High Q Resonant Sb2S3-Lithium Niobate Metasurface for Active Nanophotonics

Phase change materials (PCMs) are attracting more and more attentions as enabling materials for tunable nanophotonics. They can be processed into functional photonic devices through customized laser writing, providing great flexibility for fabrication and reconfiguration. Lithium Niobate (LN) has excellent nonlinear and electro-optical properties, but is difficult to process, which limits its application in nanophotonic devices. In this paper, we combine the emerging low-loss phase change material Sb2S3 with LN and propose a new type of high Q resonant metasurface. Simulation results show that the Sb2S3-LN metasurface has extremely narrow linewidth of 0.096 nm and high quality (Q) factor of 15,964. With LN as the waveguide layer, strong nonlinear properties are observed in the hybrid metasurface, which can be employed for optical switches and isolators. By adding a pair of Au electrodes on both sides of the LN, we can realize dynamic electro-optical control of the resonant metasurface. The ultra-low loss of Sb2S3, and its combination with LN, makes it possible to realize a new family of high Q resonant metasurfaces for actively tunable nanophotonic devices with widespread applications including optical switching, light modulation, dynamic beam steering, optical phased array and so on.

In this paper, we combine phase change material Sb 2 S 3 with LN for the first time and propose a type of resonant Sb 2 S 3 -LN metasurface, where a thin Sb 2 S 3 layer locates on top of a LN film and works as a subwavelength refractive index grating. Such a refractive index grating is comprised of periodical distributions of amorphous and crystalline Sb 2 S 3 , which can be "written", "erased" or "rewritten" with a customized writing beam (laser or ion). Simulation results show that the resonant Sb 2 S 3 -LN metasurface has extremely narrow linewidth and high Q factors. The optical spectra can be continuous tuning by not only the duty cycle of the grating, but also the crystallization fraction of the switched Sb 2 S 3 . Combining with the nonlinear and electro-optical properties of LN, the hybrid metasurface provides unprecedented possibility of active nanophotonics such as nonlinear propagation and electro-optical control.

Results and Discussion
With the ultra-low optical absorption and relatively high refractive index, phase change material Sb 2 S 3 provides a promising choice for high Q resonant nanophotonics. As is shown in Figure 1, the resonant metasurface is composed of a thin film Sb 2 S 3 grating, a LN waveguide layer and a SiO 2 substrate. After being deposited on the LN waveguide layer, a customized laser pulses or ion beam can be used to write, erase, and rewrite a functional pattern into the phase-change films [36,61]. The Sb 2 S 3 can be transformed from amorphous state to crystalline state and vice versa at specific temperature [40]. After part of a_Sb 2 S 3 is converted to c_Sb 2 S 3 , the low refractive index a_Sb 2 S 3 and high refractive index c_Sb 2 S 3 form a periodical Sb 2 S 3 subwavelength grating, which can effectively scatter free-space incident light and achieve guided mode resonances [62].The flexibility of design enables us to realize various high-Q resonant nanophotonic devices with Sb 2 S 3 .

