Doubly resonant metallic nanostructure for high conversion efficiency of second harmonic generation

doi:10.1364/OE.20.004856

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Doubly resonant metallic nanostructure for high conversion efficiency of second harmonic generation

Sinjeung Park, Jae W. Hahn, and Jae Yong Lee »View Author Affiliations

Optics Express, Vol. 20, Issue 5, pp. 4856-4870 (2012)
http://dx.doi.org/10.1364/OE.20.004856

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Abstract

The recent discovery of strong nonlinear emission in metallic nanostructures has offered possibilities for realization of functional nano photonic devices. Here, we demonstrate a novel design of a plasmonic nano device for high conversion efficiency of second harmonic generation. A 4 × 4 bowtie aperture array is fabricated to have both plasmonic resonance for local field enhancement of the fundamental wave and Fabry-Pérot resonance for high transmission of second harmonic wave. Combining nano structures for exciting surface plasmon polariton and suppressing higher order diffraction and anti-reflection layer, we achieve a second harmonic conversion efficiency of 1.4×10⁻⁸ that is nearly an order of magnitude larger than the results published in recent literatures. We also theoretically analyze evidences of the role of double resonances tuned to the fundamental wave and the second harmonic wave, resulting in the augmentation of second harmonic response approximately an order of magnitude greater than that without the help of the resonance.

1. Introduction

Nonlinear optics in the nanometer scale is getting substantial attention for its central role in the realization of novel nanophotonic devices. Although optical frequency conversion is a keystone of various nonlinear optical applications such as logic, switching, and sensing [1

J. Renger, R. Quidant, N. van Hulst, and L. Novotny, “Surface-enhanced nonlinear four-wave mixing,” Phys. Rev. Lett. 104(4), 046803 (2010). [CrossRef] [PubMed]

], it is still challenging to induce strong nonlinear response from materials subwavelength in size, such as interfaces [2

N. Kroo, G. Farkas, P. Dombi, and S. Varró, “Nonlinear processes induced by the enhanced, evanescent field of surface plasmons excited by femtosecond laser pulses,” Opt. Express 16(26), 21656–21661 (2008). [CrossRef] [PubMed]

, 3

S. Palomba and L. Novotny, “Nonlinear excitation of surface plasmon polaritons by four-wave mixing,” Phys. Rev. Lett. 101(5), 056802 (2008). [CrossRef] [PubMed]

], discrete particles [4

A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, “Near-field second-harmonic generation induced by local field enhancement,” Phys. Rev. Lett. 90(1), 013903 (2003). [CrossRef] [PubMed]

, 5

M. Lippitz, M. A. van Dijk, and M. Orrit, “Third-harmonic generation from single gold nanoparticles,” Nano Lett. 5(4), 799–802 (2005). [CrossRef] [PubMed]

], or nanostructures [6

T. Xu, X. Jiao, G. P. Zhang, and S. Blair, “Second-harmonic emission from sub-wavelength apertures: Effects of aperture symmetry and lattice arrangement,” Opt. Express 15(21), 13894–13906 (2007). [CrossRef] [PubMed]

–9

R. Zhou, H. Lu, X. Liu, Y. Gong, and D. Mao, “Second-harmonic generation from a periodic array of noncentrosymmetric nanoholes,” J. Opt. Soc. Am. B 27(11), 2405–2409 (2010). [CrossRef]

]. The task is quite straightforward in bulk optics by choosing a material with high nonlinear susceptibility and satisfying the so-called phase matching condition [10

R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic Press, Amsterdam and Boston, 2008).

]. In nanophotonics, however, the theory of nonlinear optics has not been well established, partly due to a complication that the optical near-fields around subwavelength structures are no longer plane waves of infinite extension and often experiencing considerable intensity modulation. Alternative approaches other than phase matching are therefore required for nanophotonic devices to boost nonlinear response.

Early studies have first focused on the enhanced transmission of incident light in metal nanostructures involving surface plasmon polaritons (SPPs) [1

J. Renger, R. Quidant, N. van Hulst, and L. Novotny, “Surface-enhanced nonlinear four-wave mixing,” Phys. Rev. Lett. 104(4), 046803 (2010). [CrossRef] [PubMed]

, 2

, 11

P. Genevet, J.-P. Tetienne, E. Gatzogiannis, R. Blanchard, M. A. Kats, M. O. Scully, and F. Capasso, “Large enhancement of nonlinear optical phenomena by plasmonic nanocavity gratings,” Nano Lett. 10(12), 4880–4883 (2010). [CrossRef] [PubMed]

, 12

K. D. Ko, A. Kumar, K. H. Fung, R. Ambekar, G. L. Liu, N. X. Fang, and K. C. Toussaint Jr., “Nonlinear optical response from arrays of Au bowtie nanoantennas,” Nano Lett. 11(1), 61–65 (2011). [CrossRef] [PubMed]

], with a predictable increase in the nonlinear response according to its polynomial dependence on the fundamental intensity. The large local field induced by the fundamental light in metal nano structure has been shown to greatly benefit nonlinear processes such as second harmonic generation (SHG) [11

–13

T.-D. Onuta, M. Waegele, C. C. DuFort, W. L. Schaich, and B. Dragnea, “Optical field enhancement at cusps between adjacent nanoapertures,” Nano Lett. 7(3), 557–564 (2007). [CrossRef] [PubMed]

], third harmonic generation (THG) [14

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). [CrossRef] [PubMed]

], and supercontinuum (SC) generation [15

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308(5728), 1607–1609 (2005). [CrossRef] [PubMed]

]. In the past few years, various geometries of nanostructures, differing in shape and size, have been extensively investigated to give control over the degree of field enhancement as well as its spectral resonance and spatial confinement features [16

X. Shi and L. Hesselink, “Mechanisms for enhancing power throughput from planar nano apertures for near field optical data storage,” Jpn. J. Appl. Phys. 41(Part 1, No. 3B), 1632–1635 (2002). [CrossRef]

–18

H. Guo, T. P. Meyrath, T. Zentgraf, N. Liu, L. Fu, H. Schweizer, and H. Giessen, “Optical resonances of bowtie slot antennas and their geometry and material dependence,” Opt. Express 16(11), 7756–7766 (2008). [CrossRef] [PubMed]

]. A huge enhancement of the local field has been successfully demonstrated with single hot holes including a rectangular hole with a certain aspect ratio [19

J. A. H. van Nieuwstadt, M. Sandtke, R. H. Harmsen, F. B. Segerink, J. C. Prangsma, S. Enoch, and L. Kuipers, “Strong modification of the nonlinear optical response of metallic subwavelength hole arrays,” Phys. Rev. Lett. 97(14), 146102 (2006). [CrossRef] [PubMed]

], a circular hole surrounded by ordered surface corrugations [20

A. Nahata, R. A. Linke, T. Ishi, and K. Ohashi, “Enhanced nonlinear optical conversion from a periodically nanostructured metal film,” Opt. Lett. 28(6), 423–425 (2003). [CrossRef] [PubMed]

], a bowtie antenna [12

], a nanoslit resonator surrounded by a grating-based optical antenna [21

W. Cai, A. P. Vasudev, and M. L. Brongersma, “Electrically controlled nonlinear generation of light with plasmonics,” Science 333(6050), 1720–1723 (2011). [CrossRef] [PubMed]

