Polarization-Independent Multiple Fano Resonances in Plasmonic Nonamers for Multimode-Matching Enhanced Multiband Second-Harmonic Generation Shao-Ding Liu,†,‡ Eunice Sok Ping Leong,§ Guang-Can Li,⊥ Yidong Hou,⊥ Jie Deng,§ Jing Hua Teng,§ Hock Chun Ong,∥ and Dang Yuan Lei*,⊥ †
Key Lab of Advanced Transducers and Intelligent Control System of Ministry of Education and ‡Department of Physics and Optoelectronics, Taiyuan University of Technology, Taiyuan 030024, People’s Republic of China § Institute of Materials Research and Engineering, A*STAR, 2 Fusionopolis Way, Singapore 138634 ⊥ Department of Applied Physics, The Hong Kong Polytechnic University, Hong Kong, China ∥ Department of Physics, The Chinese University of Hong Kong, Hong Kong, China S Supporting Information *
ABSTRACT: Plasmonic oligomers composed of metallic nanoparticles are one class of the most promising platforms for generating Fano resonances with unprecedented optical properties for enhancing various linear and nonlinear optical processes. For efficient generation of second-harmonic emissions at multiple wavelength bands, it is critical to design a plasmonic oligomer concurrently having multiple Fano resonances spectrally matching the fundamental excitation wavelengths and multiple plasmon resonance modes coinciding with the harmonic wavelengths. Thus far, the realization of such a plasmonic oligomer remains a challenge. This study demonstrates both theoretically and experimentally that a plasmonic nonamer consisting of a gold nanocross surrounded by eight nanorods simultaneously sustains multiple polarization-independent Fano resonances in the near-infrared region and several higher-order plasmon resonances in the visible spectrum. Due to coherent amplification of the nonlinear excitation sources by the Fano resonances and efficient scattering-enhanced outcoupling by the higher-order modes, the second-harmonic emission of the nonamer is significantly increased at multiple spectral bands, and their spectral positions and radiation patterns can be flexibly manipulated by easily tuning the length of the surrounding nanorods in the nonamer. These results provide us with important implications for realizing ultrafast multichannel nonlinear optoelectronic devices. KEYWORDS: Fano resonances, plasmonic oligomers, second-harmonic generation, higher-order plasmon modes, metallic nanostructures
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observed for the plasmonic nanostructures that possess higherorder dark subradiant modes, and the radiative losses are therefore suppressed simultaneously at several spectral positions.19,20 In general, the net dipole moment of a dark subradiant mode approaches zero, and the coupling between the dark mode and the external field is weak. Therefore, Fano resonances are often excited by breaking the structural symmetry of plasmonic
lasmonic Fano resonances originating from destructive interferences between bright superradiant and dark subradiant modes in metallic nanostructures have attracted considerable attention in recent years.1 Radiative losses at the Fano resonance positions are effectively suppressed due to excitation of the dark subradiant modes, resulting in strong near-field enhancements and structuredependent resonance line shapes.2,3 Numerous metallic nanostructures have been designed to generate Fano resonances, such as dolmen structures,4,5 ring/disk cavities,6 core/shell nanoparticles,7,8 mismatched dimers,9−12 and hybridized structures.13−18 Multiple Fano resonances are also © XXXX American Chemical Society
Received: November 4, 2015 Accepted: January 4, 2016
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Figure 1. (a) Schematic geometry of a gold nonamer, which is composed of a nanocross and eight nanorods. The angle of the cross is ψ = 90°, and the rods are placed symmetrically around the center particle. (b−f) Fabricated samples with a nominal outer rod length L = (b) 0, (c) 180, (d) 250, (e) 500, and (f) 720 nm. The other geometry parameters are the cross length C = 350 nm, the inner rod length l = 250 nm, the width w = 75 nm, the separations s = g = 30 nm, and the thickness h = 50 nm. The scale bars in (b−f) are 1 μm.
