Optical anapole mode in nanostructured lithium niobate for enhancing second harmonic generation

Yang Li; Zhijin Huang; Zhan Sui; Huajiang Chen; Xinyue Zhang; Weian Huang; Heyuan Guan; Wentao Qiu; Jiangli Dong; Wenguo Zhu; Jianhui Yu; Huihui Lu; Zhe Chen

doi:10.1515/nanoph-2020-0222

Article Open Access

Optical anapole mode in nanostructured lithium niobate for enhancing second harmonic generation

Yang Li , Zhijin Huang , Zhan Sui , Huajiang Chen , Xinyue Zhang , Weian Huang , Heyuan Guan , Wentao Qiu , Jiangli Dong , Wenguo Zhu , Jianhui Yu , Huihui Lu and Zhe Chen

Published/Copyright: June 29, 2020

Published by

Become an author with De Gruyter Brill

Submit Manuscript Author Information

From the journal Nanophotonics Volume 9 Issue 11

Abstract

Second harmonic generation (SHG) with a material of large transparency is an attractive way of generating coherent light sources at exotic wavelength range such as VUV, UV and visible light. It is of critical importance to improve nonlinear conversion efficiency in order to find practical applications in quantum light source and high resolution nonlinear microscopy, etc. Here an enhanced SHG with conversion efficiency up to 10⁻²% at SH wavelength of 282.7 nm under 11 GW/cm² pump intensity via the excitation of anapole in lithium niobite (LiNbO₃, or LN) nanodisk through the dominating d₃₃ nonlinear coefficient is investigated. The anapole has advantages of strongly suppressing far-field scattering and well-confined internal field which helps to boost the nonlinear conversion. Anapoles in LN nanodisk is facilitated by high index contrast between LN and substrate with properties of near-zero-index via hyperbolic metamaterial structure design. By tailoring the multi-layers structure of hyperbolic metamaterials, the anapole excitation wavelength can be tuned at different wavelengths. It indicates that an enhanced SHG can be achieved at a wide range of pump light wavelengths via different design of the epsilon-near-zero (ENZ) hyperbolic metamaterials substrates. The proposed nanostructure in this work might hold significances for the enhanced light–matter interactions at the nanoscale such as integrated optics.

Keywords: anapole; hyperbolic metamaterials; lithium niobate; second harmonic generation (SHG)

1 Introduction

Second harmonic generation (SHG) is a nonlinear optical process which combines two photons at the fundamental frequency (FF) and convert them into one photon at the second harmonic wavelength (SH) [1]. SHG has a wealth of applications in such as coherent laser sources [2], biological imaging microscopy [3], etc. The key of a practical SHG device is its conversion efficiency. Confining light in nonlinear material is a way of boosting nonlinear response. Due to rapid development to probe the optical field at subwavelength scale and advances in nanofabrication techniques, nonlinear optics at the nanoscale depends on the degree of the optical near-field confinement from nonlinear nanostructures without any phased-matched condition. As reported recently in diverse nonlinear nanostructures at different wavelength range, nonlinear enhancement effects from plasmonic nanostructures and dielectric metasurfaces have been extensively investigated but left nonlinear performance to be desired [4], [5], [6]. The scientific interest in nonlinear resonant phenomena for higher efficiency has been driven more by the localized resonance such as Mie-type resonances [7], [8], Fano resonance. For example, the third harmonic generation (THG) from nanostructure of gold nanodisk modulated by Fano-resonant supporting the magnetic plasmon resonance (MPR) mode and surface plasmon polaritons (SPP) can be studied about other nonlinear optical process but still with the limitation of pump threshold [9].

In recent years, there is a growing interest in the study of generating anapoles for various applications due to its strong light confinement ability [10], [11]. An anapole occurs when the far field radiation by electric dipole (ED) and toroidal dipole (TD) modes in Cartesian coordinates cancel each other out, and it is a non-radiative mode characterized by suppressing far field radiation therefore yielding a strong near field confinement [12], [13]. An efficient nonlinear device is feasible combining strong light confinement provided by anapoles and materials with high nonlinearity. As an example, the THG process has been greatly enhanced on germanium nanodisk via the excitation of anapole mode with near-infrared pump light [14]. And an anapole mode facilitate the generation of SH in LN with aluminum substrate yielding a high conversion efficiency of 1.1528 × 10⁻³% at VUV regime [15].

However, these anapoles are generated in nonlinear materials with high refractive index and a relatively narrow transparency range. In terms of wideband transparency and large nonlinearity, LN is a good choice, since it has remarkable physical properties such as electro-optic, piezoelectric, pyroelectric and SHG effect [1], [16]. It is very stable crystal with trigonal symmetry and a large transparency window. LN has a large second order nonlinearity coefficient d₃₃ of 25 pm/V which is oftentimes exploited as SHG devices by periodically poled lithium niobite (PPLN) configurations [17], [18]. A relatively low refractive index (extraordinary refractive index n_e = 2.25 at 500 nm) of LN than those such as silicon [19], [20] or germanium [14], [21] makes it rarely exploited in anapole configuration since high index contrast between substrate and material is important.

In order to enhance the index contrast between LN nanostructure and substrate, metamaterials which can be tuned to be as ENZ or even negative refractive index are chosen. Among these metamaterials, hyperbolic metamaterials (HMMs), as the topology of the isofrequency surface are hyperbolic curves, have been widely investigated recently [22]. In general, HMMs can be achieved by consisting of alternating layers of metal and dielectric [23] or as an array of nanowires [22]. Here HMMs are employed here exploiting their near ENZ and low effective permittivity property which assists a high index contrast between LN nanostructure and the substrate.

In this letter, we theoretically present a nanostructure for SHG application as shown in Figure 1. The nanostructure consists of a LN-nanodisk on the HMM substrate with a silica (SiO₂) spacer layer. A high normalized electric field intensity enhancement up to ∼35 at the resonant anapole is achieved. The SHG conversion efficiency with no need of phase-matching condition yields as high as 5.1371 × 10⁻⁵ thanks to the strong local field enhancement via anapole excitation.

$Figure 1: Schematic depiction of the proposed nanostructure for generating SH. The nanostructure consists of three parts: LN nanodisk on the top, HMM at the bottom consisting of 16 bilayers of alternating silver (Ag) [24] and silicon dioxide (SiO2) [16] layers and a SiO2 spacer layer with particular designed thickness sandwiched between LN nanodisk and HMM. The nanostructure lies on a glass substrate. The vector k→$\to {k}$ represents the wave vector of the incident light and E→$\to {E}$ indicates the x-polarized incident field.$

Figure 1:

Schematic depiction of the proposed nanostructure for generating SH. The nanostructure consists of three parts: LN nanodisk on the top, HMM at the bottom consisting of 16 bilayers of alternating silver (Ag) [24] and silicon dioxide (SiO₂) [16] layers and a SiO₂ spacer layer with particular designed thickness sandwiched between LN nanodisk and HMM. The nanostructure lies on a glass substrate. The vector k→ represents the wave vector of the incident light and E→ indicates the x-polarized incident field.

