Pronounced Fano Resonance in Single Gold Split Nanodisks with 15 nm Split Gaps for Intensive Second Harmonic Generation Shi Zhang,†,# Guang-Can Li,‡,# Yiqin Chen,†,# Xupeng Zhu,† Shao-Ding Liu,*,§ Dang Yuan Lei,*,‡ and Huigao Duan*,∥ †
School of Physics and Electronics, State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body and ∥College of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, People’s Republic of China ‡ Department of Applied Physics, The Hong Kong Polytechnic University, Hong Kong 999077, China § Department of Physics and Optoelectronics, Key Lab of Advanced Transducers and Intelligent Control System of Ministry of Education, Taiyuan University of Technology, Taiyuan 030024, People’s Republic of China S Supporting Information *
ABSTRACT: Single metallic nanostructures supporting strong Fano resonances allow more compact nanophotonics integration and easier geometrical control in practical applications such as enhanced spectroscopy and sensing. In this work, we designed a class of plasmonic split nanodisks that show pronounced Fano resonance comparable to that observed in widely studied plasmonic oligomer clusters. Using our recently developed “sketch and peel” electron-beam lithography, split nanodisks with varied diameter and split length were fabricated over a large area with high uniformity. Transmission spectroscopy measurements demonstrated that the fabricated structures with 15 nm split gap exhibit disk diameter and split length controlled Fano resonances in the near-infrared region, showing excellent agreement with simulation results. Together with the plasmon hybridization theory, in-depth full-wave analyses elucidated that the Fano resonances observed in the split nanodisks were induced by mode interference between the bright antibonding dipole mode of split disks and the subradiant mode supported by the narrow split gap. With the giant near-field enhancement enabled by the intensive Fano resonance at the tiny split gap, strong wavelength-dependent second harmonic generation was observed under nearinfrared excitation. Our work demonstrated that single split nanodisks could serve as important building blocks for plasmonic and nanophotonic applications including sensing and nonlinear optics. KEYWORDS: surface plasmon, Fano resonance, second harmonic generation, split disks, sketch and peel lithography electron generation,8 integrated optical circuits,9 enhanced nonlinear optics,10−15 photothermal therapy,16 and even color printing.17 Besides that, sophisticated engineering of phase shift with coupled plasmonic nanostructures enables directional farfield emission from quantum emitters.18 Recently, plasmonic coupling is employed to manipulate the scattering efficiency
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trong plasmonic coupling in metallic nanostructures has attracted a great deal of attention in recent years.1 According to plasmon hybridization theory, 2 the interaction of elementary plasmon modes leads to the formation of bonding and antibonding collective resonances. Meanwhile, free electrons can be confined around a narrow region due to the intense plasmon coupling between adjacent nanoparticles, which results in a dramatically enhanced near field and the generation of the so-called “hot spots”.3 This property could be very useful for a number of applications, such as single molecule detection,4 real time biosensing,5−7 hot© 2016 American Chemical Society
Received: September 5, 2016 Accepted: December 1, 2016 Published: December 1, 2016 11105
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Figure 1. Fabrication and characterization of split nanodisks. (a) Three-dimensional schematic of a single split nanodisk with radius r, gap length l, and gap width w. The thickness t of all split nanodisks in this study was fixed to be 30 nm. (b) Schematic illustration of the fabrication flow of gold split nanodisks with the SPL patterning method, where the exposed HSQ template surrounding the split disk has not been removed after step V. (c−e) Low- and high-magnification SEM images of a representative array of the prepared split nanodisks (c), a randomly selected area of the array (d), and an individual structure (e). The scale bars in (c−e) are 1 μm, 200 nm, and 100 nm, respectively.