also able to enhance optical nonlinear effects, such as second-/ third-harmonic generation (S/THG),69−72 and four-wave mixing (FWM).73 SHG is the simplest among various nonlinear optical phenomena, and it is physically forbidden within the electric dipole approximation in centrosymmetrical bulk materials. However, strong SHG can be generated in metallic nanostructures enabled by the breakdown of the centrosymmetry at the metal surface.74−78 Tremendous efforts aimed at enhancing SHG emissions with plasmonic nanostructures have been made recently.79−85 It has been shown that certain criteria have to be fulfilled to achieve strong SHG emissions: (1) nearfield enhancement amplified nonlinear source at the fundamental harmonic (FH), (2) reduced radiative loss at the FH wavelength, and (3) increased radiative scattering at the SHG wavelengths.86−88 On the one hand, the radiative loss in a plasmonic nanostructure at the FH wavelength can be effectively suppressed with the excitation of the Fano resonance, leading to an enhanced nonlinear source.69,70,89 On the other hand, by engineering the higher-order modes to enlarge their scattering intensities at the harmonic wavelengths, the outcoupling efficiency of SH emissions from a plasmonic heptamer under the excitation of a single Fano resonance can be 3 times stronger than that of a dipole antenna.90 Implementation of the above-mentioned criteria for efficient SHG in Fano resonant plasmonic structures relies on flexible spectral tunability of both Fano resonances and higher-order modes. Although the spectral positions of Fano resonances can be inductively tuned using graphene,91−93 these hybrid structures are often complex and their optical responses could, in turn, be affected with the presence of graphene. One of the simplest approaches to tune the Fano resonances is by manipulating the geometry parameters of plasmonic nanostructures. For metallic oligomer clusters, the modulation depth and the resonance energy of the generated Fano resonances can be readily modified by adjusting the particle size or interparticle separation.94−96 The Fano resonances can be tuned to the near-ultraviolet by substituting noble metals by aluminum.97 However, there are still several challenges in
nanostructures, leading to the incident polarization-dependent optical responses.6,7 Fortunately, polarization-independent Fano resonances can also be generated with plasmonic oligomer clusters,21−23 where the plasmon hybridization between the center and the surrounding particles results in the formation of two spectrally overlapped bright and dark modes, thereby leading to the generation of single Fano resonances without breaking the structural symmetry.24,25 For example, it has been shown that pronounced Fano resonances can be generated in plasmonic heptamers,21,22 pentamers,26,27 quadrumers,28−31 and trimers.32,33 Moreover, due to the strong coupling between adjacent particles, oligomer clusters often possess a bright superradiant mode and several possible dark subradiant modes as indicated by the group theory,34 providing an excellent plasmonic platform to produce multiple Fano resonances. The subradiant modes can be excited by breaking the nanocluster symmetry35−37 or using an oblique incidence, and therefore, more complex dark modes become active under radially and azimuthally polarized incidence.38−40 In particular, by introducing additional nanodisks surrounding a plasmonic heptamer, higher-order dark modes can be coupled to a broad superradiant mode without breaking the structural symmetry, giving rise to the multiple polarization-insensitive Fano resonances.41 The spectral proximity of the constructive and destructive interferences between a bright and a dark mode results in a narrow spectral dip in the scattering spectrum of a plasmonic Fano system, leading to reduced radiation losses and effective confinement of incident energy. Given these fascinating properties, Fano resonances have been widely demonstrated to be useful for label-free biosensing,42−52 surface-enhanced spectroscopy,53−56 enhanced transmission,57 nanoparticle sorting,58,59 enhanced magnetic field generation,60−62 optical switches,63 and low-loss waveguiding.64,65 With the unique ability of plasmon resonance line shaping at multiple spectral positions, Fano resonances can be used as three-dimensional plasmon rulers,66 directional antenna,67 and optical tagging.68 Recently, it has been demonstrated that Fano resonances are B
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Figure 2. (a) Measured and (b) simulated extinction spectra of the five nonamers shown in Figure 1b−f. The center panel shows the highresolution SEM images of the samples. An unpolarized white light was used in the extinction measurements. The solid lines and dots of the simulated results represent the extinction spectra at incident polarization angle θ = 0 and 45° with respect to the Y direction, respectively. The arrows in (b) indicate the wavelengths at which the near-field profile and surface charge distribution are plotted for the nonamers in Figure 4.
flexible tuning of Fano resonances: (1) The oligomer clusters reported in previous studies are mainly composed of nanodisks or nanospheres, where the spectral tunability is more limited than that with nanorods, and therefore, the nanocluster sizes have to be enlarged dramatically to extend the Fano resonances to the near-infrared spectral region. (2) The spectral contrast and the resonance energies of the multiple Fano resonances generated in oligomer clusters are simultaneously modified by adjusting a single geometry parameter, which incurs an obstacle to tune individual Fano resonances to desired spectral positions.41 These challenges have been significantly prevented from producing multimode-matching enabled multiband SHG in plasmonic Fano resonant systems. In this article, a plasmonic nonamer cluster composed of a gold nanocross surrounded with eight nanorods is designed to concurrently generate polarization-independent multiple Fano resonances in the near-infrared region and higher-order plasmon modes in the visible region. Compared with plasmonic oligomers made of circular-shaped nanodisks, the plasmon responses of the nanorods and nanocross highly depend on their aspect ratios, and thus the collective plasmon response of the nonamer cluster can be flexibly varied in the visible and near-infrared spectral regions. More importantly, it is found that one of the resonance modes can be significantly modified by manipulating the geometry parameter, while the others remain nearly unchanged in the spectrum. These unique properties make the designed nonamer an efficient generator of SH emissions at multiple spectral bands due to coherent amplification of the nonlinear excitation sources by the Fano resonances and efficient scattering-enhanced outcoupling by the higher-order modes.