a-Sb2S3 c-Sb2S3
LiNbO3 Figure 1. Schematic of a guided mode resonant grating, which consists of a grating layer composed of c_Sb 2 S 3 and a_Sb 2 S 3 , a LN waveguide layer and a SiO 2 substrate of semi-infinite thickness.
The numerical simulations are implemented in a fully three-dimensional finite element technology (in COMSOL Multiphysics). Since our structure is assumed to be "infinitely extending" in the y direction, a two-dimensional model is used for simulations (x-z plane). We use Floquet periodic boundary conditions in the x-direction, and port boundary conditions at the top and bottom of the model along the z-direction. In the simulation, silica (SiO 2 ) can be regarded as a lossless medium in the near infrared, with a refractive index of n SiO 2 = 1.45. The complex refractive indices of c_Sb 2 S 3 n c and a_Sb 2 S 3 n a are taken from experimental measurement [40], with a negligible loss at the near infrared (see the Supplementary Information Figure S1). For example, the complex refractive indices of c_Sb 2 S 3 and a_Sb 2 S 3 at the wavelength of 1550 nm are n c = 3.308 + 0i and n c = 2.712 + 0i, respectively. For a z-cut LN, we have refractive index of n o = 2.286 and n e = 2.203 [63].
The thickness of the Sb 2 S 3 and LN are T g = 40 nm and T wg = 260 nm, respectively. We set the grating period P = 800 nm and duty cycle f = 0.5, and Figure 2a gives the transmission and reflection spectra of the resonant Sb 2 S 3 -LN metasurface. For a transverse electric (TE) mode with its electric field polarized in the y-direction impinges on the metasurface at normal incidence, a sharp guided mode resonance is excited at the telecom wavelength and the reflectivity reaches nearly 100% at the resonance wavelength of 1553.00 nm. As shown in the Figure 2b, the electric field is mainly distributed in the LN waveguide layer, and the electric field component E y has been enhanced by more than 12 times at the resonance wavelength. Besides, one can also deposit a Sb 2 S 3 layer on a waveguide layer such as silicon (Si), silicon nitride (SiN) or others to achieve high Q resonances. We studied the optical spectra of a guided mode resonant grating structure with Sb 2 S 3 on Si. Similar resonances can be observed and the electric field component E y has been enhanced by more than 15 times and the Q factor reaches 744 (see the Supplementary Information Figure S2). The flexibility of design enables us to realize various high-Q resonant nanophotonic devices with Sb 2 S 3 .
Benefiting from the ability of continuous tuning of phase change materials, we can achieve flexible control of resonant wavelength by changing the geometric parameters of the metasurface. We first change the duty cycle f of the grating and obtain the reflection spectra corresponding to different duty cycles. As shown in Figure 3a, when the duty cycle reduces from f = 0.5 to f = 0.1, the resonance wavelength shifts from 1553.00 nm to 1538.26 nm, and nearly 100% reflection is achieved. At the same time, the spectral linewidth (full width at half maximum, FWHM) decreases from 4.36 nm to 0.430 nm. Herein, we give the basic relationship between the resonance mode Q factor and FWHM: where λ r denotes the resonant wavelength. Thus, the corresponding Q factor increases from 356 to 3577, with the maximal electric field enhancement increases from 12 to 41 (see the Supplementary Information Figure S3a). Then, we fix the duty cycle f = 0.5, and study the reflection spectra corresponding to different crystalline fractions η of Sb 2 S 3 . Here, the relationship between the effective dielectric constant of the Sb 2 S 3 and the crystalline fraction η is given by the Lorenz-Lorentz relationship [31]: where ε c_Sb 2 S 3 (λ) and ε a_Sb 2 S 3 (λ) are the wavelength-dependent permittivity of crystalline and amorphous Sb 2 S 3 , respectively.
And ε e f f (λ) is the effective dielectric constant of the hybridization Sb 2 S 3 . As shown in Figure 3b, when the crystalline fraction reduces from η = 1 to η = 0.2, the resonance wavelength shifts from 1553.00 nm to 1532.56 nm, maintaining nearly 100% peak reflection. At the same time, the spectral linewidth decreases from 4.36 nm to 0.096 nm, and the Q factor increases from 356 to 15,964, with the maximal electric field enhancement increase from 12 to 90 (see the Supplementary Information Figure S3b). The increase of Q factors is attributed to the reduction of scattering, i.e., coupling with the incident light with the decrease of refractive index contrast in the Sb 2 S 3 grating. These high Q resonances are possible as both Sb 2 S 3 and LN show very low losses at the telecom wavelength, which is hardly achievable for traditional phase change materials such as GST or VO 2 . Figure 3. The reflection spectra of the Sb 2 S 3 -LN metasurface with different duty cycle f (with the crystallization fraction η fixed on 1) and different crystallization fraction η (with the duty cycle f fixed on 0.5) of the Sb 2 S 3 subwavelength grating. (a) As the duty cycle f decreases from 0.5 to 0.1, the peak of the reflection spectrum shifts to the shorter wavelength, and the FWHM of the structure decreases. (b) As the crystallization fraction η decreases from 1 to 0.2, the peak of the reflection spectrum shifts to the shorter wavelength, and the FWHM of the structure decreases.

Nonlinear Optics with the Sb 2 S 3 -LN Resonant Metasurface
Since the field enhancement of the structure is very considerable, we now consider the nonlinear properties of the resonant Sb 2 S 3 -LN metasurface to explore the strong lightmatter interaction. The nonlinear Kerr effect describes the change in dielectric constant of the medium caused by the interaction of the external field and the third-order nonlinear susceptibility, and can be expressed as [64]: where χ (3) denotes the third-order nonlinear susceptibilities and |E r | denotes the strength of local electric field. For LN, the third-order susceptibility χ (3) can be obtained from: where n 2 = 1.44 × 10 −15 m 2 ⁄W is the third-order nonlinear coefficient of LN [65], Z 0 = 377 Ω is the vacuum impedance, thus the third-order nonlinear susceptibility of LN is χ (3) = 2.66 × 10 −17 m 2 /V 2 . And since the third-order nonlinear susceptibility of Sb 2 S 3 (∼ 10 −19 m 2 /V 2 ) is much smaller than that of LN, we do not take it into account in our simulation [66]. Due to the high nonlinear coefficient of LN and the strong electric field enhancement inside the LN waveguide layer, the nonlinear effect can be easily observed in the resonant metasurface. In order to obtain obvious nonlinear effect results under lower modulation power, we use the ultra-high Q factor structure parameters, with f = 0.5, η = 0.2, and other parameters are consistent with those in Figure 1. The enhancement of fields is shown in inset of Figure 4a. The reflection spectrum of the Sb 2 S 3 -LN metasurface is given in the Figure 4a with an incident intensity of 5.000 MW/m 2 , and the nonlinear spectrum is red-shifted from the resonance wavelength of 1532.564 nm to 1532.628 nm due to the decrease of the overall equivalent permittivity of the LN (the third-order susceptibility of LN is positive number). As an application of the nonlinear optical response, we can design a nonlinear optical isolator considering the asymmetry of the structure in the light propagation direction. Figure 4b gives the nonlinear non-reciprocal curves for forward and backward incident light at 1532.654 nm. With the intensity of incident light increases, the forward and backward incident light have different transmission spectra: the transmissivity of backward incident light reaches to 0 at 4.375 MW/m 2 , while that of forward is 0.67. The non-reciprocal can be adjusted through varying the parameters of the Sb 2 S 3 grating and can be obtained at the desired wavelength [64]. Besides, the proposed resonant metasurface may also be explored for other nonlinear optical applications such as second harmonic generation [67,68].  Previous experiments [40] have shown that c_Sb 2 S 3 and a_Sb 2 S 3 can exist stably under the light intensity of thousands of MW/m 2 , and in our work, the maximum intensity of the near-infrared light we use is under 12 MW/m 2 . Meanwhile, only a small part of the near-infrared light used in the study of nonlinearity and non-reciprocity will be absorbed by Sb 2 S 3 . Thus, the Sb 2 S 3 in our structure can tolerate the incident intensity mentioned above and achieve the expected nonlinear and non-reciprocal effects.

