Size and Shape Resonances in Second Harmonic Generation from

Article pubs.acs.org/JPCC

Size and Shape Resonances in Second Harmonic Generation from Silver Nanocavities Adi Salomon,† Marcin Zielinski,‡ Radoslaw Kolkowski,‡,§ Joseph Zyss,‡ and Yehiam Prior*,† †

Department of Chemical Physics, Weizmann Institute of Science, Rehovot 76100, Israel Laboratory of Photonics and Quantum Molecular, Institut d’Alembert, Ecole Normale Superieure de Cachan, 94230 Cachan, France § Institute of Physical and Theoretical Chemistry, Faculty of Chemistry, Wroclaw University of Technology, 50-370 Wroclaw, Poland ‡

ABSTRACT: The nonlinear response of subwavelength nanocavities in thin silver films are investigated. We report on significant enhancements of the second harmonic generation (SHG) when the fundamental wavelength matches dimensional resonances within the nanocavities. The nonlinear polarization properties of the nanocavities are studied as well and found to be correlated with the cavity shape and symmetry. In some nanocavities with internal nanocorrugations, giant field enhancements are observed, making them excellent candidates for high sensitivity spectroscopy.

■

INTRODUCTION Surface plasmons can be readily excited in nanostructures with dimensions smaller than visible light wavelengths. At specific optical frequencies these collective oscillations produce large polarizabilities which reinforce the local electromagnetic (EM) field and enhance the linear and nonlinear optical response of the system.1,2 Surface-enhanced Raman scattering (SERS) exemplifies a nonlinear optical effect that can be boosted by many orders of magnitude due to intensification of the EM field at or near metallic “hot spots”.3,4 Yet, though SERS was observed on rough silver surfaces already in the early 1970s, the engineering and fabrication of metallic structures with predefined shapes and sizes that give rise to enhanced local field has been rather slow. Local field enhancements can be probed also by second harmonic generation (SHG). The measured SHG intensity is proportional to (|E(ω)2∥E(2ω)|)2, where ω is the frequency of the fundamental wavelength, and thus any small modification in the EM field will be enhanced in the SHG signal.5−7 Furthermore, being a coherent process, SHG provides a direct information on the symmetry and the tensorial properties of the local fields8 which cannot be readily accessed by other techniques. Noble metals feature a centrosymmetric face cubic centered crystal structure and therefore should not give rise to SHG signal. However, SHG from metallic surfaces and spherical nanoparticles in solution has already been reported decades ago9−13 and attributed to the excitation of surface plasmons.14 Although enhanced SHG was observed from silver and gold island films already back in 1981,15 the dependency of the © XXXX American Chemical Society

SHG response on the geometrical properties (size and shape) of the metallic nanostructures is still under question.16−18 Several issues have been addressed: (1) irregularities of the metallic structure or small size variations which greatly affect its nonlinear response;16,19 (2) due to a small SHG response, ensembles of nanostructures have been measured,12,16,20−24 which is bound to affect the results due to interactions between neighboring nanostructures; (3) a major part of the studies was carried-out on gold samples irradiated by a standard 800 nm Ti:Sapphire fs lasers. This may complicate the analysis since gold does not sustain surface plasmons at the corresponding 400 nm16,17,19 second-harmonic frequency. In the present article we report on shape and size effects in the SHG response of individual subwavelength nanocavities milled in thin silver films. A significant enhancement of the SHG response is observed when the fundamental wavelength matches newly evidenced dimensional resonances within the nanocavities and the SHG emission patterns coincide with the cavity shape and symmetry. For some cavities, enhanced SHG signal are observed and accounted for by additional finer structural corrugations at the walls of the cavity or irregularities in the cavity structure. Special Issue: Ron Naaman Festschrift Received: March 27, 2013 Revised: May 31, 2013

A

dx.doi.org/10.1021/jp403010q | J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

