# Nonlinear Metasurface for Structured Light with Tunable Orbital Angular Momentum
## 4 Materials and Methods  
Design: we used the CST Microwave Studio Frequency Solver to design the linear metasurface. The refractive indices of materials were measured using a spectroscopic ellipsometer. The nonlinear  
Figure 7: Schematic and simulation results of the nonlinear tunable metasurface. (**a**) Schematic of a metasurface consisting of four quadrants with an HG input beam incident from the bottom. (**b**) Intensity and (**c**) phase distribution of the light transmitted through the metasurface at low intensity. The refractive index of ChG is \(n_{ChG}=n_{0}=2.43\). (**d**) Intensity and (**e**) phase distribution of the light transmitted through the metasurface at high intensity. The refractive index of ChG is assumed to be uniform and to have a value \(n_{ChG}=n_{0}+\Delta n=2.53\).  
simulations were performed in Comsol Multiphysics. The nonlinear coefficient was measured using a in-home Z-scan setup.  
Sample fabrication: an array of square chromium windows with size 150 \(\upmu\)m \(\times\) 150 \(\upmu\)m was fabricated on a glass substrate. Then, the As\({}_{2}\)S\({}_{3}\) film with the thickness of 500 nm was deposited on top via thermal evaporation in a Lesker PVD 75 deposition system equipped with a low temperature evaporation source. During the deposition, the substrate temperature was maintained at approximately 20 \({}^{\circ}\)C. Inside each of the Cr windows, the ChG was patterned with a square array of blocks using electron-beam lithography (Vistec EBPG5000+ 100 KV) with dosage 10.5 mC/cm\({}^{2}\). The area of the pattern is 132 \(\upmu\)m \(\times\) 132 \(\upmu\)m. The chromium around the sample played a double role: (i) it enhanced the reflectivity of the substrate enabling automatic sample alignment, and (ii) it increased the sample conductivity allowing us to avoid accumulation of charges. After exposure, the sample was immersed in a 1:1 mixture of Microposit MF-319 developer and deionized water for 32 seconds to develop. After the development, the parts unexposed by the electron beam have been removed and the thickness of the sample was found to be 400 nm using the atomic-force microscopy. Finally, six layers of Poly(methyl methacrylate) were spin-coated on the sample to provide a symmetric refractive index.  
Experiment: to characterize the fabricated metasurface, we built a Mach-Zehnder interferometer, as shown in Figure 4e. To generate an HG mode, a phase plate was inserted in the main beam path. A glass substrate spin-coated with a layer of S1813 photoresist was used as a phase plate to delay the one part of the beam by half of the wavelength. The photoresist on half of the substrate was removed using photolithography. The edge of the photoresist was placed at the center of the main beam and a spatial light filter was placed after the phase plate to filter the HG mode.  
Data availability: the data that support the findings of this study are available from the authors on reasonable request, see author contributions for specific data sets.  
[PERSON], [PERSON] and [PERSON] contributed to the initial idea. [PERSON], [PERSON], [PERSON], [PERSON] and [PERSON] performed the numerical simulation. [PERSON], [PERSON], [PERSON] and [PERSON] prepared the As\({}_{2}\)S\({}_{3}\) ChG film. [PERSON], [PERSON], [PERSON] and [PERSON] patterned the nanostructures on the samples. [PERSON], [PERSON], [PERSON], [PERSON] and [PERSON] wrote the manuscript. [PERSON] supervised the work.  
This research was funded by U.S. Office of Naval Research (N000141613020).  
The authors declare no conflict of interest.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} HG & Hermite-Gaussian \\ SLM & Spatial light modulator \\ SPP & Spiral phase plate \\ OAM & Orbital angular momentum \\ ChG & Chalcogenide glass \\ \end{tabular}