Abstract

We experimentally and theoretically investigate the influence of alumina coating on the second-harmonic generation (SHG) from split-ring resonator shaped air apertures engraved in a gold film, which are also termed as complementary split-ring resonators (CSRRs). By coating the CSRR arrays with alumina film of certain thickness, we precisely tune their electric diploe resonances (EDRs) to overlap the fundamental wavelength (FW) and realize the EDR enhanced SHG process. On this basis, by shortening the arm length of the CSRRs and then coating them with a certain thickness of the alumina film, we have achieved an SHG enhancement of nearly 1.2-fold in experiment and 8-fold in simulation compared to the CSRR array with an unshortened arm length. We attributed it to the improvement of the magnitude of the effective nonlinear source due to the realization of a doubly-resonant condition. As a flexible method, dielectric coating not only is beneficial to precisely and dynamically optimize the linear and nonlinear properties of the as-fabricated nanoscale devices but also can play the role of a protective layer, which can partially improve the damage threshold of these plasmonic nanoscale devices.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Nonlinear metasurfaces (a kind of new-fashioned artificial optical materials consisting of sub-wavelength structure elements) have received extensive attention because of their important role in nonlinear optics with their fascinating capability of generating and manipulating nonlinear harmonic signal [1,2]. Researches show that plasmonic metasurfaces formed by functional units with broken central symmetry (e.g. U-shaped [37], V-shaped [810] and T-shaped [4,11,12]) have very high second-harmonic (SH) conversion efficiency comparable to commercial nonlinear crystals. However, the low optical damage threshold of plasmonic metasurfaces caused by the ohmic loss hinders the further improvement of the SH conversion efficiency to some extent, so the focus of nonlinearity research is partly shifted to their dielectric counterparts [13,14]. Nonetheless, as a traditional optical material, plasmonic metasurfaces have their certain irreplaceability in nonlinear optics such as their very small mode volumes and characteristic that easily combine the intrinsically embedded electrical functions and optical nonlinearities. For this reason, more scientific research on the intrinsic nonlinearity of the plasmonic metasurfaces is still expected.

Since the nonlinear properties of materials are closely related to their linear properties, one feasible way for enhancing the second-harmonic generation (SHG) from metasurfaces is introducing surface lattice resonance [10,15] or surface plasmon (SP) mode [16,17] with giant local field enhancement at fundamental [18,19] or harmonic wavelengths [20,21] or both of them [22,23]. On this basis, a considerable SHG enhancement can be achieved by modifying the orientation [7] or geometric details [24] of the nanostructures to improve spatial and frequency mode matching condition. Recently, by coating gold nanoislands with a dielectric film, SHG enhancement of 45 times has been achieved [25], in which the applied fundamental wavelength of 1064 nm is far from the plasmonic resonance of the gold nanoislands, and thus the SHG enhancement is mainly attributed to the nonresonant local field enhancement. So far, it is still unknown whether the dielectric loading method could be used to enhance the SHG efficiency when the fundamental wavelength matches the plasmonic resonance.

In this paper, we investigate the influence of dielectric coating on the SHG from complementary split ring resonators (CSRRs), which have been demonstrated to exhibit a relatively high SHG efficiency [26]. By shortening the arm length of the CSRRs and coating them with a certain thickness of alumina film, we consciously tune the electric diploe resonances (EDRs) of the CSRRs to overlap the fundamental wavelength (FW) and realize the EDR-enhanced SHG process. We fabricated a series of CSRR arrays with different arm lengths and conducted alumina coating process using atomic layer deposition (ALD) to verify it. Related simulations have also been carried out.

2. Results and discussion

Figure 1(a) schematically shows a square unit cell of the dielectric-coated gold CSRR array supported on a glass substrate. The periodicities of the CSRR array in both x- and y-directions are set to px = py = 400 nm. The base length (d), the arm width (w) and the thickness (h) of the CSRRs are fixed to d = 130 nm, w = 35 nm, and h = 22 nm, respectively. The arm length (a) of the CSRR and the thickness (t) of the dielectric film are varied in our study. The CSRR arrays with an area of about 50×50 μm2 were fabricated using focused ion beam (FIB) milling. The amorphous alumina film, which was deposited onto the gold CSRRs by atomic layer deposition (ALD), was chosen as the dielectric cladding, due to its weak intrinsic second-order polarizability. During the ALD process, the deposition was performed at the operating temperature of 80℃ in order to avoid heat damage to the gold nanostructures. For numerical simulation, we used a commercial frequency-domain finite-element solver (COMSOL Multiphysics). The intrinsic magnetic response of all materials is ignored (μr = 1). The relative permittivity of gold is described by Drude model: εAu(ω) = 1 – [ω2 p / (ω2+iωγ)], where ω is the angular frequency of the incident electromagnetic wave, ωp and γ are the plasma frequency and damping rate of gold, respectively. In the simulation, we took γ = 1.075 × 1014 s-1 and ωp = 1.380 × 1016 s-1 [27]. The refractive index of the glass substrate, alumina film and air are taken to ns = 1.5, nd = 1.6 and na = 1.0, respectively. It is known that the magnetic dipole resonance of the metallic split ring resonators (SRRs) can be excited by the incident electric field perpendicular to the arm of the SRRs [3,28]. According to Babinet’s principle [29,30], electric and magnetic fields in the CSRRs are expected to be interchanged with respect to the SRRs. Hence, the magnetic dipole resonance excited by the incident arm-perpendicular polarization in the SRRs could turn into the electric dipole resonance excited by the arm-parallel polarization in the CSRRs [26]. For this reason, the electric field of the incident plane electromagnetic wave is set to be parallel to the arm of the CSRR (y-axis direction) to excite its fundamental resonance [the inset of Fig. 1(a)].

 figure: Fig. 1.

Fig. 1. (a) Schematic of a unit cell of the dielectric coated gold CSRR array on a glass substrate. Only half of the dielectric layer is shown for comparison purposes. The plane wave is incident from the substrate side along the z direction and the electric field is polarized along the y direction. (b) Measured and (c) simulated linear spectra of the CSRR arrays with different arm lengths of a = 85 nm, 95 nm, 105 nm and 115 nm. The gray dotted line represents the FW of 1540 nm. The scanning electron microscope (SEM) images (scale bar: 400 nm) of the prepared CSRRs are shown in the right panel of (b). The right panel of (c) shows the distribution of the electric field and the polarization vector in a plane that is 0.1 nm below the top surface calculated for the CSRRs with a = 115 nm at the EDR.

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Similar to the case of the magnetic dipole resonances in the SRRs [28,31], the spectral positions of the EDRs in the CSRRs are expected to be proportional to the total length (d + 2a) of the CSRRs. When the base length d is fixed, the resonant wavelength of the EDRs could then be tuned by varying the arm length a of the CSRRs. As shown in the right panel of Fig. 1(b), four arrays of the CSRRs with different arm lengths of a = 85 nm, 95 nm, 105 nm and 115 nm were prepared. The reflectance spectra of the as-prepared CSRRs (without dielectric coating) were characterized using a Fourier-transform infrared (FTIR) spectrometer and shown in the left panel of Fig. 1(b). The irregular spectrum observed in the range from 900 to 1100 nm is due to the low sensitivity of the detector in this spectral band. Apart from the irregular spectral feature, a remarkable reflection dip that is attributed to the excitation of the EDRs of the CSRRs could be clearly seen in each case. As expected, the resonant wavelength of the EDRs is found to be red-shifted with increasing the arm length a of the CSRRs. It should be noted that for a = 85 nm, 95 nm and 105 nm, the EDRs of the CSRRs are still on the blue side of the FW [1540 nm, marked by the gray dotted line in Fig. 1(b)], while the resonant wavelength of the EDR is slightly larger than the FW for a = 115 nm.

Figure 1(c) shows the simulated reflectance spectra of the CSRR arrays with the same structural parameters as the experiment and the absorption spectra are also included for completeness. It should be noted that for numerical convenience but without loss of generality, the CSRR arrays are assumed to be surrounded by a uniform dielectric medium with a refractive index of ne. Such a kind of effective medium model has been adopted to calculate the linear and nonlinear optical responses of the SRRs on a substrate, and the calculated results are found to have a good agreement with the experimental ones [24,32]. In practice, to determine an appropriate refractive index ne in the effective medium model, its value could be gradually increased from 1.0 (corresponding to the refractive index of air) until the calculated result obtained from the effective medium model shows a good agreement with that obtained from a conventional model having a substrate. In our case, a uniform dielectric environment of ne = 1.17 could be used to account for the glass substrate. The reflectance spectra calculated from the effective medium model with ne = 1.17 [Fig. 1(c)] are found to agree well with our measurements [Fig. 1(b)], faithfully reproducing the red-shifted dip upon increasing the arm length of the CSRRs. The distribution of the electric field amplitude is calculated for the CSRRs with a = 115 nm at the resonant wavelength of 1560 nm and shown in the right panel of Fig. 1(c), in which the electric fields are found to be mostly concentrated near the bulge of the CSRR. Furthermore, the polarization vector in a plane that is 0.1 nm below the top surface of the CSRR is also plotted as the white cones in the right panel of Fig. 1(c). The bulge part of the CSRR exhibits considerably larger polarizability (corresponding to larger cones) and the direction of the polarization is mainly parallel to the CSRR arm (y-axis), which implies that the observed resonance is indeed related to the excitation of the y-axis-oscillated EDR.