■

Article

EXPERIMENTAL METHODS

Nanocavities with a typical side length of 100−350 nm have been fabricated by a focused ion beam (FIB, FEI, Helios Nano Lab 600i).25 FIB milling offers a precise and reproducible fabrication tool with a resolution down to 10−20 nm. Silver films (200 nm thickness) were evaporated onto a clean fused silica substrate under high vacuum conditions, with roughness and average grain size measured to be less than 1 and 50 nm, respectively. The film quality (roughness and cleanliness) was found to be a critical parameter for high-resolution nanocavity fabrication. To have similar indices of refraction on both sides of the sample and to prevent sample oxidation, the silver surfaces were covered by a 150 nm thick polyvinyl alcohol (PVA) layer with an average refractive index in the visible to near-infrared of the order of 1.5. The nanocavities shape and size have been characterized by scanning electron microscope (SEM) before and after the SHG measurements. Samples were illuminated by a tunable Ti:sapphire laser (Spectra-Physics Mai-Tai HP, 100 fs, 80 MHz, 2−12 mWatt at the entrance lens, with a fundamental incoming beam tunable between 780 and 980 nm. The linearly polarized laser beam was focused through the glass side using a 0.7 NA objective (×60), resulting in a diffraction limited spot size of about 900 nm full width at half-maximum (d = λ/(n × NA), with λ = 940 nm, n = 1.5, and the numerical aperture NA = 0.7). The epi-reflected SH signal was collected by the same objective, and its two perpendicular polarization components were detected by two calibrated avalanche photodiodes (APD, PerkinElmer). A dichroic mirror was used to block the reflected fundamental beam, and appropriate band-pass filters (Semrock) were used to separate and isolate the SH radiation. The polarization measurements are performed at varying the input polarization angle for the linearly polarized fundamental beams by rotating a half-wavelength plate, applying subsequent corrections for the elliptization from different optical elements in the optical pathway, such as the dichroic mirror.26 The experimental setup is shown in Figure 1. Typically, for each SHG measurement, an array of ∼100 individual nanocavities has been scanned in the same experimental run to provide sufficient statistics. The average integrated SHG signal per cavity was extracted by adding up the measured SH intensity signal from all of the relevant holes and dividing the total intensity by the number of considered holes. The distance between the nanocavities (center to center) was set to be 1 μm (Figure 1a), so as to prevent excitation of collective Bloch modes and to diminish the possibility for coupling between neighbored holes.27,28

Figure 1. Experimental setup. The sample is illuminated by a tunable Ti:sapphire laser (780−980 nm). The linearly polarized laser beam is focused through the glass side using a 0.7 NA objective (×60), resulting in a spot size of about 900 nm full width at half-maximum at λ = 940 nm. The epi-reflected SH signal is collected by the same objective, and its two perpendicular polarization components were detected by two calibrated avalanche photodiodes (APD). A dichroic mirror (DM) was used to block the reflected fundamental beam was used to separate and isolate the SH radiation. The polarization measurements are performed at varying in-plane angles for the linearly polarized fundamental beams by rotating a half-wavelength plate (WP).

are not coupled to each other and can be considered as independent individual cavities. Some of the cavities give rise to suppressed or enhanced SHG response. These cavities have been found a posteriori to be blocked by metal residue or to have an addition finer corrugation inside the cavity as is discussed below. SHG as a Function of the Cavity Size and Symmetry. Next we study how the SHG response is dependent on the geometrical parameters of the cavity. Two parameters are considered: the cavity symmetry and its size. Figure 3 depicts the dependence of the SHG signal on the cavity side length, for both equilateral triangular and squares cavities. Two observations can be inferred therefrom: First, for any given cavity size, the SHG emission from the triangular cavities is much larger than that from the squares. The enhancement is ascribed to lack of inversion symmetry in the triangular holes and to its relatively sharp corners. The observed SHG response from the square holes may result from a small asymmetry in its shape (see Figure 4b inset), leading to anharmonicity in the induced electric field and thus coupling to dipolar fields. However, it should be noted that purely centro-symmetric structures may lead to a measurable SHG response, due to nonlocal effects and the related quadrupolar coupling mechanism. Dipolar coupling allowed in noncentro-symmetric structures and accounting for their associated local response is nevertheless expected to be dominant over quadrupolar coupling, as we do report here. Second, for both shapes, maxima are observed typically for a side length of about a = 150−200 nm. The observed