and spectral linewidth of single metal film-coupled nanoparticle monomers and dimers.19,20 The plasmon hybridization theory reveals that some hybridized resonances in complex nanostructures are dark or subradiant21 because their overall dipole moments approach zero, leading to effective suppression of radiative losses. Although the coupling of a dark mode with an external field is intrinsically weak, it can be indirectly excited through nearfield coupling with a bright plasmon mode, and the interference between the two modes often leads to the formation of a plasmonic Fano resonance with suppression of scattering in a narrow frequency window.22,23 A variety of metallic nanostructures such as dolmen structures,24,25 core−shell nanoparticles,26,27 ring-disk cavities,5,23 oligomer clusters,28−30 and nanoholes31 have been designed to generate Fano resonances. From the fundamental physics perspective, the strong plasmonic coupling induced generation of Fano resonances mimics the characteristic features of interacting quantum systems32 and provides an additional degree of freedom to control the radiative properties of plasmonic nanostructures, while from the application point of view, these coherent electromagnetic phenomena are able to generate interesting resonance modes with narrowed linewidths and amplified near fields that can ultimately benefit sensing,33 optical switches,34,35 low-loss waveguiding,36 enhanced spectroscopy, and nonlinear optical effects.37,38 In order to enhance the coupling strength so as to further enlarge the near-field enhancement and the modulation depth of a Fano resonance,30 it is highly desirable to design appropriate plasmonic nanostructures with extremely
small interparticle separations yet beyond the regime of spatial nonlocality and quantum tunneling.39−42 Compared with that of oligomer-like metal nanoclusters, single plasmonic structures sustaining pronounced Fano resonances are of particular importance because they allow more compact on-chip integration and convenient geometrical control for practical applications of different purposes. Although the optical responses of plasmonic oligomers can be flexibly tuned by changing either the number or the shape and spatial arrangement of constituent nanoparticles, breaking the structural symmetry in individual metal nanoparticles can also enable efficient plasmon coupling to achieve significant modulation in their optical responses. The well-known splitring resonator (SRR) is such an example that supports a strong magnetic dipole resonance,43 leading to the realization of lefthanded materials.44 Besides that, higher-order plasmon modes (quadrupole and octupole) can also be excited in a SRR,45 making it possible to flexibly engineer its radiative property.46 Due to the free electron kinetic energy at high frequencies, however, it is hard to tune the magnetic resonance of SRRs to the visible frequency range.47 Kuznetsov et al. showed that this magnetic resonance saturation effect can be avoided in a splitball resonator,48 extending the magnetic resonance frequency to around 600 nm and simultaneously achieving ultrastrong near-field enhancement within the cut region. By removing a wedge from a silver nanodisk, Fang et al. demonstrated that the interference between a narrow quadrupolar mode supported by the edge of the missing wedge slice and an antibonding bright mode of the disk leads to the formation of a very shallow Fano resonance due to the weak plasmon coupling in the cut disk.49 11106
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Figure 2. Optical properties of the split disks with varied radius. (a,c) Measured (a) and simulated (c) transmittance spectra for the split disks with increasing the radius from 75 to 200 nm, showing four sets of resonances: two sets of transmission dips marked by the green and red dashed lines, the transmission peaks marked by the blue dashed line, and the lattice resonance marked by the black dashed line. (b) Representative SEM images of the fabricated split nanodisks. The samples without removing the surrounding exposed HSQ templates were used in these measurements, and the observed plasmon resonances of the disks will shift to higher energies when the surrounding HSQ templates are removed. The scale bar at the bottom is 300 nm.
