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Abstract
It was reported previously that the quality factor of a symmetry-protected quasi-BIC mode increases as the degree of structure asymmetry is reduced. In this work, we propose and investigate an alternative approach to increase the quality factor of a quasi-BIC mode without reducing the degree of asymmetry. Specifically, we calculate the quality factor of the quasi-BIC mode of a double-gap dielectric split-ring metasurface for different split angles. It is found that the quality factor increases exponentially with the increase of the split angles while the degree of asymmetry of the structure is constant. To explain the phenomena, multipole moment decomposition of the local electromagnetic field is conducted to calculate the change of major multipole moments versus the split angles. It is revealed that the double-gap split-ring array structure stores more energy in the higher order multipoles, and the rate of radiation energy loss stays constant when the two splitting angles increase simultaneously. Additionally, the enhancement of third harmonic generation is investigated in the double-gap split-ring metasurface structure.
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1. Introduction
Bound states in the continuum (BICs) were first proposed as discrete states embedded within a continuum of quantum states by J. Neumann and E. Wigner in 1929 [1]. The concept of BICs later was adopted in different fields of wave physics including acoustics [2], microwaves [3], and photonics [4]. There are two types of BICs that have been identified and investigated in photonic systems. One type is the symmetry-protected BICs, and another is accidental BICs [5]. Symmetry-protected BICs arise from the mode decoupling between the resonant mode and the free space due to the symmetry mismatch [6–8]. Symmetry-protected BICs can only be realized at the Γ point in the reciprocal space [9]. Accidental BICs occur where all radiation channels are canceled out due to the wave interference at a certain point in the structural parameter space [10–12]. Ideally, BICs cannot be observed because BIC modes do not radiate to the far field. For ideal systems without energy internal dissipation, the quality factors of BIC modes are infinitely large. Practically, the quality factor of a BIC mode is reduced due to internal energy loss in materials [13], finite size of the device [14], and the imperfection of device fabrications [15], where the true BIC mode is transformed into a quasi-BIC mode with a finite large quality factor. Due to the large quality factor and strongly enhanced local field, quasi-BICs can be potentially used for many applications such as optical nonlinear harmonic wave generations [16,17], light-exciton strong coupling [18,19], low-threshold lasing [20,21], and ultra-sensitive photonic biosensing [22–24].
Electromagnetic resonance in an asymmetric double-gap copper split-ring metamaterial was investigated experimentally in 2007 [25]. This resonance mode can be considered as a symmetry-protected quasi-BIC mode in the split-ring structure, even though the concept of BICs in photonics [26] had not been proposed at that time. In 2019, dual quasi-BIC modes were demonstrated in a double-gap aluminum split-ring resonators array on a silicon substrate [27]. Since then, the metallic [28–31] and dielectric [8,32,33] split-ring metasurface structures have been investigated for realizing BICs modes in different spectral regions. BICs in split-ring metasurface structures have also been investigated for a variety of applications such as refractive-index sensing [34,35], high order optical harmonic wave generation [36,37], and optical modulations [38,39].
It was reported earlier that the quality factors of the symmetry-protected quasi-BIC modes increase with the reduction of the asymmetric degree of the structures [7,22,38,40–42]. In this work, we propose an approach to increase the quality factor of the quasi-BIC mode without reducing the degree of asymmetry of the structure. Specifically, we calculate the quality factor of the quasi-BIC mode of the double-gap dielectric split-ring metasurface for different splitting angles and found the quality factor increases dramatically with the increase of splitting angles. We also conduct multipole analysis of the local electromagnetic field and show the contributions of major multipole moments to the quality factor of the quasi-BIC mode. Finally, the quasi-BIC resonance enhanced third harmonic generations is investigated in the double-gap split-ring metasurface structure.
2. Quasi-BIC mode in the double-gap silicon split-ring metasurface
2.1 Asymmetric double-gap silicon split-ring metasurface
A schematic diagram of the double-gap split-ring metasurface structure is shown in Fig. 1(a) and 1(b). The structure consists of an array of asymmetric silicon double-gap split-ring resonators periodically arranged on the surface of a silicon dioxide (SiO2) substrate. The structure parameters of the double-gap split-ring resonator include the outer radius R, the inner radius r, the height h, the period P, the upper splitting angle θ1, and the lower splitting angle θ2. In the case of θ1=θ2, the double-gap split-ring resonator is symmetric along both the x and y direction. In the case of θ1≠θ2, the symmetry of the double-gap split-ring resonator is broken along the x direction. Hence, an asymmetry parameter β can be defined as β=sinα [38], where α is |θ2-θ1|/2.