■

RESULTS AND DISCUSSION SHG Response of the Individual Nanocavity. Figure 2 depicts a typical SHG measurement from individual cavities: a scanning electron micrograph of a typical triangular nanocavity array is shown with its corresponding SHG response. A typical spectrum of the SHG stemming from the nanocavity is shown in Figure 2c. No luminescence or other three photon process is observed, indicating high quality and purity of the silver film. The signals originating from the cavities are quite uniform, with a negligible background from the silver film. Almost no signal is observed between the nanocavities, and the SHG responses of cavities at the edges are similar to those which are located at the middle, confirming that the nanocavities B

dx.doi.org/10.1021/jp403010q | J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

Article

Figure 2. (a) Scanning electron micrograph image of 100 equilateral holes with side lengths of 190 nm, separated by 1 μm. The scale bar is 5 μm. The red circle indicates the focused input beam spot size in our experimental conditions. Inset: magnification of one of the holes. (b) Scanning of the SHG signal obtained from the array presented in part a under illumination of 940 nm. (c) A typical SHG spectrum of individual nanocavity. Inset: double log plot of the SHG power exhibiting a slope of 2.

Figure 3. Normalized SHG signal for individual triangular cavities (scattered triangles) and square cavities (scattered squares) as a function of their side length. The fundamental wavelength was 940 nm, and the laser power was 9 mW. For each SHG measurement, an array of ∼100 individual nanocavities has been scanned to provide good statistics. The average integrated SHG signal per cavity was extracted by adding up the measured SH intensity signal from all the relevant cavities and dividing the total intensity by the number of considered holes. Cavities which results as extremely high or low SHG have been excluded from the statistics.

resonances located at a = λ/3·n or a = λ/4·n for triangular and square cavities respectively, where λ is the fundamental wavelength and n = 1.5 is the dielectric constant of the material which is in contact with the silver film (fused silica or PVA). The data discussed in Figure 3 result from an average over the entire array of nano cavities, thus averaging over possible variations hole size. We note that the SHG signal intensity does not depend on the cavity area or the total circumference, but rather on more specific geometrical parameters.29 Clearly the SHG response is either suppressed or enhanced as function of the cavity side length for both square and triangular cavities. SHG Response as a Function of Fundamental Wavelength. As a complementary experiment and to further account for the size dependence, we measured the SHG response as a function of the fundamental wavelength, over the range of 820−980 nm. Figure 4a,b shows the result for both triangular and square holes, both with a nominal side length of a = 205− 210 nm. Clear resonances are observed, unlike the cavity size dependence; here the measurement is of the SHG from a single cavity, and therefore inaccuracies in cavity size are not averaged. Thus, a direct comparison with Figure 3 should not be attempted.

Figure 4. SHG response as a function of the fundamental wavelength for (a) triangular cavities with a side length of ∼210 nm and (b) for square cavities with a side length of ∼205 nm. Inset: SEM image of a square cavity. The laser power before the objective was 5 mW for triangular cavities and 12 mW for square cavities. The SHG signal is divided by the bare silver surface responses and is corrected according to the specifications of the optical elements. The polarization of the incident excitation beam was in the sample plane.

The results presented in Figures 3 and 4 clearly indicate that these nanocavities can be viewed as a resonator where the geometrical parameters determine the local field enhancement. In analogy to optical resonances such as microcavities,30 localized plasmons can be viewed as the cavity eigenmodes of Maxwell equations.31 While these plasmonic modes are directly coupled to the excitation beam, they may be localized in regions smaller than the wavelength of the light inducing them.32 Polarization Properties of the Nanocavities. To account for the polarization properties of these nanocavities, C

dx.doi.org/10.1021/jp403010q | J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

Article

Figure 5. Experimental polar plots of the SH emissions from (a) bare silver film, (b) a rectangular cavity, (c) a triangular hole, and (d) a triple triangle hole and their corresponding SEMs. The excitation wavelength was 940 nm, and the laser power was 8 mW for the silver film 5 mW for the rectangular cavity and 2 mW for the triangular hole. The scale bars are 200 nm each.