The paper is structured as follows: firstly, the dispersion property of the multilayered HMM is engineered and geometry parameters of nanostructure are optimized. Secondly, the scattering spectra and electric-field distributions are investigated to achieve the anapole resonance, which is further analyzed by the multipolar decomposition method. Afterwards, the far-field SHG performance is evaluated by nonlinear simulation of the optimal nanostructure. The dependences of SHG conversion efficiency with respect to the parameters of the input source are investigated. At last, comparisons of the state of the art in SHG are presented.

2 Optimization of HMM

In order to achieve high index contrast between LN nanodisk and substrate facilitating anapole excitation with low losses, a low effective refractive index substrate constituted of HMM is employed. In general, HMMs are made of alternating subwavelength-thickness layers of metal and dielectric which have opposite sign of permittivity facilitating a large tuning range of effective permittivity. The effective permittivity of HMMs are oftentimes investigated via effective medium theory (EMT) [22], [25]. In short, EMT allows to estimate the parallel component of effective permittivity ε∥<0 and perpendicular component of effective permittivity ε⊥>0 of HMMs which is related to filling fraction and the permittivity of the constituent materials.

The filling fraction of the metal (ρ) is defined as follow [22]:

(1)ρ=dmetaldmetal+ddielectric

where dmetal and ddielectric are the thicknesses of the metallic and the dielectric layers respectively. The equations for estimating the effective permittivity of the parallel εxx=εyy=ε∥ and perpendicular εzz=ε⊥ components based on field boundary conditions in Maxwell’s equations are as follows [26]:

(2)ε∥=ρεmetal+(1−ρ)εdielectric

(3)ε⊥=εmetalεdielectricρεdielectric+(1−ρ)εmetal

where εmetal and εdielectric are the permittivities of the metallic and the dielectric layers respectively. According to the sign of ε∥ and ε⊥, HMMs are classifies as Type I and Type II. Type I corresponds to a positive ε∥ and negative ε⊥. Whereas, Type II is reversed. Since the parallel index contrast is a key in the excitation of anapoles, a low or even negative ε∥ corresponding to Type II HMMs is chosen. On the other hand, the Type II HMMs with uniaxial anisotropic εxx, εyy<0;εzz>0 show more metallic characteristics such as low transmission and high reflection which is beneficial for supporting the anapole excitation inside LN nanodisk [27], [28].

The hyperbolic dispersion of HMM allows a wavelength range to cover the pump light wavelength to achieve the target wavelength of SHG around 200–300 nm. In terms of metallic materials, silver (Ag) which has small absorption loss and small real part of the permittivity in the targeted wavelength is more suitable than some others such as gold (Au) [24] or aluminum (Al) [16]. With regarding to dielectric material, SiO₂ which has weak absorption and small permittivity in the targeted wavelength is chosen. On the other hand, the chosen material Ag and SiO₂ are oftentimes investigated in thick film layer configurations in the literature with mature film deposition technique guaranteeing the possibility of structure fabrications.

We can tailor the dispersion of HMMs by appropriate filling fraction of metal (Ag) and dielectric (SiO₂). In this study, HMM is chosen as 16 pairs of alternating layers of Ag and SiO₂ thin films, with thicknesses of 30 and 15 nm respectively. The total thickness of the bilayer consisting of Ag and SiO₂ is fixed at 45 nm since this thickness yields small transmission losses and the filling fraction of the metal (ρ) is set as 0.67 in order to achieve short SH wavelength.

The ENZ wavelength versus the filling fraction of the metal (ρ) is investigated by EMT and it is depicted in Figure 2A. Taking into account the feasible film deposition thickness and the operation wavelength regime, a filling fraction of (ρ) is chosen as 0.67 (shown as dashed line in Figure 2A), which yields Ag thickness T (Ag) = 30 nm and SiO₂ thickness T (SiO₂) = 15 nm where the period is fixed at 45 nm. The ENZ wavelength occurs at around 330.8 nm. In terms of the total number of alternating thin film pairs, a number of 16 pairs is chosen to provide optimal performance since it yields a good compromise between the fabrication feasibility and small transmission losses.

$Figure 2: Optical properties of the HMM configuration. (Color online) (A) ENZ wavelength as a function of filling fraction of the metal (Ag) versus dielectric (SiO2). The inset is the schematic of the Ag/SiO2 multilayered HMM with ρ=0.67$\rho =0.67$, corresponding Ag thickness T (Ag) = 30 nm and SiO2 thickness T (SiO2) = 15 nm, where ENZ occurs at around 330.8 nm. (B) Real and imaginary parts of the parallel and perpendicular component of effective permittivity as functions of wavelength for Ag/SiO2 HMM with multilayered structures with filling fraction of the metal versus SiO2ρ=0.67$\rho =0.67$. The blue area corresponds to Type II HMM where parallel component of effective permittivity ε∥<0${\boldsymbol{\varepsilon }}_{\parallel }{< }0$ and perpendicular component of effective permittivity ε⊥>0${\boldsymbol{\varepsilon }}_{\perp }{ >}0$.$

Figure 2:

Optical properties of the HMM configuration. (Color online) (A) ENZ wavelength as a function of filling fraction of the metal (Ag) versus dielectric (SiO₂). The inset is the schematic of the Ag/SiO₂ multilayered HMM with ρ=0.67, corresponding Ag thickness T (Ag) = 30 nm and SiO₂ thickness T (SiO₂) = 15 nm, where ENZ occurs at around 330.8 nm. (B) Real and imaginary parts of the parallel and perpendicular component of effective permittivity as functions of wavelength for Ag/SiO₂ HMM with multilayered structures with filling fraction of the metal versus SiO₂ρ=0.67. The blue area corresponds to Type II HMM where parallel component of effective permittivity ε∥<0 and perpendicular component of effective permittivity ε⊥>0.

The parallel and perpendicular component of effective permittivity corresponding to 16 pairs of alternating layers of Ag and SiO₂ thin films (30 nm Ag and 15 nm SiO₂) as functions of wavelength are shown in Figure 2B where the blue area corresponds to Type II HMM regime. This HMM configuration will be employed as a low effective index substrate supporting LN nanodisk whereas the material and thickness of terminating layer i.e. interfacing between HMM and LN nanodisk will be tuned according to its ability of high field enhancement which will be presented in the next section.

