# Nonlinear Metasurface for Structured Light with Tunable Orbital Angular Momentum
## 2 Results
### Reconfigurable Beam with OAM
Therefore, these two structures can be used to realize the proposed nonlinear metasurface enabling the intensity-dependent OAM switching. The maximum refractive index change inside ChG is \(\Delta n=0.12\) and the maximum intensity inside the ChG blocks is 150 GW/cm\({}^{2}\), as found in the simulation results. The damage threshold of ChG with different compositions measured by the femtosecond laser has been studied by [PERSON] et al. and [PERSON] et al. at the near-infrared and mid-infrared wavelengths, respectively [39; 40]. Due to the short pulse duration (100 fs) and a low repetition rate (1 KHz), the damage threshold of ChGs is much larger than the peak intensity required for our reconfigurable metasurface. Moreover, it has been reported that if As\({}_{2}\)S\({}_{3}\) is properly doped with silver, the nonlinear coefficient of the silver-doped ChG film can be up to two orders of magnitude larger than the nonlinear coefficient of the undoped As\({}_{2}\)S\({}_{3}\) film [41]. In this case, the required peak intensity will decrease to approximately 1 GW/cm\({}^{2}\), making the proposed device more energy efficient. Besides energy efficiency, another advantage of the silver-doped ChG with larger nonlinear coefficient is that it may result in a much larger refractive index change \(\Delta n\). In our current design with the pure As\({}_{2}\)S\({}_{3}\), \(\Delta n\approx 0.1\). Realization of a 180\({}^{\circ}\) phase change with the current value of \(\Delta n\approx 0.1\) requires the resonances to be very sharp which places a stringent requirements on the fabrication precision to ensure the rapid phase change, which is beyond our ability right now. However, if a larger \(\Delta n\) can be introduced by the silver-doped ChG, the design may tolerate more fabrication imperfection. The deposition and patterning processes of the silver-doped ChG film will be studied in the future to experimentally realize the reconfigurable metasurface which produces output structured light with tunable topological charges. When the input intensity increased from 1.94 GW/cm\({}^{2}\) to 1.98 GW/cm\({}^{2}\), the phase of the light transmitted through the structure with the side-length \(l=760\) nm jumped by approximately 90\({}^{\circ}\), as shown in Figure 5e. The origin of this phase jump can be understood by looking at Figure 6 where the electric- and magnetic-field distributions in a unit cell for four selected input intensities are plotted. As shown in Figure 6a,b,e,f, the field distributions were very similar when the input intensity increased from 1 kW/cm\({}^{2}\) to 1.94 GW/cm\({}^{2}\) and they possess only a magnetic-resonance revealed as a vortex-like electric field distribution. When the input intensity increased, the resonances became closer to each other. In Figure 6c,d,g,h, the field distributions are very similar when the input intensity increases from 1.98 GW/cm\({}^{2}\) to 4 GW/cm\({}^{2}\) and both electric- and magnetic-resonances are present at the operation wavelength. As the light intensity increases, the electric-resonance shifts closer to the operation wavelength and as it overlaps with the magnetic resonance it leads to an abrupt phase jump by 90\({}^{\circ}\). Upon the change in the input intensity from 1 kW/cm\({}^{2}\) to 4 GW/cm\({}^{2}\), the phase changed by 180\({}^{\circ}\) due to the changes in the relative spectral position of the electric and magnetic resonances. Figure 7b,c, respectively. The dark center in Figure 7b and the spiral phase distribution in Figure 7c show that the OAM is carried by the transmitted beam. In this case, the refractive index of ChG is \(n_{ChG}=n_{0}=2.43\). To simulate the nonlinear metasurface, the refractive index of ChG is set as \(n_{ChG}=n_{0}+\Delta n=2.53\). Therefore, the phase acquired in quadrants II and IV of the metasurface changed by \(180^{\circ}\).