nanorods with lengths l and L, respectively. The distance between the inner and outer ring layers is denoted as g, and s is the separation between the nanocross and the inner ring layer. The width of the nanorods and the nanocross is denoted as w, and h is the structure thickness. The angle of the nanocross is ψ = 90°, and the surrounding nanorods are placed symmetrically around the central particle. Therefore, the nonamer has a fourfold symmetry (D4h point group). Rahmani et al. have shown that plasmonic nanoclusters with rotational symmetry exhibit polarization-invariant far-field response though their near-field distribution profiles highly depend on incidence polarization position due to superposition of nondegenerate eigenmodes.25 Similarly, the far-field optical response of the symmetric nonamers is polarization-independent at normal incidence. In addition, since the optical properties of the constituent nanoparticles of the nonamer can be easily tuned by manipulating their aspect ratio, the collective plasmon response of the whole structure is expected to be easily tuned over a wide spectral region. In the experiment, we have fabricated a series of nonamer arrays with variable nanorod length of the outer ring layer using e-beam lithography. Figure 1b−f represents the corresponding scanning electron microscopy (SEM) images, all exhibiting good reproducibility over a large area. The nominal periodicities in both X and Y directions are 1.15 μm, and the nanorod lengths L of the outer ring layer are 0, 180, 250, 500, and 720 nm, respectively. The other geometry parameters are designed to be C = 350 nm, l = 250 nm, w = 75 nm, g = 30 nm, s = 30 nm, and h = 50 nm. The high-resolution SEM images shown in the middle panel of Figure 2 demonstrate that the measured geometric parameters of the fabricated samples are very close to the designed values, with a typical deviation within ±5 nm. The black line in Figure 2a represents the measured extinction spectrum for a pentamer (L = 0), and only one pronounced Fano resonance appears around 1500 nm. However, the plasmonic coupling through near-field inter-
RESULTS AND DISCUSSION Multiple Fano Resonances in Plasmonic Nonamers. Figure 1a shows the geometry of the designed gold nonamer, where a nanocross with length C is placed in the center of the cluster, and the inner and outer ring layers are made up of four C
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Figure 3. Calculated extinction (left panel) and absorption (right panel) intensities as functions of the nanorod length L and incident wavelength. The white dotted lines indicate the nanorod lengths corresponding to the extinction spectra shown in Figure 2, and the dashed lines are guides for the eye of the four sets of Fano resonances.
Figure 4. Field enhancement (|E|/|Einc|) distribution and surface charge distribution of the five nonamers at different spectral positions: (a) 1765 and (b) 1545 nm corresponding to the bright superradiant mode and the Fano resonance mode of the pentamer, respectively; (c)1765, (d) 1064, and (e) 1548 nm corresponding to the superradiant mode, the first and second Fano resonances of the nonamer with L = 180 nm; (f) 1310 and (g) 1559 nm corresponding to the first and second Fano resonances of the nonamers with L = 250 nm; (h) 1456 and (i) 1873 nm corresponding to the third and fourth Fano resonances of the nonamer with L = 500 nm; and (j) 1456 nm corresponding to the third Fano resonance of the nonamer with L = 720 nm.
actions between the nanocross and the two ring layers results in the generation of multiple Fano resonances when the outer ring layer of nanorods is introduced to form a nonamer. For example, two prominent Fano resonances appear in the spectrum for the nonamer with L = 180 nm (the red line),
and the lower-energy resonance is almost at the same spectral position as that of the pentamer while the new resonance appears around 1000 nm. When the rod length is enlarged to 250 nm (the blue line), the lower-energy Fano resonance remains at the same position as that of L = 180 nm while a D
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ACS Nano perceivable kink,41 instead of a spectral dip, emerges around 1300 nm. Further increase of the rod length to 500 nm (the ocean green line) retrieves the generation of double Fano resonances at lower energies with significantly improved spectral contrast compared to L = 180 nm. The surrounding nanorods overlap with each other when the rod length is 720 nm, thereby forming a square ring (the magenta line) and resulting in the disappearance of the lower-energy Fano resonance compared to L = 500 nm. The measured extinction spectra show good agreement with the simulation results shown in Figure 2b (solid lines). The slight differences between the measured and simulated spectra can be attributed to the size variations among the clusters in the nonamer arrays. In order to increase the observability of the optical response variation with the nanorod geometry, the calculated extinction and absorption spectra of the nonamer are shown in the contour plots as a function of nanorod length L and incident wavelength in Figure 3, which reveals the presence of four sets of Fano resonances. When L < 250 nm, double Fano resonances can be observed in the spectra: a higher-energy one red shifting linearly with the increase of L (the first one, marked with light blue dashed line) and the other at lower energy that is insensitive to the nanorod length L (the second one, marked with green dashed line). When the nanorod length is in the range of 250 nm < L < 320 nm, the first Fano resonance vanishes, as observed in Figure 2, and the modulation depth of the second Fano resonance decreases at the same time. When L > 320 nm, another two sets of Fano resonances appear in the spectra. For the newly appearing Fano resonance with higher energy (the third one, marked with yellow dashed line), there is a minor change for the resonance energy with the increasing of L. The other newly appearing