# Nonlinear Metasurface for Structured Light with Tunable Orbital Angular Momentum
## 2 Results
### Reconfigurable Beam with OAM  
In this section, we demonstrate that the third-order nonlinearity (Kerr effect) of ChG can be used to achieve the switching of the output beam OAM from positive to negative. The refractive index of the ChG \(n_{ChG}\) can be efficiently changed as a function of the input light intensity due to its large nonlinear Kerr response described by \(n_{ChG}=n_{0}+\Delta n=n_{0}+n_{2}I\). Here, \(n_{0}\) is the linear refractive index of the ChG, \(n_{2}=7.9\times 10^{-13}\) cm\({}^{2}\)/W is the nonlinear coefficient measured by our in-home Z-scan setup, and \(\Delta n\) is the refractive index change of the ChG corresponding the input beam intensity \(I\). Figure 5 shows the result of the nonlinear studies of ChG nano-blocks with different side-length. The input intensity was varied from \(1\) kW/cm\({}^{2}\), which is low enough to avoid significant refractive index change, to \(4\) GW/cm\({}^{2}\). As shown in Figure 5a,b, for \(l=700\) nm, around the wavelengths of electric and magnetic resonances indicated by the dashed lines, the phase change of the transmitted light is around \(180^{\circ}\). However, at these two wavelength, the transmittance is close to zero as the two resonances are spectrally separated. Therefore, this structure is not suitable to design a nonlinear  
Figure 4: **(a)** Fabrication process for ChG-based all dielectric metasurfaces involves the following steps: fabrication of a chromium window with the size of 150 \(\upmu\)m \(\times\) 150 \(\upmu\)m; deposition of an As\({}_{2}\)S\({}_{3}\) film; exposure of the As\({}_{2}\)S\({}_{3}\) using electron beam; development of the exposed sample. **(b)** Scanning electron microscopy image of the fabricated metasurface with four quadrants. **(c)** Intensity and **(d)** phase of simulation results of an HG beam transmitted through the metasurface. **(e)** Schematic of the Mach–Zehner interferometer used to characterize the fabricated metasurface. **(f–h)** Experimental results obtained with the fabricated metasurface. **(f)** Intensity distribution of the output OAM beam. **(g,h)** Interference of the output OAM beam and a reference Gaussian beam showing a spiral-shaped and fork-like intensity distributions (see text for details). metasurface. As explained above, with the increase of the side-length, the two resonances shift closer to each other, and as they overlap, nearly 100% transmission can be achieved with the phase change covering the entire 360\({}^{\circ}\). For the side-length 760 nm, the two resonances are both located around the wavelength 1550 nm. As seen in Figure 5, the maximum 180\({}^{\circ}\) phase change is achieved at the wavelength of 1572 nm. This wavelength is indicated by the white dashed line in Figure 5a-d and it is the operation wavelength of the OAM beam converter. When the input intensity increases, the phase of the transmitted light changes by 180\({}^{\circ}\) and the transmittance at the intensity levels of interest remains higher than 60%, as shown in Figure 5c,d. As illustrated by Figure 1, while the phase in the even quadrants changes 180\({}^{\circ}\), the phase of odd quadrants should remain the same. Therefore, to realize the intensity-dependent switching, we build the odd quadrants with side-length 520 nm for which the resonances are far away from the operation wavelength of 1572 nm. As shown in Figure 5f, for low intensity 1 kW/cm\({}^{2}\), the phase introduced by the structure with side-lengths of 760 nm and 520 nm differs by approximately 90\({}^{\circ}\). The phase of the beam transmitted through the even quadrants (built of the cubes with the side-length of \(l=760\) nm) grows with the increase of the input intensity while the phase in the odd quadrants remains constant. When the intensity increases to 4 GW/cm\({}^{2}\), the phase difference between the odd and even quadrants increases to 270\({}^{\circ}\), while the transmittance remains higher than 60%.