Fig. 1. (a) Schematic diagram of the asymmetric double-gap silicon split-ring metasurface structure. (b) Top view (x-y plane) of the asymmetric split-ring metasurface structure. The structure parameters include the outer radius R, the inner radius r, the height h, the period P, the upper splitting angle θ1, and the lower splitting angle θ2.
Finite-difference time-domain (FDTD) simulations using a Lumerical FDTD software are carried out to calculate the transmittance spectra and the electromagnetic field distributions of the double-gap split-ring resonators array. In the simulations, the simulation domain is a three-dimensional region where periodic boundary conditions are used in the boundaries of the simulation domain in the ± x and ± y directions. The perfect matching layer (PML) boundary condition is utilized in the boundaries in the ± z directions. The refractive indices of Si and SiO2 are set to 3.48 and 1.45 in the near infrared-region (NIR), respectively. A plane wave polarizing along the x direction with the amplitude of 1 V/m is normally incident onto the metasurface from above. A frequency-domain field profile monitor is placed at the half height of the double-gap split-ring resonator to obtain the electromagnetic field profile and a frequency-domain power monitor is placed below the double-gap split-ring metasurface to record the transmittance power.
The transmittance spectra of the double-gap split-ring metasurface structure with different α are simulated and plotted in Fig. 2(a). The lower splitting angle θ2 is fixed at 20° and the upper splitting angle θ1 is changed from 10° to 20° in the step of 2°. The other geometric parameters are R = 350 nm, r = 180 nm, h = 150 nm, P = 1000 nm and are fixed in all simulations. As shown in Fig. 2(a), when the double-gap split-ring resonator is symmetric, (i.e., α=0°), the metasurface structure has almost 100% transmittance in the whole spectral wavelength ranging from 1550 nm to 1600 nm. When the double-gap split-ring resonator is asymmetric, such as α=1°, an ultra-narrow transmittance dip emerges at the wavelength of 1566.8 nm. Because the perturbation introduced by breaking the symmetry of the double-gap split-ring metasurface structure establishes a radiative channel between the bound state and the free space, making the true BIC convert into the quasi-BIC. Moreover, as α increases, the transmittance dip becomes wider due to more energy radiating to the free space and the resonance wavelength red shifts evidently. The quality factors of the quasi-BIC mode for different asymmetry parameters can be calculated from [14]
where ω0 is the resonance frequency, and γ is the overall damping rate of the resonance mode. The overall damping rate γ can be obtained by fitting the transmittance curves in Fig. 2(a) with the classical Fano formula [43], where a, b, and c are real constants. The quality factors versus different asymmetry parameters are calculated and shown in Fig. 2(b). It is seen that the quality factor is as high as 32764 when the asymmetry parameter β=sin(1°). The data points in Fig. 2(b) are well fitted by the function of Q = 10.1×β-2, indicating that the quality factor Q is inversely proportional to the square of asymmetry parameter β. When the asymmetry parameter approaches 0, the quality factor approaches infinity. Therefore, the smaller the asymmetry parameter, the higher the quality factor of the quasi-BIC mode. Reducing the asymmetry parameter is a traditional approach used to design high-Q metasurface structures based on symmetry-protected quasi-BIC mode. Figure 2(c) shows the transmittance spectra of the double-gap split-ring metasurface structure with θ1 = 10° and θ2 = 20° and the amplitude of the electric field at two positions in the nanogaps of the resonator. The blue solid line represents the transmittance spectrum of the double-gap split-ring metasurface structure. It is seen that the wavelength of the transmittance dip is 1583.9 nm. The black solid line represents the amplitude of the electric field of point A which is located at the small angle gap of the resonator as seen in the inset of Fig. 2(c). The black dashed line is the amplitude of the electric field of point B which is located at the large angle gap of the resonator. As shown in Fig. 2(c), the electric field enhancements at point A and point B reach the maximum value at the resonance wavelength of 1583.8 nm. The electric field enhancement at point A in the small angle gap is larger than that at point B in the large angle gap. Also, it can be seen that there is a 0.1 nm resonance wavelength difference between the near-field and the far-field.Fig. 2. (a) Evolution of transmittance spectra of the double-gap silicon split-ring metasurface structure with different α. (b) The quality factor Q as a function of the asymmetry parameter β. The red solid line represents the fitting result. (c) The transmittance spectrum of the double-gap split-ring metasurface structure with θ1 = 10° and θ2 = 20°, and the electric field enhancements of point A and point B as functions of wavelength. The red stars in the inset represent the positions of point A and point B.