Fano resonance has a lower resonance energy (the fourth one, marked with blue dashed line), and it is red shifting with the increasing of L. Once the outermost nanorods connect with each other (L > 570 nm), the fourth Fano resonance disappears. The above identification of the four sets of Fano resonances is further supported by the electric near-field distribution at respective wavelengths. The top panel of Figure 4a shows the near-field enhancement (|E|/|Einc|) distribution at the cross section of the pentamer (25 nm above the pentamer−substrate interface) at a wavelength of 1765 nm, and the bottom panel shows the corresponding surface charge distribution. Both panels show that the localized plasmons of the nanocross and the surrounding nanorods oscillate in-phase, resulting in a bright superradiant mode with a broad line width. In contrast, the plasmons of the nanocross oscillate out-of-phase with the surrounding nanorods at a wavelength of 1545 nm (see Figure 4b), leading to cancellation of their dipole moments and reduced radiative damping, that is, forming a subradiant collective mode. The subradiant mode spectrally overlaps with the bright mode, and their destructive interference results in the formation of the Fano resonance, as shown in Figure 2a (black line). The generation of this Fano resonance in the pentamer shares the same physical mechanism as that in the oligomer clusters composed of metal nanodisks.21,22 When the outer ring layer with a nanorod length of L = 180 nm is introduced to form a plasmonic nonamer, the localized plasmons of the individual nanoparticles also oscillate inphase for the bright collective resonance at a wavelength of 1765 nm (Figure 4c). However, due to the nanorod-length mismatch-induced symmetry breaking, the four pairs of
surrounding nanorods can be considered as asymmetric nanorod dimers, which all possess a subradiant bonding dipole mode with their plasmons oscillating out-of-phase.9 The nearfield distribution at the first Fano resonance position (1064 nm) reveals that the subradiant bonding dipolar mode of the dimers on the left and the right side is efficiently excited (see Figure 4d), leading to a suppressed radiative damping and the formation of the spectral dip (see Figure 2a). Similar to the pentamer case, the out-of-phase oscillation of the localized plasmons of the nanocross and nanorods in the nonamer with L = 180 nm gives rise to a subradiant resonance mode at a wavelength of 1548 nm (see Figure 4e), and its destructive interference with the bright superradiant mode at a wavelength of 1765 nm leads to the formation of the second Fano resonance (see the second spectral dip of the red line in Figure 2a). Since the resonance energy of the bonding dipole mode decreases with increasing L, the first Fano resonance shifts to lower energies accordingly (see Figure 3). When the nanorod length of the outer ring layer is enlarged to 250 nm, equal to that of the inner ring layer, the surrounding nanorod pairs evolve into symmetric dimers, and the subradiant bonding dipole mode cannot be effectively excited under normal incidence (see Figure 4f for a wavelength of 1310 nm). As a result, the first Fano resonance disappears in the extinction spectrum (see Figure 2a) while the second Fano resonance preserves and red shifts slightly, consistent with the near-field and surface charge profiles at a wavelength of 1559 nm. On the one hand, a common feature shared by the surface charge distributions for the pentamer and the nonamers with L = 180 and 250 nm at their second subradiant resonance positions (see Figure 4b,e,g) is that the localized plasmons of the center nanocross always oscillate out-of-phase with respect to the surrounding nanorod dimers at the left and right sides. On the other hand, the center nanocross in both nonamers are often weakly excited at their first subradiant resonance positions (see Figure 4d,f), while the bonding dipolar mode of the nanorod dimers on the left and right sides forms a quadrupole-like higher-order mode with reduced radiative damping. In the following, we will show that when the length of the nanorods in the outer ring layer is further enlarged, the collective dark resonances due to out-of-phase oscillation of plasmons in the center nanocross and the two nanorod ring layers can be excited, resulting in the formation of the third and the fourth Fano resonances and more plasmonic hot spots due to strong near-field coupling between adjacent layers. Figure 4h shows the near-field enhancement and surface charge distributions of the third Fano resonance in the nonamer with L = 500 nm, where the plasmons of the nanocross and the surrounding nanorods at the left and right sides all are excited effectively. Although the surface charges on the center nanocross and the inner ring layer of the nanorods oscillate out-of-phase, similar to that of the pentamer and the nonamer with L = 180 and 250 nm at their second subradiant resonance positions, the surface charges of the nanocross oscillate in-phase with that of the outer ring layer, completely different from the scenario shown in Figure 4e,g. As a result, the strong near-field coupling also occurs between the two nanorod layers in addition to between the nanocross and the inner nanorods (see the top panel of Figure 4h) and consequently generates a larger number of plasmonic hot spots than in the nonamer with L = 180 and 250 nm. The cancellation of the dipole moments between the nanorod layers and the nanocross results in a subradiant collective mode, and the destructive interference E
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Figure 5. Near-field enhancement and surface charge distribution for the four Fano resonances in the two nonamers with (a,b) L = 180 nm and (c,d) L = 500 nm excited by an incident polarization angle θ = 45°: (a) 1064 and (b) 1548 nm corresponding to the first and second Fano resonances for L = 180 nm; (c) 1456 and (d) 1873 corresponding to the third and fourth Fano resonances for L = 500 nm.