Since the fundamental resonance dominates the SHG in typical nanostructures [3,19,26], we focus on the influence of dielectric coating on the EDRs of the gold CSRR arrays. The measured EDR resonant wavelengths of the CSRR arrays with different arm lengths of a = 85 nm, 95 nm, 105 nm and 115 nm are shown in Fig. 2(a) as a function of the alumina film thickness t. It is noted that before depositing the alumina film (t = 0 nm) the EDRs of the CSRRs with a = 85 nm, 95 nm and 105 nm are on the blue-side of the FW of 1540 nm [marked as a horizontal dashed line in Fig. 2(a)]. With increasing the thickness of the deposited alumina film, the EDRs are found to be gradually red-shifted, and thus the EDRs of the CSRRs with a = 85 nm, 95 nm and 105 nm could overlap with the FW at a certain alumina thickness, which ensures the resonance condition could be fulfilled in the SHG process. Since it is difficult to experimentally characterize the exact geometrical parameters of the deposited alumina film, the effective medium model is also used in the case of the CSRRs with dielectric coating. As a first step, we assume that the CSRRs are covered with an alumina film with an infinity thickness, which corresponds to a conventional model having a half-space glass substrate and a half-space covering alumina. By gradually varying the refractive index of the uniform environment in the effective medium model and comparing the results to that obtained from the conventional model, we found that a uniform dielectric environment of ne = 1.57 could account for the glass substrate and the covering alumina layer with an infinite thickness. Therefore, to account for both the glass substrate and the alumina film with a finite thickness, the refractive index of the uniform dielectric environment used in the effective medium model should fall within a range from ne = 1.17 (corresponding to t = 0 nm) to ne = 1.57 (corresponding to t = ∞). Figure 2(b) summarizes the EDR positions extracted from the simulated reflectance spectra of the CSRRs with different arm lengths as a function of the refractive index ne. It is seen that the simulated EDR positions are red-shifted almost linearly with increasing the refractive index ne, and at a certain ne the EDRs of the CSRRs with a = 85 nm, 95 nm and 105 nm could overlap with the FW, which is consistent with the experiments. It is also noted that with increasing the alumina thickness the EDR positions are expected to asymptotically red-shift to a limit where the CSRRs are covered by an infinite thick alumina, as evidenced by a decrease in the slope of the EDR red-shifts [Fig. 2(a)]. Therefore, it is reasonable to assume that the relation between the refractive index ne of the uniform environment used in the effective medium model and the alumina thickness t follows a simple inverse proportional function ne = 1.57 − [0.4/(kt + 1)], where the unit of t is nm. By fitting the function to the experimental results, the factor k is determined to be k = 0.035. The obtained inverse proportional function is plotted in the inset of Fig. 2(b). It should be pointed out that this approximate function is only used for the qualitative comparison between experiment and simulation results in the following discussions.

 figure: Fig. 2.

Fig. 2. (a) Measured and (b) simulated EDR positions of the CSRR arrays with different arm lengths as a function of the alumina thickness t and the refractive index ne of a uniform environment, respectively. Spheres are experimental data and circles are simulated data. Lines are provided to guide the eye. The horizontal dotted line represents the FW of 1540 nm. Inset in (b): The approximate function that relates the refractive index ne of the uniform environment to the alumina thickness t.

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In the following, we investigated the influence of dielectric coating on the SHG of these gold CSRR arrays. In nonlinear measurements, we excited these CSRR arrays with a femtosecond laser (repeat frequency is 50 MHz, pulse width < 0.1 ps), which is normally incident from the substrate side. The electric field was polarized along the arm of the CSRRs, and the FW was fixed at 1540 nm. As schematically shown in Fig. 3, the laser was focused to the samples by a 50× long focal length lens, and the spot diameter was about 20 μm. The SH signal was collected by a 50× objective lens, filtered out the fundamental wave components by a band-pass filter, and finally entered the EMCCD through a spectrometer. Polarization selection was realized via controlling the linear polarizer in front of the spectrometer.

 figure: Fig. 3.

Fig. 3. Schematic of the experimental setup for the SHG measurement. LPF: long-pass filter; L1-L3: lens; SPF: short-pass filter; LP: linear polarizer; EMCCD: electron multiplying charge coupled device. The Fourier images of the sample is recorded by the EMCCD.

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Figure 4(a) shows that the slope of the measured SH intensity from a typical alumina coated CSRR array versus the incident power is nearly 2, which further confirms that the collected signal is the SH. The polarization of the SHG was also examined and shown in the inset of Fig. 4(a). It is seen that for the fundamental wave polarized along the y-axis (parallel to the CSRR arm), the x-axis polarization component (represented by XY, blue curve) of the SHG is significantly smaller than the y-axis polarization component (represented by YY, red curve), which implies that the SHG polarization is mostly oriented along the y-axis and is consistent with the previous reports [26,33]. For idea CSRRs, the XY component is expected to be zero due to the inversion symmetry with respect to the x-axis. However, the imperfections of the fabricated CSRRs, such as the length or width difference between the left and right arms [see the SEM images in Fig. 1(b)], could break the inversion symmetry with respect to the x-axis, which could be attributed to the experimentally observed non-zero XY component.

 figure: Fig. 4.

Fig. 4. (a) Dependency between the radiated SH intensity from an alumina coated CSRR array and the incident FW power in double logarithmic coordinates. The slope of nearly 2 confirms the occurrence of a second-order nonlinear process. The hollow circles are experimental data and the black line is the linear fitting curve. Inset shows the analyzing of the SHG polarization. XY (blue curve) represents that the polarization of the fundamental wave is along the y-axis (parallel to the CSRR arm) while the transmission axis of the polarizer is along the x-axis. YY (red curve) represents that both the polarization of the fundamental wave and the transmission axis of the polarizer are along the y-axis. (b) Measured and (c) simulated SHG intensity of the CSRR arrays with different arm lengths as a function of the alumina thickness and the refractive index of uniform environment, respectively. The scale of the x-axis in (c) has been modified with a function ne = 1.57 - [0.4 / (0.035t + 1)] for easy comparison.

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Figure 4(b) shows the measured SH intensity of the CSRR arrays with different arm lengths as a function of the alumina film thickness. In our experiments, we performed a nonlinear optical measurement every time a 3-nm-thick alumina film was deposited onto the CSRRs. For the CSRR array with a = 115 nm (black spheres), it is seen from Fig. 4(b) that the SH intensity decreases monotonically with increasing the alumina film thickness, which could be ascribed to that the EDRs move further away from the FW as the alumina film becomes thicker [see black curve in Fig. 2(a)]. For the convenience of discussion, all the measured SH intensities in Fig. 4(b) are normalized with the SH intensity of the uncoated CSRR array with a = 115 nm. For the CSRR array with a = 105 nm (red spheres), its initial EDR peak located on the blue side of the FW. As demonstrated above, with increasing the alumina film thickness, the EDR first gradually approaches the FW and then crosses over the FW as the alumina film thickness is further increased [see red curve in Fig. 2(a)]. Correspondingly, the SHG intensity is found to initially increase with the increase of the alumina thickness and then gradually decrease after reaching its maximum. The maximum value is over 1.7-fold of its initial value (t = 0 nm). With increasing the alumina film thickness, the SHG intensity measured for the CSRR arrays with a = 95 nm and 85 nm (blue and green spheres) shows the similar trend to the CSRR array with a = 105 nm.

We also used COMSOL to perform nonlinear simulations in which the nonlinear Helmholtz equation was solved. In brief, the linear polarization of the CSRRs was first calculated at the FW under the y-polarized incident pump. Then, the nonlinear surface current density on the CSRRs was calculated based on the hydrodynamic model [11,34], which act as a nonlinear source in the simulation and eventually feedback the SH radiation. In the nonlinear simulations, the effective medium model is also applied. In previous reports [24,32], it has been demonstrated that the nonlinear results calculated from the effective medium model with the same uniform environment refractive index ne at both FW and SH could have a good agreement with the experimental ones. Hence, in our simulations, the same ne is also used for both FW and SH. The simulated SH nonlinear response of the alumina coated CSRR arrays is shown in Fig. 4(c) and the scale of the x-axis in the figure has been modified with a function ne = 1.57 - [0.4 / (0.035t + 1)] for easy comparison. For the CSRR array with a = 115 nm (black circles), it is seen that the SH intensity decreases monotonically with increasing the refractive index ne, which could be ascribed to that the EDRs move further away from the FW as the alumina film becomes thicker [see black curve in Fig. 2(b)]. For the CSRR array with a = 105 nm (red spheres), its initial EDR peak located on the blue side of the FW. For the CSRR arrays with a = 105 nm, 95 nm and 85 nm (red, blue and green circles), their initial EDR peaks located on the blue side of the FW. With increasing the refractive index ne, the EDR peaks could approach the FW and pass it as the refractive index ne becomes larger [see red, blue and green curves in Fig. 2(b)]. Correspondingly, the SHG intensity of this array experienced a significant increase with the increase of the refractive index ne, and then gradually decreased after reaching its maximum. The trend of the SHG intensity shows a good consistency between the experimental and simulation results.

To further explore the physical implications of enhancing the SHG of the CSRR arrays by dielectric coating, we turn our attention to the doubly-resonant condition. Figures 5(a) and 5(b) show the simulated absorption of the CSRR arrays with a = 85 nm, 95 nm, 105 nm and 115 nm at the FW of 1540 nm and the SH wavelength of 770 nm, respectively, as a function of the uniform environment refractive index ne. For direct comparison, the refractive indices ne at which the SHG of the CSRR arrays with different arm lengths achieve the maximum intensity are marked by the vertical dotted lines [the corresponding ne is extracted from Fig. 4(c)]. The absorption peaks observed at the FW [Fig. 5(a)] are attributed to the excitation of the EDRs. It is seen from Fig. 5(b) that absorption peaks are also observed at the SH wavelength, implying the existence of the higher-order resonance. The magnetic field distribution is calculated for the CSRR array with a = 115 nm at ne = 1.34 and shown in the inset of Fig. 5(b), from which we could identify this high-order resonance as the magnetic quadrupole resonance.

 figure: Fig. 5.