pattern to achieve better resolution over large areas.51 Figure 1b shows the SPL fabrication process of an array of gold split nanodisks. Briefly, a hydrogen silsesquioxane (HSQ) resist layer was spin-coated on a quartz substrate (Step I), and then the outline of the designed split disks was sketched on the HSQ layer by a focused electron beam, followed with the development in a salty solution to obtain an HSQ template (Step II). Subsequently, a 30 nm-thick gold film was conformally evaporated on the template (Step III), on which an adhesive polymer layer was poured to selectively peel off the gold at the top and outside of the template (Steps IV and V). Note that in the following studies, the HSQ template was kept on the substrate, and it is optically transparent in the spectral range of interest. SEM images of the samples after and before removing the exposed HSQ template have been shown in Figure S1 in the Supporting Information. Figure 1c shows the scanning electron microscopy (SEM) image of an array of split nanodisks with 200 nm radius and 600 nm pitch, exhibiting good uniformity over the whole array. The enlarged SEM image of a randomly selected area shown in Figure 1d further confirms the reproducibility from disk to disk. As shown in Figure 1e, a closer look at a specific split disk reveals a ∼15 nm split gap in the radial direction. Figure S2 in Supporting Information presents the SEM images of arrays of gold split nanodisks with other dimensions, further demonstrating the excellent capability of the SPL process for direct and reliable definition of plasmonic split disks. Polarization-Selective and Diameter-Dependent Optical Properties of Split Nanodisks. To systematically study the optical properties of the designed split nanodisks, we first prepared six structures with radii varied from 75 to 200 nm in squared arrays of 100 μm × 100 μm at the same pitch of 600 nm. The split length of structures equals to their respective
Very recently, Sartorello et al. showed that the coupling strength in a cut disk could be enhanced by reducing the cutting slit width to ∼30 nm, resulting in an amplified coherent nonlinear response with the presence of a Fano resonance in the visible region upon exciting the magnetic plasmon mode of the structure at ∼1400 nm.50 In this work, we make a step forward to fabricate single plasmonic split nanodisks with extremely narrow split gaps (down to ∼15 nm over 300 nm length) using our recently developed “sketch and peel” lithography (SPL) method.51 The significant reduction in the gap width enables much stronger coherent plasmonic coupling at the gap region, thus pushing the Fano resonance wavelength to ∼1000 nm. Enabled by the giant field enhancement in the split nanogap, intensive second harmonic generation (SHG) was realized upon exciting at the Fano resonance position, indicating the important role of plasmonic Fano resonances in nonlinear optics and also the promising applications of plasmonic split nanodisks in on-chip nanophotonic device integration.
RESULTS AND DISCUSSION Design and Fabrication. Figure 1a schematically illustrates the designed gold split nanodisk with radius r, split length l, and gap width w, on a quartz substrate. To enlarge the plasmon coupling strength and thus obtain significantly enhanced near field at the split gap, the gap width should be as small as possible and also uniform along the whole split, indicating an aspect ratio larger than 10 (assume 10 nm gap width and 100 nm split length). This is immensely challenging, if not impossible, for conventional electron-beam lithography (EBL) patterning due to the unavoidable proximity effect in exposure. Our recently developed SPL approach can well mitigate the proximity effect by exposing only the outlines of a designed 11107
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Figure 3. Resonance modes analysis and the corresponding calculated charge density and near-field enhancement distributions of the split and perfect disks with a radius of 200 nm. (a) The calculated transmittance spectra of split and perfect disks with different incident polarizations. (b) The hybridization schemes of the split nanodisks. (c) The charge density (upper panels) and near-field enhancement |E|/|Einc| (lower panels) distributions around the labeled positions, where the lower-left corner shows the corresponding maximum near-field enhancement factor.
