1. INTRODUCTION

Recently, metamaterials have shown a plenty of intriguing phenomena absent in natural materials that can be applied in fascinating applications such as invisibility cloaking [1,2], negative refractive index [3,4], perfect absorbers [5,6], superlenses [7–9], and anomalous wavefront deflection [10]. Specifically, the metamaterials consist of a periodic structure of “meta-atoms,” which is a metallic resonator made of a metal structure at the micrometer scale. Its optical properties depend on not only the unit cells but also the coupling between the unit cells, which is controlled by the designed shape, size, and arrangement of the structures [11–15]. Plasmonic split-ring resonators (SRRs) and closed-ring resonators (CRRs) are two fundamental functional units of metamaterials showing excellent optical properties within a wide spectrum range from microwave to visible light that can interact with the electric field and magnetic field of electromagnetic waves [3]. In the terahertz (THz) regime, they act as important supplements to the limited natural THz materials [16,17], realizing electromagnetic coupling in the resonators. The electromagnetic coupling effect of metamaterials has triggered many appealing phenomena including Fano resonances [18–23], plasmon-induced transparency (PIT) [24,25], and high-quality factor resonances [26]. Notably, PIT is an imitation of quantum phenomenon in metamaterial systems, with the merit of being not limited to the quantum mechanical system. Within the PIT phenomenon, a pair of different modes destructively interfere with each other, giving rise to a transmission window. The PIT effect has a fascinating property of slow light that can be designed for slow light applications [27,28].

Transmission of a metadevice can be actively modulated by several approaches, including the mechanical [29], electrical [30–32], thermal [33–38], and optical methods [39–50]. Particularly, for the optical method, the metamaterials are often hybridized with dielectric materials [51], such as semiconductors [27,30,42,44–46,49,52–58], superconductors [59–61] and graphene [62–64], and phase-change materials [65], the conductivity of which can be reversibly controlled by varying the incident optical pump. These methods have successfully realized the active modulation of strength and group delay. Thanks to the excellent properties of the photoexcited carriers and the mature technologies of fabricating microelectronic and photoelectronic devices, the semiconductors are of great importance in alternative dielectric materials. As an indirect semiconductor, germanium (Ge) possesses great photoelectronic properties such as a large carrier mobility, a high carrier concentration, and an indirect energy gap of 0.66 eV [66]. It is possible to lower the indirect bandgap of Ge via the approaches of doping [67], strain engineering [68], and hybridization with other materials [69,70]. Additionally, as an optical gain material by outer stimuli, Ge is in favor of forming a population inversion and promoting the inter-band radiative recombination. Moreover, the ultrafast relaxation of photoexcited carriers of Ge has been investigated by using ultrafast transient absorption spectroscopy [66] and ultra-broadband mid-infrared spectroscopy [71]. It is found that electron intervalley scattering in Ge is at the sub-picosecond time scale [72]. Recently, Ge film was first hybridized with metamaterials to realize an ultrafast photoswitching behavior in planar metadevices with a sub-picosecond decay constant [39]. However, modulation of the PIT phenomenon is limited to only one incident polarization, which hinders the development of anisotropic metadevices. It is important to stress that the anisotropy of photonic devices is widely researched as well as the widespread applications of anisotropic devices in sensing, communication, and molecular spectroscopy [73–77]. Thus, a key issue in this context that has yet to be investigated is the intrinsic linear dichroism in THz regime pertaining to the intrinsic nature of materials.

In this work, an active ultrafast, anisotropic, and all-optical switching of the PIT effect is numerically and experimentally established in a Ge-hybridized metadevice by means of varying the exterior pump power. In this metadevice, a golden structural array of SRRs and CRRs is fabricated on the noncrystalline Ge film, which is sputtered on a 2 mm thick quartz substrate. The occurrence and disappearance of the PIT effect are attributed to the change of photoinduced conductivity in Ge film, which shunts the capacitive gaps of the SRRs and thus affects the THz transmission of the metamaterial device. Additionally, the polarization dependence of the PIT effect is ascribed to the structure anisotropy of the metamaterial in a pair of orthometric directions. As a result, PIT phenomena are observed in the transmission windows at 0.78 THz and 1.07 THz for vertical and horizontal polarizations, respectively. By altering the exterior optical pump, the PIT effect was almost completely switched off, acquiring an ultrahigh modulation depth up to 99.06%. Benefiting from the defect states in noncrystalline Ge that act as the trap-assisted recombination sites in the forbidden band, an ultrashort period time was measured within 3 ps, which is shorter than 17 ps in previous work [39]. Furthermore, the decay constant extracted from the single exponential fitting is $\sim 700\mathrm{fs}$.