2.2 High quality factor of the quasi-BIC mode enabled by large double splitting angles
The quality factor of the quasi-BIC mode in the double-gap split-ring metasurface structure can also be increased by increasing the double splitting angles simultaneously while the asymmetry parameter is kept as a constant. The average of double splitting angles can be characterized by the average splitting angle φ=(θ1+θ2)/2. Figure 3(a) shows the transmittance spectra of the double-gap split-ring metasurface structure with different average splitting angles φ and a fixed asymmetry parameter β=sin(5°). When the average splitting angle φ increases, there is a distinct blueshift in the resonance wavelength, and the spectral linewidth of the transmittance dip becomes narrower. When φ=65°, the linewidth of the transmittance dip is about 0.09 nm and the corresponding quality factor reaches as high as 16364. Furthermore, the quality factors versus the average splitting angles φ for different asymmetry parameters are calculated and shown in Fig. 3(b). It can be seen that for every fixed asymmetry parameter, the quality factor increases dramatically as the average splitting angle φ increases. Specifically, for the asymmetry parameter β=sin(3°), the quality factor increases from 7530 to 44744 as the average splitting angle φ increases from 25° to 65°. Thus, the quality factor of the double-gap split-ring metasurface structure can also be increased by increasing the average splitting angle not only reducing the asymmetry parameter. Figure 3(c) shows the quality factors versus asymmetry parameters for different average splitting angles φ=25°, 35°, 45°, 55°, and 65°. The asymmetry parameter is changed by rotating the left half of the split-ring resonator clockwise and the right half of the split-ring resonator counterclockwise for the same degree to ensure the constant of the average splitting angle. As shown in Fig. 3(c), the quality factor increases as the asymmetry parameter decreases for the fixed average splitting angle. To consider both the effects of the asymmetry parameter and the splitting angles on the quality factor, we write the quality factor in the form of
where A(φ) is a function of the average splitting angle φ. To determine A(φ), the data points in Fig. 3(c) are fitted by using Eq. (3), and the five solid lines shown in Fig. 3(c) represent the fitting results of the quality factors for the asymmetry parameters. It is found that the quality factor is proportional to the inverse square of the asymmetry parameter for different average splitting angles. Also, A(φ) is obtained from the fitting results and is 20.7, 31.0, 44.0, 68.1, and 123.0 for different average splitting angles φ of 25°, 35°, 45°, 55°, and 65°, respectively. The values of A(φ) obtained above for different average splitting angle φ are plotted and shown in Fig. 3(d). It is seen that A(φ) can be well fitted by an exponential function of A(φ) = 1.3×eφ/14.7 + 15.2. Thus, the complete form of the Eq. (3) isFig. 3. (a) The transmittance spectra of the double-gap split-ring metasurface structure with different average splitting angles φ when the asymmetry parameter β is fixed as β=sin(5°). (b) The quality factors versus average splitting angles for different asymmetry parameters. (c) The quality factors versus asymmetry parameters for different average splitting angles. (d) The exponential fitting for A(φ) versus the average splitting angle φ.
From Eq. (4), it can be seen that for a fixed asymmetry parameter β, the quality factor increases exponentially with the average splitting angle φ. Given any specific splitting angle θ1 and θ2, the quality factor of the quasi-BIC mode in the double-gap split-ring metasurface structure can be predicted by using Eq. (4). Furthermore, as the average splitting angle keeps increasing, the transmittance dip will gradually disappear and the quality factor approaches infinity.