], etc., yielding a strong nonlinear response as a consequence. The mechanism responsible for such enhancement is a transmission resonance involving SPPs generated in certain metal nanostructures, with their strong fields interacting constructively. Furthermore, employing multiple nanostructures into a periodic array has been shown to boost the local field intensity by an order of magnitude greater than that of an isolated structure [12

, 22

Y. Chu, E. Schonbrun, T. Yang, and K. B. Crozier, “Experimental observation of narrow surface plasmon resonances in gold nanoparticle arrays,” Appl. Phys. Lett. 93(18), 181108 (2008). [CrossRef]

, 23

B. Auguié and W. L. Barnes, “Collective resonances in gold nanoparticle arrays,” Phys. Rev. Lett. 101(14), 143902 (2008). [CrossRef] [PubMed]

]. This type of enhancement occurs when an ensemble of metallic apertures can act together by an electrodynamic coupling provided that the wave vectors of an SPP excitation and a 2-D grating are appropriately matched in momentum [24

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998). [CrossRef]

]. Many experiments have revealed a good correlation between the enhanced transmission of a fundamental light and the increase of nonlinear response.

There has been, however, a notion [12

] that a stronger local field with resonance matching is not necessarily the only prerequisite for a stronger nonlinear emission. This implies that the intensity enhancement of a fundamental light is not the essential limiting factor and other mechanisms may be introduced to boost nonlinear response further. Another factor that plays an important role in the nonlinear optics using nanostructures can be their symmetry. In SHG, for instance, it is crucial to incorporate a nonlinear medium or morphological features lacking in inversion symmetry into nanostructures. Several investigations have found that reducing the geometrical symmetry in metal nanostructures [7

M. W. Klein, C. Enkrich, M. Wegener, and S. Linden, “Second-harmonic generation from magnetic metamaterials,” Science 313(5786), 502–504 (2006). [CrossRef] [PubMed]

–9

R. Zhou, H. Lu, X. Liu, Y. Gong, and D. Mao, “Second-harmonic generation from a periodic array of noncentrosymmetric nanoholes,” J. Opt. Soc. Am. B 27(11), 2405–2409 (2010). [CrossRef]

, 25

Y. Zhang, N. K. Grady, C. Ayala-Orozco, and N. J. Halas, “Three-dimensional nanostructures as highly efficient generators of second harmonic light,” Nano Lett. 11(12), 5519–5523 (2011). [CrossRef] [PubMed]

] can also be of significant benefit to SHG, while even a centrosymmetric structure can exhibit a nonzero second-order susceptibility arising from symmetry breaking at an interface, sufficient to produce scattered emission of SHG [6

]. Notably, a dielectric nanoparticle capped with a tilted hemispherical metal layer has demonstrated an intense SHG with conversion efficiencies similar to those of inorganic SHG crystals [25

]. Despite the significant findings and progresses made so far, our understanding of the nonlinearity of plasmonic nanostructures is as yet incomplete and new approaches can still be implemented to improve their nonlinear response.

In this paper, we design and experimentally demonstrate a scheme for plasmonic nano photonic devices to achieve enhanced SH response by taking advantage of “double resonances” with a fundamental and SH light at the same time. Along with the well-known benefit of enhanced fundamental intensity, the transmission resonance at SH wavelength is introduced to effectively extract the SH wave generated in the metallic nanostructure. The idea of using double resonance of plasmonic nanostructures has been previously proposed to enhance the effective nonlinearity of a metamaterial consisting of nanoparticles with third-order nonlinear dielectric core coated by metallic shell [26

A. A. Zharov and N. A. Zharova, “Double-resonance plasmon-driven enhancement of nonlinear optical response in a metamaterial with coated nanoparticles,” JETP Lett. 92(4), 210–213 (2010). [CrossRef]

]. By means of a theoretical model, it has been predicted that a giant enhancement in third harmonic response would occur when the linear dipole response of a metamaterial at the fundamental frequency and its harmonic can be simultaneously tuned into resonance with each surface plasmon modes of different type. This requirement is, to some extent, analogous to the phase matching condition to be met for coherent signal buildup in an efficient frequency conversion using bulk nonlinear materials. We here hypothesize that the efficiency of nonlinear signal buildup and out-coupling from a nanostructure is proportional to its linear transmission at the SH wavelength and that their resonance properties possess spectral similarity to each other. Based on these assumptions, we explore a configuration of metallic bowtie nano-apertures (BNA) that allow for a strong plasmonic resonance with the fundamental and a concomitant Fabry-Pérot-like (FP-like) resonance occurring at half the wavelength of the fundamental. To maximize the SH conversion efficiency of the plasmonic device, we integrate such BNAs for excitation of SPP modes into a device structure being able to suppress higher-order diffraction and support anti-reflection layers.

We first work out a design of doubly resonant BNA in a silver film by performing finite-difference time-domain (FDTD) simulations. Spectral profiles of the linear transmission in symmetric and asymmetric BNAs are tailored to exhibit strong resonances at the fundamental and corresponding SH wavelengths. The BNAs are then further engineered into 4 × 4 square periodic arrays, which allow for an extra gain in the SH signal emanating in the zeroth diffraction order from the array structures. In the experiment, the forward-transmitted SH radiation from the BNA arrays is measured to assess optical conversion efficiency as a function of the fundamental wavelength. The normalized-to-area efficiency at the designed resonance wavelength is found to exhibit a nonlinear enhancement that cannot be attributed solely to the enhanced fundamental intensity. Combined with the observation of an increase in SH response by an order of magnitude further, spectral analysis of the measured SH efficiency against theoretical predictions is carried out to indicate the effect of implementing a resonance for SH transmission.

2. Designing doubly resonant metallic bowtie apertures (BNAs)

It has been well recognized that subwavelength metallic bowtie structures can lead to a drastic increase of the applied field tightly bound within the feed gap region, arising from localized surface plasmon resonances (SPRs) at the tip of two sharp ridges and their strong electrodynamic coupling. Metallic bowtie apertures (BNAs) may support multiple transmission resonances of different origins, involving a SPR peak and several FP-like features occurring at shorter wavelengths. With incident fields at the SPR wavelength, surface plasmon polaritons (SPPs) are most favorably excited around the aperture edge [18

] to produce the highest amplitude of local fields. The SPR wavelength depends critically on the geometry of BNAs including gap size, ridge shape, aperture side lengths, etc. The parasitic resonance features, what we referred to as FP-like peaks, also exhibit similar enhancements in transmission. They are, however, more likely to depend on the thickness of metal films in which BNAs are formed, for being associated with the channel wall current of the structure [18

]. In designing BNAs for an enhanced SH response, we here attempt to use double resonances, one at the SPR wavelength for a fundamental light and the other at a FP-like peak tuned to the corresponding SH wavelength. Combined with the field enhancement of the fundamental, we anticipate a further increase in the SHG output, resulting from such BNAs that represent a channel-like resonance in the transmission of SH light as well as its coherent buildup.