Electro-Optical Tunability of the Sb 2 S 3 -LN Resonant Metasurface
Now, we turn to investigate the electro-optical properties of the resonant Sb 2 S 3 -LN metasurface. As shown in the Figure 5a, we now add a pair of Au electrodes at the side of the Sb 2 S 3 grating (electrical isolation between the electrodes and phase change material can be realized with an insulator layer when necessary). The length along the y direction of the Sb 2 S 3 grating is set as L = 10 µm, which is much larger than that of the resonant wavelength (it is regard as infinite in the y direction in simulations for simplicity). To demonstrate the super reconfiguration ability of the proposed structure, we first tune the resonant wavelength as an example of rewriting the Sb 2 S 3 grating by varying the period from P = 800 nm to P = 650 nm, with f = 0.5, η = 0.2 (the high Q parameters), and other parameters are same with that of in Figure 1. As we rewrite the period to be P = 650 nm, the resonance wavelength moves from 1532.564 nm to 1293.682 nm, as shown in Figure 5b. We next add gate voltage from the electrode in x-direction of the LN for dynamic electro-optical tuning, and thus the change of n o along with the voltage can be described that [69]: where r 22 = 6.8 pm/V is the electro-optic coefficient of LN and E 0y is the electric field applied to the LN layer (along with the Y axis of LN). As we add different gate voltages, n o will vary along with the gate voltage (see the Supplementary Information Figure S5), and thus we can tune the reflection spectra of the Sb 2 S 3 -LN metasurface with the electric signal. As shown in the Figure 5c, with the gate voltage increases from 0 V to 200 V, the resonant wavelength shifts from 1293.682 nm to 1293.358 nm, while maintaining 100% reflection. Such a shift is 2.79 times larger than the FWHM of the resonance and thus enough to induce vivid change of the optical spectra. It should be mentioned that for a larger electro-optic coefficient of r 33 = 33 pm/V, the gate voltage will be much lower for the same effects.

Conclusions
In summary, we have demonstrated a type of resonant Sb 2 S 3 -LN metasurface and shown its promising applications in active nanophotonics. The proposed structure includes a subwavelength grating layer composed of low-loss phase change material Sb 2 S 3 and a waveguide layer composed of LN. We can deposit the phase change material Sb 2 S 3 on LN, and then use customized laser pulses to realize the required structure [36] (e.g., the grating structure), which overcomes the difficulty of processing of LN in nanoscale. Numerical simulations indicate that the resonant metasurface shows considerable nonlinear and electro-optic effects. In addition, the optical spectra can be continuously adjusted with lithography-free method, as the different duty cycle and the crystalline fraction can be achieved by the laser or ion beam. Other methods, such as electrothermal switching [15,35], could also be applied to induce the crystallization and amorphization of phase change materials.The optical switching of chalcogenide phase change materials can be realized at the nanosecond scale and previous work has demonstrated tuning of phase change optical devices at the speed of tens of MHz [17]. For the practical application of our proposed device, the patterns in the phase change material will be fixed unless one wants to rewrite the structure to change its working wavelength. And the dynamic electro-optical modulation or nonlinear effects can be realized by the LN, whose intrinsic response can be as fast as ∼ f s and previous work has demonstrated LN modulators up to 100 GHz [50]. Represented by Sb 2 S 3 , other ultra-low loss of PCMs in the near infrared, such as Sb 2 Se 3 [40] or Ge 2 Sb 2 Se 4 Te 1 (GSST) [70], can also be applied to combining with LN, makes it possible to realize a new family of high Q resonant metasurfaces for active nanophotonic devices with widespread applications including optical switches, light modulation, dynamic beam steering, optical phased array, optical artificial network and so on.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.

Conflicts of Interest:
The authors declare no conflict of interest.