The electromagnetic field distributions of the double-gap split-ring resonator are calculated and plotted in Fig. 4 and Fig. 5. Figures 4(a)-(d) show the electric field distributions in the x-y plane of the double-gap split-ring resonator in a unit cell for different splitting angles. The upper splitting angle θ1 is increased from 30° to 60° and the lower splitting angle θ2 is increased simultaneously from 40° to 70° in the step of 10° while the asymmetry parameter β is fixed at β=sin(5°). It is seen that the electric field enhancements are mainly localized in the two gaps. As the two splitting angles increase, the electric field and the volume of the enhancement region increase. Figure 5(a) to 5(d) show the magnetic field distributions in the x-y plane of the double-gap split-ring resonator with the fixed asymmetry parameter β=sin(5°) in a unit cell for different splitting angles. As shown in Fig. 5, the magnetic field enhancements are mainly localized in the center region of the split-ring resonator. As the two splitting angles increase, the magnetic field and the volume of the enhancement region increase. Therefore, a higher quality factor resonance mode and stronger electromagnetic field enhancements can be obtained by increasing the splitting angles of the double split-ring resonators.
Fig. 4. Electric field distributions at the resonance wavelength in the x-y plane of the double-gap split-ring resonator with different upper and lower splitting angles, where (a) θ1 = 30° and θ2 = 40°, (b) θ1 = 40° and θ2 = 50°, (c) θ1 = 50° and θ2 = 60°, (d) θ1 = 60° and θ2 = 70°.
Fig. 5. Magnetic field distributions at the resonance wavelength in the x-y plane of the double-gap split-ring resonator with different upper and lower splitting angles, where (a) θ1 = 30° and θ2 = 40°, (b) θ1 = 40° and θ2 = 50°, (c) θ1 = 50° and θ2 = 60°, (d) θ1 = 60° and θ2 = 70°.
3. Multipole analysis of the quasi-BIC mode in the metasurface structure
To explain the phenomenon that increasing the average splitting angle φ results in increasing the quality factor of the quasi-BIC mode, we conduct the multipole moment analysis of the local electromagnetic field. An open-source MATLAB-based code for multipole decomposition in the Cartesian coordinate system is used to calculate the moments of electric dipole, magnetic dipole, electric quadrupole, and magnetic quadrupole, respectively from the displacement electric current density j(r) by j(r)= -iωε0(n2-1)E(r) [44]. Here, r is the spatial position vector, E(r) is the electric field distribution, ω is the angular frequency of the light, ε0 is the electric permittivity of vacuum, and n is the refractive indices of the materials. To obtain the electric field distribution, a 3D Fourier transform (DFT) monitor encircling the double-gap split-ring in a unit cell is utilized together with a 3D index monitor that has the same dimensions.
Figure 6(a) shows the calculated electric field profile of the double-gap split-ring resonator with θ1 = 10° and θ2 = 20° at resonance wavelength in the x-y plane. The arrows indicate the direction of the displacement density. As shown in Fig. 6(a), the electric field enhancement is mainly localized in the gap of the split-ring and the displacement current forms a loop (white arrows) circulating clockwise in the x-y plane. Figure 6(b) shows the magnetic field profile at resonance wavelength in the x-z plane. The magnetic field enhancement is mainly concentrated in the center region of the spit-ring. Two magnetic fields (white arrows) loop with opposite directions, generating a magnetic dipole moment along the z direction.
Fig. 6. (a) The electric field profile in the x-y plane of the resonator at resonance wavelength, where the white arrows represent the direction of induced displacement currents. (b) The magnetic field profile in the x-z plane crossing a resonator (y = 0) at resonance wavelength and the white arrows represent the direction of the magnetic field.
After calculating the induced displacement current density j(r), four multipole moments including electric dipole (P), magnetic dipole (M), electric quadrupole (Qe), and magnetic quadrupole (Qm), are calculated with j(r) by using following equations [45],
Fig. 7. The amplitude of components of the (a) electric dipole moment, (b) magnetic dipole moment, (c) electric quadrupole moment, and the (d) magnetic quadrupole moment versus wavelength, respectively.