We first explore the design for doubly resonant BNAs in a silver film on a Si₃N₄-on-quartz substrate [Fig. 1(a) ]. Silver is chosen as a film material because it is metallic in the broad spectrum ranging from visible to near-infrared and a large field enhancement can be expected due to its high dielectric constant in the real part relative to the imaginary part [27

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, Berlin and Heidelberg, 1988).

]. The silicon nitride (Si₃N₄) layer, described in detail in a later section, is introduced for implementing BNAs in a periodic array to augment the SH emission in the experiment. We assume BNAs that are illuminated by a fundamental light tunable from 800 nm to 900 nm in wavelength. Therefore the SPR wavelength of the BNAs should reside the fundamental wavelength range and this condition dictates that a FP-like SH resonance be occurring at half the fundamental wavelength, between 400 nm to 450 nm.

Fig. 1 (a) The geometrical configuration for a metallic BNA array generating SH emission in the forward direction, where a laser beam illuminates the BNAs milled in the silver film on a Si₃N₄-on-quartz substrate. The incident beam is polarized parallel to the bowtie axes that are laid horizontally in the figure. The silicon nitride layer of thickness

d

= 300 nm is used in implementing BNAs in a periodic array with a spacing

a_{0}

= 400 nm. The silver film thickness

t

is optimized for enhancing SH response and set to 50 nm. (b) Simulated linear spectral transmission of single BNAs exhibiting double resonances due to the surface plasmon resonance and FP-like behavior of the metallic nanostructures.). Curves represent the linear dipole response of an individual BNA, quantified by normalized intensity of the electric field with horizontal (x) polarization at the center on the aperture’s exit plane. FDTD calculations are made from the pulse response of the BNAs with an outline length of 70 nm and ridge gap of 20 nm, varying in the silver film thickness

t

as 30 nm (red), 50 nm (blue), and 80 nm (greenThe dashed lines are guides to the eye, representing the design wavelengths for the fundamental (860 nm) and SH (430 nm) light.

Using FDTD simulations with a commercial software (Optiwave OptiFDTD), we optimize a set of parameters regarding the BNA geometry to tailor the spectral profiles of linear transmission for such BNAs. A doubly resonant design can be obtained, for example, with a 50-nm-thick silver BNA having the outline length of 70 nm and the ridge gap of 20 nm, permitting a SPR peak centered at 860 nm and an isolated FP-like peak at 435 nm as shown in Fig. 1(b). For an incident beam polarized parallel to the bowtie axis (along the x-axis), the SPR peak is found to enhance the fundamental intensity by a factor of about 60 and the FP-like peak of the same order arises at nearly SH wavelength. Changing either the thickness or the lateral layout of a BNA would in general lead to a simultaneous modification of each resonance peak in its intensity as well as center wavelength. As an illustration, the linear transmission characteristics of BNAs in Fig. 1(b) clearly reveals such spectral behavior with the thickness variation. With a decreasing silver film thickness, the field enhancement effect with the fundamental gets higher while the two resonance peaks become more separated to mismatch in wavelengths for an efficient SHG. For a given wavelength of the fundamental light, a number of iterations might be required in the simulation to maximize the fundamental field enhancement and to tune appreciable FP-like resonance to the SH wavelength at the same time.

To elucidate the linear response of a single BNA under double-resonance condition, electric-field maps of the 50-nm-thick silver BNA with the same design as that in Fig. 1(b) are computed. As a substantial modulation of the fields in the plasmonic interaction of a BNA is known to occur for the light polarization parallel to the bowtie axis, we consider only x-components of the field

E_{x}

throughout this paper. Figures 2(a-c) and 2(d-f) compare the characteristics of the fundamental SPR mode (excited at 860 nm) and the FP-like mode (excited at 430 nm), in the xz and yz cross sections through the middle of the two bowtie tips and on the xy plane at the aperture exit. A close examination of Fig. 2(a-c) indicates that the SPR induces strong fields localized at the vicinity of the two bowtie tips and the fields in the entrance and exit planes are coupled through the waveguide mode bound within the feed gap region, resulting in a drastic field enhancement of the incident light by orders of magnitude. It is obvious from Fig. 2(d-f) that the FP-like resonance transmission is quite different from the SPR transmission in the nature of field enhancement. Compared with the SPR mode, the FP-like resonance produces no hot spots on the entrance plane and much weaker fields within the feed gap region. On the other hand, the field intensity is maximum on the exit plane with hot spots near the bowtie tips. It is also seen that the FP-like resonance supports fields to build up gradually along the channel walls of the bowtie tips.

Fig. 2 FDTD-simulated electric-field amplitude distributions of a doubly resonant BNA with the same design and illumination used in Fig. 1(b). The fundamental SPR mode excited at 860 nm wavelength, is mapped in the (a) xz and (b) yz cross sections through the middle of the two bowtie tips and on the (c) xy plane at the aperture exit. (d-f) Corresponding cross sectional features of the FP-like resonance with an incident light at 430 nm wavelength. In all figures, the BNA’s bowtie axis and the direction of light polarization are fixed along the x-axis. Color bars are scaled as electric field amplitude normalized to the incident field. The dimension of the cross sections is in the unit of nm.

The field enhancement and mode structures resulting from these resonant responses play an important role in the efficient SHG from the metallic BNA without a nonlinear medium. Since the second-order nonlinear susceptibility

χ_{(s)}^{(2)}

can be nonzero only at the BNA edges and walls, the SPR-enhanced fundamental field

E_{x} (ω)

around the bowtie tips is crucial to induce a large nonlinear polarization

P_{N L (s)} (2 ω) = ε_{0} χ_{(s)}^{(2)} E_{x} (ω) E_{x} (ω)

at the SH harmonic frequency. With the local dipole source

P_{N L (s)} (2 ω)

predominantly formed down along the channel walls at the gap, the harmonic field

E_{x} (2 ω) \propto P_{N L (s)} (2 ω)

is then generated with a polarization nearly parallel to the walls’ surface normal [25

]. Here, a linear response of the BNA at the harmonic frequency

2 ω

is believed to determine how efficiently the harmonic fields add up to the exit plane, thereby the effective

χ_{e f f}^{(2)}

of the BNA device. According to the previous theoretical study [26

], the resonance gain in the linear field response at the harmonic frequency is directly conveyed to the proportional increase in the nonlinear response. Combined with enhanced fundamental fields [Fig. 2(a)], a strong field-buildup at the harmonic wavelength along the channel walls [Fig. 2(d)], would therefore allow the doubly resonant BNA to increase SHG efficiency significantly, based on the reasoning described above.