Fig. 5. Simulated absorption of the CSRR arrays with different arm lengths at the (a) FW of 1540 nm and (b) SH wavelength of 770 nm as a function of the uniform environment ne. Vertical dotted lines represent the values of ne = 1.17 (black), 1.235 (red), 1.315 (blue), 1.385 (green) at which the SHG intensity achieves the maximum for the CSRR arrays with different arm lengths of a = 115 nm, 105 nm, 95 nm, 85 nm, respectively. The scale of the x-axis has been modified with a function ne = 1.57 - [0.4 / (0.035t + 1)] for comparison. The inset in (b) shows the distribution of the magnetic field and polarization vector at the absorption peak at the SH wavelength for the CSRR arrays with a = 115 nm. (c) The distribution of the three components of the SH-generated polarization vector in two planes that are 0.1 nm below the top surface of the CSRR (red arrows) and 0.1 nm above the bottom surface of the CSRR (blue arrows). The center of the arrow is positioned at the arrow position. The right half of the panels: CSRRs with a = 115 nm, ne = 1.17. The left half of the panels: CSRRs with a = 85 nm, ne = 1.385.

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It should be emphasized that the SHG density could be affected by the local field enhancement factor at both the FW and SH wavelength [21,25,32]. For the CSRR arrays with a = 115 nm and 105 nm, the absorption peaks at the FW are far away from the peaks at the SH wavelength [black and red curves in Fig. 5(a) vs that in Fig. 5(b)]. This case could be regarded as a singly-resonant condition, in which the EDRs at the FW play a dominant role in the SHG intensity, and thus the maxima of absorption at the FW and the SHG intensity occur at almost the same ne, i.e., the black and red vertical dotted lines overlap with the corresponding absorption peaks at the FW [Fig. 5(a)]. For the CSRR array with a = 95 nm, the absorption peaks at the FW and SH wavelength become closer [blue curves in Figs. 5(a) and 5(b)]. The magnetic quadrupole resonance at the SH wavelength is expected to play a certain role in the SHG density, which is also evident by the occurrence of a deviation between the values of ne at which the absorption and the SHG intensity achieve the maximum [blue curve and vertical dotted line in Fig. 5(a)]. In particular, when the arm length of the CSRR is taken to a = 85 nm, the absorption peaks at the FW and SH wavelength almost overlap with each other [green curve in Figs. 5(a) and 5(b)]. In this case, the doubly-resonant condition could be fulfilled. In addition to the overlap between the values of ne at which the absorption at the FW and the SHG intensity achieve the maximum, the maxima of absorption at the SH wavelength and the SHG intensity also occur at almost the same ne [green curves and vertical dotted line in Figs. 5(a) and 5(b)]. In our study, the polarization of both the fundamental and SH wave are along the y-axis, which could typically give rise to strong SH signals [25]. Furthermore, associated with the excitation of the magnetic quadrupole resonance at the SH wavelength, the bulge part of the CSRR is found to exhibit a relatively large polarizability and the direction of polarization is along the y-axis [the inset of Fig. 5(b)], which shows a good overlap with the EDR-induced polarization in the bulge part [the inset of Fig. 1(c)]. Therefore, the maximum SHG intensity in the CSRR array with a = 85 nm could be much larger than that in the array with a = 115 nm.

Figure 5(c) shows the distributions of the three components of the SH-generated polarization vector calculated at ne = 1.17 for the CSRRs with a = 115 nm and at ne = 1.385 for the CSRRs with a = 85 nm. For clarity, the SH-generated polarization is taken in two parallel planes: one is 0.1 nm below the top surface of the CSRR (red arrows), and the other is 0.1 nm above the bottom surface of the CSRR (blue arrows). Due to the inversion symmetry with respect to the x-axis, only half of the gold CSRR is shown here. It is seen that the z components of the SH-generated polarization in the top and bottom planes and the x components on the left part and right part of the CSRR will cancel out due to their opposite pointing directions, while the y components in the top and bottom planes have the same pointing directions. As a result, the y components oscillate in phase, and generate the y-axis polarized SHG. It is also found that the magnitude of the y component of the SH-generated polarization in the case of the CSRR with a = 85 nm (left panel) is much larger than that in the case of the CSRR with a = 115 nm (right panel). As demonstrated above, the absorption peaks at the FW and the SH wavelength for the CSRRs with a = 115 nm are spectrally separated from each other (corresponding to the singly-resonant condition), while these two absorption peaks for the CSRRs with a = 85 nm almost overlap with each other (corresponding to the doubly-resonant condition). Noting that the absorption at the FW, i.e., the contributions of the fundamental wave to the SH-generated polarization [25], are almost the same under these two conditions [see Fig. 5(a)], which implies that the contributions of the higher-order resonance at the SH wavelength should be taken into account in the observed SH-generated polarization enhancement. Therefore, in addition to the EDR at the FW, the magnetic quadrupole resonance at the SH wavelength could also play an important role in the SHG process.

3. Summary

In conclusion, the effects of the dielectric coating on the linear optical response and nonlinear SHG of the gold CSRRs have been theoretically and experimentally investigated. The combination of shortening the arm length of the CSRRs and coating them with a dielectric film has been demonstrated as an efficient method to spectrally tune the plasmonic resonances. This provides an opportunity to simultaneously overlap the EDR and magnetic quadrupole resonance of the dielectric-coated CSRRs with the fundamental and SH wave to fulfill the doubly-resonant condition. Compared to the SHG intensity under the singly-resonant condition, an SHG enhancement of nearly 1.2-fold in experiment and 8-fold in simulation has been obtained under the doubly-resonant condition. The dielectric coating method could not only tune and improve the linear/non-linear optical properties of the metallic nanostructures, but also act as a protective layer to partially improve the damage threshold of the plasmonic nanoscale devices.

Funding

National Key Research and Development Program of China (2017YFA0303700); National Natural Science Foundation of China (11621091, 11674168, 11774162, 11834007).

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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15. D. C. Hooper, C. Kuppe, D. Wang, W. Wang, J. Guan, T. W. Odom, and V. K. Valev, “Second Harmonic Spectroscopy of Surface Lattice Resonances,” Nano Lett. 19(1), 165–172 (2019). [CrossRef]  

16. S.A. Maier, Plasmonics: fundamentals and applications (Springer Science & Business Media, 2007). [CrossRef]  

17. M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics 6(11), 737–748 (2012). [CrossRef]  

18. R. Czaplicki, M. Zdanowicz, K. Koskinen, J. Laukkanen, M. Kuittinen, and M. Kauranen, “Dipole limit in second-harmonic generation from arrays of gold nanoparticles,” Opt. Express 19(27), 26866–26871 (2011). [CrossRef]  

19. F. B. Niesler, N. Feth, S. Linden, and M. Wegener, “Second-harmonic optical spectroscopy on split-ring-resonator arrays,” Opt. Lett. 36(9), 1533–1535 (2011). [CrossRef]  

20. C. Hubert, L. Billot, P. M. Adam, R. BAchelot, P. Royer, J. Grand, D. Gindre, K. D. Dorkenoo, and A. Fort, “Role of surface plasmon in second harmonic generation from gold nanorods,” Appl. Phys. Lett. 90(18), 181105 (2007). [CrossRef]  

21. B. Metzger, L. Gui, J. Fuchs, D. Floess, M. Hentschel, and H. Giessen, “Strong Enhancement of Second Harmonic Emission by Plasmonic Resonances at the Second Harmonic Wavelength,” Nano Lett. 15(6), 3917–3922 (2015). [CrossRef]  

22. K. Thyagarajan, S. Rivier, A. Lovera, and O. J. Martin, “Enhanced second-harmonic generation from double resonant plasmonic antennae,” Opt. Express 20(12), 12860–12865 (2012). [CrossRef]  

23. M. Celebrano, X. Wu, M. Baselli, S. Grossmann, P. Biagioni, A. Locatelli, C. De Angelis, G. Cerullo, R. Osellame, B. Hecht, L. Duo, F. Ciccacci, and M. Finazzi, “Mode matching in multiresonant plasmonic nanoantennas for enhanced second harmonic generation,” Nat. Nanotechnol. 10(5), 412–417 (2015). [CrossRef]  

24. S. D. Liu, P. Yue, M. Q. Zhu, J. Wen, and D. Lei, “Restoring the silenced surface second-harmonic generation in split-ring resonators by magnetic and electric mode matching,” Opt. Express 27(19), 26377–26391 (2019). [CrossRef]  

25. S. Chervinskii, K. Koskinen, S. Scherbak, M. Kauranen, and A. Lipovskii, “Nonresonant Local Fields Enhance Second-Harmonic Generation from Metal Nanoislands with Dielectric Cover,” Phys. Rev. Lett. 120(11), 113902 (2018). [CrossRef]  

26. N. Feth, S. Linden, M. W. Klein, M. Decker, F. B. 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]  

27. P. Ginzburg, A. V. Krasavin, G. A. Wurtz, and A. V. Zayats, “Nonperturbative Hydrodynamic Model for Multiple Harmonics Generation in Metallic Nanostructures,” ACS Photonics 2(1), 8–13 (2015). [CrossRef]  

28. S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004). [CrossRef]  

29. F. Falcone, T. Lopetegi, M. A. Laso, J. D. Baena, J. Bonache, M. Beruete, R. Marques, F. Martin, and M. Sorolla, “Babinet principle applied to the design of metasurfaces and metamaterials,” Phys. Rev. Lett. 93(19), 197401 (2004). [CrossRef]  

30. T. Zentgraf, T. P. Meyrath, A. Seidel, S. Kaiser, H. Giessen, C. Rockstuhl, and F. Lederer, “Babinet’s principle for optical frequency metamaterials and nanoantennas,” Phys. Rev. B 76(3), 033407 (2007). [CrossRef]  

31. C. Rockstuhl, T. Zentgraf, H. Guo, N. Liu, C. Etrich, I. Loa, K. Syassen, J. Kuhl, F. Lederer, and H. Giessen, “Resonances of split-ring resonator metamaterials in the near infrared,” Appl. Phys. B 84(1-2), 219–227 (2006). [CrossRef]  

32. K. O’Brien, H. Suchowski, J. Rho, A. Salandrino, B. Kante, X. Yin, and X. Zhang, “Predicting nonlinear properties of metamaterials from the linear response,” Nat. Mater. 14(4), 379–383 (2015). [CrossRef]  