From the results shown in Fig. 7, the moments of Px, Mz, $Q_{x y}^e$, and $Q_{z z}^m$ are major multipole moments. Next, the amplitudes of Px, Mz, $Q_{x y}^e$, and $Q_{z z}^m$ as functions of the average splitting angle φ are calculated and plotted in Fig. 8(a) to 8(d) with the fixed asymmetry parameter β=sin(5°). As shown in Fig. 8(a), the electric dipole moment Px remains almost constant as the average splitting angle increases, indicating that the rate of radiation energy loss from the double-gap split-ring metasurface structure is almost unchanged. Figure 8(b) shows that the magnetic dipole moment Mz increases as the average splitting angle increases. However, since Mz oscillates along the z direction, it only radiates in the x-y plane and the radiated energy is absorbed and recycled by neighboring resonators. Thus, Mz does not contribute to the quality factor of the quasi-BIC mode in the double-gap split-ring metasurface structure. As shown in Fig. 8(c) and 8(d), both the electric quadrupole moment Qe xy and the magnetic quadrupole moment $Q_{z z}^m$ increase with the increasing average splitting angle. Since the quadrupolar consists of a pair of antiphase dipoles and the radiations of the pair of antiphase dipoles are canceled out in the far field due to the symmetry configuration, the quadrupole mode is non-radiative. As the quadrupole moments increase, the energy stored inside the double-gap split-ring metasurface increases but with less radiation energy loss.
Fig. 8. The amplitude of the (a) electric dipole moment Px, (b) magnetic dipole moment Mz, (c) electric quadrupole moment $Q_{x y}^e$, and the (d) magnetic quadrupole moment $Q_{z z}^m$ versus average splitting angle φ, respectively.
In our double-gap split-ring metasurface structure, the electric and magnetic dipole moments oscillating in the x-y plane have contributions to the far-field radiated power of the double-gap split-ring metasurface since these dipole moments radiate in the ± z direction. From the results shown in Fig. 7(a) and 7(b), the electric dipole moment Px and the magnetic dipole moment My are mainly responsible for the far-field radiated power of the metasurface structure. The radiated powers Ip and IM caused by Px and My in a unit cell can be obtained with the following formulas respectively [45],
The radiated powers of Px and My versus the incident wavelength are calculated and compared in Fig. 9. It can be seen that the electric dipole moment Px has the highest radiated power. The magnetic dipole moment My has the second largest radiated power at resonance wavelength, while My is strongly suppressed, resulting in less radiation energy loss compared with that of the electric dipole moment Px. Therefore, the radiation of the far field of quasi-BIC mode in the double-gap split-ring metasurface structure is mainly attributed to the electric dipole moment Px.
As discussed above, the rate of energy radiation to the far field is primarily determined by the x component of the electric dipole moment Px. The Px is approximately a constant as the two splitting angles increase as shown in Fig. 8(a), indicating that the rate of radiation energy loss from the double-gap split-ring metasurface structure is almost constant. The energy stored locally in the split-ring structure is dominated by the electric quadrupole moment $Q_{x y}^e$ and the magnetic quadrupole moment $Q_{z z}^m$ and increases as the two split angles increase as shown in Fig. 8(c) and 8(d). Consequently, the quality factor of the quasi-BIC resonant mode increases as the split angles increase, since the double-gap split-rings store more energy while the rate of energy radiation is constant as the two split angles increase simultaneously.
4. Enhancement for third harmonic generation at the quasi-BIC mode
The enhanced electromagnetic field at the quasi-BIC mode can enhance nonlinear responses of the metasurface structure, such as second harmonic generation (SHG) [46] or third harmonic generation (THG) [47]. It has been reported that silicon has been used as an ideal nonlinear optical material for studying the enhancement of THG signal due to its high refractive index, low loss in the infrared region, and large third-order nonlinear susceptibility (χ (3) ≈ 2.79 × 10−18 m2·V-2) [48]. In this work, the quasi-BIC enhanced THG in the asymmetric double-gap silicon split-ring metasurface is investigated by using FDTD simulations. In the FDTD simulations, the electric and magnetic fields are computed at every point of the Yee lattice during successive time steps by solving discretized Maxwell’s equations [49]. A plane wave with the peak electric field amplitude of 1.0 × 107 V/m and pulse length of 1000 fs is set to simulate a femtosecond pulsed optical wave. A point time monitor is placed below the metasurface structure to obtain the spectrum of the Fourier transform of the time signal. The electric polarization density P in the direction of incident polarization can be expressed as
where χ(1) is the linear electric susceptibility, χ(2) is the second-order nonlinear electric susceptibility which is zero here, χ(3) is the third-order nonlinear electric susceptibility of the silicon material, and E is the electric field component in the direction of polarization.Figure 10(a) shows calculated THG intensities generated from the silicon double-gap split-ring metasurface structure and from an un-patterned silicon film with the same thickness of 150 nm. The metasurface structure with the asymmetry parameter β=sin(5°) and the average splitting angle φ=25° is taken as an example in calculating the THG intensity shown in Fig. 10(a). The red solid line is the THG intensity of the double-gap split-ring metasurface structure versus wavelength. By pumping at the resonance wavelength of 1571.88 nm, the THG intensity of the asymmetric double-gap split-ring metasurface structure reaches the maximum (1.46606 × 107 W/m2) at the wavelength of 523.96 nm. The blue dashed line is the THG intensity of the bare Si film and achieves the peak value of 22352.4 W/m2 at 523.96 nm wavelength. Therefore, the THG intensity of the asymmetric double-gap split-ring metasurface structure is 656 times higher than that of the bare Si film with the same thickness. Figure 10(b) shows the dependence of THG intensity of the double-gap split-ring metasurface structure on the pumping wavelength. The THG intensity changes drastically as the pumping wavelength across the quasi-BIC resonance wavelength. When the pumping wavelength is at the quasi-BIC resonance wavelength of 1571.88 nm, the THG intensity reaches the maximal value and is dramatically reduced off the resonance wavelength.