Here, an attempt can be made to simply evaluate the influence of the two different types of resonant linear response on the SHG enhancement. Translating the theoretical implication of the proposal for double-resonance plasmonics [26

] into our case, we worked out a relation between the second-order nonlinearity enhancement and the strength of linear dipole response. If a plasmonic nanostructure’s effective linear dipole moment under an incident field

E_{0} (ω)

is quantifiable with the field enhancement

E_{e f f} (ω) = G (ω) E_{0} (ω)

within the nanostructure, then the effective nonlinear polarization approximates to

P_{e f f} (2 ω) = f ε_{0} χ_{s}^{(2)} G (2 ω) [G^{2} (ω) E_{0}^{2} (ω)]

, where

f

is a constant determined by the nanostructure configuration,

ε_{0}

is the vacuum permittivity, and

G (ω)

is the gain factor. Accordingly, the SHG intensity can be expressed as

I_{S H G} \propto | P_{e f f} (2 ω) |^{2} \propto | G (2 ω) |^{2} | G (ω) |^{4}

. For a metallic BNA, the field enhancement factor

E_{e f f} / E_{0}

in linear transmission is a good relative measure of

G

, which can be evaluated from the normalized transmission intensity

| E_{T} / E_{0} |^{2}

at the center on the aperture’s exit plane. One can readily see how the nanostructure’s SHG efficiency depends on its linear response at the fundamental (

ω

) and SH (

2 ω

) frequency. In addition to the widespread recognition that the plasmonic SHG increases with the fundamental intensity enhancement quadratically, the SHG can further benefit from the linear resonant response at its second harmonics. Therefore, the optimization of SHG efficiency can be achieved by tuning both the SPR resonance at

ω

and FP-like resonance at

2 ω

so that the product of

| E_{T} (ω) / E_{0} (ω) |^{4}

and

| E_{T} (2 ω) / E_{0} (2 ω) |^{2}

is maximized.

3. The Effect of FP-like resonances on SH light buildup through a BNA

In this study, we raised a conjecture that the FP-like transmission property of a metallic nanostructure at the SH wavelength can play a vital role in the SH buildup and its out-coupling from the structure. To put it differently, an extra resonant condition is presumed for SH dipoles, strongly induced by an SPR enhancement of the fundamental intensity, to constructively add their nonlinear radiation up within the plasmonic structure. The two mechanisms are, however, subject to rather different boundary conditions. Hence we need to examine the aforementioned correlation between the FP-like transmission and the efficiency of SH buildup by a direct calculation of SHG output under the fundamental irradiation.

For the doubly resonant BNA designs, we numerically calculate the relative spectral efficiency of SH signal buildup that is observable at the exit plane of the nanostructure. The simulation is largely divided into three steps. (i) We calculate 3-dimensional distribution of the localized electric fields in a BNA illuminated by a fundamental light varying in wavelength from 600 nm to 1200 nm. The Lorentz-Drude model is used to describe the dispersive properties of silver. With a horizontally (along the x-axis) polarized incident light, x-components of the near-field

E_{x}

are greatly enhanced and make a major contribution to the second-order nonlinear polarization, whereas the residual

E_{y}

components can be neglected. (ii) From the complex electric fields of the fundamental

E_{x}

, induced 2nd-order nonlinear polarization is created over the BNA surface. The strength of local SH dipole source at each point on the silver-air interface is calculated from

P_{N L (s), n} (2 ω) = ε_{0} χ^{(2)}_{(s), n n n} E_{x} (ω) E_{x} (ω)

using a second-order susceptibility that is assumed to be a constant over the wavelength range of the fundamental and have only surface normal (

\hat{n}

) tensor components. In the previous investigation of SHG from silver surfaces [28

E. K. L. Wong and G. L. Richmond, “Examination of the surface second harmonic response from noble metal surfaces at infrared wavelengths,” J. Chem. Phys. 99(7), 5500–5507 (1993). [CrossRef]

], its dispersive behavior was found to show a good agreement with that of the imaginary part of the linear dielectric constant of bulk silver, where the imaginary part which is nearly constant over the entire SPR band of our interest. Here, the spectral dependence of SH dipole intensity is computed in a relative fashion. We further assume that the dominant contribution to SH emission originates from the nonlinear dipoles on the aperture wall at the ridge gap [9

R. Zhou, H. Lu, X. Liu, Y. Gong, and D. Mao, “Second-harmonic generation from a periodic array of noncentrosymmetric nanoholes,” J. Opt. Soc. Am. B 27(11), 2405–2409 (2010). [CrossRef]

]. In general, the nonlinear polarization responsible for SH emission can be induced on both the whole surface of aperture edge and the lateral surface of metal films. It has been pointed out, however, that the SH contribution from the aperture wall is much larger than that of other regions, owing to the enhanced field intensity [29

P. Schön, N. Bonod, E. Devaux, J. Wenger, H. Rigneault, T. W. Ebbesen, and S. Brasselet, “Enhanced second-harmonic generation from individual metallic nanoapertures,” Opt. Lett. 35(23), 4063–4065 (2010). [CrossRef] [PubMed]

]. (iii) Based on a FDTD method, SH radiations from such nonlinear dipole sources are summed up on the aperture’s exit plane and the spectral intensity of SH response is evaluated from the sum of absolute squares of

E_{x}

and

E_{y}

We carried out the simulation to investigate the spectral behavior of SH response from the doubly resonant BNAs described in the previous section. For comparison, we also examined another BNA of the same layout but with a different silver film thickness

t

= 80 nm, which revealed a mismatch between the FP-like peak and the SH wavelength of an SPR resonance as seen in Fig. 1(b). Starting with the calculation of 3-D electric field distribution of the fundamental, we could obtain linear transmission characteristics of the BNAs as a function of incident light wavelength ranging from 600 nm to 1200 nm, as shown in Fig. 3(a) . Induced SH dipole sources depending on the complex amplitude of the fundamental field, were allocated to the silver-air interface and then the relative spectral intensity of SH emission could be evaluated, as given by Fig. 3(c). The doubly resonant BNA with 50 nm silver thickness shows superior SHG intensity compared with 80 nm silver thickness, seemingly reflecting the difference in the field enhancement factor for the fundamental intensity. We note, however, that the result indeed contains contribution from the difference in SH buildup efficiency as well. To exclude the influence of fundamental intensity and thereby isolate the SH buildup characteristics, we normalized the strength of nonlinear dipoles using the local fundamental fields whose intensities were equalized in wavelengths and for the two different BNA designs. As a consequence, genuine SH buildup efficiency was obtained as Fig. 3(b) in which the results (dashed lines) are compared with the corresponding FP-like resonance curves (solid lines).

Fig. 3 Theoretical prediction of the spectral intensity of the fundamental and SH response from doubly resonant BNAs for the design shown in Fig. 1(b). (a) Linear transmission of the BNAs as a function of the incident fundamental wavelength, evaluated from normalized intensity of the electric field with horizontal (x) polarization at the center on the aperture’s exit plane. (b) Relative efficiency of the SH signal buildup as a function of the SH wavelength of the fundamental (dashed lines), corresponding to the right vertical scale in arbitrary units. Here, the influence of the fundamental intensity difference was excluded by normalizing the strength of the SH dipole excitation. For comparison, the linear transmission curves at SH wavelengths (solid lines) are also plotted, corresponding to the left vertical scale. (c) Spectral profiles of overall SH emission intensity at the exit plane, obtained by multiplying the square of the fundamental intensity transmission (a) with the SH buildup efficiency (b).