33. X. Yang, C. Zhang, M. Wan, Z. Chen, and Z. Wang, “Engineered second-harmonic diffraction from highly transmissive metasurfaces composed of complementary split-ring resonators,” Opt. Lett. 41(13), 2938–2941 (2016). [CrossRef]  

34. C. Ciracì, E. Poutrina, M. Scalora, and D. R. Smith, “Origin of second-harmonic generation enhancement in optical split-ring resonators,” Phys. Rev. B 85(20), 201403 (2012). [CrossRef]  

References

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  1. G. Li, S. Zhang, and T. Zentgraf, “Nonlinear photonic metasurfaces,” Nat. Rev. Mater. 2(5), 17010 (2017).
    [Crossref]
  2. A. Krasnok, M. Tymchenko, and A. Alu, “Nonlinear metasurfaces: a paradigm shift in nonlinear optics,” Mater. Today 21(1), 8–21 (2018).
    [Crossref]
  3. M. W. Klein, C. Enkrich, M. Wegener, and S. Linden, “Second-harmonic generation from magnetic metamaterials,” Science 313(5786), 502–504 (2006).
    [Crossref]
  4. M. W. Klein, M. Wegener, N. Feth, and S. Linden, “Experiments on second- and third-harmonic generation from magnetic metamaterials,” Opt. Express 15(8), 5238–5247 (2007).
    [Crossref]
  5. F. B. Niesler, N. Feth, S. Linden, J. Niegemann, J. Gieseler, K. Busch, and M. Wegener, “Second-harmonic generation from split-ring resonators on a GaAs substrate,” Opt. Lett. 34(13), 1997–1999 (2009).
    [Crossref]
  6. S. Linden, F. B. Niesler, J. Forstner, Y. Grynko, T. Meier, and M. Wegener, “Collective effects in second-harmonic generation from split-ring-resonator arrays,” Phys. Rev. Lett. 109(1), 015502 (2012).
    [Crossref]
  7. W. Y. Tsai, T. L. Chung, H. H. Hsiao, J. W. Chen, R. J. Lin, P. C. Wu, G. Sun, C. M. Wang, H. Misawa, and D. P. Tsai, “Second Harmonic Light Manipulation with Vertical Split Ring Resonators,” Adv. Mater. 31(7), 1806479 (2019).
    [Crossref]
  8. B. K. Canfield, S. Kujala, K. Jefimovs, J. Turunen, and M. Kauranen, “Linear and nonlinear optical responses influenced by broken symmetry in an array of gold nanoparticles,” Opt. Express 12(22), 5418–5423 (2004).
    [Crossref]
  9. B. K. Canfield, S. Kujala, K. Jefimovs, Y. Svirko, J. Turunen, and M. Kauranen, “A macroscopic formalism to describe the second-order nonlinear optical response of nanostructures,” J. Opt. A: Pure Appl. Opt. 8(4), S278–S284 (2006).
    [Crossref]
  10. R. Czaplicki, A. Kiviniemi, M. J. Huttunen, X. Zang, T. Stolt, I. Vartiainen, J. Butet, M. Kuittinen, O. J. F. Martin, and M. Kauranen, “Less Is More: Enhancement of Second-Harmonic Generation from Metasurfaces by Reduced Nanoparticle Density,” Nano Lett. 18(12), 7709–7714 (2018).
    [Crossref]
  11. C. Ciracì, E. Poutrina, M. Scalora, and D. R. Smith, “Second-harmonic generation in metallic nanoparticles: Clarification of the role of the surface,” Phys. Rev. B 86(11), 115451 (2012).
    [Crossref]
  12. R. Czaplicki, J. Makitalo, R. Siikanen, H. Husu, J. Lehtolahti, M. Kuittinen, and M. Kauranen, “Second-Harmonic Generation from Metal Nanoparticles: Resonance Enhancement versus Particle Geometry,” Nano Lett. 15(1), 530–534 (2015).
    [Crossref]
  13. L. Ghirardini, L. Carletti, V. Gili, G. Pellegrini, L. Duo, M. Finazzi, D. Rocco, A. Locatelli, C. De Angelis, I. Favero, M. Ravaro, G. Leo, A. Lemaitre, and M. Celebrano, “Polarization properties of second-harmonic generation in AlGaAs optical nanoantennas,” Opt. Lett. 42(3), 559–562 (2017).
    [Crossref]
  14. X. Y. Zhang, Q. T. Cao, Z. Wang, Y. X. Liu, C. W. Qiu, L. Yang, Q. H. Gong, and Y. F. Xiao, “Symmetry-breaking-induced nonlinear optics at a microcavity surface,” Nat. Photonics 13(1), 21–24 (2019).
    [Crossref]
  15. D. C. Hooper, C. Kuppe, D. Wang, W. Wang, J. Guan, T. W. Odom, and V. K. Valev, “Second Harmonic Spectroscopy of Surface Lattice Resonances,” Nano Lett. 19(1), 165–172 (2019).
    [Crossref]
  16. S.A. Maier, Plasmonics: fundamentals and applications (Springer Science & Business Media, 2007).
    [Crossref]
  17. M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics 6(11), 737–748 (2012).
    [Crossref]
  18. R. Czaplicki, M. Zdanowicz, K. Koskinen, J. Laukkanen, M. Kuittinen, and M. Kauranen, “Dipole limit in second-harmonic generation from arrays of gold nanoparticles,” Opt. Express 19(27), 26866–26871 (2011).
    [Crossref]
  19. F. B. Niesler, N. Feth, S. Linden, and M. Wegener, “Second-harmonic optical spectroscopy on split-ring-resonator arrays,” Opt. Lett. 36(9), 1533–1535 (2011).
    [Crossref]
  20. C. Hubert, L. Billot, P. M. Adam, R. BAchelot, P. Royer, J. Grand, D. Gindre, K. D. Dorkenoo, and A. Fort, “Role of surface plasmon in second harmonic generation from gold nanorods,” Appl. Phys. Lett. 90(18), 181105 (2007).
    [Crossref]
  21. B. Metzger, L. Gui, J. Fuchs, D. Floess, M. Hentschel, and H. Giessen, “Strong Enhancement of Second Harmonic Emission by Plasmonic Resonances at the Second Harmonic Wavelength,” Nano Lett. 15(6), 3917–3922 (2015).
    [Crossref]
  22. K. Thyagarajan, S. Rivier, A. Lovera, and O. J. Martin, “Enhanced second-harmonic generation from double resonant plasmonic antennae,” Opt. Express 20(12), 12860–12865 (2012).
    [Crossref]
  23. M. Celebrano, X. Wu, M. Baselli, S. Grossmann, P. Biagioni, A. Locatelli, C. De Angelis, G. Cerullo, R. Osellame, B. Hecht, L. Duo, F. Ciccacci, and M. Finazzi, “Mode matching in multiresonant plasmonic nanoantennas for enhanced second harmonic generation,” Nat. Nanotechnol. 10(5), 412–417 (2015).
    [Crossref]
  24. S. D. Liu, P. Yue, M. Q. Zhu, J. Wen, and D. Lei, “Restoring the silenced surface second-harmonic generation in split-ring resonators by magnetic and electric mode matching,” Opt. Express 27(19), 26377–26391 (2019).
    [Crossref]
  25. S. Chervinskii, K. Koskinen, S. Scherbak, M. Kauranen, and A. Lipovskii, “Nonresonant Local Fields Enhance Second-Harmonic Generation from Metal Nanoislands with Dielectric Cover,” Phys. Rev. Lett. 120(11), 113902 (2018).
    [Crossref]
  26. N. Feth, S. Linden, M. W. Klein, M. Decker, F. B. 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]
  27. P. Ginzburg, A. V. Krasavin, G. A. Wurtz, and A. V. Zayats, “Nonperturbative Hydrodynamic Model for Multiple Harmonics Generation in Metallic Nanostructures,” ACS Photonics 2(1), 8–13 (2015).
    [Crossref]
  28. S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
    [Crossref]
  29. F. Falcone, T. Lopetegi, M. A. Laso, J. D. Baena, J. Bonache, M. Beruete, R. Marques, F. Martin, and M. Sorolla, “Babinet principle applied to the design of metasurfaces and metamaterials,” Phys. Rev. Lett. 93(19), 197401 (2004).
    [Crossref]
  30. T. Zentgraf, T. P. Meyrath, A. Seidel, S. Kaiser, H. Giessen, C. Rockstuhl, and F. Lederer, “Babinet’s principle for optical frequency metamaterials and nanoantennas,” Phys. Rev. B 76(3), 033407 (2007).
    [Crossref]
  31. C. Rockstuhl, T. Zentgraf, H. Guo, N. Liu, C. Etrich, I. Loa, K. Syassen, J. Kuhl, F. Lederer, and H. Giessen, “Resonances of split-ring resonator metamaterials in the near infrared,” Appl. Phys. B 84(1-2), 219–227 (2006).
    [Crossref]
  32. K. O’Brien, H. Suchowski, J. Rho, A. Salandrino, B. Kante, X. Yin, and X. Zhang, “Predicting nonlinear properties of metamaterials from the linear response,” Nat. Mater. 14(4), 379–383 (2015).
    [Crossref]
  33. X. Yang, C. Zhang, M. Wan, Z. Chen, and Z. Wang, “Engineered second-harmonic diffraction from highly transmissive metasurfaces composed of complementary split-ring resonators,” Opt. Lett. 41(13), 2938–2941 (2016).
    [Crossref]
  34. C. Ciracì, E. Poutrina, M. Scalora, and D. R. Smith, “Origin of second-harmonic generation enhancement in optical split-ring resonators,” Phys. Rev. B 85(20), 201403 (2012).
    [Crossref]

2019 (4)

W. Y. Tsai, T. L. Chung, H. H. Hsiao, J. W. Chen, R. J. Lin, P. C. Wu, G. Sun, C. M. Wang, H. Misawa, and D. P. Tsai, “Second Harmonic Light Manipulation with Vertical Split Ring Resonators,” Adv. Mater. 31(7), 1806479 (2019).
[Crossref]