oligomer cluster is often governed by its structural symmetry. Since the nonamer is designed to have the D4h point group symmetry, its far-field response is expected to be polarizationindependent. The circular points in Figure 2b represent the calculated extinction spectra for an incident polarization angle θ = 45°, and the spectra are exactly the same as that for θ = 0 (solid line in the same figure). Figure S2 compares the extinction spectra calculated at incidence polarization along one symmetric (θ = 0) and two nonsymmetric axes (θ = 15 and 35°), which show exactly the same spectral response for each nonamer. Although the extinction properties of the nonamers are polarization-independent, their near-field distributions change dramatically by manipulating the incident polarization, particularly important for plasmonic hot spot engineering. Figure 5 shows the near-field distributions and surface charge profiles at the Fano resonance positions for the nonamers with L = 180 and 500 nm excited under incident polarization θ = 45°. As can be seen from the surface charge profiles (bottom panels), the longitudinal plasmons of all the surrounding nanorods are excited. At the first Fano resonance for L = 180 nm, the subradiant collective resonance at a wavelength of 1064 nm is related to the excitation of bonding dipole modes of the four nanorod dimers (bottom panel of Figure 5a), with plasmonic hot spots generated in all the gap regions of the nanorod dimers (top panel). At the spectral position of the second Fano resonance, the localized plasmons of the nanocross oscillate out-of-phase with that of the four inner nanorods, forming a collective subradiant mode (bottom panel of Figure 5b) and generating strong near-field hot spots only at the gap regions between the nanocross and the inner nanorods (top panel). At the third Fano resonance in the nonamer with L = 500 nm, the longitudinal plasmons of the inner nanorods oscillate out-of-phase with respect to that of both nanocross and outer nanorods (bottom panel of Figure 5c), and there exist plasmon hot spots in all the gap regions between adjacent nanoparticles (top panel). The surface charge profile at the fourth Fano resonance for L = 500 nm at θ = 45° is reversed inphase compared to the third one, but the near-field distribution is almost preserved. Enhanced Multiband Second-Harmonic Generation. Due to concurrent excitations of the multiple Fano resonances,
with a broad bright mode (near-field and surface charge distributions not shown) leads to the formation of the third Fano resonance. More interestingly, one can clearly see from Figure 3 that the spectral position of this Fano resonance is almost independent of the length of the outer nanorods. For example, even when the four outer nanorods connect with each other at L = 720 nm, the resonance energy, the near-field distribution, and the surface charge profile all are almost unchanged compared to L = 500 nm (see Figure 3 and Figure 4j). Unlike the first three ones, both near-field distribution and surface charge profile of the fourth Fano resonance is distinctively different due to the involvement of the top and bottom nanorod dimers in the near-field coupling. As can be seen from the top panel of Figure 4i, there exist strong plasmonic hot spots not only in the gaps of all nanorod dimers but also at the regions between the corners of the four outer nanorods. The surface charge profile in the bottom panel of Figure 4i shows that the localized plasmons of the top and bottom (left and right sides) nanorod dimers oscillate in-phase (out-of-phase) with respect to that of the center nanocross, leading to an amplification (a cancellation) of their dipole moments. It is also worthwhile pointing out that multipolar plasmons are excited on the left- and right-side inner nanorods. By further enlarging L, the dipole resonance of the outer nanorods shifts to lower energies, and consequently, the resonance energy of the fourth Fano resonance red shifts. At L = 720 nm, the dipole resonance of the outer nanorods can no longer be excited, and thus the fourth Fano resonance vanishes from the spectrum. These results indicate that, by adjusting the length of the outer nanorods, the first and the fourth Fano resonances can be well tuned while the spectral positions of the second and the third Fano resonances are almost unchanged. This property makes the nonamer system a promising platform for plasmon resonance shaping and allows easy tuning of multiple Fano resonances to desired spectral positions. Furthermore, the simulation results also reveal that some of the Fano resonances can be easily adjusted to the visible by simply scaling down the geometry parameters (Figure S1). Polarization-Independent Fano Resonances. The polarization dependence of the far-field response of an F
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Figure 6. (a) Measured SHG emission spectrum for the nonamer with L = 180 nm excited with an FH wavelength of 880 nm with an incident average power of 54 mW. The inset shows the log−log plot of the measured SH intensity as a function of incident power (blue empty circles), with a linear fit to the measured data (blue line). (b) Normalized measured (red solid circles) and simulated (blue empty circles) SH emission intensities as a function of excitation wavelength. The blue and red solid lines are a guide for the eye. The insets show two SH emission mappings at 440 (left) and 475 nm (right). Each image has a dimension of 50 μm × 50 μm, the same as the area of each nonamer array. (c,d) FH near-field distributions at (c) 880 and (d) 950 nm. (e,f) Normalized SH near-field distribution at (e) 440 and (f) 475 nm, where the inset in (f) shows the ratio of the SH near-field intensity at the two wavelengths along the white dashed lines in (e,f). (g,h) Angular plots of the SH far-field emission intensity at (g) 440 and (h) 475 nm in the y−z plane perpendicular to the sample surface, where both intensities are scaled by a factor of 200.