The SH signal buildup shows a resonant behavior fairly similar to the FP-like resonance in their spectral shape, while distorted and shifted to some degree. It is also interesting to find that there is a discrepancy in the proportionality of SH buildup efficiency to FP-like resonance for the two BNA designs. Although FP-like resonance peaks of the two designs differ by less than 30%, SH buildup efficiency of the BNA of 80 nm thickness is almost an order of magnitude smaller than that of 50 nm thickness. The cause of this discrepancy may be inferred from difference in the spatial feature of local electric fields of fundamental wave exciting SH dipoles. In the BNA of 50 nm thickness, SH dipoles around the FP-like resonance are excited by the fundamental fields being resonant with the aperture’s SPP modes. The BNA of 80 nm thickness, on the other hand, has its FP-like resonance at 515 nm, detuned way off from the SH wavelength (405 nm) of the fundamental’s resonance (810 nm). The numerical observation suggests that resonant characteristics of BNAs at the SH wavelength, incorporating with the fundamental resonance, can be a significant factor to be considered for increasing the efficiency of SHG.

4. Implementing doubly resonant BNAs in a periodic array

Pursuing higher efficiency of SHG in practical applications, we consider employing doubly resonant BNAs in a periodic array that emanates SH radiation in the zeroth diffraction order. The array configuration of silver BNAs and substrate material structure are determined, by taking a fundamental wavelength

λ_{0}

= 860 nm and its SH wavelength at

λ_{S H}

= 430 nm as primary design parameters.

To avoid the far-field diffraction loss of SH light emitted by a square array of BNAs, the array period

a_{0}

needs to be kept smaller than the SH wavelength

λ_{S H}

, permitting only the zeroth diffraction order. At the same time, the array period

a_{0}

should match the wavelength of SPP modes excited by the incident light at wavelength

λ_{0}

, in order for an array of BNAs to exhibit extraordinary optical transmission with a further local field enhancement compared with the case of a single aperture [24

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998). [CrossRef]

]. These concurrent requirements dictate that

a_{0} = λ_{0} {[(ε_{m} + ε_{d}) / ε_{m} ε_{d}]}^{1 / 2} < 0.5 λ_{0}

, where

λ_{0}

is the incident light wavelength,

ε_{m}

, the permittivity of metal, and

ε_{d}

, the permittivity of dielectric. Accordingly, a dielectric with refractive index greater than

{[4 ε_{m} / (ε_{m} - 4)]}^{1 / 2}

is required for a metal-dielectric interface. When using a thin silver film (

ε_{m}

= −29.518 +

i

2.018 at the fundamental wavelength of 860 nm [30

A. D. Rakić, A. B. Djurišić, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. 37(22), 5271–5283 (1998). [CrossRef] [PubMed]

]) in which BNAs are milled, the minimum refractive index of a dielectric is 1.88. We choose to use silicon nitride (Si₃N₄) for the dielectric because of its appropriate refractive index

n

= 1.993 and transparency at the wavelength of 860 nm [31

T. Bååk, “Silicon oxynitride; a material for GRIN optics,” Appl. Opt. 21(6), 1069–1072 (1982). [CrossRef] [PubMed]

]. Then, the optimal period

a_{0}

of arrayed BNAs in a silver film is readily determined as 400 nm. Being sandwiched between a silver film and a quartz substrate, a silicon nitride layer is required to have a thickness of 300 nm, designed for anti-reflection of the fundamental wave at the interface of silicon nitride and quartz. The layer is also thick enough to prevent the SPP fields from reaching the quartz substrate.

In the implementation of doubly resonant BNA arrays, we explore the use of asymmetric design for individual BNAs in addition to symmetric ones, as breaking symmetry in the shape of nanostructures is known to be advantageous for enhancing SH response [7

M. W. Klein, C. Enkrich, M. Wegener, and S. Linden, “Second-harmonic generation from magnetic metamaterials,” Science 313(5786), 502–504 (2006). [CrossRef] [PubMed]

–9

R. Zhou, H. Lu, X. Liu, Y. Gong, and D. Mao, “Second-harmonic generation from a periodic array of noncentrosymmetric nanoholes,” J. Opt. Soc. Am. B 27(11), 2405–2409 (2010). [CrossRef]

]. Generally speaking, SH polarizability may exist over the whole volume of nanostructures, not limited at their interfaces [32

Y. Zeng, W. Hoyer, J. Liu, S. W. Koch, and J. V. Moloney, “Classical theory for second-harmonic generation from metallic nanoparticles,” Phys. Rev. B 79(23), 235109 (2009). [CrossRef]

]. In a nanostructure consisting of centrosymmetric media only, however, a dominant source of SH dipoles arise only at the interface where broken inversion symmetry can be introduced [12

, 32

Y. Zeng, W. Hoyer, J. Liu, S. W. Koch, and J. V. Moloney, “Classical theory for second-harmonic generation from metallic nanoparticles,” Phys. Rev. B 79(23), 235109 (2009). [CrossRef]

]. The effective nonlinear susceptibility of such nanostructures depends particularly on their geometry, thereby playing a significant role in the SH response [8

B. K. Canfield, H. Husu, J. Laukkanen, B. Bai, M. Kuittinen, J. Turunen, and M. Kauranen, “Local field asymmetry drives second-harmonic generation in non-centrosymmetric nanodimers,” Nano Lett. 7(5), 1251–1255 (2007). [CrossRef] [PubMed]

, 29

, 33

J. R. Heflin, C. Figura, D. Marciu, Y. Liu, and R. O. Claus, “Thickness dependence of second-harmonic generation in thin films fabricated from ionically self-assembled monolayers,” Appl. Phys. Lett. 74(4), 495–497 (1999). [CrossRef]

]. One can have control over breaking symmetry in nanostructures by either changing their geometrical shape or using oblique angles of light incidence. The resulting asymmetric distribution of the local fields allows for a higher effective susceptibility than that with a symmetric field distribution [6

We worked out symmetric and asymmetric designs of individual BNAs to be implemented in the aforementioned square array arrangement. Both types of BNAs were designed to permit double resonances at the fundamental wavelength

λ_{0}

= 860 nm and its SH wavelength

λ_{S H}

= 430 nm. As delineated in Fig. 4(a) , the geometry of a symmetric BNA in a 50-nm-thick silver film has a square outline of 70 nm in both side and a ridge gap of 20 nm. Asymmetric design of a BNA was performed by changing lengths of the two ridges, with all the other parameters kept the same as those of the symmetric design. The asymmetric BNA was designed to have the lateral layout shown in Fig. 4(b), which was found to produce asymmetry between the electric field amplitudes

E_{1}

and

E_{2}

at the tip of the two ridges with a ratio of

E_{1} / E_{2}

= 0.46. The asymmetry introduced in the present design, compares to that obtainable with oblique light incidence on a symmetric device at an angle as large as 70 degrees. The linear transmission characteristics of the BNA designs is given in Fig. 4(c), clearly showing the desirable double-resonance features. The asymmetric BNA exhibits its plasmonic and FP-like resonance peaks at 880 nm and 450 nm, respectively, both resonances being shifted together to slightly longer wavelengths than the designed ones. However, SH wavelengths of the plasmonic resonance band can still be overlapped well with the FP-like resonance band. At the moment, it also seems apparent from Fig. 4(c) that our asymmetric BNA design is of inferior performance in SH conversion compared with the symmetric BNA. Nevertheless, the increase of effective nonlinear susceptibility due to breaking symmetry might be a contributing factor that allows the asymmetric design to outperform the symmetric one.