we first study the SHG emission pattern from the silver film itself since surface imperfections and roughness may contribute to the observed signal. Figure 5a depicts both the X and the Y components of the SH emission collected from the silver film. Two perpendicular dipolar lobes pattern are observed, and the total signal may be summed into a circular, polarization independent, intensity plot. These polar plots provide a typical signature of the incoherent process, namely, hyper Raman scattering (HRS) and results from contributions of randomly oriented dipoles. These dipoles are induced in individual silver grains (diameter ∼50 nm) and are excited within the ∼900 nm diameter fundamental beam at very high laser power. The situation is very different when a single rectangular nanocavity is irradiated. In a rectangular cavity the excited dipole has a welldefined orientation, and therefore the SH response is highly dependent on the input beam polarization. This is clearly seen in Figure 5b, where the SHG intensity is noticeable when both illumination and detection have horizontal (x-axis) polarization and is suppressed for the orthogonal (y-axis) analysis polarization. Moreover, even though the cavity is much smaller than the beam area, the oscillating dipole inside the rectangular cavity gives rise to a relatively strong nonlinear response which overwhelms the incoherent response of the silver film around the cavity. Next we study the emission pattern from cavities with different shapes and symmetries. The 3-fold symmetry cavities (Figures 5c,d) for any given side length yielded a very clear octupolar (J = 3) polarization pattern, a signature for a 3-fold symmetry object.33,34 The nonintuitive 4-fold symmetry pattern for the triangles results from our measurement setup. We do not rotate the sample but rather rotate the angle of polarization of the input beam, for a fixed sample and fixed polarization analyzers. Thus, two polarization projections are involved, which together give rise to the apparent flower-shaped 4-fold symmetry. While, in linear measurements, these emission patterns can be ascribed to an isotropic field distribution (J = 0), in SHG, contributions to the second-order susceptibility χ(2) tensor preclude a dipolar J = 1 component by

virtue of the 3-fold symmetry of nanotriangles, whereas even order components (J = 0 and 2) are assumed negligible assuming Kleinman symmetry. In the χ(2) tensor rotational spectrum, this leaves only a J = 3 component. Furthermore, the observed SHG in our cavities is purely local, and contributions from gradient of fundamental field (retardation effect) or from coupling to higher order gradient in the induced polarization are negligible. These high-quality polar plots which coincide with the cavity contour shape indicate that the SHG emission is barely affected by contribution from the silver film, making them an excellent candidate for studying their coupling to neighboring cavities and to molecular systems. Hot Spots. As was noted above, some nanocavities gave rise to enhanced SHG signals which were several orders of magnitude stronger than the radiation observed from nominally identical cavities. Figure 6 illustrates such a case for a set of

Figure 6. Left: scanning of the SHG signal from array of isolated 330 nm side length equilateral triangles separated by 1 μm. While the average signal is about 120 counts/0.2 s, some of the “hot spot” triangles give rise to signals which are 200 times higher (25 000 counts/0.2 s). Right: SEM images of two “hot spots” as marked in the left panel. The giant SHG signal results from corrugated walls of the triangular hole. D

dx.doi.org/10.1021/jp403010q | J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