X. Y. Zhang, Q. T. Cao, Z. Wang, Y. X. Liu, C. W. Qiu, L. Yang, Q. H. Gong, and Y. F. Xiao, “Symmetry-breaking-induced nonlinear optics at a microcavity surface,” Nat. Photonics 13(1), 21–24 (2019).
[Crossref]

D. C. Hooper, C. Kuppe, D. Wang, W. Wang, J. Guan, T. W. Odom, and V. K. Valev, “Second Harmonic Spectroscopy of Surface Lattice Resonances,” Nano Lett. 19(1), 165–172 (2019).
[Crossref]

S. D. Liu, P. Yue, M. Q. Zhu, J. Wen, and D. Lei, “Restoring the silenced surface second-harmonic generation in split-ring resonators by magnetic and electric mode matching,” Opt. Express 27(19), 26377–26391 (2019).
[Crossref]

2018 (3)

S. Chervinskii, K. Koskinen, S. Scherbak, M. Kauranen, and A. Lipovskii, “Nonresonant Local Fields Enhance Second-Harmonic Generation from Metal Nanoislands with Dielectric Cover,” Phys. Rev. Lett. 120(11), 113902 (2018).
[Crossref]

R. Czaplicki, A. Kiviniemi, M. J. Huttunen, X. Zang, T. Stolt, I. Vartiainen, J. Butet, M. Kuittinen, O. J. F. Martin, and M. Kauranen, “Less Is More: Enhancement of Second-Harmonic Generation from Metasurfaces by Reduced Nanoparticle Density,” Nano Lett. 18(12), 7709–7714 (2018).
[Crossref]

A. Krasnok, M. Tymchenko, and A. Alu, “Nonlinear metasurfaces: a paradigm shift in nonlinear optics,” Mater. Today 21(1), 8–21 (2018).
[Crossref]

2017 (2)

2016 (1)

2015 (5)

K. O’Brien, H. Suchowski, J. Rho, A. Salandrino, B. Kante, X. Yin, and X. Zhang, “Predicting nonlinear properties of metamaterials from the linear response,” Nat. Mater. 14(4), 379–383 (2015).
[Crossref]

M. Celebrano, X. Wu, M. Baselli, S. Grossmann, P. Biagioni, A. Locatelli, C. De Angelis, G. Cerullo, R. Osellame, B. Hecht, L. Duo, F. Ciccacci, and M. Finazzi, “Mode matching in multiresonant plasmonic nanoantennas for enhanced second harmonic generation,” Nat. Nanotechnol. 10(5), 412–417 (2015).
[Crossref]

B. Metzger, L. Gui, J. Fuchs, D. Floess, M. Hentschel, and H. Giessen, “Strong Enhancement of Second Harmonic Emission by Plasmonic Resonances at the Second Harmonic Wavelength,” Nano Lett. 15(6), 3917–3922 (2015).
[Crossref]

P. Ginzburg, A. V. Krasavin, G. A. Wurtz, and A. V. Zayats, “Nonperturbative Hydrodynamic Model for Multiple Harmonics Generation in Metallic Nanostructures,” ACS Photonics 2(1), 8–13 (2015).
[Crossref]

R. Czaplicki, J. Makitalo, R. Siikanen, H. Husu, J. Lehtolahti, M. Kuittinen, and M. Kauranen, “Second-Harmonic Generation from Metal Nanoparticles: Resonance Enhancement versus Particle Geometry,” Nano Lett. 15(1), 530–534 (2015).
[Crossref]

2012 (5)

C. Ciracì, E. Poutrina, M. Scalora, and D. R. Smith, “Second-harmonic generation in metallic nanoparticles: Clarification of the role of the surface,” Phys. Rev. B 86(11), 115451 (2012).
[Crossref]

M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics 6(11), 737–748 (2012).
[Crossref]

S. Linden, F. B. Niesler, J. Forstner, Y. Grynko, T. Meier, and M. Wegener, “Collective effects in second-harmonic generation from split-ring-resonator arrays,” Phys. Rev. Lett. 109(1), 015502 (2012).
[Crossref]

K. Thyagarajan, S. Rivier, A. Lovera, and O. J. Martin, “Enhanced second-harmonic generation from double resonant plasmonic antennae,” Opt. Express 20(12), 12860–12865 (2012).
[Crossref]

C. Ciracì, E. Poutrina, M. Scalora, and D. R. Smith, “Origin of second-harmonic generation enhancement in optical split-ring resonators,” Phys. Rev. B 85(20), 201403 (2012).
[Crossref]

2011 (2)

2009 (1)

2008 (1)

2007 (3)

T. Zentgraf, T. P. Meyrath, A. Seidel, S. Kaiser, H. Giessen, C. Rockstuhl, and F. Lederer, “Babinet’s principle for optical frequency metamaterials and nanoantennas,” Phys. Rev. B 76(3), 033407 (2007).
[Crossref]

M. W. Klein, M. Wegener, N. Feth, and S. Linden, “Experiments on second- and third-harmonic generation from magnetic metamaterials,” Opt. Express 15(8), 5238–5247 (2007).
[Crossref]

C. Hubert, L. Billot, P. M. Adam, R. BAchelot, P. Royer, J. Grand, D. Gindre, K. D. Dorkenoo, and A. Fort, “Role of surface plasmon in second harmonic generation from gold nanorods,” Appl. Phys. Lett. 90(18), 181105 (2007).
[Crossref]

2006 (3)

B. K. Canfield, S. Kujala, K. Jefimovs, Y. Svirko, J. Turunen, and M. Kauranen, “A macroscopic formalism to describe the second-order nonlinear optical response of nanostructures,” J. Opt. A: Pure Appl. Opt. 8(4), S278–S284 (2006).
[Crossref]

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

C. Rockstuhl, T. Zentgraf, H. Guo, N. Liu, C. Etrich, I. Loa, K. Syassen, J. Kuhl, F. Lederer, and H. Giessen, “Resonances of split-ring resonator metamaterials in the near infrared,” Appl. Phys. B 84(1-2), 219–227 (2006).
[Crossref]

2004 (3)

S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
[Crossref]

F. Falcone, T. Lopetegi, M. A. Laso, J. D. Baena, J. Bonache, M. Beruete, R. Marques, F. Martin, and M. Sorolla, “Babinet principle applied to the design of metasurfaces and metamaterials,” Phys. Rev. Lett. 93(19), 197401 (2004).
[Crossref]

B. K. Canfield, S. Kujala, K. Jefimovs, J. Turunen, and M. Kauranen, “Linear and nonlinear optical responses influenced by broken symmetry in an array of gold nanoparticles,” Opt. Express 12(22), 5418–5423 (2004).
[Crossref]

Adam, P. M.

C. Hubert, L. Billot, P. M. Adam, R. BAchelot, P. Royer, J. Grand, D. Gindre, K. D. Dorkenoo, and A. Fort, “Role of surface plasmon in second harmonic generation from gold nanorods,” Appl. Phys. Lett. 90(18), 181105 (2007).
[Crossref]

Alu, A.

A. Krasnok, M. Tymchenko, and A. Alu, “Nonlinear metasurfaces: a paradigm shift in nonlinear optics,” Mater. Today 21(1), 8–21 (2018).
[Crossref]

BAchelot, R.

C. Hubert, L. Billot, P. M. Adam, R. BAchelot, P. Royer, J. Grand, D. Gindre, K. D. Dorkenoo, and A. Fort, “Role of surface plasmon in second harmonic generation from gold nanorods,” Appl. Phys. Lett. 90(18), 181105 (2007).
[Crossref]

Baena, J. D.

F. Falcone, T. Lopetegi, M. A. Laso, J. D. Baena, J. Bonache, M. Beruete, R. Marques, F. Martin, and M. Sorolla, “Babinet principle applied to the design of metasurfaces and metamaterials,” Phys. Rev. Lett. 93(19), 197401 (2004).
[Crossref]

Baselli, M.

M. Celebrano, X. Wu, M. Baselli, S. Grossmann, P. Biagioni, A. Locatelli, C. De Angelis, G. Cerullo, R. Osellame, B. Hecht, L. Duo, F. Ciccacci, and M. Finazzi, “Mode matching in multiresonant plasmonic nanoantennas for enhanced second harmonic generation,” Nat. Nanotechnol. 10(5), 412–417 (2015).
[Crossref]

Beruete, M.

F. Falcone, T. Lopetegi, M. A. Laso, J. D. Baena, J. Bonache, M. Beruete, R. Marques, F. Martin, and M. Sorolla, “Babinet principle applied to the design of metasurfaces and metamaterials,” Phys. Rev. Lett. 93(19), 197401 (2004).
[Crossref]

Biagioni, P.

M. Celebrano, X. Wu, M. Baselli, S. Grossmann, P. Biagioni, A. Locatelli, C. De Angelis, G. Cerullo, R. Osellame, B. Hecht, L. Duo, F. Ciccacci, and M. Finazzi, “Mode matching in multiresonant plasmonic nanoantennas for enhanced second harmonic generation,” Nat. Nanotechnol. 10(5), 412–417 (2015).
[Crossref]

Billot, L.

C. Hubert, L. Billot, P. M. Adam, R. BAchelot, P. Royer, J. Grand, D. Gindre, K. D. Dorkenoo, and A. Fort, “Role of surface plasmon in second harmonic generation from gold nanorods,” Appl. Phys. Lett. 90(18), 181105 (2007).
[Crossref]

Bonache, J.

F. Falcone, T. Lopetegi, M. A. Laso, J. D. Baena, J. Bonache, M. Beruete, R. Marques, F. Martin, and M. Sorolla, “Babinet principle applied to the design of metasurfaces and metamaterials,” Phys. Rev. Lett. 93(19), 197401 (2004).
[Crossref]

Busch, K.

Butet, J.

R. Czaplicki, A. Kiviniemi, M. J. Huttunen, X. Zang, T. Stolt, I. Vartiainen, J. Butet, M. Kuittinen, O. J. F. Martin, and M. Kauranen, “Less Is More: Enhancement of Second-Harmonic Generation from Metasurfaces by Reduced Nanoparticle Density,” Nano Lett. 18(12), 7709–7714 (2018).
[Crossref]

Canfield, B. K.