Fig. 4 Lateral geometry of (a) a symmetric BNA and (b) an asymmetric BNA in doubly resonant designs. (c) Corresponding linear transmission, evaluated at the center of the aperture on the BNA’s exit plane, as a function of the wavelength of incident light polarized along the x-axis (parallel to the bowtie axis). The linear transmission curves represent the spectral dependence of the local field enhancement factor relative to the incident light intensity.

5. Experiments

In the fabrication of a plasmonic device with doubly resonant BNA array, a 300-nm-thick silicon nitride layer was first deposited on a quartz substrate by PECVD (Unaxis VL-LA-PECVD) and a 50-nm-thick silver film was then coated using electron-beam evaporation method (ULVAC El-5). The root-mean-square roughness of the silver film is 1.3 nm thereby SH light is not generated by the surface roughness. The BNA arrays were milled in the silver film by focused ion beam (FIB, SII SMI3050) under 30 kV acceleration voltage, 1 pA current and 5 μs dwell time. The symmetric and asymmetric apertures were fabricated into 4 × 4 square arrays with a period of 400 nm, as shown in scanning electron microscope (SEM, Hitachi S-4200) images in Fig. 5(a) and 5(b), respectively.

Fig. 5 SEM images of (a) symmetric BNAs and (b) asymmetric BNAs fabricated into 4 × 4 arrays. (c) A schematic of the experimental setup used to investigate the characteristics of the SH emission from the BNA arrays.

The experimental setup for the SH measurements is shown schematically in Fig. 5(c). A mode-locked femtosecond Ti:Sapphire laser (Coherent Mira 900) with the pulse duration of 150 fs and the repetition rate of 76 MHz was used as the fundamental light source with its wavelength tunable from 810 nm to 890 nm. The spectral bandwidth of the laser was approximately 11 nm in the operating wavelength range. The polarization of the fundamental wave was adjusted at the laser output using the combination of a half-wave plate and a polarizer. The horizontally polarized beam was focused by a microscope objective (20 × , NA 0.35, Nachet PL-FL20) to illuminate the device with a spot size of 6 μm. The position of the device was controlled by a 3-axis translation stage. A rotation stage was also used to fine control the incident angle of the fundamental wave. Another objective lens identical to the focusing objective, collected the fundamental and SH lights emanating from the device. A long-pass dichroic mirror (with cutoff wavelength at 567 nm) dumped the fundamental wave out and directed the SH wave to a photon multiplier tube (PMT, Dongwoo Optron PDS-1). A stack of two colored-glass bandpass filters (Schott BG39, Transmission factor T0.6 for 400 nm – 500 nm) was used to purify SH emission by completely removing the residuals of fundamental wave reflected off at the dichroic mirror, where the transmission factor for the fundamental wave was T < 10⁻¹⁰ . To increase the signal-to-noise ratio of SH measurements, a lock-in detection of the PMT signal was carried out using a lock-in amplifier (Signal Recovery 7280 DSP) with a chopper frequency at 500 Hz. In the alignment of an incident fundamental wave to a designated position of the aperture array, we observed microscope images of the device and the laser spot in the transmission mode. The fundamental wave transmitted through the device was attenuated by a ND filter (OD = 3.0) before a CCD camera (Thorlabs DCU224C) to record microscope images.

6. Results and discussion

Before carrying out the SH measurement, we first tested the durability of the device against laser-induced structural damages. By monitoring the change in fundamental transmission through the device with the incident power and exposure time, we experimentally determined to keep the maximum incident power at 7.5 mW (within the spot diameter of 6 μm), which was more than 5 times below the measured damage threshold. Since the 4 × 4 BNA arrays were fabricated in the area of 1.3 μm × 1.3 μm, the effective fundamental power falling on the device area is smaller than the incident power of a whole beam. The effective power was calculated in the area of 1.6 μm × 1.6 μm considering to the effect of collecting charges at the outermost BNAs. The ratio of the effective power to the whole power was estimated to be 0.18, and the “incident power” in the rest of this paper refers to the effective fundamental power. To quantify the detected SH signals as optical power, we also carefully calibrated the PMT’s signal response to optical power in the SH wavelength range and characterized the spectral transmission of the collecting objective, the dichroic mirror, and the colored-glass bandpass filters.

We observed the SH emission signal from the BNA arrays illuminated by the fundamental wave at 860 nm wavelength. The fundamental power incident on the BNA arrays was varied up to 1.35 mW. As shown in Fig. 6 , the quadratic dependence of the observed signal on the fundamental input power was verified for both the symmetric and asymmetric BNA arrays. The result clearly indicates that the detected signal is mainly due to the SH response of the BNA arrays.

Fig. 6 SH emission power measured as a function of the input power of the fundamental laser at 860 nm in the symmetric and asymmetric BNA arrays. Each set of experimental data was fit to a power law curve (solid line) with an exponent close to 2.

By tuning the fundamental wavelength from 810 and 890 nm, we measured the wavelength-dependent SH conversion of the BNA arrays for a fundamental power kept at 1.35 mW. The wavelength dependent SH signals from the symmetric and asymmetric BNA arrays are depicted in Fig. 7 . Based on the BNA transmission characteristics given in Fig. 4(c), symmetric BNAs would be supposed to exhibit superior SH conversion compared with asymmetric BNAs. In terms of field enhancement in the fundamental intensity and resonance matching, SH conversion would be more efficient with symmetric BNAs than the asymmetric ones by at least several factors. Therefore this observation, compared with the theoretical prediction regarding the local field enhancement only, reflects that mechanisms other than the fundamental intensity are involved in determining the strength of SH response. It can be inferred that the effective nonlinear susceptibility is increased in the asymmetric BNAs due to their broken symmetry in the structure and the local field distribution. Like Fig. 4(c), resonances of the asymmetric BNA shift to slightly longer wavelengths and can be meet the condition of the double resonances. Solid lines in Fig. 7 display SHG intensity of the BNA arrays estimated from the simulation results. The measured SH signals from the asymmetric array as well as the symmetric BNA array correspond to the simulated spectral response. The results show that theoretical prediction adequately reflects SHG process in BNAs with double resonance.

Fig. 7 Wavelength-dependent SH emission power from the symmetric (squares) and asymmetric (circles) BNA arrays with a fundamental input power of 1.35 mW. The solid lines in the figure represent the simulated spectral response of the BNA arrays used to generate the SH signals.