2. RESULTS AND DISCUSSION

A. Sample Characterization

The metamaterial device is depicted in Fig. 1. Pumped by a series of laser pulses with a wavelength of 800 nm, the metamaterial device realizes an active anisotropic modulation of THz transmission, which is illustrated in Fig. 1(a). A metamaterial unit cell with real proportion is characterized in Fig. 1(b), which comprises a CRR surrounded by two pairs of SRRs. A bar located in the middle of the CRR is used to split the CRR into two parts. Notably, these two pairs of SRRs are different in size. Moreover, their gaps are orthogonal to each other in direction, and they are designed for the polarization dependence in the THz modulation. The centers of adjacent units are 140 μm and 110 μm away from each other along the $x$ axis and $y$ axis, respectively. A 125 nm thick Ge film was sputtered on the quartz substrate. The well-designed metal structure made of 240 nm thick gold (Au) and 10 nm thick titanium (Ti) was evaporated on the Ge layer using a standard photolithography technique and e-beam evaporation, with its optical microscope image shown in Fig. 1(c). The inset image characterized the surface morphology of a meta-atom. It shows a metal structure with a height of 250 nm.

 

Fig. 1. (a) Schematic illustration of the ultrafast THz polarization-dependent metamaterial device configuration for OPTP spectral measurement. (b) Schematic of the metamaterial unit cell. The geometric parameters are listed as follows: $L_x=120\mathrm{\mu m}$, $L_y=50\mathrm{\mu m}$, $l_{xx}=26\mathrm{\mu m}$, $l_{xy}=25\mathrm{\mu m}$, $l_{yx}=50\mathrm{\mu m}$, $l_{yy}=15\mathrm{\mu m}$, $w=5\mathrm{\mu m}$, $g=5\mathrm{\mu m}$, $d=5\mathrm{\mu m}$, $h=200\mathrm{nm}$. (c) Optical microscopy image of the metadevice. The inset shows the surface morphology measured by the atomic force microscope (AFM).

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B. Experimental Section

Fabrication of the Ge-based Metadevice: First, a 2 mm thick quartz substrate is cleaned by a standard semiconductor cleaning process. After successively being cleaned by No. 1 liquid, No. 2 liquid, and deionized water, the quartz substrate is rid of organic matter, inorganic matter, and particles. Second, Ge film is uniformly sputtered on the cleaned quartz substrate with a thickness of 125 nm. Third, photolithography is employed for the graphics transfer. The photoresist is spin-coated on the quartz substrate and processed by soft bake. After that, it is exposed to laser, developed in developing liquid, and processed by oxygen gas in sequence, in order to wipe off the residual photoresist. Fourth, Ti (employed for the chromium adhesion layer) and Au are sputtered onto the treated substrate in turn for a thickness of 10 nm and 200 nm. Finally, through lift-off technology, the substrate is rid of photoresist and unwanted metal and is left with the designed metal graphics.

Experimental Measurement Section: The transmission spectra of the metaphotonic device are analyzed by the optical-pump THz-probe (OPTP) terahertz time-domain spectrometer system (TTT-02-OPTP) from TuoTuo Technology. 800 nm femtosecond laser pulses ($\sim 100\mathrm{fs}$ duration of full width at half-maximum, 1 kHz repetition rate) are generated from a Ti:sapphire regenerative amplifier. A part of the laser pulses are employed as the external optical pumping. The THz probe pulses are generated from nonlinear crystals (ZnTe) stimulated by the other part of the laser pulses, arriving several picoseconds later than the laser pulses at the metamaterial device. The THz spot ($\sim 2.2\mathrm{mm}$ in diameter) on the device is completely covered by the laser spot ($\sim 5\mathrm{mm}$ in diameter). The THz beam irradiates perpendicularly to the surface of metamaterial device with the polarizations along the $x$ axis and $y$ axis, respectively, as illustrated in Fig. 1(b). The THz transmission in the time domain is recorded from the transient transmission amplitude with a certain temporal interval (0–17 ps) and subsequently transformed in the frequency domain using a standard Fourier transform analysis. The transmission spectrum in the frequency domain is normalized by a reference signal passing through an identical bare quartz substrate. All the measurements are carried out at room temperature and in a dry atmosphere to avoid water vapor absorption of the THz beam.