Article

Films and Ag Film over Polymer Nanosphere Surfaces Supported on Glass. J. Chem. Phys. 1993, 99 (3), 2101−2115. (5) Stockman, M. I.; Bergman, D. J.; Anceau, C.; Brasselet, S.; Zyss, J. Enhanced Second-Harmonic Generation by Metal Surfaces with Nanoscale Roughness: Nanoscale Dephasing, Depolarization, And Correlations. Phys. Rev. Lett. 2004, 92 (5), 057402. (6) Anceau, C.; Brasselet, S.; Zyss, J.; Gadenne, P. Local SecondHarmonic Generation Enhancement on Gold Nanostructures Probed by Two-Photon Microscopy. Opt. Lett. 2003, 28 (9), 713−715. (7) Schuller, J. A.; Barnard, E. S.; Cai, W. S.; Jun, Y. C.; White, J. S.; Brongersma, M. L. Plasmonics for Extreme Light Concentration and Manipulation. Nat. Mater. 2010, 9 (3), 193−204. (8) Le Floc’h, V.; Brasselet, S.; Roch, J.-F.; Zyss, J. Monitoring of Orientation in Molecular Ensembles by Polarization Sensitive Nonlinear Microscopy. J. Phys. Chem. B 2003, 107 (45), 12403− 12410. (9) Brown, F.; Parks, R. E.; Sleeper, A. M. Nonlinear Optical Reflection from a Metallic Boundary. Phys. Rev. Lett. 1965, 14 (25), 1029−&. (10) Vance, F. W.; Lemon, B. I.; Hupp, J. T. Enormous HyperRayleigh Scattering from Nanocrystalline Gold Particle Suspensions. J. Phys. Chem. B 1998, 102 (50), 10091−10093. (11) Johnson, R. C.; Li, J. T.; Hupp, J. T.; Schatz, G. C. HyperRayleigh Scattering Studies of Silver, Copper, and Platinum Nanoparticle Suspensions. Chem. Phys. Lett. 2002, 356 (5−6), 534−540. (12) Chandra, M.; Das, P. K. “Small-Particle Limit” in the Second Harmonic Generation from Noble Metal Nanoparticles. Chem. Phys. 2009, 358 (3), 203−208. (13) Moran, A. M.; Sung, J. H.; Hicks, E. M.; Van Duyne, R. P.; Spears, K. G. Second Harmonic Excitation Spectroscopy of Silver Nanoparticle Arrays. J. Phys. Chem. B 2005, 109 (10), 4501−4506. (14) Agarwal, G. S.; Jha, S. S. Surface-Enhanced Raman-Scattering in a 2-Oscillator Electromagnetic Model. Phys. Rev. B 1982, 26 (8), 4013−4021. (15) Wokaun, A.; Bergman, J. G.; Heritage, J. P.; Glass, A. M.; Liao, P. F.; Olson, D. H. Surface Second-Harmonic Generation from Metal Island Films and Microlithographic Structures. Phys. Rev. B 1981, 24 (2), 849−856. (16) van Nieuwstadt, J. A. H.; Sandtke, M.; Harmsen, R. H.; Segerink, F. B.; Prangsma, J. C.; Enoch, S.; Kuipers, L. Strong Modification of the Nonlinear Optical Response of Metallic Subwavelength Hole Arrays. Phys. Rev. Lett. 2006, 97, 146102. (17) Schon, P.; Bonod, N.; Devaux, E.; Wenger, J.; Rigneault, H.; Ebbesen, T. W.; Brasselet, S. Enhanced Second-Harmonic Generation from Individual Metallic Nanoapertures. Opt. Lett. 2010, 35 (23), 4063−4065. (18) Hanke, T.; Cesar, J.; Knittel, V.; Trugler, A.; Hohenester, U.; Leitenstorfer, A.; Bratschitsch, R. Tailoring Spatiotemporal Light Confinement in Single Plasmonic Nanoantennas. Nano Lett. 2012, 12 (2), 992−996. (19) Yin, L.; Vlasko-Vlasov, V. K.; Rydh, A.; Pearson, J.; Welp, U.; Chang, S. H.; Gray, S. K.; Schatz, G. C.; Brown, D. B.; Kimball, C. W. Surface Plasmons at Single Nanoholes in Au Films. Appl. Phys. Lett. 2004, 85 (3), 467−469. (20) Nappa, J.; Russier-Antoine, I.; Benichou, E.; Jonin, C.; Brevet, P. F. Second Harmonic Generation from Small Gold Metallic Particles: From the Dipolar to the Quadrupolar Response. J. Chem. Phys. 2006, 125 (18), 184712. (21) Nappa, J.; Revillod, G.; Russier-Antoine, I.; Benichou, E.; Jonin, C.; Brevet, P. F. Electric Dipole Origin of the Second Harmonic Generation of Small Metallic Particles. Phys. Rev. B 2005, 71 (16), 165407. (22) Czaplicki, R.; Zdanowicz, M.; Koskinen, K.; Laukkanen, J.; Kuittinen, M.; Kauranen, M. Dipole Limit in Second-Harmonic Generation from Arrays of Gold Nanoparticles. Opt. Express 2011, 19 (27), 26866−26871. (23) Awada, C.; Jonin, C.; Kessi, F.; Adam, P. M.; Kostcheev, S.; Bachelot, R.; Royer, P.; Samah, M.; Russier-Antoine, I.; Benichou, E.; Bachelier, G.; Brevet, P. F. Polarized Second Harmonic Response of