nm (Figure 6c) is weaker than that at 950 nm (Figure 6d). This is consistent with the observation from Figure 2 that the energy gap between the 880 nm incidence and the first Fano resonance is larger than that for the 950 nm incidence. Because a stronger near-field enhancement at the FH wavelength indicates a stronger nonlinear source for SHG, the SH near-field intensity at the nonamer surface for the 950 nm incidence would thus be much larger than that for the 880 nm incidence (Figure 6e,f). This discrepancy between the experimental results and the calculated field enhancement factor at the FH wavelength suggests that the collected SH far-field emission intensity also relies on other factors such as the scattering efficiency at the SH wavelength.86,87,90 In fact, a closer look into the ratio of the SH near-field intensity along the white dashed lines in Figure 6e,f at the two wavelengths (inset of Figure 6f) reveals that the electric field in the free space is indeed stronger at a wavelength of 440 nm than that for 475 nm (light yellow regions). This suggests that the scattering efficiency at the 440 nm SH wavelength is larger than that at 475 nm. As a result, although the SH emission for the 880 nm incidence has a weaker near-field intensity than the 950 nm counterpart, the converted harmonic energies can be more effectively coupled out to the free space for collection due to the larger scattering efficiency at 440 nm. Although the operation wavelength range in our experiment is restricted to below 980 nm, spectrally separated from the Fano resonances in the nonamers, we have indeed observed that the SH emission intensity increases with the FH wavelength approaching the first Fano resonance (λ > 960 nm, red circular points, Figure 6b), in good agreement with our theoretical calculation result (blue circular points, Figure 6b). The asymmetric angular intensity distribution profiles shown in
the radiative losses of the nonamers are suppressed simultaneously at the respective spectral positions in the near-infrared region. In the meantime, the plasmonic hot spots with strong near-field enhancements in the nonamers are expected to amplify the nonlinear excitation sources for SHG. Finally, the higher-order resonance modes in the visible region arising from plasmon hybridization of multipolar resonances sustained by the nanorods and nanocross can possibly be coupled with the nonlinear signals, leading to enhanced scattering of SH emissions. Therefore, the above-mentioned criteria for achieving effective SHG at multiple wavelength bands can be fully fulfilled with the designed plasmonic nonamers. Figure 6a presents the nonlinear emission spectrum for the nonamer with L = 180 nm excited by a 500 fs pulse laser at an output wavelength of 880 nm with an average power of 54 mW, and an emission peak appears around 440 nm. The inset is a log−log plot of the SH emission intensity as a function of incident power, which exhibits a clear quadratic dependence, confirming the measured signals coming from SHG. The red circular points in Figure 6b show the measured wavelengthdependent SH emission intensity by varying the FH excitation wavelength from 850 to 980 nm. An intensity maximum is observed at the FH wavelength of 880 nm, and the left inset shows the corresponding emission image, demonstrating a much stronger intensity than that at 950 nm excitation (right inset). The blue circular points in Figure 6b show the calculation result for the same system using a perturbative approach,75 which shows good agreement with experiment. However, the near-field distribution at the FH wavelength reveals that the field enhancement factor at a wavelength of 880 G
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Figure 7. Calculated SHG emitted by the designed clusters with L = (a) 0, (b) 180 nm, (c) 250 nm, (d) 500 nm, and (e) 720 nm. The top panels show the scattering spectra (black dashed lines) of the designed oligomers under oblique incidence in the SH wavelength range and the absorption (red solid lines) and extinction (blue solid lines) spectra in the FH wavelength range. The middle panels present the FH wavelength-dependent SH (red lines) and FH (blue lines) near-field intensities, and the bottom panels show the corresponding SH far-field intensities (the same as Figure 6b). The near- and far-field intensities are normalized, and the data for L = 0, 180, and 250 nm are scaled by a factor of 3.
thus expect that the SHG intensities can be several orders larger than that at the off-resonance condition, as presented in Figure 6. To illustrate clearly the enhanced multiband SH emissions in the plasmonic nonamers, the near-field distributions at the corresponding FH and SH wavelengths as well as the angular distributions of the SH emission intensities are presented in Figures S5−S7 in the Supporting Information, respectively. The top four panels in Figure S5 consistently demonstrate that, due to efficient suppression of the radiative losses at the four Fano resonance positions in the nonamers, the near-field intensity at the FH wavelengths are significantly enhanced, leading to amplified nonlinear excitation sources and thereby generating the relatively strong SH emissions (top four panels, Figures S6 and S7). The bottom two panels in Figure S5 show that the FH near-field intensities at the higher-order scattering peaks are often smaller than that for the nearby Fano resonances, indicating the formation of weaker nonlinear excitation sources. Due to the larger scattering efficiency at the emission wavelengths, the SH far-field intensity can also be very strong, as observed from Figure 7 as well as the bottom two panels in Figure S7. Detailed discussions on the multimode-matching realization for the plasmonic nonamers can be found in the Supporting Information. For the off-resonance excitation of SHG shown in Figure 6, the generated nonlinear sources are weak and thereby lowintensity SH emissions. Figure S8a plots the variation of SH farfield intensity in logarithmic scale for the nonamer with L = 180 nm, and the emission intensities at the Fano resonance positions (on-resonance excitation) are about 2 orders stronger than that at the 880 nm incidence (off-resonance excitation). Note that the scattering spectra in the SH wavelength range shown in Figure 7 are calculated with an obliquely incident plane wave. This excitation condition is distinctively different from that of the nonlinear sources originating from various localized electric dipoles perpendicular to the surface of the
Figure 6g,h are inconsistent with dipolar emission, indicating significant contribution from higher multipoles. This also corroborates the important role of the far-field scattering in the SH emission intensity. To better understand the interplay of plasmonic near-field enhancement and far-field scattering efficiency in the SHG, Figure 7 comprehensively compares the linear and nonlinear responses of the designed nonamers in the spectral range of 800−2100 nm and in the corresponding SH wavelength range. The top panels show the scattering spectra (black dashed lines, top axes) of the nonamers in the SH wavelength range and their absorption (red solid lines, bottom axes) and extinction (blue solid lines, bottom axes) spectra used to locate the Fano resonance positions. The middle panels present the wavelength-dependent SH (red lines) and FH (blue lines) near-field intensities, and the bottom panels show the corresponding SH far-field intensities calculated with the same method as Figure 6b. On the one hand, the SH far-field intensity peaks marked with the magenta bars match exactly the scattering peaks in the SH wavelength range but not necessarily occur at all the SH near-field intensity peaks. This can be straightforwardly understood from the fact that the scattering process plays a dominant role in the far-field response rather than in the nearfield regime. On the other hand, the Fano resonance bands corresponding to the absorption peaks in the FH wavelength range generally coincide with both near- and far-field SH emission peaks in the SH wavelength range (light blue, green, yellow, and blue bars) because the amplification of the nonlinear sources by plasmonic Fano-resonance-induced nearfield enhancement dominates the whole SHG efficiency at these spectral positions. These results conclusively point out that efficient SHG at multiple wavelength bands requires the use of plasmonic nanostructures with both Fano resonances at the FH wavelengths and scattering peaks (or relatively high scattering intensity) in the corresponding SH wavelengths. Under these on-resonant mode-matching conditions, we can H
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nanocross surrounded by eight nanorods. Due to the high structural symmetry and strong electromagnetic coupling between adjacent nanoparticles, the plasmonic nonamers can sustain multiple polarization-independent Fano resonances in the near-infrared region and also higher-order plasmon resonances in the visible spectrum. The collective plasmon responses of the nonamers can be flexibly adjusted to desired spectral positions by virtue of their enhanced spectral tunability. More importantly, we have shown that the nonlinear sources for SHG in the nonamers can be significantly amplified by exciting the multiple Fano resonances, and that the outcoupling efficiency of SH emissions can be dramatically boosted up with the higher-order plasmon resonances at the corresponding SH wavelengths. The multimode-matching condition can thus be achieved by manipulating the geometry parameters of the nonamers, making them an excellent platform for enhanced multiband SHG. These results provide us with important implications for realizing ultrafast multichannel nonlinear optoelectronic devices.