radius and the corresponding SEM images of the prepared split disks are shown in Figure 2b. Figure 2a shows the measured transmittance spectra of the arrays under quasi-normal incidence with polarization perpendicular to split gap (ypolarized incidence). The transmittance spectra were based on the measured intensity of the transmitted light from the single patch of nanostructure array (I) and the bare quartz substrate with the same area size as the array (I0), and the transmittance spectra T were obtained by normalization as T ∝ I/I0. The samples without removing the surrounding exposed HSQ templates were used in these measurements (the same as Figure S1b, Supporting Information). Compared with that of the samples after removing the HSQ templates (Figure S1a, Supporting Information), plasmon resonances of the disks only shift to lower energies because of the enlarged refractive index of the surrounding mediums. As can be seen from Figure 2a, the smallest structure with r = 75 nm (magenta line) exhibits two transmission dips, and their positions gradually shift to lower energies with increasing the disk size, as indicated by the red and green dashed lines. Interestingly, a small transmittance peak appears at around 750 nm in the spectrum for the split disk with r = 125 nm (green line in Figure 2a), and it develops into a prominent asymmetric peak at around 1000 nm for the structure with r = 200 nm (red line in Figure 2a), as indicated by the blue dashed line. These results agree well with the simulation results shown in Figure 2c. Note that the lattice resonances at around 870 nm (determined by the pitch of the array and the index of the substrate) in the simulated spectra
were not effectively excited in experiment because of the quasinormal incidence condition and also the spectral overlapping with the peak marked in blue. Due to high structural anisotropy in the split nanodisks, switching the incident polarization to be parallel to split gap (x-polarized incidence) dramatically changes their transmission responses. Figure S3a in the Supporting Information presents the measured transmittance spectra of the same structures illuminated with light of polarization parallel to their gaps, which exhibit only a single distinct transmittance dip and the long-wavelength one disappears, agreeing well with the simulation results in Figure S3c in the Supporting Information. Full-Wave Mode Analysis Revealing Co-Existence of Magnetic Resonance, Fano Resonance, Dipole Mode, and Lattice Resonance. To understand the mode nature of the transmission peaks and dips observed for the split disks in Figure 2, we further analyzed the plasmon hybridization scheme and their near-field properties with full-wave electromagnetic simulations, in comparison with a perfect disk. Figure 3a compares the transmittance spectra of the 200 nm-radius split disk under orthogonal incident polarization with that for the complete disk of the same size. In order to better visualize the spectral features of the four sets of resonances, the region enclosed in the yellow square is zoomed-in in the inset of Figure 3a. The zoomed-in spectrum indicates that in addition to the prominent resonance peak around 1000 nm, there is a small resonance peak around 940 nm, and the corresponding resonance is also observed in the measured spectrum (red line 11108
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Figure 4. Split-length-dependent Fano resonance under y-polarized incidence. (a) Experimentally measured transmittance spectra of the arrays composed of 150 nm-radius split nanodisks with the split length of 75, 150, 225, and 300 nm, respectively. (b) SEM images of the fabricated split nanodisks with different split length. (c) The corresponding calculated transmittance spectra of the split nanodisks.
that the antibonding dipole mode (DAB) is excited. There is a broad linewidth for the DAB hybridized mode, and the linewidth increases with the increasing of the disk size (red dashed lines in Figure 2), indicating the strong radiative losses of the DAB resonance. As for the transmission peak around position 3 (Figure 3c), near-field distributions reveal the excitation of the bonding quadrupole mode (QB), and radiative damping is effectively suppressed around this spectral position. The subradiant QB mode is spectral overlapped with the bright DAB mode, and the destructive interference leads to the formation of a pronounced Fano resonance. As a result, the incident energy can be effectively confined in the gap region, and the maximum nearfield enhancement factor can be as large as 122. Besides that, the charge density and near-field enhancement distributions of position 4 indicate that the corresponding antibonding quadrupole mode QAB is excited around 936 nm, which leads to the generation of a higher order Fano resonance. Although the modulation depth of this Fano resonance is weak, the maximum near-field enhancement factor can be as large as 78 due to the strong plasmon coupling and suppressed radiative losses. For