C. Simulation and Experiment Results

The PIT phenomenon refers to the quantum destructive interference between two pathways in atomic systems, leading to a narrow transmission window. The underlying physics is intuitively explained as follows. The electromagnetic field of the THz beam excites a weakly coupled fundamental odd eigenmode in SRRs because of their asymmetric structure. In addition, besides the SRRs, a strong even eigenmode of coupled electric dipole oscillation along the direction of THz polarization is excited in CRRs. These two oscillation modes couple back and forth between the SRRs and CRRs, which results in the PIT effect. A transmission dip can be observed in the CRRs and SRRs at different frequencies by numerical calculations as depicted in Fig. 7 (see Appendix A). The near-field electromagnetic coupling promotes the coupling of oscillation modes in the CRRs and SRRs.

To improve the sensitivity of this device, we use the Ge film as photoactive material, whose short gap (5 μm) is designed to lower the threshold for switching off the near-field coupling of inductive-capacitive (LC) resonance and dipole resonance. The incident optical pump photoexcites the Ge film and enhances its photoconductivity. As a result, the capacitance at the gaps of the CRRs and SRRs is reduced, which weakens the coupling of the oscillation modes between the CRRs and SRRs and thus decreases the resonance amplitude at the PIT window. It can be found from Fig. 1(b) that this metadevice consists of two kinds of symmetric structures along the $x$ axis and $y$ axis, respectively.

The experimentally measured and numerically calculated transmission spectra in the frequency domain are shown in Fig. 2, accounting for different optical pump fluences (from 0 to $1000\mathrm{\mu J}/{\mathrm{cm}}^2$) and conductivity of Ge (from 0 to 1600 S/m). The strong resonance features shown in Figs. 2(a) and 2(b) represent the transmission properties of planar metamaterial structure without an exterior pump in THz $x$ polarization and $y$ polarization, respectively. Particularly, the strong resonance leads to typical transmission peaks located at 0.79 THz and 1.04 THz for THz $x$ polarization and $y$ polarization, respectively. It is obvious that the transparency windows differ from each other in frequency by 0.25 THz, which exhibits a typical polarization-dependent property. After the optical pump beam photoexcites the hybrid metamaterial sample, the reduction of the transmission amplitude of the PIT window is clearly observed. Under the illumination of the THz beam in $x$ polarization, and with the incident pump fluence increasing from 0 to $1000\mathrm{\mu J}/{\mathrm{cm}}^2$ (incident power from 0 to $1000\mathrm{mW}/{\mathrm{cm}}^2$), the transmission amplitude at the PIT window continuously decreased and finally switched off. The relative transmission, denoted as the amplitude difference between the transmission peak and the first transmission dip, decreased from 65.75% ($\mathrm{d}{T}_M$) without an exterior pump to 0.62% ($\mathrm{d}{T}_m$) at $1000\mathrm{\mu J}/{\mathrm{cm}}^2$, with the calculated modulation depth of 99.06%. Here the normalized modulation depth is defined as $(\mathrm{d}{T}_M-\mathrm{d}{T}_m)/\mathrm{d}{T}_M$. The relative modulation depth is shown in Fig. 8 (see Appendix A). With the pump power increasing, the relative modulation depth gradually decreases from 1 to 0.94% at THz $x$ polarization and even lower than 0 at THz $y$ polarization. It shows a maximum relative modulation depth as high as 99.06% and exceeds 100%. For the THz $y$ polarization, the relative transmission decreases from 61.63% without an exterior pump to 1.34% at $500\mathrm{\mu J}/{\mathrm{cm}}^2$, associated with the normalized modulation depth of 97.83%. The corresponding simulated results for THz $x$ polarization and $y$ polarization are depicted in Figs. 2(c) and 2(d), respectively. The simulations were performed using the finite-difference time-domain (FDTD) method, with the conductivity of golden metamaterials fixed at $3\times {10}^7\mathrm{S}/\mathrm{m}$. Considering that pump fluence changes from 0 to $1000\mathrm{\mu J}/{\mathrm{cm}}^2$, the conductivity of the semiconductor coated on the metamaterials was set from 0 to 1600 S/m. Importantly, the simulated modulation depths are 97.50% and 98.82% for THz $x$ polarization and $y$ polarization, respectively. Obviously, the experimental results are in great agreement with the simulations. The delicate differences between them may be caused by the mismatching between the fabricated device and the designed structure.