B. K. Canfield, S. Kujala, K. Jefimovs, Y. Svirko, J. Turunen, and M. Kauranen, “A macroscopic formalism to describe the second-order nonlinear optical response of nanostructures,” J. Opt. A: Pure Appl. Opt. 8(4), S278–S284 (2006).
[Crossref]

B. K. Canfield, S. Kujala, K. Jefimovs, J. Turunen, and M. Kauranen, “Linear and nonlinear optical responses influenced by broken symmetry in an array of gold nanoparticles,” Opt. Express 12(22), 5418–5423 (2004).
[Crossref]

Cao, Q. T.

X. Y. Zhang, Q. T. Cao, Z. Wang, Y. X. Liu, C. W. Qiu, L. Yang, Q. H. Gong, and Y. F. Xiao, “Symmetry-breaking-induced nonlinear optics at a microcavity surface,” Nat. Photonics 13(1), 21–24 (2019).
[Crossref]

Carletti, L.

Celebrano, M.

L. Ghirardini, L. Carletti, V. Gili, G. Pellegrini, L. Duo, M. Finazzi, D. Rocco, A. Locatelli, C. De Angelis, I. Favero, M. Ravaro, G. Leo, A. Lemaitre, and M. Celebrano, “Polarization properties of second-harmonic generation in AlGaAs optical nanoantennas,” Opt. Lett. 42(3), 559–562 (2017).
[Crossref]

M. Celebrano, X. Wu, M. Baselli, S. Grossmann, P. Biagioni, A. Locatelli, C. De Angelis, G. Cerullo, R. Osellame, B. Hecht, L. Duo, F. Ciccacci, and M. Finazzi, “Mode matching in multiresonant plasmonic nanoantennas for enhanced second harmonic generation,” Nat. Nanotechnol. 10(5), 412–417 (2015).
[Crossref]

Cerullo, G.

M. Celebrano, X. Wu, M. Baselli, S. Grossmann, P. Biagioni, A. Locatelli, C. De Angelis, G. Cerullo, R. Osellame, B. Hecht, L. Duo, F. Ciccacci, and M. Finazzi, “Mode matching in multiresonant plasmonic nanoantennas for enhanced second harmonic generation,” Nat. Nanotechnol. 10(5), 412–417 (2015).
[Crossref]

Chen, J. W.

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Martin, O. J. F.

R. Czaplicki, A. Kiviniemi, M. J. Huttunen, X. Zang, T. Stolt, I. Vartiainen, J. Butet, M. Kuittinen, O. J. F. Martin, and M. Kauranen, “Less Is More: Enhancement of Second-Harmonic Generation from Metasurfaces by Reduced Nanoparticle Density,” Nano Lett. 18(12), 7709–7714 (2018).
[Crossref]

Meier, T.

S. Linden, F. B. Niesler, J. Forstner, Y. Grynko, T. Meier, and M. Wegener, “Collective effects in second-harmonic generation from split-ring-resonator arrays,” Phys. Rev. Lett. 109(1), 015502 (2012).
[Crossref]

Metzger, B.

B. Metzger, L. Gui, J. Fuchs, D. Floess, M. Hentschel, and H. Giessen, “Strong Enhancement of Second Harmonic Emission by Plasmonic Resonances at the Second Harmonic Wavelength,” Nano Lett. 15(6), 3917–3922 (2015).
[Crossref]

Meyrath, T. P.

T. Zentgraf, T. P. Meyrath, A. Seidel, S. Kaiser, H. Giessen, C. Rockstuhl, and F. Lederer, “Babinet’s principle for optical frequency metamaterials and nanoantennas,” Phys. Rev. B 76(3), 033407 (2007).
[Crossref]

Misawa, H.

W. Y. Tsai, T. L. Chung, H. H. Hsiao, J. W. Chen, R. J. Lin, P. C. Wu, G. Sun, C. M. Wang, H. Misawa, and D. P. Tsai, “Second Harmonic Light Manipulation with Vertical Split Ring Resonators,” Adv. Mater. 31(7), 1806479 (2019).
[Crossref]

Moloney, J. V.

Niegemann, J.

Niesler, F. B.

O’Brien, K.

K. O’Brien, H. Suchowski, J. Rho, A. Salandrino, B. Kante, X. Yin, and X. Zhang, “Predicting nonlinear properties of metamaterials from the linear response,” Nat. Mater. 14(4), 379–383 (2015).
[Crossref]

Odom, T. W.

D. C. Hooper, C. Kuppe, D. Wang, W. Wang, J. Guan, T. W. Odom, and V. K. Valev, “Second Harmonic Spectroscopy of Surface Lattice Resonances,” Nano Lett. 19(1), 165–172 (2019).
[Crossref]

Osellame, R.

M. Celebrano, X. Wu, M. Baselli, S. Grossmann, P. Biagioni, A. Locatelli, C. De Angelis, G. Cerullo, R. Osellame, B. Hecht, L. Duo, F. Ciccacci, and M. Finazzi, “Mode matching in multiresonant plasmonic nanoantennas for enhanced second harmonic generation,” Nat. Nanotechnol. 10(5), 412–417 (2015).
[Crossref]

Pellegrini, G.

Poutrina, E.

C. Ciracì, E. Poutrina, M. Scalora, and D. R. Smith, “Second-harmonic generation in metallic nanoparticles: Clarification of the role of the surface,” Phys. Rev. B 86(11), 115451 (2012).
[Crossref]

C. Ciracì, E. Poutrina, M. Scalora, and D. R. Smith, “Origin of second-harmonic generation enhancement in optical split-ring resonators,” Phys. Rev. B 85(20), 201403 (2012).
[Crossref]

Qiu, C. W.

X. Y. Zhang, Q. T. Cao, Z. Wang, Y. X. Liu, C. W. Qiu, L. Yang, Q. H. Gong, and Y. F. Xiao, “Symmetry-breaking-induced nonlinear optics at a microcavity surface,” Nat. Photonics 13(1), 21–24 (2019).
[Crossref]

Ravaro, M.

Rho, J.

K. O’Brien, H. Suchowski, J. Rho, A. Salandrino, B. Kante, X. Yin, and X. Zhang, “Predicting nonlinear properties of metamaterials from the linear response,” Nat. Mater. 14(4), 379–383 (2015).
[Crossref]

Rivier, S.

Rocco, D.

Rockstuhl, C.

T. Zentgraf, T. P. Meyrath, A. Seidel, S. Kaiser, H. Giessen, C. Rockstuhl, and F. Lederer, “Babinet’s principle for optical frequency metamaterials and nanoantennas,” Phys. Rev. B 76(3), 033407 (2007).
[Crossref]

C. Rockstuhl, T. Zentgraf, H. Guo, N. Liu, C. Etrich, I. Loa, K. Syassen, J. Kuhl, F. Lederer, and H. Giessen, “Resonances of split-ring resonator metamaterials in the near infrared,” Appl. Phys. B 84(1-2), 219–227 (2006).
[Crossref]

Royer, P.

C. Hubert, L. Billot, P. M. Adam, R. BAchelot, P. Royer, J. Grand, D. Gindre, K. D. Dorkenoo, and A. Fort, “Role of surface plasmon in second harmonic generation from gold nanorods,” Appl. Phys. Lett. 90(18), 181105 (2007).
[Crossref]

Salandrino, A.

K. O’Brien, H. Suchowski, J. Rho, A. Salandrino, B. Kante, X. Yin, and X. Zhang, “Predicting nonlinear properties of metamaterials from the linear response,” Nat. Mater. 14(4), 379–383 (2015).
[Crossref]

Scalora, M.

C. Ciracì, E. Poutrina, M. Scalora, and D. R. Smith, “Origin of second-harmonic generation enhancement in optical split-ring resonators,” Phys. Rev. B 85(20), 201403 (2012).
[Crossref]

C. Ciracì, E. Poutrina, M. Scalora, and D. R. Smith, “Second-harmonic generation in metallic nanoparticles: Clarification of the role of the surface,” Phys. Rev. B 86(11), 115451 (2012).
[Crossref]

Scherbak, S.

S. Chervinskii, K. Koskinen, S. Scherbak, M. Kauranen, and A. Lipovskii, “Nonresonant Local Fields Enhance Second-Harmonic Generation from Metal Nanoislands with Dielectric Cover,” Phys. Rev. Lett. 120(11), 113902 (2018).
[Crossref]

Seidel, A.

T. Zentgraf, T. P. Meyrath, A. Seidel, S. Kaiser, H. Giessen, C. Rockstuhl, and F. Lederer, “Babinet’s principle for optical frequency metamaterials and nanoantennas,” Phys. Rev. B 76(3), 033407 (2007).
[Crossref]

Siikanen, R.

R. Czaplicki, J. Makitalo, R. Siikanen, H. Husu, J. Lehtolahti, M. Kuittinen, and M. Kauranen, “Second-Harmonic Generation from Metal Nanoparticles: Resonance Enhancement versus Particle Geometry,” Nano Lett. 15(1), 530–534 (2015).
[Crossref]

Smith, D. R.

C. Ciracì, E. Poutrina, M. Scalora, and D. R. Smith, “Second-harmonic generation in metallic nanoparticles: Clarification of the role of the surface,” Phys. Rev. B 86(11), 115451 (2012).
[Crossref]

C. Ciracì, E. Poutrina, M. Scalora, and D. R. Smith, “Origin of second-harmonic generation enhancement in optical split-ring resonators,” Phys. Rev. B 85(20), 201403 (2012).
[Crossref]

Sorolla, M.

F. Falcone, T. Lopetegi, M. A. Laso, J. D. Baena, J. Bonache, M. Beruete, R. Marques, F. Martin, and M. Sorolla, “Babinet principle applied to the design of metasurfaces and metamaterials,” Phys. Rev. Lett. 93(19), 197401 (2004).
[Crossref]

Soukoulis, C. M.