comparison, the blue and black lines in Figure 3a represent the transmittance spectra for the split and perfect disks under x-polarized incidence, respectively, which are almost identical with a broad transmission dip at around 1140 nm (positions 5 and 5′). The corresponding surface charge and near-field distributions in the right two panels of Figure 3c indicate that this transmission dip can be attributed to the excitation of the electric dipole mode in both structures. Since the radiative loss of an electric dipole mode is in general stronger than a quadruple mode, the near-field enhancement factors at the transmission dip position of the two structures are only about 19 and 17, much smaller than that at the Fano resonance positions of the split disk. It is also worth mentioning that there is a lattice resonance around 870 nm in the simulated
in Figure 2a). The ability to detect such a weak spectral feature experimentally further confirms that high-quality nanostructures with well-defined geometries can be reliably fabricated with our SPL process. According to the plasmon hybridization theory, optical responses of the split nanodisk are caused by the hybridization of plasmon modes between a complete disk and a rectangular nanohole. For example, the upper panel of Figure 3b shows the hybridization scheme between the electric dipole modes of the nanodisk (DD) and the nanohole (DH), which leads to the formation of a bonding (DB) and an antibonding dipole mode (DAB),49 and there are strong radiative efficiencies for both hybridized resonances. Besides that, the lower panel of Figure 3b shows that the interaction between the quadrupole modes of individual nanostructures (QD and QH) results in the generation of a bonding (QB) and an antibonding quadrupole mode (QAB). Due to the subradiant nature of the element quadrupole modes, radiative losses of both hybridized quadrupole modes can be weak. The four transmission dips and peaks of the split disk with incident polarization perpendicular to split gap are labeled as positions 1−4 in sequence from long to short wavelength, and the corresponding charge density (upper panels) and near-field enhancement (lower panels) distributions are shown in the left four panels of Figure 3c. The charge and field distribution at position 1 reveal the excitation of the bonding dipole mode (DB), which can also be seen as a magnetic dipole mode, in close analogy to that of the split-ring and split-ball resonators.43,48 The intense plasmonic coupling at the narrow split gap results in a giant near-field enhancement of more than two orders of magnitude though the selected wavelength is detuned from the actual resonance position. The second column of Figure 3c shows the near-field distributions around position 2. It is worth noting that the selected spectral position is away from the transmission dip to avoid the influence of the higher order resonances. It is found 11109
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Figure 5. SHG with the single split and perfect nanodisks (r = 150 nm, l = 225 nm, and w = 15 nm). (a) Measured SH emission spectra with incident wavelength 1000 nm and the incident power density around 106 W/cm2. (b) The log−log plot of the measured SHG intensity of the split nanodisk and incident power density, where the incident wavelength was 1000 nm and the polarization was perpendicular with the split gap. (c) Measured SH emission spectra of the split nanodisk with various fundamental wavelengths under y-polarized incidence, where the incident power density is identical with that of (a). (d−f) Calculated scattering spectra (d), FH near-field enhancement (e), and SH emission intensity versus the incident wavelength (f) for the single split and perfect nanodisks, where the blue lines represent for the split nanodisk with y-polarized incidence, the red and black lines represent for the split and perfect nanodisks with x-polarized incidence, and the pink data points (error bar included) in (f) represent the experimental results. (g−i) FH near-field enhancement distributions (left column), normalized SH near-field distributions (middle column), and angular plots of the SH far-field emissions (xz plane, right column) when the incidence wavelength is around the Fano resonance position (g) and the electric dipole modes (h) and (i), where the numbers at the lower-left corner of the left columns show the maximum FH near-field enhancement factor.