3 Results and discussions

3.1 Optimization of LN nanostructure

The purpose to optimize the nanostructured LN-nanodisk geometry is to obtain high field enhancement in nonlinear material therefore enhancing nonlinear response. In order to achieve that, the spacer layer between LN nanodisk and HMMs is SiO₂ since it has negligible absorption loss within the considered wavelength range. The optimal thickness of SiO₂ spacer layer and geometries of LN nanodisk are determined via three-dimensional finite-difference time-domain (Lumerical FDTD) simulations. The incident field is a broad bandwidth total-field scattered-field (TFSF) source and the simulated structure is shown in Figure 1. Perfectly matched layer (PML) boundary conditions are employed in all three dimensions simulating a finite structure size. The optimal SiO₂ spacer layer thickness is the one that allows high field enhancement in LN nanostructure [29], [30]. Therefore, the averaged intensity enhancement which is defined as the ratio of the averaged volumetric field integration in LN nanoparticle with that of field amplitude E0 in the incident wave as 〈|E/E0|2〉.

Figure 3A shows the calculated maximum averaged intensity enhancement when varying the spacer thickness T whereas the LN nanodisk is centered on top with parameters of diameter (D = 432 nm) and height (H = 104 nm). The maximum averaged intensity enhancement 〈|E/E0|2〉 achieves at 21nm-thickness SiO₂ layer. The averaged intensity enhancement of the optimal SiO₂ spacer layer (black curve) and 0nm-thickness SiO₂ spacer layer (red curve) are calculated wavelength by wavelength with monochromatic wave excitation as shown in Figure 3B. The highest field enhancement occurs around 565.4 nm and it yields 1.3 times field enhancement compared with 0nm-thickness SiO₂ spacer layer configurations.

Figure 3:

Optimization of the spacer-layer thickness. (Color online) (A) Calculated maximum averaged electric field intensity enhancement as a function of SiO₂ spacer thickness T whereas the LN nanodisk is centered on top with parameters of diameter (D = 432 nm) and height (H = 104 nm). The data points are fitted. (B) Averaged intensity enhancement versus wavelength of 21nm-thickness SiO₂ layer (black curve) and 0nm-thickness SiO₂ layer (red curve). The insets show the electric field distributions at the highest field enhancement mode of each configuration respectively.

In terms of the geometries of the nanostructure, LN (nanodisk) is the most efficient scatter comparing to other shapes such as cube or sphere [31]. A highly efficient scattering together with high index contrast are promising to the excitation of anapole which yields large field enhancement. Three-dimensional FDTD numerical simulations are employed to analyze different height and diameter of the LN nanodisk whereas the averaged field enhancement is calculated. Figure 4A, B shows the normalized maximum electric field intensity enhancement versus varying one parameter while the other one is fixed, which indicates the optimization locates in the vicinity of the diameter (D) of 432 nm and the height (H) of 104 nm.

$Figure 4: Numerical analyses of the LN-nanodisk geometries and the field distributions of different HMM filling fraction of the metal. (Color online) (A) Normalized maximum electric field intensity enhancement of varying the height of LN nanodisk, while diameter is fixed to 432 nm. The coarse optimal D is around 432 nm. (B) Normalized electric field intensity enhancement of varying the diameter of LN nanodisk, while height is fixed to 70 nm. The coarse optimal H is around 104 nm. The data points are fitted. (C) Fine optimization of LN nanodisk geometries around the vicinity of coarse optimal one (D = 432 nm, H = 104 nm) and the optimal one is depicted by the dashed blue circle corresponding to parameters of D = 432 nm, H = 104 nm. (D) Normalized electrical field intensity enhancement distributions |E/E0|2${\vert E/{E}_{0}\vert }^{2}$ for the different HMM filling fraction of the metal (ρ$\rho $) at ρ=0.13$\rho =0.13$ (at wavelength of 595.2 nm), 0.3 (at wavelength of 573.9 nm), 0.45 (at wavelength of 569.7 nm) and 0.7 (at wavelength of 565.4 nm), respectively.$

Figure 4:

Numerical analyses of the LN-nanodisk geometries and the field distributions of different HMM filling fraction of the metal. (Color online) (A) Normalized maximum electric field intensity enhancement of varying the height of LN nanodisk, while diameter is fixed to 432 nm. The coarse optimal D is around 432 nm. (B) Normalized electric field intensity enhancement of varying the diameter of LN nanodisk, while height is fixed to 70 nm. The coarse optimal H is around 104 nm. The data points are fitted. (C) Fine optimization of LN nanodisk geometries around the vicinity of coarse optimal one (D = 432 nm, H = 104 nm) and the optimal one is depicted by the dashed blue circle corresponding to parameters of D = 432 nm, H = 104 nm. (D) Normalized electrical field intensity enhancement distributions |E/E0|2 for the different HMM filling fraction of the metal (ρ) at ρ=0.13 (at wavelength of 595.2 nm), 0.3 (at wavelength of 573.9 nm), 0.45 (at wavelength of 569.7 nm) and 0.7 (at wavelength of 565.4 nm), respectively.

Fine optimization of LN nanodisk geometries around the vicinity of coarse optimal one (D = 432 nm, H = 104 nm) is performed and the result is shown in Figure 4C. The optimal one is depicted by the dashed blue circle corresponding to parameters of diameter (D = 432 nm) and height (H = 104 nm) which yields high field enhancement. A suitable height-to-diameter ratio (height/diameter defined as the geometrical aspect ratio) is also important for the potential of anapole excitations [19], [32] and here the optimal aspect ratio height/diameter is ∼0.24. Based on the above optimized structural parameters, Figure 4D shows the corresponding local field distribution under different metal filling fraction of HMM, which reveals the hyperbolic dispersion of HMM can manipulate the anapole field confinement.

Total scattering spectra of the optimal nanostructure are simulated and the averaged field enhancement factor in the wavelength range between 200 and 1000 nm is investigated as shown in Figure 5A, C.

$Figure 5: Simulation scattering spectra and field distributions of the nanostructures. (Color online) LN nanodisk placed on SiO2 substrate: (A) The top figure corresponds to the normalized scattering cross section and the bottom corresponds the intensity enhancement 〈|E/E0|2〉$\langle {\vert E/{E}_{0}\vert }^{2}\rangle $. (B) Normalized electrical field intensity enhancement distributions 〈|E/E0|2〉$\langle {\vert E/{E}_{0}\vert }^{2}\rangle $ in xy-, xz-, and yz-planes at the incident wavelength of 588.8 nm correspond to the dashed cured outlined mode in Figure 5A. LN nanodisk placed at the center with 21 nm SiO2 spacer layer and 16 pairs of HMM (ρ=0.67$\rho =0.67$) sitting on glass substrate as the simulated nanostructure presented in Figure 1: (C) Top figure corresponds to the normalized scattering cross section and the bottom corresponds 〈|E/E0|2〉$\langle {\vert E/{E}_{0}\vert }^{2}\rangle $. (D) Normalized electrical field intensity enhancement distributions |E/E0|2${\vert E/{E}_{0}\vert }^{2}$ at 565.4 nm. The distributions of the normalized electric field in xy-, xz-, and yz-planes correspond to the dashed cured outlined mode in Figure 5C. The nanostructure of xz and yz cross sections are outline with white solid lines. Here the height (H = 104 nm) and diameter (D = 432 nm) of LN nanodisk are the same for all parts of the figure. The gray dashed lines show the mode of the highest field enhancement.$