S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
[Crossref]

Stolt, T.

R. Czaplicki, A. Kiviniemi, M. J. Huttunen, X. Zang, T. Stolt, I. Vartiainen, J. Butet, M. Kuittinen, O. J. F. Martin, and M. Kauranen, “Less Is More: Enhancement of Second-Harmonic Generation from Metasurfaces by Reduced Nanoparticle Density,” Nano Lett. 18(12), 7709–7714 (2018).
[Crossref]

Suchowski, H.

K. O’Brien, H. Suchowski, J. Rho, A. Salandrino, B. Kante, X. Yin, and X. Zhang, “Predicting nonlinear properties of metamaterials from the linear response,” Nat. Mater. 14(4), 379–383 (2015).
[Crossref]

Sun, G.

W. Y. Tsai, T. L. Chung, H. H. Hsiao, J. W. Chen, R. J. Lin, P. C. Wu, G. Sun, C. M. Wang, H. Misawa, and D. P. Tsai, “Second Harmonic Light Manipulation with Vertical Split Ring Resonators,” Adv. Mater. 31(7), 1806479 (2019).
[Crossref]

Svirko, Y.

B. K. Canfield, S. Kujala, K. Jefimovs, Y. Svirko, J. Turunen, and M. Kauranen, “A macroscopic formalism to describe the second-order nonlinear optical response of nanostructures,” J. Opt. A: Pure Appl. Opt. 8(4), S278–S284 (2006).
[Crossref]

Syassen, K.

C. Rockstuhl, T. Zentgraf, H. Guo, N. Liu, C. Etrich, I. Loa, K. Syassen, J. Kuhl, F. Lederer, and H. Giessen, “Resonances of split-ring resonator metamaterials in the near infrared,” Appl. Phys. B 84(1-2), 219–227 (2006).
[Crossref]

Thyagarajan, K.

Tsai, D. P.

W. Y. Tsai, T. L. Chung, H. H. Hsiao, J. W. Chen, R. J. Lin, P. C. Wu, G. Sun, C. M. Wang, H. Misawa, and D. P. Tsai, “Second Harmonic Light Manipulation with Vertical Split Ring Resonators,” Adv. Mater. 31(7), 1806479 (2019).
[Crossref]

Tsai, W. Y.

W. Y. Tsai, T. L. Chung, H. H. Hsiao, J. W. Chen, R. J. Lin, P. C. Wu, G. Sun, C. M. Wang, H. Misawa, and D. P. Tsai, “Second Harmonic Light Manipulation with Vertical Split Ring Resonators,” Adv. Mater. 31(7), 1806479 (2019).
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Turunen, J.

B. K. Canfield, S. Kujala, K. Jefimovs, Y. Svirko, J. Turunen, and M. Kauranen, “A macroscopic formalism to describe the second-order nonlinear optical response of nanostructures,” J. Opt. A: Pure Appl. Opt. 8(4), S278–S284 (2006).
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B. K. Canfield, S. Kujala, K. Jefimovs, J. Turunen, and M. Kauranen, “Linear and nonlinear optical responses influenced by broken symmetry in an array of gold nanoparticles,” Opt. Express 12(22), 5418–5423 (2004).
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D. C. Hooper, C. Kuppe, D. Wang, W. Wang, J. Guan, T. W. Odom, and V. K. Valev, “Second Harmonic Spectroscopy of Surface Lattice Resonances,” Nano Lett. 19(1), 165–172 (2019).
[Crossref]

Vartiainen, I.

R. Czaplicki, A. Kiviniemi, M. J. Huttunen, X. Zang, T. Stolt, I. Vartiainen, J. Butet, M. Kuittinen, O. J. F. Martin, and M. Kauranen, “Less Is More: Enhancement of Second-Harmonic Generation from Metasurfaces by Reduced Nanoparticle Density,” Nano Lett. 18(12), 7709–7714 (2018).
[Crossref]

Wan, M.

Wang, C. M.

W. Y. Tsai, T. L. Chung, H. H. Hsiao, J. W. Chen, R. J. Lin, P. C. Wu, G. Sun, C. M. Wang, H. Misawa, and D. P. Tsai, “Second Harmonic Light Manipulation with Vertical Split Ring Resonators,” Adv. Mater. 31(7), 1806479 (2019).
[Crossref]

Wang, D.

D. C. Hooper, C. Kuppe, D. Wang, W. Wang, J. Guan, T. W. Odom, and V. K. Valev, “Second Harmonic Spectroscopy of Surface Lattice Resonances,” Nano Lett. 19(1), 165–172 (2019).
[Crossref]

Wang, W.

D. C. Hooper, C. Kuppe, D. Wang, W. Wang, J. Guan, T. W. Odom, and V. K. Valev, “Second Harmonic Spectroscopy of Surface Lattice Resonances,” Nano Lett. 19(1), 165–172 (2019).
[Crossref]

Wang, Z.

X. Y. Zhang, Q. T. Cao, Z. Wang, Y. X. Liu, C. W. Qiu, L. Yang, Q. H. Gong, and Y. F. Xiao, “Symmetry-breaking-induced nonlinear optics at a microcavity surface,” Nat. Photonics 13(1), 21–24 (2019).
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W. Y. Tsai, T. L. Chung, H. H. Hsiao, J. W. Chen, R. J. Lin, P. C. Wu, G. Sun, C. M. Wang, H. Misawa, and D. P. Tsai, “Second Harmonic Light Manipulation with Vertical Split Ring Resonators,” Adv. Mater. 31(7), 1806479 (2019).
[Crossref]

Wu, X.

M. Celebrano, X. Wu, M. Baselli, S. Grossmann, P. Biagioni, A. Locatelli, C. De Angelis, G. Cerullo, R. Osellame, B. Hecht, L. Duo, F. Ciccacci, and M. Finazzi, “Mode matching in multiresonant plasmonic nanoantennas for enhanced second harmonic generation,” Nat. Nanotechnol. 10(5), 412–417 (2015).
[Crossref]

Wurtz, G. A.

P. Ginzburg, A. V. Krasavin, G. A. Wurtz, and A. V. Zayats, “Nonperturbative Hydrodynamic Model for Multiple Harmonics Generation in Metallic Nanostructures,” ACS Photonics 2(1), 8–13 (2015).
[Crossref]

Xiao, Y. F.

X. Y. Zhang, Q. T. Cao, Z. Wang, Y. X. Liu, C. W. Qiu, L. Yang, Q. H. Gong, and Y. F. Xiao, “Symmetry-breaking-induced nonlinear optics at a microcavity surface,” Nat. Photonics 13(1), 21–24 (2019).
[Crossref]

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X. Y. Zhang, Q. T. Cao, Z. Wang, Y. X. Liu, C. W. Qiu, L. Yang, Q. H. Gong, and Y. F. Xiao, “Symmetry-breaking-induced nonlinear optics at a microcavity surface,” Nat. Photonics 13(1), 21–24 (2019).
[Crossref]

Yang, X.

Yin, X.

K. O’Brien, H. Suchowski, J. Rho, A. Salandrino, B. Kante, X. Yin, and X. Zhang, “Predicting nonlinear properties of metamaterials from the linear response,” Nat. Mater. 14(4), 379–383 (2015).
[Crossref]

Yue, P.

Zang, X.

R. Czaplicki, A. Kiviniemi, M. J. Huttunen, X. Zang, T. Stolt, I. Vartiainen, J. Butet, M. Kuittinen, O. J. F. Martin, and M. Kauranen, “Less Is More: Enhancement of Second-Harmonic Generation from Metasurfaces by Reduced Nanoparticle Density,” Nano Lett. 18(12), 7709–7714 (2018).
[Crossref]

Zayats, A. V.

P. Ginzburg, A. V. Krasavin, G. A. Wurtz, and A. V. Zayats, “Nonperturbative Hydrodynamic Model for Multiple Harmonics Generation in Metallic Nanostructures,” ACS Photonics 2(1), 8–13 (2015).
[Crossref]

M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics 6(11), 737–748 (2012).
[Crossref]

Zdanowicz, M.

Zeng, Y.

Zentgraf, T.

G. Li, S. Zhang, and T. Zentgraf, “Nonlinear photonic metasurfaces,” Nat. Rev. Mater. 2(5), 17010 (2017).
[Crossref]

T. Zentgraf, T. P. Meyrath, A. Seidel, S. Kaiser, H. Giessen, C. Rockstuhl, and F. Lederer, “Babinet’s principle for optical frequency metamaterials and nanoantennas,” Phys. Rev. B 76(3), 033407 (2007).
[Crossref]

C. Rockstuhl, T. Zentgraf, H. Guo, N. Liu, C. Etrich, I. Loa, K. Syassen, J. Kuhl, F. Lederer, and H. Giessen, “Resonances of split-ring resonator metamaterials in the near infrared,” Appl. Phys. B 84(1-2), 219–227 (2006).
[Crossref]

Zhang, C.

Zhang, S.

G. Li, S. Zhang, and T. Zentgraf, “Nonlinear photonic metasurfaces,” Nat. Rev. Mater. 2(5), 17010 (2017).
[Crossref]

Zhang, X.

K. O’Brien, H. Suchowski, J. Rho, A. Salandrino, B. Kante, X. Yin, and X. Zhang, “Predicting nonlinear properties of metamaterials from the linear response,” Nat. Mater. 14(4), 379–383 (2015).
[Crossref]

Zhang, X. Y.

X. Y. Zhang, Q. T. Cao, Z. Wang, Y. X. Liu, C. W. Qiu, L. Yang, Q. H. Gong, and Y. F. Xiao, “Symmetry-breaking-induced nonlinear optics at a microcavity surface,” Nat. Photonics 13(1), 21–24 (2019).
[Crossref]

Zhou, J. F.

S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
[Crossref]

Zhu, M. Q.