 

Fig. 2. Experimentally measured spectral dispersion of transmission spectra for the polarization-related metadevice in THz (a) $x$-polarized and (b) $y$-polarized pumps, considering a series of selected fluences. The corresponding numerically simulated transmission spectra for THz (c) $x$-polarized and (d) $y$-polarized light, with the labeled conductivity of the Ge film representing the pump level.

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Figure 3 shows the electrical field confined in the metamaterial device at 0.79 THz in THz $x$ polarization. It is shown in Fig. 3(a) that without an exterior pump, the amplitude of the electric field in the gaps of SRRs is stronger than in other areas, which is consistent with the PIT effect. With the increment of the exterior pump fluence, the conductivities in the gaps of the SRRs and the gaps between the SRRs and CRRs continually increase to 400 S/m and 800 S/m. The increase of conductivity destroyed the coupling between the odd eigenmode and the even eigenmode, reducing the intensity of the electric field confined in the gaps as shown in Figs. 3(b) and 3(c). As depicted in Fig. 3(d), when the conductivity of the Ge film reached 1600 S/m, corresponding to the external pump fluence of $1000\mathrm{\mu J}/{\mathrm{cm}}^2$, the confined electric field and PIT phenomenon almost disappear. A similar feature is found in the confined electrical field in THz $y$ polarization, with the results illustrated in Fig. 9 (see Appendix A).

 

Fig. 3. Numerically calculated $z$-component field distributions in the transverse plane of a metamaterial unit at 0.79 THz, in the case of THz $x$ polarization, accounting for Ge conductivity varying from 0 to 1600 S/m.

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The modulation of the dispersion properties in metadevices usually occurs when the PIT phenomenon is experimentally observed. When the THz wave packets pass through the device, the modification of the dispersion properties leads to the slow light effect, accompanied by the change of group velocity. The active modulation of slow light through a device is beneficial to both fundamental scientific research and the implementation of optical techniques. The group delay spectrum is described as a time delay of a THz wave packet passing through the sample, in comparison to that through the air. It is defined as $t_g=-\mathrm{d}({\mathit{\Phi }}_{\mathrm{sam}}-{\mathit{\Phi }}_{\mathrm{ref}})/\mathrm{d}\omega$, where $\omega$ is the angular frequency ($\omega =2\pi f$), and ${\mathit{\Phi }}_{\mathrm{sam}}$ and ${\mathit{\Phi }}_{\mathrm{ref}}$ are transmission phases in the cases of the THz wave packet passing through the sample and the sapphire reference, respectively. The phase spectra were retrieved from the time-domain-spectroscopy (TDS) measurement. The active group delay modulations are depicted in Fig. 4. In this experiment, the group delay modulation is considered to be caused by the transmission resonance of the metadevice. The measured group delays for $x$ polarization and $y$ polarization are shown in Figs. 4(a) and 4(b), with the pump fluence changing from 0 to $1000\mathrm{\mu J}/{\mathrm{cm}}^2$. When the metadevice was illuminated by a THz beam with $x$ polarization, as shown in Fig. 4(a), a pair of maximum negative group delays was located at around 0.65 THz and 0.93 THz. Usually the slow light region is located between these two frequencies, where the group delay is positive. The maximum group delay was measured to be 1.49 ps at 0.78 THz. Similarly, as shown in Fig. 4(b), when the metadevice was illuminated by a THz beam with $y$ polarization, the maximum negative group delays were found at around 0.88 THz and 1.26 THz. Alternatively, the maximum positive group delay was measured to be 0.92 ps at 0.98 THz. On the other hand, the simulated group delay spectra for THz $x$ polarization and $y$ polarization are shown in Figs. 4(c) and 4(d), with the conductivity of Ge varying from 0 to 1600 S/m. The simulated group delay was calculated from the transmission FDTD simulation system. Despite that there is a slight difference between the numerically simulated group delay spectra and the experimentally measured results, the overall shape and the location of the simulated group delay peaks and dips are consistent with the experimental results. We attribute these minor differences to the mismatch in dimensions of the fabricated device and the designed structure.