Figure 5:

Simulation scattering spectra and field distributions of the nanostructures. (Color online) LN nanodisk placed on SiO₂ substrate: (A) The top figure corresponds to the normalized scattering cross section and the bottom corresponds the intensity enhancement 〈|E/E0|2〉. (B) Normalized electrical field intensity enhancement distributions 〈|E/E0|2〉 in xy-, xz-, and yz-planes at the incident wavelength of 588.8 nm correspond to the dashed cured outlined mode in Figure 5A. LN nanodisk placed at the center with 21 nm SiO₂ spacer layer and 16 pairs of HMM (ρ=0.67) sitting on glass substrate as the simulated nanostructure presented in Figure 1: (C) Top figure corresponds to the normalized scattering cross section and the bottom corresponds 〈|E/E0|2〉. (D) Normalized electrical field intensity enhancement distributions |E/E0|2 at 565.4 nm. The distributions of the normalized electric field in xy-, xz-, and yz-planes correspond to the dashed cured outlined mode in Figure 5C. The nanostructure of xz and yz cross sections are outline with white solid lines. Here the height (H = 104 nm) and diameter (D = 432 nm) of LN nanodisk are the same for all parts of the figure. The gray dashed lines show the mode of the highest field enhancement.

The top figures of Figure 5A, C correspond normalized scattering cross section where a pronounced dip indicating suppression of far field radiation is observed in the scattering cross-section spectrum. The bottom figures of Figure 5A, C correspond respectively the averaged intensity enhancement 〈|E/E0|2〉 of LN nanodisk placed on SiO₂ substrate at 588.8 nm and LN nanodisk placed on HMM substrate at 565.4 nm, where a 〈|E/E0|2〉 of 8.7 enhancement is obtained for case of the HMM substrate, which is higher than the case of SiO₂ substrate and other reported nanostructures [15] thanks to the high index contrast between LN nanodisk and HMM substrate. For the case of HMM substrate, the largest enhancement 〈|E/E0|2〉 occurs at a wavelength of 565.4 nm which locates at the decreasing slop near the dip wavelength of the total scattering cross section.

Figure 5B, D shows respectively the normalized electrical field intensity enhancement distributions in xy-, xz-, and yz-planes corresponding to the dashed cured outlined mode in Figure 5A, C. The maximum value of the normalized electric field intensity enhancement distributions |E/E0|2 in Figure 5D can reach up to ∼35, which is a high value compared to the case of SiO₂ substrate shown in Figure 5B and those reported in references [15], [20], [30], which shows the electric field is confined better inside the LN nanodisk with HMM substrate. With this large field enhancement obtained and the large index contrast between LN nanodisk and HMMs, we will investigate whether this mode is an anapole or not via multipolar decomposition in the next section.

3.2 Multipolar decomposition

In order to understand the origin of the large obtained field enhancement at the local dip wavelength of the total scattering cross section, multipolar decomposition analysis is performed. The total scattering cross section can be decomposed as the sum of radiations from different electric and magnetic multipoles as follows [33], [34]:

(4)Csca=πk2∑l=1∞∑m=−ll(2l+1)[|aE(l, m)|2+|aM(l, m)|2]

where k is the incident wave vector, l is the order of the multipole and m is the amount of the z-component of angular momentum carried per photon.

In view of each multipole mode of multipole decomposition influenced by the nanostructural properties including the effects of spacer layer and complicated substrate on spectral shifts [32], [35], [36], the decomposition up to quadrupoles while neglecting other higher order multipoles is performed by finite element method (COMSOL Multiphysics) in spherical coordinates for the stability of calculations and the result is shown in Figure 6A. Due to the neglect of other higher order multipoles’ contributions, the sum scattering cross section is a bit different from that displayed in the top figure of Figure 5C where all the multipoles contributions are taken into account [37], [38]. In general, different local dips in the sum scattering cross section correspond to anapoles of different order with different purity which are related to the degree of far field radiation extinction by destructive interference between Cartesian ED and TD modes. As such, the contributions from each multipole term can be clearly identified. Whereas at the local dip wavelength, spherical ED mode takes up an important portion. The dashed circled out local dip in Figure 6A indicates the effectively suppressed far field radiation which is termed anapole leading to a significant drop of the sum scattering cross section. Upon analyzing multipole contributions to the light–matter interactions, one can note that nearby the local dip wavelength of the spherical ED mode, the spherical magnetic quadrupole (MQ) resonance contributes to the far field radiation, making the anapole mode pure incompletely. Meanwhile, the contributions from spherical magnetic dipole (MD) and electric quadrupole (EQ) modes are negligible.

Figure 6:

Multipolar analysis of light scattering by the nanostructure. (Color online) (A) Multipoles decomposition of the studied nanostructure in spherical coordinates. Sum stands for sum scattering cross section from the decomposed multipoles up to the 2nd order, spherical ED for electric dipole, MD for magnetic dipole, EQ for electric quadrupole and MQ for magnetic quadrupole. (B) Cartesian multipolar expansion of Cartesian ED and TD for toroidal dipole. The gray dashed line indicates the wavelength of the destructively interference as the first-order anapole excitation. The inset shows the electric field distribution at the first-order anapole mode.

The spherical ED mode of radiation suppression in spherical coordinates normally is caused by interference with other multipoles. In order to find out this, TD mode which is neglected in spherical coordinates [39] multipolar decomposition is calculated by integration of the currents within the nanostructure in Cartesian coordinates.

In Cartesian coordinates, the radiated moments of Cartesian ED and TD can be derived from the scattering current density J→ as follows [40], [41].

(5)ED:P→=1−iω∫J→d3r

(6)TD:T→=110c∫[(r→⋅J→)r→−2r2J→]d3r

where c is the speed of light in vacuum, P→=−ikT→ represents the contributions of the electric dipole and toroidal dipole modes in current Cartesian coordinates [12]. Figure 6B shows the Cartesian ED and TD multipole contributions in Cartesian coordinates. The slight wavelength difference between the scattering dip of spherical ED mode and the crossing point of the Cartesian ED and TD contributions results from the material losses [42].

The intersection between the Cartesian ED and TD modes near 580.8 nm (gray dashed line in Figure 6B corresponding to the first-order anapole of this nanostructure) shows the destructively interference in the far field which yields to the excitation of anapole. The slight difference between the intersecting wavelength at 580.8 nm for far field and the resonant wavelength at 565.4 nm for near field (gray dashed line in Figure 5C) indicates the deviation of anapole wavelength resulting from the mismatch between the resonant positions in the near field and far field [43]. Therefore, both the suppression of spherical ED far field radiation and the intersection between the Cartesian ED and TD modes unambiguously reveal the physical origins of the first-order anapole mode of the nanostructure. The first-order anapole mode brings enhancement of the near field for realizing a large enhancement in SHG.

