot (z = ~0.55 μm) is estimated to be ~12.8 fs (Fig.
5(b)).
#212831 - $15.00 USD Received 28 May 2014; revised 2 Jul 2014;
accepted 2 Jul 2014; published 9 Jul 2014(C) 2014 OSA 14 July 2014
| Vol. 22, No. 14 | DOI:10.1364/OE.22.017360 | OPTICS EXPRESS
17367
-
In order to measure the actual temporal behavior of the enhanced
field near the hot spot, an autocorrelation measuring device of
Michelson interferometer type was installed behind the apparatus of
TPL measurement of Fig. 4(a). As in the previous TPL experiments,
the GDD was minimized using a pair of chirped mirrors and a wedge
pair. Subsequently, it was possible to measure the interferometric
autocorrelation signal (IAC) of the temporal profile of the
incident laser pulse using a two-photon absorption detector with a
1:8 ratio (the dashed line (red) in Fig. 5(c)). The pulse duration
(ti) obtained from the IAC signal is measured ~12 fs, which is
nearly FT-limited pulse duration in consideration of the spectral
bandwidth of the incident laser. As discussed earlier, the TPL
signal has a quadratic dependence, which enables the direct
detection of the IAC signal via the TPL signal from the PMT in Fig.
4(a). Besides, the TPL signal yields a long decay time, which is
not the case for ordinary second harmonic signals. Thus, it was
possible to monitor the IAC signal by slowly translating the moving
mirror of the interferometer setup (solid blue line in Fig. 5(c)).
From the IAC signal of the enhanced field detected by the PMT, the
pulse duration (tTPL) was measured to be 13.6 fs which is slightly
longer than the FDTD-estimated value of 12.8 fs. The discrepancy
may be attributable to the fabrication imperfection of the
funnel-waveguide. Besides, the TPL signal experiences absorption
loss during its escape from the waveguide backwards through the
inlet aperture. Accordingly, the TPL signal generated from the
large z partition (z > 0.55 μm) within the hot spot volume
contributes more than that of the small z partition (z < 0.55
μm), thereby broadening the pulse duration observed at the inlet
aperture even though the actual pulse duration within the hot spot
may be shorter than the measured value.
-20 0 20-1
0
1
Incident field (ti = 12 fs) Enhanced field (te = 12.8 fs)
Nor
mal
ized
E-fi
eld
(a. u
.)
Time (fs)
(b)
-20 0 20
0
2
4
6
8
10 Incident field (ti = 12 fs) Enhanced field (tTPL = 13.6
fs)
PM
T si
gnal
(a. u
.)
Delay time (fs)
(c)
0 5 10 15 20 25 300
5
10
15
20
25
30
ti (fs)
0.0
0.2
0.4
0.6
0.8
1.0
t e (fs
)
(t e-t i
)/t0
(d)
0.0 0.2 0.4 0.6 0.8760
780
800
820
Cen
ter W
avel
engt
h (n
m)
z (μm)
11
12
13
14
15
16
17
t e (f
s)
(a)Highest |E|2
enhancement
Exit aperture
FDTD simulation
IAC experiment
0 0.5 1 z (μm)
Fig. 5. Temporal characteristics of the enhanced field at the
hot spot of the funnel-waveguide. (a) FDTD calculation results
showing how the pulse duration (solid red line) as well as the
center wavelength (dotted blue line) of the enhanced field varies
along the distance from the exit aperture. (b) FDTD calculation
results for the incident field versus the enhanced field in their
temporal profiles at the maximum field position. The notations ti
and te denote the given incident pulse duration and the enhanced
pulse duration, respectively. (c) Experimental results for the IAC
signal of the incident and enhanced field actually measured with a
Michelson interferometer. (d) FDTD calculation results for the
relation between ti and te at the maximum field position. The
degree of temporal pulse broadening is defined as (te-ti)/t0 with
t0 ( = 2.67 fs) being the one-oscillation period of the incident
field centered at an 800 nm wavelength.
#212831 - $15.00 USD Received 28 May 2014; revised 2 Jul 2014;
accepted 2 Jul 2014; published 9 Jul 2014(C) 2014 OSA 14 July 2014
| Vol. 22, No. 14 | DOI:10.1364/OE.22.017360 | OPTICS EXPRESS
17368
-
Figure 5(d) presents another FDTD simulation result showing a
direct comparison of pulse duration between the incident field and
the enhanced field right at the location of the maximum field
enhancement. The incident field was assumed as a FT-limited pulse
of an 800 nm center wavelength with the pulse duration varying in
the range of 3 to 30 fs. Over the entire range of simulation, the
computed value of te is found to closely follow the incident laser
pulse duration within a single oscillation cycle (t0 = 2.67 fs),
even though the relative broadening factor ((te-ti)/t0) appears to
be increasing as ti becomes shorter. This simulation result
supports that the funnel-waveguide is capable of enhancing the
intensity of a few-cycle incident pulse without significant pulse
broadening.
4. Conclusions
Our FDTD simulation performed in this investigation shows that
the proposed 3-D metallic funnel-waveguide is an effective
nanostructure for strong field enhancement of ultrashort light
pulses. The hot spot volume of 20-dB intensity enhancement is
estimated to be ~107 nm3 wherein the incident pulse power is
concentrated with a 53% power coupling efficiency. The instant peak
pulse power is enhanced to be twice the incident laser power due to
the constructive interference of the trailing edge of the incoming
pulse with its the leading edge reflected backwards by the mode
cutoff from the hot spot. Our TPL-exploited experiment confirms
that the maximum enhancement factor reaches 165. In addition, the
ultrafast dephasing profile of the localized field in the hot spot
is identified through the interferometric autocorrelation of the
TPL signal. No thermal or ablation damage is seen even for a ~0.5
TWcm−2 incident laser field, which implies that the peak pulse
intensity can be enhanced to at least 80 TWcm−2 strong enough to
produce extreme ultraviolet light by means of higher harmonic
generation.
Acknowledgments
This work was supported by the National Honor Scientist Research
Program from National Research Foundation of the Republic of Korea
(NRF).
#212831 - $15.00 USD Received 28 May 2014; revised 2 Jul 2014;
accepted 2 Jul 2014; published 9 Jul 2014(C) 2014 OSA 14 July 2014
| Vol. 22, No. 14 | DOI:10.1364/OE.22.017360 | OPTICS EXPRESS
17369