 

Fig. 4. Experimentally measured group delay spectra of the polarization-related metadevice for THz (a) $x$ polarization and (b) $y$ polarization, in the case of a series of selected fluences. The corresponding numerical results for (c) $x$ polarization and (d) $y$ polarization, with the conductivity of Ge film representing the pump level.

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Figure 5 depicts the temporal evolution of the THz transmission amplitude spectra of the metamaterial device pumped by a fluence of $1000\mathrm{\mu J}/{\mathrm{cm}}^2$. The time delay shown on the abscissa axis refers to a relative time delay between the arrival of the pump beam and the THz probe illuminating at the same position. The time delay can be controlled by moving the translational time delay stage with a certain interval. At a specific time delay, the THz probe pulse passing through the metaphotonic device is converted into the frequency domain using a standard Fourier transform, from which the transmission-frequency graph can be obtained. Figures 5(a) and 5(b) show the transmission amplitude of the metamaterial device for THz $x$ polarization and $y$ polarization, respectively. The red region and blue region correspond to the relatively high and low transmission rate, respectively. When the THz probe pulse arrived earlier than the pump pulse, it showed a typical PIT effect in accordance with the black curves shown in Figs. 2(a) and 2(b). When the time delay increased, the dark blue areas became lighter and connected, which means that the PIT effect was switched off. It took around 3 ps and 3.5 ps for the metadevice to switch off the PIT effect and recover to its original state for THz $x$ polarization and $y$ polarization, respectively. The difference of the recovery time in Figs. 5(a) and 5(b) stems from the anisotropy of the metadevice. Because of the impingement of the pump pulse on the Ge film, a large number of carriers were excited to the conduction band and short-circuited the gaps in the SRRs, which weakened the oscillation mode coupling between the SRRs and CRRs. As time went by, plentiful carriers transited to the valence band due to the radiation recombination and non-radiation recombination. The oscillation modes began to couple back and forth between the SRRs and CRRs again, which resulted in the resurgence of the PIT effect. Similarly, the temporal evolution of the group delay is depicted in Fig. 10 (see Appendix A).

 

Fig. 5. Color map showing the transient evolution of THz transmission amplitude against frequency and time delay pumped with fluence of $1000\mathrm{\mu J}/{\mathrm{cm}}^2$ over an entire on-off photoswitching cycle.

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The negative differential transmission ($-\mathrm{\Delta }T/T_0$) of the Ge film coated on quartz substrate as a function of a series of selected pump fluences is depicted in Fig. 6. Here $\mathrm{\Delta }T=T-T_0$ is the change of transmission, and $T$ and $T_0$ are the transmission of the THz wave through the sample with and without the pump, respectively. A stronger optical pump pulse enhanced the photoconductive free carriers’ density, resulting in the increase of relative change in transmission. The measured maximal amplitude of transmission increases from 14.6% at $500\mathrm{\mu J}/{\mathrm{cm}}^2(\text{power}\text{of}500\mathrm{mW}/{\mathrm{cm}}^2)$ to 35.4% at $1500\mathrm{\mu J}/{\mathrm{cm}}^2(\text{power\hspace{0.17em}}\text{\hspace{0.17em}of}1500\mathrm{mW}/{\mathrm{cm}}^2)$. The full recovery time was measured to be 3 ps. The relative change in Fig. 6 manifests a single exponential decay. Therefore, we use the convolution of a single exponential function and the instrument response function to fit the experimentally measured relative change of transmission. The formula is given as follows [39]:

 

Fig. 6. Negative differential transmission of 125 nm thick Ge film coated on quartz substrate pumped for a series of selected powers (as labeled). The experimental measurement is fitted using a single exponential function. These plots are vertically arranged for distinct comparison.