ACS Photonics (1)

P. Ginzburg, A. V. Krasavin, G. A. Wurtz, and A. V. Zayats, “Nonperturbative Hydrodynamic Model for Multiple Harmonics Generation in Metallic Nanostructures,” ACS Photonics 2(1), 8–13 (2015).
[Crossref]

Adv. Mater. (1)

W. Y. Tsai, T. L. Chung, H. H. Hsiao, J. W. Chen, R. J. Lin, P. C. Wu, G. Sun, C. M. Wang, H. Misawa, and D. P. Tsai, “Second Harmonic Light Manipulation with Vertical Split Ring Resonators,” Adv. Mater. 31(7), 1806479 (2019).
[Crossref]

Appl. Phys. B (1)

C. Rockstuhl, T. Zentgraf, H. Guo, N. Liu, C. Etrich, I. Loa, K. Syassen, J. Kuhl, F. Lederer, and H. Giessen, “Resonances of split-ring resonator metamaterials in the near infrared,” Appl. Phys. B 84(1-2), 219–227 (2006).
[Crossref]

Appl. Phys. Lett. (1)

C. Hubert, L. Billot, P. M. Adam, R. BAchelot, P. Royer, J. Grand, D. Gindre, K. D. Dorkenoo, and A. Fort, “Role of surface plasmon in second harmonic generation from gold nanorods,” Appl. Phys. Lett. 90(18), 181105 (2007).
[Crossref]

J. Opt. A: Pure Appl. Opt. (1)

B. K. Canfield, S. Kujala, K. Jefimovs, Y. Svirko, J. Turunen, and M. Kauranen, “A macroscopic formalism to describe the second-order nonlinear optical response of nanostructures,” J. Opt. A: Pure Appl. Opt. 8(4), S278–S284 (2006).
[Crossref]

Mater. Today (1)

A. Krasnok, M. Tymchenko, and A. Alu, “Nonlinear metasurfaces: a paradigm shift in nonlinear optics,” Mater. Today 21(1), 8–21 (2018).
[Crossref]

Nano Lett. (4)

R. Czaplicki, A. Kiviniemi, M. J. Huttunen, X. Zang, T. Stolt, I. Vartiainen, J. Butet, M. Kuittinen, O. J. F. Martin, and M. Kauranen, “Less Is More: Enhancement of Second-Harmonic Generation from Metasurfaces by Reduced Nanoparticle Density,” Nano Lett. 18(12), 7709–7714 (2018).
[Crossref]

R. Czaplicki, J. Makitalo, R. Siikanen, H. Husu, J. Lehtolahti, M. Kuittinen, and M. Kauranen, “Second-Harmonic Generation from Metal Nanoparticles: Resonance Enhancement versus Particle Geometry,” Nano Lett. 15(1), 530–534 (2015).
[Crossref]

D. C. Hooper, C. Kuppe, D. Wang, W. Wang, J. Guan, T. W. Odom, and V. K. Valev, “Second Harmonic Spectroscopy of Surface Lattice Resonances,” Nano Lett. 19(1), 165–172 (2019).
[Crossref]

B. Metzger, L. Gui, J. Fuchs, D. Floess, M. Hentschel, and H. Giessen, “Strong Enhancement of Second Harmonic Emission by Plasmonic Resonances at the Second Harmonic Wavelength,” Nano Lett. 15(6), 3917–3922 (2015).
[Crossref]

Nat. Mater. (1)

K. O’Brien, H. Suchowski, J. Rho, A. Salandrino, B. Kante, X. Yin, and X. Zhang, “Predicting nonlinear properties of metamaterials from the linear response,” Nat. Mater. 14(4), 379–383 (2015).
[Crossref]

Nat. Nanotechnol. (1)

M. Celebrano, X. Wu, M. Baselli, S. Grossmann, P. Biagioni, A. Locatelli, C. De Angelis, G. Cerullo, R. Osellame, B. Hecht, L. Duo, F. Ciccacci, and M. Finazzi, “Mode matching in multiresonant plasmonic nanoantennas for enhanced second harmonic generation,” Nat. Nanotechnol. 10(5), 412–417 (2015).
[Crossref]

Nat. Photonics (2)

M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics 6(11), 737–748 (2012).
[Crossref]

X. Y. Zhang, Q. T. Cao, Z. Wang, Y. X. Liu, C. W. Qiu, L. Yang, Q. H. Gong, and Y. F. Xiao, “Symmetry-breaking-induced nonlinear optics at a microcavity surface,” Nat. Photonics 13(1), 21–24 (2019).
[Crossref]

Nat. Rev. Mater. (1)

G. Li, S. Zhang, and T. Zentgraf, “Nonlinear photonic metasurfaces,” Nat. Rev. Mater. 2(5), 17010 (2017).
[Crossref]

Opt. Express (5)

Opt. Lett. (5)

Phys. Rev. B (3)

C. Ciracì, E. Poutrina, M. Scalora, and D. R. Smith, “Second-harmonic generation in metallic nanoparticles: Clarification of the role of the surface,” Phys. Rev. B 86(11), 115451 (2012).
[Crossref]

C. Ciracì, E. Poutrina, M. Scalora, and D. R. Smith, “Origin of second-harmonic generation enhancement in optical split-ring resonators,” Phys. Rev. B 85(20), 201403 (2012).
[Crossref]

T. Zentgraf, T. P. Meyrath, A. Seidel, S. Kaiser, H. Giessen, C. Rockstuhl, and F. Lederer, “Babinet’s principle for optical frequency metamaterials and nanoantennas,” Phys. Rev. B 76(3), 033407 (2007).
[Crossref]

Phys. Rev. Lett. (3)

F. Falcone, T. Lopetegi, M. A. Laso, J. D. Baena, J. Bonache, M. Beruete, R. Marques, F. Martin, and M. Sorolla, “Babinet principle applied to the design of metasurfaces and metamaterials,” Phys. Rev. Lett. 93(19), 197401 (2004).
[Crossref]

S. Chervinskii, K. Koskinen, S. Scherbak, M. Kauranen, and A. Lipovskii, “Nonresonant Local Fields Enhance Second-Harmonic Generation from Metal Nanoislands with Dielectric Cover,” Phys. Rev. Lett. 120(11), 113902 (2018).
[Crossref]

S. Linden, F. B. Niesler, J. Forstner, Y. Grynko, T. Meier, and M. Wegener, “Collective effects in second-harmonic generation from split-ring-resonator arrays,” Phys. Rev. Lett. 109(1), 015502 (2012).
[Crossref]

Science (2)

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

S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
[Crossref]

Other (1)

S.A. Maier, Plasmonics: fundamentals and applications (Springer Science & Business Media, 2007).
[Crossref]

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (5)

Fig. 1.
Fig. 1. (a) Schematic of a unit cell of the dielectric coated gold CSRR array on a glass substrate. Only half of the dielectric layer is shown for comparison purposes. The plane wave is incident from the substrate side along the z direction and the electric field is polarized along the y direction. (b) Measured and (c) simulated linear spectra of the CSRR arrays with different arm lengths of a = 85 nm, 95 nm, 105 nm and 115 nm. The gray dotted line represents the FW of 1540 nm. The scanning electron microscope (SEM) images (scale bar: 400 nm) of the prepared CSRRs are shown in the right panel of (b). The right panel of (c) shows the distribution of the electric field and the polarization vector in a plane that is 0.1 nm below the top surface calculated for the CSRRs with a = 115 nm at the EDR.
Fig. 2.
Fig. 2. (a) Measured and (b) simulated EDR positions of the CSRR arrays with different arm lengths as a function of the alumina thickness t and the refractive index ne of a uniform environment, respectively. Spheres are experimental data and circles are simulated data. Lines are provided to guide the eye. The horizontal dotted line represents the FW of 1540 nm. Inset in (b): The approximate function that relates the refractive index ne of the uniform environment to the alumina thickness t.
Fig. 3.
Fig. 3. Schematic of the experimental setup for the SHG measurement. LPF: long-pass filter; L1-L3: lens; SPF: short-pass filter; LP: linear polarizer; EMCCD: electron multiplying charge coupled device. The Fourier images of the sample is recorded by the EMCCD.
Fig. 4.
Fig. 4. (a) Dependency between the radiated SH intensity from an alumina coated CSRR array and the incident FW power in double logarithmic coordinates. The slope of nearly 2 confirms the occurrence of a second-order nonlinear process. The hollow circles are experimental data and the black line is the linear fitting curve. Inset shows the analyzing of the SHG polarization. XY (blue curve) represents that the polarization of the fundamental wave is along the y-axis (parallel to the CSRR arm) while the transmission axis of the polarizer is along the x-axis. YY (red curve) represents that both the polarization of the fundamental wave and the transmission axis of the polarizer are along the y-axis. (b) Measured and (c) simulated SHG intensity of the CSRR arrays with different arm lengths as a function of the alumina thickness and the refractive index of uniform environment, respectively. The scale of the x-axis in (c) has been modified with a function ne = 1.57 - [0.4 / (0.035t + 1)] for easy comparison.
Fig. 5.
Fig. 5. Simulated absorption of the CSRR arrays with different arm lengths at the (a) FW of 1540 nm and (b) SH wavelength of 770 nm as a function of the uniform environment ne. Vertical dotted lines represent the values of ne = 1.17 (black), 1.235 (red), 1.315 (blue), 1.385 (green) at which the SHG intensity achieves the maximum for the CSRR arrays with different arm lengths of a = 115 nm, 105 nm, 95 nm, 85 nm, respectively. The scale of the x-axis has been modified with a function ne = 1.57 - [0.4 / (0.035t + 1)] for comparison. The inset in (b) shows the distribution of the magnetic field and polarization vector at the absorption peak at the SH wavelength for the CSRR arrays with a = 115 nm. (c) The distribution of the three components of the SH-generated polarization vector in two planes that are 0.1 nm below the top surface of the CSRR (red arrows) and 0.1 nm above the bottom surface of the CSRR (blue arrows). The center of the arrow is positioned at the arrow position. The right half of the panels: CSRRs with a = 115 nm, ne = 1.17. The left half of the panels: CSRRs with a = 85 nm, ne = 1.385.

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