3.3 Nonlinear simulations

Thanks to the anapole excitation in the nanostructure, maximum field enhancement reaches up to ∼35. SHG is studied employing the optimized parameters from above with LN nanodisk lying on HMMs and the substrate is SiO₂ (schematically shown in Figure 1). Phase-matching conditions [1] is not necessary due to the nanometrical thickness of the structure. In general, the nonlinear coefficient matrix of trigonal symmetric structure is as follows [1]:

(7)dijk=[0000d31−d22−d22d220d3100d31d31d33000]

In LN the largest second order nonlinear susceptibility is d33=−41.7 pm/V. Only the diagonal terms of second order nonlinear susceptibility will be considered in calculating nonlinear polarizations via FDTD Solutions. The peak pump intensity of the normal incident Gaussian pulse is set to I0=5.31GW/cm2 (corresponding to the incident electric field amplitude of 1.9995ℒ108 V/m). Referring to the anapole resonance wavelength obtained by linear scattering, the central wavelength of the source is at 565.4 nm with the full-width at half-maximum (FWHM) of 8.8 THz and a pulse duration of 90 fs, the sampling range of fundamental wavelength is selected as 560.7–570.2 nm for nonlinear simulations. It is a beam with a spot size one-micron wide in x-direction in the simulation estimating nonlinear response. The obtained far-field power spectrum is shown in Figure 7A where there are two peaks corresponding to pump and SH respectively. Figure 7B indicates the SHG contribution of the proposed nanostructure presented in Figure 1 is mainly attributed to LN nanodisk when comparing with the case of bare HMM without LN nanodisk, and the case of LN nanodisk on SiO₂ substrate and on Ag substrate, respectively. As expected, the high fundamental field observed in Figure 7C induces an enhancement of the SHG field localized inside the LN nanodisk as shown in Figure 7D for the proposed nanostructure.

Figure 7:

Nonlinear simulations of the nanostructure. (Color online) (A) Normalized nonlinear far-field power spectrum with spectral color where SH wavelength is at 282.7 nm and the fundamental wavelength is at 565.4 nm. (B) Normalized nonlinear far-field spectra of SHG for the LN nanodisk with HMM substrate (blue solid line), the bare HMM without LN nanodisk (red solid line), the LN nanodisk on SiO₂ substrate (purple solid line) and on Ag substrate (green solid line) respectively. (C) and (D) Normalized field intensity distributions in the xy planes at fundamental and SH wavelength respectively. The white solid lines depict the xy cross sections of the proposed nanostructure.

The SHG conversion efficiency is estimated via the equation as follows [44], [45]:

(8)ηSH=PSHPFF

PFF is the power of the fundamental wavelength i.e. the pump light, PSH is the power at the SH wavelength. Where P=12∫real(S→)⋅dA, and S→ is Poynting vector S→=±(E→ℒH→)/2 and A is the cross-sectional area of the Gaussian beam. The SHG conversion efficiency obtained in Figure 7A reaches up to 5.1371ℒ10−5 at the absolute power of 3.0027ℒ10−4 W with λ=565.4nm. Meanwhile, considering the properties of the source, it is suitable to calculate the dimensional SHG efficiency described as follows [46], [47]:

(9)ηdimSH=PSHPFF2 (W−1)

The parameters are the same as in Equation (8). The dimensional SHG efficiency calculated by the absolute pump power from the nanostructure reaches 0.1711 W⁻¹ at λ=565.4nm. As can be seen from Figure 7B, the contribution of HMM benefits from the higher index contrast with the LN nanodisk to achieve the higher confinement filed for SHG than that of SiO₂ substrate. However, the LN nanodisk on Ag substrate with an index contrast slightly higher than that of HMM substrate generates the lower SHG efficiency of 6.8643ℒ10−6 at λ=535.6nm due to the material of Ag with higher lossy than the HMM. Low losses are essentials for SHG generation efficiency which can be achieved well with tunable dispersion of HMM. It is revealed in Figure 7C, D that the strong enhancement of SHG conversion efficiency originated mainly from the localized concentrated electromagnetic field in the LN nanodisk induced by the anapole mode (i.e. at fundamental wavelength). The SHG conversion efficiency can be improved by optimizing the pump light conditions such as pulse duration and peak intensity. The results of the obtained SHG conversion efficiency with respect to pulse duration and peak intensity are shown in Figure 8 where the structure parameters are the same as that employed in Figure 7A. And the SHG power as a function of pump intensity is shown in the inset of Figure 8B.

Figure 8:

Optimizing calculations of the pump light conditions. (Color online) (A) SHG conversion efficiency versus different pump light pulse duration. (B) SHG conversion efficiency as a function of pump light peak intensity varying from 2 to 50 GW/cm². The inset shows the log–log plot of quadratic dependence of the SHG power on the peak pump intensity at 565.4 nm fundamental wavelength. A fit to this data produces a black line with a slope of 1.99, which is very close to the theoretical prediction of two reasonably well.

As can be seen from Figure 8A, the optimal value of pulse duration is about 90 fs which yields a SHG conversion efficiency up to 5.1371 × 10⁻⁵. When the incident pulse duration is more than 90 fs, the SHG conversion efficiency will saturate and be no longer significantly decreased but approach the saturation gradually, which is typical of cavity phenomena [48], [49]. With regard to pump light peak intensity, the optical damage threshold of LN is considered as larger than 70 GW/cm² [1]. Due to the relatively small distance between the first silver film and the focal plane of the pump light, the laser-induced damage threshold of silver for ultrashort pulse about 0.5 ps is as high as 166 GW/cm² [50] and it will increase with shortening the pulse duration [51]. Therefore, the largest peak intensity in Figure 8B is considered only up to 50 GW/cm² and the largest obtained SHG conversion efficiency is at the order of ∼10⁻⁴. Also as shown in the inset of Figure 8B, the SHG power is proportional to the square of the pump intensity, which shows a very good agreement with the second-order nature of the SHG, confirming the SHG process.

As shown above in the article, the anapole-assisted nanostructure obtained here is to enhance nonlinear effects efficiently. Table 1 shows the comparisons of the optical field enhancement and SHG conversion efficiency of different structures where the proposed nanostructure in this article appears in bold. The SHG conversion efficiency is high up to the order of ∼10⁻⁴, which exceeds several orders higher than the case of other configurations such as nanoantennas and metasurfaces. Due to the optimized geometric parameters vary with the nanostructure, the volume of the nanostructure in this work is different from that of other nanostructures, and even smaller than that of most other nanostructures. Hence, the proposed nanostructure yielding higher conversion efficiency through anapole enhancement of the electromagnetic field might find applications in such as nanophotonics and biophotonics.

Table 1:

Comparisons of the electric-field enhancement and SHG conversion efficiency of different structures.