spectra, as indicated by the near-field distributions in the Supporting Information (Figure S4). However, due to the quasi-normal incidence condition in the experiments, the lattice resonance was not effectively excited in the measured spectra. Symmetry Breaking Enabled Large Modulation Depth in Fano Resonance. The spectral modulation depth of a plasmonic Fano resonance is of critical importance for practical applications, e.g., ensuring reliable spectral shift detection for biosensing. Although the modulation depth of the fundamental Fano resonance generated in the split nanodisks studied in Figures 2 and 3 is significantly enlarged due to stronger plasmonic near-field coupling at the narrower split gap compared with that of the cut nanodisks reported in previous studies,49,50 it is still weaker than that achieved with plasmonic oligomer structures.22,29,30 Here we demonstrate that the modulation depth of the Fano resonance supported in single plasmonic split nanodisks can be enhanced by increasing the gap length in this section. The fundamental Fano resonance of split nanodisk is governed by the bonding quadrupole mode. Therefore, the modulation depth can be tuned by manipulating the geometry of the gap. Figure 4a shows the measured transmission spectra of the 150 nm-radius split nanodisks with different split length l under y-polarized incidence, and the corresponding magnified SEM images are represented in Figure 4b. When the split length equals the radius (l = 150 nm, the
black lines in Figures 2a and 4a), there is a weak Fano resonance around 760 nm. By reducing the split length to 75 nm (the purple line, Figure 4a), radiative losses of the whole structure cannot be determined by such a small cut, and the Fano resonance disappears from the spectrum. On the contrary, radiative losses can be more effectively suppressed when l is enlarged to 225 nm (the red line, Figure 4a), and a very strong Fano resonance is observed around 1000 nm, where the modulation depth is comparable with that of the dolmen and oligomer structures.22,29,30 In addition, by fitting the spectrum according to an analytical Fano interference model,33 the quality factor of the Fano resonance in the split disk was calculated to be about 21 (Figure S5, Supporting Information), while it is only about 5 for the electric dipole mode of the perfect and split disk under x-polarized incidence. It is worth noting that here single nanoparticles are used to generate such a strong Fano resonance, which could be promising for more compact integration and easier geometry control in practical applications. Further enlarge l to 300 nm, that is, a half disk dimer, the Fano resonance disappears from the spectrum again, and only the bonding dipole mode is excited (the cyan line, Figure 4a). In Figure 4c, we show the calculated spectra of each array. The simulation results agree very well with the measurements except for the aforementioned lattice resonance, and more systematic simulation results with different gap 11110
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two electric dipole modes are presented in the left panels of Figure 5g−i, respectively. The integrated near-field enhancement over the surface of the nanodisks against the incident wavelength is shown in Figure 5e. Indeed, the near-field enhancement around the Fano resonance is the strongest within the discussed spectral range, and the maximum field enhancement is about 100 at the Fano resonance position, while it is only about 28 and 23 for the two electric dipole modes, respectively. Besides that, it is found that the maximum near-field enhancement is slightly red-shifted compared with that of the scattering minimum of the Fano resonance. Due to the intrinsic damping, energy shift between near and far-field responses is a common phenomenon in plasmonic nanostructures.61,62 Previous studies have shown that for a plasmonic Fano structure, the maximum near-field intensity enhancement corresponds to the central frequency of the asymmetric modulation for the Fano resonance, but does not correspond to the scattering dip spectral position.63,64 Therefore, there is an energy detuning between the maximum near-field enhancement and the scattering minimum for the split nanodisks. Since the SH emission is governed by the FH near-field enhancement, an amplified nonlinear source can be achieved with the excitation of the Fano resonance. As a result, the calculated SH near-field distribution for the Fano resonance is much stronger than that of the electric dipole modes (middle panels, Figure 5g−i), and the SH far-field emission is the strongest due to the enormously enhanced nonlinear source by the Fano resonance (right panels, Figure 5g−i). By adjusting the incident wavelength, the blue (split disk, y-polarized), red (split disk, x-polarized), and black (perfect disk, x-polarized) lines in Figure 5f show the variations of the calculated SH emissions, and the experimental results are shown by pink data points with error bar, which was calculated from three sets of measured data. The variations of the simulation and experiment agree well with each other. To rule out the contribution of the excitation of higher order resonances, the scattering spectra of the split disk under oblique incidence have been calculated as shown in Figure S8 in the Supporting Information, and no higher order resonance is found around the SH wavelength range. Therefore, the SH emission with the split disk is not amplified with plasmon resonances, even though, with the strongly enhanced nonlinear source due to the excitation of Fano resonance, the SH emission intensity with