triangular holes, all with a a = 320 nm side length and illuminated by a 940 nm input beam. To account for these enhanced signals, we examined more closely the relevant individual holes and invariably found an additional finer internal structure resulting from either incomplete drilling of the metal layer or additional roughness or finer corrugation at the walls of the holes. These imperfect nanocavities are shown in Figure 6. Significant enhancements of EM fields might be explained by scattering of the input beam due to the small-sized structures, something that leads to coupling to any localized modes. The extreme sensitivity of these structures to corrugation and internal fine structure are the subject of current investigations. The observation of these EM field enhancements may eventually lead to controlled fabrication of specific structures where strong enhancement of the electric fields may enable very sensitive detection, possibly down to the single molecule level.35,36

■

CONCLUSIONS In conclusion we have shown experimentally that the side length of individual nanocavities strongly affects their nonlinear behavior while their emitted harmonic polarization pattern is abiding to their shape and results from excitation of surface plasmon localized modes. These localized modes are trapped in the nanocavities and therefore give rise to relatively high EM enhancement which might affect linear optical behavior as well.37−41 We note that an increase of 1−2 orders of magnitude in the emitted SHG intensity was observed when small changes in the geometrical parameters of the nanocavity were introduced. Understanding the nanocavity, symmetry, contour shape, and size effects on the EM field enhancement and its emitted harmonic polarization pattern opens up the possibility of designing artificial nanomaterials with modulated emission pattern and high sensitivity. These nanoplasmonic cavities can be used for SERS, data storage, high resolution sensing, optical switches and photochemistry42 at the nanoscale43 and openingup to the exploitation of the tensor dimensions inherent to nonlinear optics.

■

AUTHOR INFORMATION

Corresponding Author

*Phone: +972-8-9344008; e-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS We acknowledge the support of the Israel Science Foundation and Weizmann-CNRS NaBi LEA laboratory. Part of this work is supported by a grant from the Grand Center for Sensors and Security and the James Franck Program.

■

REFERENCES

(1) de Abajo, F. J. G. Colloquium: Light Scattering by Particle and Hole Arrays. Rev. Mod. Phys. 2007, 79 (4), 1267−1290. (2) Zijlstra, P.; Orrit, M. Single Metal Nanoparticles: Optical Detection, Spectroscopy and Applications. Rep. Prog. Phys. 2011, 74, 106401. (3) Nie, S.; Emory, S. R. Probing Single Molecules and Single Nanoparticles by Surface-Enhanced Raman Scattering. Science 1997, 275 (5303), 1102−1106. (4) Vanduyne, R. P.; Hulteen, J. C.; Treichel, D. A. Atomic-Force Microscopy and Surface-Enhanced Raman-Spectroscopy. 1. Ag Island E

dx.doi.org/10.1021/jp403010q | J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