Structure	Structure parameter (diameter [D]; height [H])	FF power or peak pump intensity (λFF)	〈\|E/E0\|2〉	\|E/E0\|2	ηSH	ηdimSH (W⁻¹)
Plasmonic and dielectric chiral nanostructure [52]	Gold nanosphere (D = 200 nm)	2 W (520 nm)	-	-	∼10⁻¹¹	-
Nanocrystalline nanoparticle [53]	Si nanoparticle (D = 350 nm)	30 GW/cm² (1050 nm)	-	-	1.5 × 10⁻⁶	2.2 × 10⁻⁵
Metal–dielectric hybrid nanoantennas [54]	AlGaAs nanodisk (D = 760 nm, H = 200 nm)	1.6 GW/cm² (1554 nm)	-	20	5 × 10⁻⁶	-
AlGaAs-on-AlOx nanodimers [55]	Al_0.18Ga_0.82 As cylinder (D = 670 nm, H = 400 nm)	1.6 GW/cm² (1550 nm)	-	-	∼4 × 10⁻⁶	-
LiNbO₃ nanodisks on an Al substrate [15]	LN nanodisk (D = 256 nm, H = 70 nm)	5.31 GW/cm² (351.3 nm)	∼6	∼22	1.1528 × 10⁻⁵	-
Free-standing disk nanoantennas [56]	GaAs/AlGaAs disk (D = 440 nm, H = 210 nm)	1 GW/cm² (800 nm)	-	-	1.9 × 10⁻⁵	0.063
Nanostructured lithium niobite (this article)	LN nanodisk (D = 432 nm, H = 104 nm)	5.31 GW/cm² (565.4 nm)	8.7	∼35	5.1371 × 10⁻⁵	0.1711

4 Conclusion

In conclusion, an approach to enhance the near-field effects of nanostructure with higher index contrast between LN and HMM with low losses has been investigated in SHG numerically. The electric-field enhancement associated with optical anapole mode which occurs at the wavelength of 565.4 nm enhances efficiently nonlinear interactions where the achieved SHG conversion efficiency yields up to 10⁻⁴ under pump intensity of 11 GW/cm². The HMMs assisted anapole excitation in low refractive index material may also work for other materials in order to obtain an efficient nonlinear conversion. In such a configuration, the design of structure by tuning dispersion and optimization of geometric parameters for anapole excitation can also be applied to other nanostructures. The great flexibility for high tuning efficiency in these nanostructures might find some applications, such as spectrally selective device and compact optical device.

Corresponding authors: Wentao Qiu, Key Laboratory of Optoelectronic Information and Sensing Technologies of Guangdong Higher Education Institutes, Jinan University, Guangzhou 510632, China, E-mail: qiuwentao16@163.com; and Huihui Lu, Guangdong Provincial Key Laboratory of Optical Fiber Sensing and Communications, Jinan University, Guangzhou 510632, P.R. China, E-mail: thuihuilu@jnu.edu.cn.

^aYang Li and Zhijin Huang: These authors equally contributed to this work.

Funding source: National Natural Science Foundation of China

Funding source: Guangdong Special Support Program

Funding source: Guangdong Natural Science Funds for Distinguish Young Scholar

Funding source: Science Foundation of Guangdong Province

Funding source: Fundamental Research Funds for the Central Universities

Acknowledgments

This work was supported by the National Natural Science Foundation of China (61775084, 61505069, 61705089, 61705087), Guangdong Special Support Program (2016TQ03X962), Guangdong Natural Science Funds for Distinguish Young Scholar (2015A030306046), Science Foundation of Guangdong Province (2020A151501791), Fundamental Research Funds for the Central Universities (21619409, 21619410).

Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
Research funding: None declared.
Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

References

[1] R. W. Boyd, Nonlinear Optics. San Diego, CA, Elsevier, 2003.Search in Google Scholar

[2] L. P. Gonzalez, D. C. Upchurch, P. G. Schunemann, L. Mohnkern, and S. Guha, “Second-harmonic generation of a tunable continuous-wave CO2 laser in orientation-patterned gaas,” Opt. Lett., vol. 38, pp. 320–322, 2013. https://doi.org/10.1364/ol.38.000320.Search in Google Scholar

[3] P. Campagnola, “Second harmonic generation imaging microscopy: applications to diseases diagnostics,” Anal. Chem., vol. 83, pp. 3224–3231, 2011. https://doi.org/10.1021/ac1032325.Search in Google Scholar PubMed PubMed Central

[4] S. Chen, W. Wong, Y. Pun, K. Cheah, and G. Li, “Surface plasmon-enhanced third harmonic generation from gold–polymer hybrid plasmonic crystal,” Adv. Opt. Mater., vol. 1, pp. 522–526, 2013. https://doi.org/10.1002/adom.201300144.Search in Google Scholar

[5] D. Smirnova and Y. S. Kivshar, “Multipolar nonlinear nanophotonics,” Optica, vol. 3, pp. 1241–1255, 2016. https://doi.org/10.1364/optica.3.001241.Search in Google Scholar

[6] N. Panoiu, W. Sha, D. Lei and G. Li, “Nonlinear optics in plasmonic nanostructures,” J. Opt., vol. 20, p. 083001, 2018. https://doi.org/10.1088/2040-8986/aac8ed.Search in Google Scholar

[7] D. Smirnova, A. I. Smirnov and Y. S. Kivshar, “Multipolar second-harmonic generation by mie-resonant dielectric nanoparticles,” Phys. Rev. A, vol. 97, p. 013807, 2018. https://doi.org/10.1103/physreva.97.013807.Search in Google Scholar

[8] D. A. Smirnova, A. B. Khanikaev, L. A. Smirnov, and Y. S. Kivshar, “Multipolar third-harmonic generation driven by optically induced magnetic resonances,” ACS Photonics, vol. 3, pp. 1468–1476, 2016. https://doi.org/10.1021/acsphotonics.6b00036.Search in Google Scholar

[9] H. Liu, G. X. Li, K. F. Li, et al., “Linear and nonlinear fano resonance on two-dimensional magnetic metamaterials,” Phys. Rev. B, vol. 84, p. 235437, 2011. https://doi.org/10.1103/physrevb.84.235437.Search in Google Scholar

[10] V. Savinov, N. Papasimakis, D. P. Tsai, and N. I. Zheludev, “Optical anapoles,” Commun. Phys., vol. 2, p. 69, 2019. https://doi.org/10.1038/s42005-019-0167-z.Search in Google Scholar

[11] K. Koshelev, G. Favraud, A. Bogdanov, Y. Kivshar, and A. Fratalocchi, “Nonradiating photonics with resonant dielectric nanostructures,” Nanophotonics, vol. 8, pp. 725–745, 2019. https://doi.org/10.1515/nanoph-2019-0024.Search in Google Scholar