It is found that the maximum SH signals from the asymmetric BNAs are almost twice as large as that from the symmetric ones. The SH power conversion efficiencies for the maximum SH signals were measured to be 7.6 × 10⁻⁹ at the symmetric BNA and 1.4 × 10⁻⁸ at the asymmetric BNA. Among many studies on the SHG in metallic nanostructures, only a few works reported their results in terms of the conversion efficiency [9

R. Zhou, H. Lu, X. Liu, Y. Gong, and D. Mao, “Second-harmonic generation from a periodic array of noncentrosymmetric nanoholes,” J. Opt. Soc. Am. B 27(11), 2405–2409 (2010). [CrossRef]

, 21

W. Cai, A. P. Vasudev, and M. L. Brongersma, “Electrically controlled nonlinear generation of light with plasmonics,” Science 333(6050), 1720–1723 (2011). [CrossRef] [PubMed]

, 25

, 34

M. W. Klein, M. Wegener, N.-A. Feth, and S. Linden, “Experiments on second- and third-harmonic generation from magnetic metamaterials: erratum,” Opt. Express 16(11), 8055 (2008). [CrossRef]

–36

H. Lu, X. Liu, R. Zhou, Y. Gong, and D. Mao, “Second-harmonic generation from metal-film nanohole arrays,” Appl. Opt. 49(12), 2347–2351 (2010). [CrossRef] [PubMed]

]. The highest conversion efficiency of SHG in a metallic nanostructure was reported for nanocups exploiting structural plasmonic resonance [25

]. Here, we note that our result in the asymmetric aperture array represents an improvement of nearly an order of magnitude in the SHG conversion efficiency, compared with the SHG conversion efficiency ( = 1.8 × 10⁻⁹) of nanocups [25

We briefly extend our discussion regarding on large enhancement of the SHG conversion efficiency of a nano photonic device demonstrated in this work. The discussion needs to be made by evaluating each contribution from different idea or design adopted in the device since our metallic nanostructure incorporates several ideas described in the previous section. The BNA was designed to have double resonances i.e., plasmonic resonance for fundamental wave and Fabry-Pérot resonance for SH wave. When we calculated the SHG from a BNA with a simple analytical model, we obtained one order of magnitude enhancement of SHG due to the double resonance of the BNA. We increased the transmission of the fundamental wave through BNAs by matching the spacing between bowtie apertures to the wavelength of SPP being excited on the metal surface. In addition to the increase of fundamental wave transmission due to SPP coupling, the aperture spacing concomitantly smaller than SH wavelength allows only the zeroth order diffraction of SH wave after the exit plane of BNA, facilitating a coherent addition of the SH waves generated in aperture elements. Small gain in enhancement of the conversion efficiency is also added due to anti-reflection film for fundamental wave on front surface of the device. It is difficult to quantitatively analyze each contribution mentioned above, since the SHG is not simply proportional to square of the transmission field at the exit of the aperture and coherent addition of SH waves is the result of coupling of SH waves generated in different aperture elements. We presume that the overall enhancement factor resulting from the phase matching of SPP, coherent addition of SH waves, and anti-reflection of the fundamental wave, becomes larger by more than one order of magnitude.

7. Conclusions

In conclusion, we report on a deliberate design of a nano photonic device for SHG and experimentally demonstrate large enhancement of SHG conversion efficiency with a metallic bowtie nano-apertures (BNAs) which are employed into a 4 × 4 square periodic array. We perform finite-difference time-domain (FDTD) simulations to tailor spectral transmission of a BNA in a silver film to be doubly resonant with the fundamental and SH wavelengths. The wavelength conversion efficiency of the BNA array, combined with the analysis of its spectral dependence on the fundamental, is assessed to show evidences of the role of additional resonance tuned to the SH transmission, resulting in the augmentation of SH response approximately an order of magnitude greater than that without the help of SH resonance. SHG conversion efficiency is further improved with the SPP excitation for enhanced transmission of fundamental wave, suppression of higher order diffraction for coherent coupling of SH waves, and anti-reflection layer on entrance metal surface. We finally achieve the SHG conversion efficiency of the nano photonic device to be 1.4 × 10⁻⁸ for the asymmetric type BNA, which is an order of magnitude larger than the results published in recent literatures.

Acknowledgments

The authors are grateful to Yongwoo Kim at Yonsei University for FIB fabrication of the aperture arrays. They also thank Ju Hyeon Park at KRISS for the assistance in the experiments. S.P. and J.W.H. acknowledge NRF grant funded by the Korea government (MEST) (No.2011-0030630). J.Y.L. acknowledges Korea MEST/NRF grant (No. 2011-0020504).

References and links

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2.	N. Kroo, G. Farkas, P. Dombi, and S. Varró, “Nonlinear processes induced by the enhanced, evanescent field of surface plasmons excited by femtosecond laser pulses,” Opt. Express 16(26), 21656–21661 (2008). [CrossRef] [PubMed]
3.	S. Palomba and L. Novotny, “Nonlinear excitation of surface plasmon polaritons by four-wave mixing,” Phys. Rev. Lett. 101(5), 056802 (2008). [CrossRef] [PubMed]
4.	A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, “Near-field second-harmonic generation induced by local field enhancement,” Phys. Rev. Lett. 90(1), 013903 (2003). [CrossRef] [PubMed]
5.	M. Lippitz, M. A. van Dijk, and M. Orrit, “Third-harmonic generation from single gold nanoparticles,” Nano Lett. 5(4), 799–802 (2005). [CrossRef] [PubMed]
6.	T. Xu, X. Jiao, G. P. Zhang, and S. Blair, “Second-harmonic emission from sub-wavelength apertures: Effects of aperture symmetry and lattice arrangement,” Opt. Express 15(21), 13894–13906 (2007). [CrossRef] [PubMed]
7.	M. W. Klein, C. Enkrich, M. Wegener, and S. Linden, “Second-harmonic generation from magnetic metamaterials,” Science 313(5786), 502–504 (2006). [CrossRef] [PubMed]
8.	B. K. Canfield, H. Husu, J. Laukkanen, B. Bai, M. Kuittinen, J. Turunen, and M. Kauranen, “Local field asymmetry drives second-harmonic generation in non-centrosymmetric nanodimers,” Nano Lett. 7(5), 1251–1255 (2007). [CrossRef] [PubMed]
9.	R. Zhou, H. Lu, X. Liu, Y. Gong, and D. Mao, “Second-harmonic generation from a periodic array of noncentrosymmetric nanoholes,” J. Opt. Soc. Am. B 27(11), 2405–2409 (2010). [CrossRef]
10.	R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic Press, Amsterdam and Boston, 2008).
11.	P. Genevet, J.-P. Tetienne, E. Gatzogiannis, R. Blanchard, M. A. Kats, M. O. Scully, and F. Capasso, “Large enhancement of nonlinear optical phenomena by plasmonic nanocavity gratings,” Nano Lett. 10(12), 4880–4883 (2010). [CrossRef] [PubMed]
12.	K. D. Ko, A. Kumar, K. H. Fung, R. Ambekar, G. L. Liu, N. X. Fang, and K. C. Toussaint Jr., “Nonlinear optical response from arrays of Au bowtie nanoantennas,” Nano Lett. 11(1), 61–65 (2011). [CrossRef] [PubMed]
13.	T.-D. Onuta, M. Waegele, C. C. DuFort, W. L. Schaich, and B. Dragnea, “Optical field enhancement at cusps between adjacent nanoapertures,” Nano Lett. 7(3), 557–564 (2007). [CrossRef] [PubMed]
14.	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). [CrossRef] [PubMed]
15.	P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308(5728), 1607–1609 (2005). [CrossRef] [PubMed]
16.	X. Shi and L. Hesselink, “Mechanisms for enhancing power throughput from planar nano apertures for near field optical data storage,” Jpn. J. Appl. Phys. 41(Part 1, No. 3B), 1632–1635 (2002). [CrossRef]
17.	E. X. Jin and X. Xu, “Finite-difference time-domain studies on optical transmission through planar nano-apertures in a metal Film,” Jpn. J. Appl. Phys. 43(1), 407–417 (2004). [CrossRef]
18.	H. Guo, T. P. Meyrath, T. Zentgraf, N. Liu, L. Fu, H. Schweizer, and H. Giessen, “Optical resonances of bowtie slot antennas and their geometry and material dependence,” Opt. Express 16(11), 7756–7766 (2008). [CrossRef] [PubMed]
19.	J. A. H. van Nieuwstadt, M. Sandtke, R. H. Harmsen, F. B. Segerink, J. C. Prangsma, S. Enoch, and L. Kuipers, “Strong modification of the nonlinear optical response of metallic subwavelength hole arrays,” Phys. Rev. Lett. 97(14), 146102 (2006). [CrossRef] [PubMed]
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21.	W. Cai, A. P. Vasudev, and M. L. Brongersma, “Electrically controlled nonlinear generation of light with plasmonics,” Science 333(6050), 1720–1723 (2011). [CrossRef] [PubMed]
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30.	A. D. Rakić, A. B. Djurišić, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. 37(22), 5271–5283 (1998). [CrossRef] [PubMed]
31.	T. Bååk, “Silicon oxynitride; a material for GRIN optics,” Appl. Opt. 21(6), 1069–1072 (1982). [CrossRef] [PubMed]
32.	Y. Zeng, W. Hoyer, J. Liu, S. W. Koch, and J. V. Moloney, “Classical theory for second-harmonic generation from metallic nanoparticles,” Phys. Rev. B 79(23), 235109 (2009). [CrossRef]
33.	J. R. Heflin, C. Figura, D. Marciu, Y. Liu, and R. O. Claus, “Thickness dependence of second-harmonic generation in thin films fabricated from ionically self-assembled monolayers,” Appl. Phys. Lett. 74(4), 495–497 (1999). [CrossRef]
34.	M. W. Klein, M. Wegener, N.-A. Feth, and S. Linden, “Experiments on second- and third-harmonic generation from magnetic metamaterials: erratum,” Opt. Express 16(11), 8055 (2008). [CrossRef]
35.	N. Feth, S. Linden, M. W. Klein, M. Decker, F. B. P. Niesler, Y. Zeng, W. Hoyer, J. Liu, S. W. Koch, J. V. Moloney, and M. Wegener, “Second-harmonic generation from complementary split-ring resonators,” Opt. Lett. 33(17), 1975–1977 (2008). [CrossRef] [PubMed]
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OCIS Codes
(190.2620) Nonlinear optics : Harmonic generation and mixing
(190.4360) Nonlinear optics : Nonlinear optics, devices
(240.6680) Optics at surfaces : Surface plasmons
(350.4238) Other areas of optics : Nanophotonics and photonic crystals
(310.6628) Thin films : Subwavelength structures, nanostructures