nanostructures. Since the excitation of the higher-order resonances with oblique incidence relies on retardation effect, the coupling between the incidence and some of the higherorder resonances can be relatively weak, especially for the resonances within the interband electronic transition wavelength range. Figure S9a shows the simulated scattering spectrum for the nonamer of L = 180 nm illuminated by an oblique incidence (black dashed line), and the scattering intensity decreases monotonically with increasing incidence wavelength. This seems in contradiction to both simulated (blue empty circles) and measured (red solid circles) SH emission peaks observed around 440 nm (Figure 6), with the former evaluated with the FH near-field enhancement. When the real SH nonlinear sources (i.e., many localized electric dipoles perpendicular to the surface of the nonamer are considered), the scattering spectrum and the SH emission spectrum show good agreement, as shown in Figure S9b. Since the scattering intensity can also be amplified by the electric dipoles, the scattering spectrum calculated with the SH nonlinear sources cannot be used to directly identify the net contribution by the enhanced far-field scattering at the higherorder resonances. To further distinguish the respective effects of the enhanced far-field scattering and the enhanced nonlinear sources, the SH emission in a gold nanorod dimer is investigated in Figure S10.78 Although only the bonding dipole mode of the dimer is efficiently excited at 1575 nm for the FH incidence, an additional SH emission peak is observed at the FH wavelength of 1365 nm with intensity stronger than that of 1575 nm. By investigating the higher-order resonance modes of the dimer, it is concluded that the SHG peak corresponding to the 1365 nm FH incidence is related to the excitation of the antibonding quadrupole mode at the SH wavelength because their near-field distribution profiles have the same characteristics.78 The stronger emission peak at 1365 nm of the nanorod dimer is used to have a quantitative comparison with the SH emission intensity of the nonamers. For the nonamer with L = 500 nm, the SH emission intensity related to the third and the fourth Fano resonances are about 3.6 and 6.8 times larger than that of the dimer antenna. By carefully engineering the geometry parameters of the nonamer, the SH emission intensity is expected to be further enhanced when the Fano resonances and the higher-order modes match exactly the FH and SH wavelengths, respectively. It is also worth noting that the interband electronic transitions of gold can be an obstacle to achieve strong scattering for SH emissions at a wavelength below 550 nm. This obstacle can be overcome by using alternative plasmonic materials such as aluminum with which Fano resonances and strong scattering have been realized in the near-ultraviolet spectral range,97 and thus it is possible to achieve enhanced SH emissions below 550 nm with aluminum nanoparticles. Finally, Figure 5 has shown that, although the far-field response of the nonamers is polarization-independent, the FH near-field distribution can be tuned by the incident polarization. Since the intensity of the nonlinear sources is governed by the FH near-field profile, the SH emissions can thus be adjusted by manipulating the incident polarization (Figure S8b), which will be investigated in our future studies.