[12] K. V. Baryshnikova, D. A. Smirnova, B. S. Luk’yanchuk, and Y. S. Kivshar, “Optical anapoles: concepts and applications,” Adv. Opt. Mater., vol. 7, p. 1801350, 2019. https://doi.org/10.1002/adom.201801350.Search in Google Scholar

[13] L. Xu, M. Rahmani, K. Zangeneh Kamali, et al., “Boosting third-harmonic generation by a mirror-enhanced anapole resonator,” Light Sci. Appl., vol. 7, p. 44, 2018. https://doi.org/10.1038/s41377-018-0051-8.Search in Google Scholar PubMed PubMed Central

[14] G. Grinblat, Y. Li, M. P. Nielsen, R. F. Oulton, and S. A. Maier, “Efficient third harmonic generation and nonlinear subwavelength imaging at a higher-order anapole mode in a single germanium nanodisk,” ACS Nano, vol. 11, pp. 953–960, 2017. https://doi.org/10.1021/acsnano.6b07568.Search in Google Scholar PubMed

[15] K.-H. Kim and W.-S. Rim, “Anapole resonances facilitated by high-index contrast between substrate and dielectric nanodisk enhance vacuum ultraviolet generation,” ACS Photonics, vol. 5, pp. 4769–4775, 2018. https://doi.org/10.1021/acsphotonics.8b01287.Search in Google Scholar

[16] E. D. Palik, Handbook of Optical Constants of Solids. San Diego, CA, Academic Press, 1998.Search in Google Scholar

[17] A. Rao, M. Malinowski, A. Honardoost, et al., “Second-harmonic generation in periodically-poled thin film lithium niobate wafer-bonded on silicon,” Opt. Express, vol. 24, pp. 29941–29947, 2016. https://doi.org/10.1364/oe.24.029941.Search in Google Scholar PubMed

[18] C. Wang, C. Langrock, A. Marandi, et al., “Ultrahigh-efficiency wavelength conversion in nanophotonic periodically poled lithium niobate waveguides,” Optica, vol. 5, pp. 1438–1441, 2018. https://doi.org/10.1364/optica.5.001438.Search in Google Scholar

[19] Y. Yang, V. A. Zenin, and S. I. Bozhevolnyi, “Anapole-assisted strong field enhancement in individual all-dielectric nanostructures,” ACS Photonics, vol. 5, pp. 1960–1966, 2018. https://doi.org/10.1021/acsphotonics.7b01440.Search in Google Scholar

[20] T. Shibanuma, G. Grinblat, P. Albella, and S. A. Maier, “Efficient third harmonic generation from metal-dielectric hybrid nanoantennas,” Nano Lett., vol. 17, pp. 2647–2651, 2017. https://doi.org/10.1021/acs.nanolett.7b00462.Search in Google Scholar PubMed

[21] G. Grinblat, Y. Li, M. P. Nielsen, R. F. Oulton and S. A. Maier, “Enhanced third harmonic generation in single germanium nanodisks excited at the anapole mode,” Nano Lett., vol. 16, pp. 4635–4640, 2016. https://doi.org/10.1021/acs.nanolett.6b01958.Search in Google Scholar PubMed

[22] P. Shekhar, J. Atkinson, and Z. Jacob, “Hyperbolic metamaterials: fundamentals and applications,” Nano Converg., vol. 1, p. 14, 2014. https://doi.org/10.1186/s40580-014-0014-6.Search in Google Scholar PubMed PubMed Central

[23] O. Kidwai, S. V. Zhukovsky, and J. Sipe, “Effective-medium approach to planar multilayer hyperbolic metamaterials: strengths and limitations,” Phys. Rev. A, vol. 85, p. 053842, 2012. https://doi.org/10.1103/physreva.85.053842.Search in Google Scholar

[24] P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B, vol. 6, pp. 4370–4379, 1972. https://doi.org/10.1103/physrevb.6.4370.Search in Google Scholar

[25] L. Ferrari, C. Wu, D. Lepage, X. Zhang, and Z. Liu, “Hyperbolic metamaterials and their applications,” Prog. Quantum Electron., vol. 40, pp. 1–40, 2015. https://doi.org/10.1016/j.pquantelec.2014.10.001.Search in Google Scholar

[26] B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B, vol. 74, p. 115116, 2006. https://doi.org/10.1103/physrevb.74.115116.Search in Google Scholar

[27] D. Korobkin, B. Neuner, C. Fietz, N. Jegenyes, G. Ferro, and G. Shvets, “Measurements of the negative refractive index of sub-diffraction waves propagating in an indefinite permittivity medium,” Opt. Express, vol. 18, pp. 22734–22746, 2010. https://doi.org/10.1364/oe.18.022734.Search in Google Scholar PubMed

[28] Z. Huang, T. B. Norris, and E. Narimanov, “Nanoscale fingerprinting with hyperbolic metamaterials,” APL Photonics, vol. 4, p. 026103, 2019. https://doi.org/10.1063/1.5079736.Search in Google Scholar

[29] K. V. Sreekanth, M. Elkabbash, Y. Alapan, A. R. Rashed, U. A. Gurkan, and G. Strangi, “A multiband perfect absorber based on hyperbolic metamaterials,” Sci. Rep., vol. 6, p. 26272, 2016. https://doi.org/10.1038/srep26272.Search in Google Scholar PubMed PubMed Central

[30] L. Sabri, Q. Huang, J. N. Liu and B. T. Cunningham, “Design of anapole mode electromagnetic field enhancement structures for biosensing applications,” Opt. Express, vol. 27, pp. 7196–7212, 2019. https://doi.org/10.1364/oe.27.007196.Search in Google Scholar

[31] J. Van De Groep and A. Polman, “Designing dielectric resonators on substrates: combining magnetic and electric resonances,” Opt. Express, vol. 21, pp. 26285–26302, 2013. https://doi.org/10.1364/oe.21.026285.Search in Google Scholar PubMed

[32] R. Wang and L. Dal Negro, “Engineering non-radiative anapole modes for broadband absorption enhancement of light,” Opt. Express, vol. 24, pp. 19048–19062, 2016. https://doi.org/10.1364/oe.24.019048.Search in Google Scholar PubMed

[33] P. Grahn, A. Shevchenko, and M. Kaivola, “Electromagnetic multipole theory for optical nanomaterials,” New J. Phys., vol. 14, p. 093033, 2012. https://doi.org/10.1088/1367-2630/14/9/093033.Search in Google Scholar

[34] C. F. Bohren and D. R. Huffman. Absorption and Scattering of Light by Small Particles. New York, John Wiley & Sons, 2008.Search in Google Scholar

[35] A. I. Kuznetsov, A. E. Miroshnichenko, Y. H. Fu, J. Zhang, and B. Luk’yanchuk, “Magnetic light,” Sci. Rep., vol. 2, p. 492, 2012. https://doi.org/10.1038/srep00492.Search in Google Scholar PubMed PubMed Central