ToC Category:
Nonlinear Optics

History
Original Manuscript: December 1, 2011
Revised Manuscript: February 4, 2012
Manuscript Accepted: February 9, 2012
Published: February 13, 2012

Virtual Issues
Vol. 7, Iss. 4 Virtual Journal for Biomedical Optics

Citation
Sinjeung Park, Jae W. Hahn, and Jae Yong Lee, "Doubly resonant metallic nanostructure for high conversion efficiency of second harmonic generation," Opt. Express 20, 4856-4870 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-5-4856

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References

J. Renger, R. Quidant, N. van Hulst, and L. Novotny, “Surface-enhanced nonlinear four-wave mixing,” Phys. Rev. Lett.104(4), 046803 (2010). [CrossRef] [PubMed]
N. Kroo, G. Farkas, P. Dombi, and S. Varró, “Nonlinear processes induced by the enhanced, evanescent field of surface plasmons excited by femtosecond laser pulses,” Opt. Express16(26), 21656–21661 (2008). [CrossRef] [PubMed]
S. Palomba and L. Novotny, “Nonlinear excitation of surface plasmon polaritons by four-wave mixing,” Phys. Rev. Lett.101(5), 056802 (2008). [CrossRef] [PubMed]
A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, “Near-field second-harmonic generation induced by local field enhancement,” Phys. Rev. Lett.90(1), 013903 (2003). [CrossRef] [PubMed]
M. Lippitz, M. A. van Dijk, and M. Orrit, “Third-harmonic generation from single gold nanoparticles,” Nano Lett.5(4), 799–802 (2005). [CrossRef] [PubMed]
T. Xu, X. Jiao, G. P. Zhang, and S. Blair, “Second-harmonic emission from sub-wavelength apertures: Effects of aperture symmetry and lattice arrangement,” Opt. Express15(21), 13894–13906 (2007). [CrossRef] [PubMed]
M. W. Klein, C. Enkrich, M. Wegener, and S. Linden, “Second-harmonic generation from magnetic metamaterials,” Science313(5786), 502–504 (2006). [CrossRef] [PubMed]
B. K. Canfield, H. Husu, J. Laukkanen, B. Bai, M. Kuittinen, J. Turunen, and M. Kauranen, “Local field asymmetry drives second-harmonic generation in non-centrosymmetric nanodimers,” Nano Lett.7(5), 1251–1255 (2007). [CrossRef] [PubMed]
R. Zhou, H. Lu, X. Liu, Y. Gong, and D. Mao, “Second-harmonic generation from a periodic array of noncentrosymmetric nanoholes,” J. Opt. Soc. Am. B27(11), 2405–2409 (2010). [CrossRef]
R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic Press, Amsterdam and Boston, 2008).
P. Genevet, J.-P. Tetienne, E. Gatzogiannis, R. Blanchard, M. A. Kats, M. O. Scully, and F. Capasso, “Large enhancement of nonlinear optical phenomena by plasmonic nanocavity gratings,” Nano Lett.10(12), 4880–4883 (2010). [CrossRef] [PubMed]
K. D. Ko, A. Kumar, K. H. Fung, R. Ambekar, G. L. Liu, N. X. Fang, and K. C. Toussaint., “Nonlinear optical response from arrays of Au bowtie nanoantennas,” Nano Lett.11(1), 61–65 (2011). [CrossRef] [PubMed]
T.-D. Onuta, M. Waegele, C. C. DuFort, W. L. Schaich, and B. Dragnea, “Optical field enhancement at cusps between adjacent nanoapertures,” Nano Lett.7(3), 557–564 (2007). [CrossRef] [PubMed]
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). [CrossRef] [PubMed]
P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science308(5728), 1607–1609 (2005). [CrossRef] [PubMed]
X. Shi and L. Hesselink, “Mechanisms for enhancing power throughput from planar nano apertures for near field optical data storage,” Jpn. J. Appl. Phys.41(Part 1, No. 3B), 1632–1635 (2002). [CrossRef]
E. X. Jin and X. Xu, “Finite-difference time-domain studies on optical transmission through planar nano-apertures in a metal Film,” Jpn. J. Appl. Phys.43(1), 407–417 (2004). [CrossRef]
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