Fig. 10. (a) Quasi-BIC enhanced THG intensity spectra (red solid line) and the THG intensity in the reference Si thin film of same thickness (blue dashed line) pumped at the quasi-BIC resonance wavelength of 1571.88 nm. (b) The peak THG intensity of a quasi-BIC mode versus the excitation wavelength. (c) Polar plot of THG intensity versus the polarization angle of excitation laser. (d) Enhancement factor for THG and quality factor versus the average splitting angle φ.
Figure 10(c) is the polar plot of THG intensity versus the polarization angle of incident light with respect to the x direction. As the polarization rotates from 0 to π/2, the THG intensity changes from the maximum (1.46606 × 107 W/m2) to the minimum (66958.5 W/m2). Further increasing the polarization angle, the THG intensity increases from the minimum to the minimum again. At polarizing angles of π/2 and 3π/2, the quasi-BIC mode is not excited because the double-gap split-ring metasurface structure is symmetric with respect to the direction of the polarization. Thus, the quasi-BIC mode plays a critical role in the THG signal enhancement. Figure 10(d) shows the enhancement factor of THG intensity and the quality factor as a function of the average splitting angle from the double-gap split-ring metasurface structure with the asymmetry parameter fixed as β=sin(5°). Here the enhancement factor is defined as the ratio of THG intensity in the patterned Si split-ring metasurface structure to that in the un-patterned Si film of the same thickness. When φ=65°, the THG signal of split-ring metasurface structure is 147 times of intensity stronger than that from the bare Si film. As the average splitting angle decreases from 65° to 10°, the enhancement factor increases from 147 to 4501. The THG intensity in the Si split-ring metasurface is affected by the amount of silicon materials involved in the nonlinear interactions and the electric field enhancement localized in the silicon nanostructure. As the average splitting angle decreases, though the quality factor decreases, the amount of silicon materials increases and the localized electric field inside the silicon nanostructure decreases slightly, resulting in a higher THG intensity. Figure 10(d) indicates that double-gap split-ring metasurface structures with small splitting angles produce large enhanced nonlinear optical THG signals.
5. Summary
In this work, we proposed a new approach to increase the quality factor of the quasi-BIC mode in an asymmetric double-gap silicon split-ring metasurface structure by using large split angles. We found the quality factor of the quasi-BIC mode increases exponentially with the increase of double split angles when the degree of asymmetry of double-gap split-rings is kept constant. We also conducted the multipole moment analysis of the local electromagnetic field and investigated the contributions of major electromagnetic multipole moments to the quality factor of the quasi-BIC mode. It was revealed that the double-gap split-ring metasurface stores more electrometric energy locally and the rate of radiation energy loss stays constant when the two splitting angles increase simultaneously, giving rise to higher quality factors for the double-gap split-ring metasurface with large split angles. Finally, the enhancement of quasi-BIC mode for the third harmonic generation was investigated in reference with the THG generated in a bare Si film of the same thickness. The large angle double-gap split-ring metasurface can be easily fabricated with less demanding fabrication accuracy.
Funding
Yiwu Research Institute of Fudan University Research Fund; Yanchang Petroleum-Fudan University Research Fund.
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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