[36] A. B. Evlyukhin, S. M. Novikov, U. Zywietz, et al., “Demonstration of magnetic dipole resonances of dielectric nanospheres in the visible region,” Nano Lett., vol. 12, pp. 3749–3755, 2012. https://doi.org/10.1021/nl301594s.Search in Google Scholar PubMed

[37] R. M. Bakker, D. Permyakov, Y. F. Yu, et al., “Magnetic and electric hotspots with silicon nanodimers,” Nano Lett., vol. 15, pp. 2137–2142, 2015. https://doi.org/10.1021/acs.nanolett.5b00128.Search in Google Scholar PubMed

[38] L. Wang, S. Kruk, L. Xu, et al., “Shaping the third-harmonic radiation from silicon nanodimers,” Nanoscale, vol. 9, pp. 2201–2206, 2017. https://doi.org/10.1039/c6nr09702b.Search in Google Scholar PubMed

[39] W. Liu, J. Zhang, and A. E. Miroshnichenko, “Toroidal dipole-induced transparency in core-shell nanoparticles,” Laser Photonics Rev., vol. 9, pp. 564–570, 2015. https://doi.org/10.1002/lpor.201500102.Search in Google Scholar

[40] J. Chen, J. Xiang, S. Jiang, Q. Dai, S. Tie, and S. Lan, “Multipole radiations from large gold nanospheres excited by evanescent wave,” Nanomaterials, vol. 9, p. 175, 2019. https://doi.org/10.3390/nano9020175.Search in Google Scholar PubMed PubMed Central

[41] A. E. Miroshnichenko, A. B. Evlyukhin, Y. F. Yu, et al., “Nonradiating anapole modes in dielectric nanoparticles,” Nat. Commun, vol. 6, p. 8069, 2015. https://doi.org/10.1038/ncomms9069.Search in Google Scholar PubMed PubMed Central

[42] T. Feng, Y. Xu, W. Zhang, and A. E. Miroshnichenko, “Ideal magnetic dipole scattering,” Phys. Rev. Lett., vol. 118, p. 173901, 2017. https://doi.org/10.1103/physrevlett.118.173901.Search in Google Scholar PubMed

[43] P. Alonso-González, P. Albella, F. Neubrech, et al., “Experimental verification of the spectral shift between near- and far-field peak intensities of plasmonic infrared nanoantennas,” Phys. Rev. Lett., vol. 110, p. 203902, 2013. https://doi.org/10.1103/physrevlett.110.203902.Search in Google Scholar PubMed

[44] Z. Huang, H. Lu, H. Xiong, et al., “Fano resonance on nanostructured lithium niobate for highly efficient and tunable second harmonic generation,” Nanomaterials, vol. 9, p. 69, 2019. https://doi.org/10.3390/nano9010069.Search in Google Scholar PubMed PubMed Central

[45] X. Guo, C.-L. Zou, and H. X. Tang, “Second-harmonic generation in aluminum nitride microrings with 2500%/w conversion efficiency,” Optica, vol. 3, p. 1126, 2016. http://dx.doi.org/10.1364/OPTICA.3.001126.10.1364/OPTICA.3.001126Search in Google Scholar

[46] S. Campione, A. Benz, M. B. Sinclair, F. Capolino, and I. Brener, “Second harmonic generation from metamaterials strongly coupled to intersubband transitions in quantum wells,” Appl. Phys. Lett., vol. 104, p. 131104, 2014. https://doi.org/10.1063/1.4870072.Search in Google Scholar

[47] M. Celebrano, X. Wu, M. Baselli, et al., “Mode matching in multiresonant plasmonic nanoantennas for enhanced second harmonic generation,” Nat. Nanotechnol., vol. 10, p. 412, 2015. https://doi.org/10.1038/nnano.2015.69.Search in Google Scholar PubMed

[48] M. Vincenti, D. De Ceglia, V. Roppo, and M. Scalora, “Harmonic generation in metallic, gaas-filled nanocavities in the enhanced transmission regime at visible and UV wavelengths,” Opt. Express, vol. 19, pp. 2064–2078, 2011. https://doi.org/10.1364/oe.19.002064.Search in Google Scholar

[49] V. Roppo, F. Raineri, C. Cojocaru, et al., Generation efficiency of the second harmonic inhomogeneous component, arXiv preprint arXiv:1010.4693 2010. https://doi.org/10.1364/np.2010.nme41.Search in Google Scholar

[50] L. Gallais and M. Commandré, “Laser-induced damage thresholds of bulk and coating optical materials at 1030 nm, 500 fs,” Appl. Opt., vol. 53, pp. A186–A196, 2014. https://doi.org/10.1364/ao.53.00a186.Search in Google Scholar PubMed

[51] R. M. Wood, Laser-Induced Damage of Optical Materials. Boca Raton, FL, CRC Press, 2003.10.1887/0750308451Search in Google Scholar

[52] X. Y. Z. Xiong, A. Al-Jarro, L. J. Jiang, N. C. Panoiu, and W. E. I. Sha, “Mixing of spin and orbital angular momenta via second-harmonic generation in plasmonic and dielectric chiral nanostructures,” Phys. Rev. B, vol. 95, p. 165432, 2017. https://doi.org/10.1103/physrevb.95.165432.Search in Google Scholar

[53] S. V. Makarov, M. I. Petrov, U. Zywietz, et al., “Efficient second-harmonic generation in nanocrystalline silicon nanoparticles,” Nano Lett., vol. 17, pp. 3047–3053, 2017. https://doi.org/10.1021/acs.nanolett.7b00392.Search in Google Scholar PubMed

[54] V. F. Gili, L. Ghirardini, D. Rocco, et al., “Metal–dielectric hybrid nanoantennas for efficient frequency conversion at the anapole mode,” Beilstein J. Nanotechnol., vol. 9, pp. 2306–2314, 2018. https://doi.org/10.3762/bjnano.9.215.Search in Google Scholar PubMed PubMed Central

[55] D. Rocco, V. F. Gili, L. Ghirardini, et al., “Tuning the second-harmonic generation in algaas nanodimers via non-radiative state optimization [invited],” Photonics Res., vol. 6, p. B6, 2018. https://doi.org/10.1364/prj.6.0000b6.Search in Google Scholar

[56] M. Timofeeva, L. Lang, F. Timpu, et al., “Anapoles in free-standing iii–v nanodisks enhancing second-harmonic generation,” Nano Lett., vol. 18, pp. 3695–3702, 2018. https://doi.org/10.1021/acs.nanolett.8b00830.Search in Google Scholar PubMed

Received: 2020-04-01

Accepted: 2020-06-06

Published Online: 2020-06-29

This work is licensed under the Creative Commons Attribution 4.0 International License.

Articles in the same Issue

https://doi.org/10.1515/nanoph-2020-0222

Keywords for this article

anapole; hyperbolic metamaterials; lithium niobate; second harmonic generation (SHG)

Creative Commons

BY 4.0