the Fano resonance is about 5 times stronger than that of the electric dipole modes. It is also noted that instead of dipolar emissions, the SHG far-field scattering patterns correspond to different higher order multipolar emissions. As a centrosymmetric object, the nonlinear responses of the perfect nanodisks are similar to that of perfect nanospheres, where the SH emissions can be dominated by the quadrupolar response for small nanoparticles,65 and the octupolar term should be considered for larger nanoparticles with retardation effects.66 As a results, there is a similar SHG far-field scattering pattern for the perfect nanodisk compared with that of perfect nanospheres (right panel, Figure 5i).65,66 As for the split nanodisks, the structural symmetry is broken with the presence of the nanogap. However, when the incident polarization is along the x-axis, the quadrupolar mode (QD mode in Figure 3b) of the nanodisk can still be excited with the SH nonlinear source. Compared with the perfect nanodisk, there is only a minor change for the near- and far-field responses for the split nanodisk under xpolarized incidence (Figure 5h). On the contrary, the linear and
lengths are represented in Figure S6 in the Supporting Information. In order to better show the physical origin that leads to the Fano resonance with strong modulation depth, the spectra and near-field distributions of single split nanodisks with different gap lengths are, respectively, presented in Figure S7 in the Supporting Information, where the influence of the lattice mode is eliminated in this case. It is found that the energy detuning between the superradiant and subradiant mode is modified by adjusting the gap length. When the energy detuning approachs zero (l ∼ 200 nm), the coupling strength can be strongly enhanced, resulting in the formation of the Fano resonance with a strong modulation depth. Fano Resonance Enhanced Second Harmonic Generation. Due to the strong plasmon coupling around the narrow gap, giant near-field enhancement and strong Fano resonance are realized with single split nanodisks. Besides that, the surrounding HSQ template can be possibly removed by etching. Therefore, the split nanodisk with narrow gap can be a promising platform for applications in biosensing and enhanced spectroscopy. For example, nonlinear optical effects such as SHG in metallic nanostructures highly depend on localized electric-field enhancements around the fundamental harmonic (FH) wavelength.12,13,52−57 Previous studies have shown that with the suppressed radiative losses, the nonlinear source of SHG can be amplified by the excitation of the Fano resonance, thereby forming enhanced SHG.10,11,58,59 For the fabricated single split nanodisks, plasmon coupling is significantly enhanced by the narrow gap, and radiative losses can be simultaneously suppressed with the excitation of the Fano resonance. Therefore, one can expect that the nonlinear source can be dramatically enhanced, and strong SH emissions can be possibly achieved by using the split nanodisks. The 150 nm-radius split disk with l = 225 nm, which has the strong Fano resonance, is used for the SHG measurements. When the incidence is around 1000 nm (matches with the Fano resonance), and the polarization is perpendicular to the split gap; the blue line in Figure 5a represents the typical SH emission spectrum, where a strong emission peak appears at 500 nm. On the contrary, the emissions are very weak for the split and perfect nanodisks when the polarization is along the xaxis (the red and black lines, Figure 5b). By manipulating the incidence, the open circular points in Figure 5b show the log− log plot of the relationship between the measured SH emission intensity and the incident power density using the Fano resonance of the split nanodisk. A linear fit reveals that the slope is about 1.92, indicating the measured signals are SH emissions. By adjusting the FH wavelength for the split nanodisk under y-polarized incidence, the SH emission spectra shown in Figure 5c indeed reveal that the emission intensity is the strongest when the incidence is around the Fano resonance (i.e., 1000 nm). In order to verify the experimental results, the SH emissions of the single split and perfect nanodisks are calculated with a perturbative approach.60 The blue line in Figure 5d shows the calculated scattering spectrum of the single split nanodisk under y-polarized incidence. The pronounced Fano resonance is around the same spectral position as that of the split nanodisk array (Figure 4), and the spectral features are also similar to each other despite of the lattice resonance. For comparison, the red and black lines represent the scattering spectra of the split and perfect nanodisks under x-polarized excitation. The nearfield enhancement distributions at the Fano resonance and the 11111