METHODS Sample Fabrication. The gold nonamers were written via standard e-beam lithography (EBL, ELS-7000, Elionix) using a bilayer resist followed by a lift-off process. The sample fabrication was done as follows. A 10 mm × 10 mm × 0.4 mm quartz substrate was cleaned in an ultrasonic bath of acetone followed by isopropyl alcohol and dried using a nitrogen gun. The bilayer resist consisted of a 110 nm thick PMMA at the bottom and a ∼60 nm thick ZEP at the top. The resist was soft-baked at 180 °C for 2 min. A conductive liquid, e-spacer (Showa Denko), was then spin-coated at 1500 rpm as the topmost layer to reduce the charging effect. The EBL writing process was carried out at an acceleration voltage of 100 kV, beam current of 50 pA, and at a dose of 1600 μC/cm2. After writing, the e-spacer was removed with DI water and the resists were developed in o-xylene for 10 s. The structures were then etched with RIE etcher (Plasmalab 80plus, Oxford) for 10 s. Finally, the sample was coated with 3 nm thick Cr film followed by 50 nm thick Au film at a deposition rate of 1 and 2 Å/s, respectively, at a base pressure of 2.5 × 10−6 Torr in an ebeam evaporator (Denton Vacuum, Explorer). The lift-off process was carried out in acetone bath and ultrasonic for 5 min. Extinction Measurement. The unpolarized extinction spectra of the samples were recorded by a Fourier transform infrared microscope (Bruker Hyperion 1000/2000) at normal incidence, combining a visible and a near-infrared light source. The incident light was focused on the nanostructures through a condenser, and the transmitted light was collected through a reflective objective (magnification 36×, numerical aperture 0.5). The detection area was 50 μm × 50 μm, the same as the area of each nonamer array, which was selected by the illumination and detection apertures. The transmission spectra were normalized with respect to the transmission through a bare quartz substrate, and the extinction spectra were calculated as 1 − transmittance. SHG Measurement. All the wavelength-dependent SHG measurements were carried out on 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 is about 500 fs and 80 MHz, and the mean power density at the sample plane is about 50 MW/cm2 after focused by an objective (magnification 100×, numerical aperture 0.95). The SH emission intensity at each wavelength was obtained by integrating the emission signal within the SH wavelength window (20 nm) over the area of each nonamer array (50 μm × 50 μm). Electromagnetic Simulation. The finite-difference time-domain method was used to calculate the absorption, scattering and extinction spectra, near-field enhancement, and surface charge distribution. In the simulation, the complex dielectric constants of gold were taken from the measured data.98 The refractive index of the surrounding medium
CONCLUSION In conclusion, we have achieved enhanced multiband SH emissions with plasmonic nonamers consisting of a gold I
DOI: 10.1021/acsnano.5b06956 ACS Nano XXXX, XXX, XXX−XXX
Article
ACS Nano of the nonamers was supposed to be n = 1.25 to compensate the substrate effect. Perfectly matched layers around the nanostructures were used to simulate the open space, and a normal incident pulse with linear polarization was used as the excitation source. Nonlinear simulations using the finite element method (COMSOL Multiphysics) simulations were performed to calculate the SH emissions from the plasmonic nonamers. First, we solved the linear scattering response for the structures at the FH wavelength with a y-polarized incidence and calculated the nonlinear source with the FH field distribution. Second, we solved the linear scattering response of the structures at the SHG wavelength by using the nonlinear source derived from the first step. Because gold is a centrosymmetric material, the second-order surface susceptibility tensor can be reduced to three independent components: χ⊥⊥⊥, χ⊥∥∥, and χ∥∥⊥, where ⊥ and ∥ represent the orientations perpendicular and parallel to the surface of a structure, respectively. In our simulations, only the dominant component χ⊥⊥⊥ was considered.75 The surface nonlinear polarization can then be written as PSurf,⊥(r, 2ω) = χ⊥⊥⊥E⊥(r, ω)E⊥(r, ω), and the surface nonlinear current (nonlinear source) can be calculated via JSurf,⊥(r, 2ω) = ∂PSurf,⊥(r, 2ω)/∂t. The SHG field was obtained by solving the Maxwell equations with the use of the weak form. The electric field integration value over the structure surface was used as the near-field intensity, and the integrated far-field scattering over a solid angle range determined by the objective lens was used for collecting the SHG farfield intensity (numerical aperture 0.95, corresponding to an inclination angle of ∼71°).
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsnano.5b06956. Figures S1−S10 (PDF)
AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
ACKNOWLEDGMENTS S.-D.L. acknowledges the financial support by the National Natural Science Foundation of China (Grant Nos. 11304219 and 11574228) and the Program for the Top Young Academic Leaders of Higher Learning Institutions of Shanxi. E.S.P.L. and J.H.T. acknowledge the support by the Institute of Materials Research and Engineering, A*STAR. Y.H., G.-C.L., and D.Y.L. acknowledge the support by the Hong Kong Polytechnic University (Grant No. 1-ZVAW) and the Hong Kong Research Grants Council (ECS Grant No. 509513). REFERENCES (1) Luk’yanchuk, B.; Zheludev, N. I.; Maier, S. A.; Halas, N. J.; Nordlander, P.; Giessen, H.; Chong, C. T. The Fano Resonance in Plasmonic Nanostructures and Metamaterials. Nat. Mater. 2010, 9, 707−715. (2) Le, F.; Brandl, D. W.; Urzhumov, Y. A.; Wang, H.; Kundu, J.; Halas, N. J.; Aizpurua, J.; Nordlander, P. Metallic Nanoparticle Arrays: a Common Substrate for Both Surface-Enhanced Raman Scattering and Surface-Enhanced Infrared Absorption. ACS Nano 2008, 2, 707− 718. (3) Christ, A.; Martin, O. J.; Ekinci, Y.; Gippius, N. A.; Tikhodeev, S. G. Symmetry Breaking in a Plasmonic Metamaterial at Optical Wavelength. Nano Lett. 2008, 8, 2171−2175. (4) Zhang, S.; Genov, D. A.; Wang, Y.; Liu, M.; Zhang, X. PlasmonInduced Transparency in Metamaterials. Phys. Rev. Lett. 2008, 101, 047401. J
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DOI: 10.1021/acsnano.5b06956 ACS Nano XXXX, XXX, XXX−XXX