Article

Square, Hexagonal and Random Arrays of Gold Metallic Nanocylinders. Opt. Mater. 2011, 33 (9), 1440−1444. (24) Xu, T.; Jiao, X.; Zhang, G. P.; Blair, S. Second-Harmonic Emission from Sub-Wavelength Apertures: Effects of Aperture Symmetry and Lattice Arrangement. Opt. Express 2007, 15 (21), 13894−13906. (25) Nagpal, P.; Lindquist, N. C.; Oh, S. H.; Norris, D. J. Ultrasmooth Patterned Metals for Plasmonics and Metamaterials. Science 2009, 325 (5940), 594−597. (26) Zielinski, M.; Oron, D.; Chauvat, D.; Zyss, J. Second-Harmonic Generation from a Single Core/Shell Quantum Dot. Small 2009, 5 (24), 2835−2840. (27) Hentschel, M.; Saliba, M.; Vogelgesang, R.; Giessen, H.; Alivisatos, A. P.; Liu, N. Transition from Isolated to Collective Modes in Plasmonic Oligomers. Nano Lett. 2010, 10 (7), 2721−2726. (28) Halas, N. J.; Lal, S.; Chang, W. S.; Link, S.; Nordlander, P. Plasmons in Strongly Coupled Metallic Nanostructures. Chem. Rev. 2011, 111 (6), 3913−3961. (29) Hanke, T.; Krauss, G.; Trautlein, D.; Wild, B.; Bratschitsch, R.; Leitenstorfer, A. Efficient Nonlinear Light Emission of Single Gold Optical Antennas Driven by Few-Cycle Near-Infrared Pulses. Phys. Rev. Lett. 2009, 103 (25), 257404. (30) Bogomolny, E.; Djellali, N.; Dubertrand, R.; Gozhyk, I.; Lebental, M.; Schmit, C.; Ulysse, C.; Zyss, J. Trace Formula for Dielectric Cavities. II. Regular, Pseudointegrable, And Chaotic Examples. Phys. Rev. E 2011, 83 (3), 036208. (31) Cole, R. M.; Baumberg, J. J.; Garcia de Abajo, F. J.; Mahajan, S.; Abdelsalam, M.; Bartlett, P. N. Understanding Plasmons in Nanoscale Voids. Nano Lett. 2007, 7 (7), 2094−2100. (32) Wang, F.; Shen, Y. R. General Properties of Local Plasmons in Metal Nanostructures. Phys. Rev. Lett. 2006, 97 (20), 206806. (33) Zyss, J. Molecular Engineering Implications of Rotational Invariance in Quadratic Nonlinear Optics: From Dipolar to Octupolar Molecules and Materials. J. Chem. Phys. 1993, 98, 6583. (34) Brasselet, S.; Zyss, J. Multipolar Molecules and Multipolar Fields: Probing and Controlling the Tensorial Nature of Nonlinear Molecular Media. J. Opt. Soc. Am. B 1998, 15 (1), 257−288. (35) Hrelescu, C.; Sau, T. K.; Rogach, A. L.; Jackel, F.; Feldmann, J. Single Gold Nanostars Enhance Raman Scattering. Appl. Phys. Lett. 2009, 94 (15), 153113. (36) Talley, C. E.; Jackson, J. B.; Oubre, C.; Grady, N. K.; Hollars, C. W.; Lane, S. M.; Huser, T. R.; Nordlander, P.; Halas, N. J. SurfaceEnhanced Raman Scattering from Individual Au Nanoparticles and Nanoparticle Dimer Substrates. Nano Lett. 2005, 5 (8), 1569−1574. (37) Kim, J. H.; Moyer, P. J. Transmission Characteristics of Metallic Equilateral Triangular Nanohole Arrays. Appl. Phys. Lett. 2006, 89 (12), 121106. (38) Chang, S. H.; Gray, S. K.; Schatz, G. C. Surface Plasmon Generation and Light Transmission by Isolated Nanoholes and Arrays of Nanoholes in Thin Metal Films. Opt. Express 2005, 13 (8), 3150− 3165. (39) Fan, W. J.; Zhang, S.; Minhas, B.; Malloy, K. J.; Brueck, S. R. J. Enhanced Infrared Transmission through Subwavelength Coaxial Metallic Arrays. Phys. Rev. Lett. 2005, 94 (3), 4406. (40) van der Molen, K. L.; Klein Koerkamp, K. J.; Enoch, S.; Segerink, F. B.; van Hulst, N. F.; Kuipers, L. Role of Shape and Localized Resonances in Extraordinary Transmission through Periodic Arrays of Subwavelength Holes: Experiment and Theory. Phys. Rev. B 2005, 72 (4), 045421. (41) Koerkamp, K. J. K.; Enoch, S.; Segerink, F. B.; van Hulst, N. F.; Kuipers, L. Strong Influence of Hole Shape on Extraordinary Transmission through Periodic Arrays of Subwavelength Holes. Phys. Rev. Lett. 2004, 92 (18), 183901. (42) Salomon, A.; Genet, C.; Ebbesen, T. W. Molecule-Light Complex: Dynamics of Hybrid Molecule-Surface Plasmon States. Angew. Chem., Int. Ed. 2009, 48 (46), 8748−8751. (43) Kim, S.; Jin, J. H.; Kim, Y. J.; Park, I. Y.; Kim, Y.; Kim, S. W. High-Harmonic Generation by Resonant Plasmon Field Enhancement. Nature 2008, 453 (7196), 757−760. F

dx.doi.org/10.1021/jp403010q | J. Phys. Chem. C XXXX, XXX, XXX−XXX