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or chromium adhesion layer was used. The deposited gold at the outside and top of the HSQ templates was peeled off by UV-cured optical adhesive (NOA-61, Norland Products Inc.), and only the inside gold structures remained for optical measurements. In a typical peeling process, optical adhesive was poured onto the gold-coated sample, keeping static for 1 min. Subsequently, the adhesive was cured under the illumination of ultraviolet for 20 min. Finally, the gold structures were obtained after peeling off the cured adhesive. Scanning Electron Microscopy. The fabricated structures were characterized by field-emission scanning electron microscopy (FESEM, Carl-Zeiss Sigma HD). The accelerating voltage and the working distance were 1 kV and 3.5 mm, respectively. Note that low voltage and small working distance were used to enable highresolution SEM imaging for the gold structures on the insulating quartz substrate. Transmittance Measurements. Polarization-resolved transmittance spectra were collected by a Fourier transform infrared microscope (Bruker Hyperion 1000/2000) equipped with a visible and a near-infrared light source and corresponding detectors. A condenser was used to focus the incident light to the sample plane at quasi-normal incidence (∼23.6°), and a reflective objective (magnification 15× , numerical aperture 0.4) was used to collect the transmitted light. The transmittance spectra were normalized with respect to the transmittance through a quartz substrate. SHG Measurements. The wavelength-dependent SHG was measured with a commercial laser scanning confocal microscope system (Leica, TCS SP5), combined with a Ti:sapphire femtosecond laser (Spectra-physics, Mai Tai HP). The time duration and repetition rate of the laser pulse were about 500 fs and 80 MHz, respectively. The measurement setup is schemed in Figure S10a in the Supporting Information. The mean power density at the sample plane was around 106 W/cm2 on condition that the magnification and numerical aperture of the focused objective were 100× and 0.95, respectively. The SHG intensity at each wavelength was obtained through integrating the emission signal within the second harmonic wavelength window (20 nm) over the area of each split disk array (100 μm × 100 μm). Electromagnetic Simulations. Finite-difference time-domain method was used to calculate the transmittance spectra and the corresponding charge and near-field distributions with a commercial software (Lumerical Solutions). The dielectric constant of gold was from the database of Johnson-Christy.67 Perfectly matched layers were used in simulation at z direction, periodic boundary condition was employed for x and y directions, and the period at both directions is 600 nm. The reserved exposed HSQ was replaced by SiO2 (Palik).68 The SH emissions from the single split and solid nanodisks are calculated with the finite element method (FEM, COMSOL Multiphysics). First, the linear scattering response of the disks is solved at the FH wavelength, and the FH near-field distributions are used to calculate the nonlinear source. Then, the linear scattering response at the SH wavelength is calculated by using the nonlinear source derived from the first step. In the simulations, only the dominant component χ⊥⊥⊥ of the second order surface susceptibility tensor is considered, where ⊥ represents the orientation perpendicular to the surface of the structure.60 The surface nonlinear polarization is written as PSurf,⊥(r, 2ω) = χ⊥⊥⊥E⊥(r, ω)E⊥(r, ω), and the SH nonlinear source is calculated by JSurf,⊥(r, 2ω) = ∂PSurf,⊥(r, 2ω)/∂t. With the use of the weak form, the SH near and far-field distributions are obtained by solving the Maxwell equations. The near-field intensity is calculated by integrating the electric field over the structure surface, and the integrated far-field scattering over a solid angle range determined by the objective lens (numerical aperture 0.95) is used for collecting the SH emissions.
nonlinear responses change dramatically for the split disk under y-polarized incidence (Figure 5g), where the quadrupolar mode (QD) of the perfect disk can no longer be sustained, the SH near-field distributions are totally different from the other two cases, and there are qualitatively changes of the SH far-field scattering patterns. The conversion efficiencies with individual disks have also been calculated (Figure S9, Supporting Information), where the SH conversion efficiency is supposed to be ηSHG = ScaSH/ExtFH, and ScaSH and ExtFH are the scattering and extinction cross sections around the second and the FH wavelengths, respectively. Please note that this definition is different from that of the traditionally used method in experiments, where the efficiency is calculated by the SHG emission intensity divided by the pump intensity. The calculated SH conversion efficiency for the Fano resonance is larger than 10−11 (with incidence around 1000 nm, Figure S9a, Supporting Information), and it can be enlarged to about 10−10 when the incidence is approaching the magnetic dipole mode of the split disk (with incidence around 2550 nm). For the perfect disk, the maximum SH conversion efficiency is