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Table 1. Exponential Decay Time of the Relative Change of Fitted THz Transmission in Quartz Substrate Coated by Ge, Pumped by a Series of Exterior Lasers^a

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3. CONCLUSION

In conclusion, we have presented a profound experimental and numerical analysis of the ultrafast, anisotropic, and all-optical modulation of the PIT effect in a Ge-hybridized metadevice. These devices consist of a specific arrangement of SRRs and CRRs. It is found that PIT phenomena are observed in transmission windows at different frequencies for the vertical and horizontal THz polarizations, respectively. With the increase of the exterior pump power, the PIT effects at different frequencies were both almost completely switched off, resulting in an ultrahigh modulation depth up to 99.06%. Additionally, it is feasible to conduct the observable modulation of group delay by varying the exterior pump, which exhibits great potential for active ultrafast slow light devices. Last but not least, the ultrashort recovery time was experimentally measured at the picosecond time scale, with the decay constant extracted at the sub-picosecond time scale. This work aims to pave the way for ultrafast and anisotropic all-optical switching platforms.

APPENDIX A

The transmission spectra of individual CRRs and SRRs are studied by numerical calculation. The near-field coupling of the CRRs and SRRs gives rise to a sharp transmission window at the frequency between transmission dips of the CRRs and SRRs shown in Fig. 7. The relative modulation depth is shown in Fig. 8

 

Fig. 7. Transmission spectra of SRR resonators and CRR resonators for (a) $x$ polarization and (b) $y$ polarization, with conductivity of 0 S/m.

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Fig. 8. Relative modulation depth as a function of pump power.

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Figure 9 shows the electrical field confined in the metamaterial device under the illumination of a THz beam with $y$ polarization. Without pumping, the amplitude of the electric field in the gap of the SRRs is stronger than in other areas, which is in accordance with the PIT phenomenon. When varying the pump fluence, the corresponding conductivities in the gaps of the SRRs and the gaps between the SRRs and CRRs are set to be 400 S/m and 800 S/m, respectively. The increase of conductivity destroys the coupling between the odd eigenmode and the even eigenmode, which weakens the intensity of the electric field confined in the gaps. When the conductivity of the Ge film reachs 1600 S/m, corresponding to the external pump fluence of $1000\mathrm{\mu J}/{\mathrm{cm}}^2$, the confined electric field and PIT phenomenon almost disappear.

 

Fig. 9. Numerically calculated $z$-component field distributions in the transverse plane of a unit of the metamaterial for the THz $y$ polarization, accounting for the conductivity of Ge varying from 0 to 1600 S/m.

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Figure 10 shows the temporal evolution of the THz transmission group delay spectra, pumped by $1000\mathrm{mW}/{\mathrm{cm}}^2$. It exhibits a similar trend with the THz transmission amplitude spectra depicted in Fig. 4.

 

Fig. 10. Contour map showing the transient evolution of THz group delay against frequency and time delay over an entire on-off photoswitching cycle, under a pump fluence of $1000\mathrm{\mu J}/{\mathrm{cm}}^2$.

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By fitting a single exponential function to the experimental measurement, the decay constants ${\tau }_1$ are shown in Table 1. When the pump power increases, ${\tau }_1$ manifests a delicate ascenscion from 785 to 868 fs.

Funding

National Natural Science Foundation of China (11802339, 11804387, 11805276, 11902358, 61801498, 61805282); Scientific Researches Foundation of National University of Defense Technology (ZK16-03-59, ZK18-01-03, ZK18-03-22, ZK18-03-36); Natural Science Foundation of Hunan Province (2016JJ1021); Open Director Fund of State Key Laboratory of Pulsed Power Laser Technology (SKL2018ZR05); Open Research Fund of Hunan Provincial Key Laboratory of High Energy Technology (GNJGJS03); Opening Foundation of State Key Laboratory of Laser Interaction with Matter (SKLLIM1702); Youth Talent Lifting Project (17-JCJQ-QT-004).

Acknowledgment

The authors are grateful to Prof. Lei Shi from Fudan University for providing the FDTD software.

Disclosures

The authors declare no conflicts of interest.

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