# Nonlinear Metasurface for Structured Light with Tunable Orbital Angular Momentum
## 2 Results  
### Beam-Converter Metasurface Design  
The operation principle of our reconfigurable metasurface is illustrated in Figure 1. The metasurface transformed an input Hermite-Gaussian (HG) beam into an OAM beam with counter-clockwise or clockwise wavefront, depending on the intensity of the incoming light. In the linear regime--for low input intensity--the phase acquired in the even quadrants (II and IV) was 90\({}^{\circ}\) larger than in the odd quadrants (I and III). Consequently, the input HG beam was transmitted through the metasurface and the resulting phase distribution directly after the metasurface is given by \(\phi=(N-1)90^{\circ}\), where \(N\) enumerated the quadrants. Although in the near-field the phase of the transmitted beam changes in a stepwise manner, in the far-field, the wavefront became helical with a counter-clockwise direction of rotation corresponding to a positive OAM, as shown in Figure 1a. Furthermore, the metasurface was designed such that for a high-intensity input beam, the phase introduced in the even quadrants was increased by 180\({}^{\circ}\) respect to the low-intensity regime. Figure 1b shows that in this case, the phase distribution at the output increased in the clockwise direction. In contrast with the low-intensity regime shown in Figure 1a, for high input intensity, the output beam acquired a negative OAM. The reconfigurability of the output beam was enabled by the design of the metasurface utilizing Mie-resonances in conjunction with highly nonlinear ChGs, as described below in detail. Figure 1: Working principle of a nonlinear metasurface with reconfigurable output beam. The color maps show the phase of the input and output beams, and the phase shifts introduced by the metasurface. (**a**) At low intensity, upon transmission through the metasurface, the input Hermite–Gaussian (HG) beam acquires a non-uniform phase distribution leading to generation of a beam carrying a positive orbital angular momentum (OAM). (**b**) At high intensity, the phase in even quadrants changes by 180\({}^{\circ}\); the output beam possesses a negative OAM, as opposed to the low-intensity case. In this section, we will demonstrate the design principle of the metasurface that converts HG beams into OAM beams. In Section 2.2, we compare the results of the experimental measurements with simulations for the mode converter operating in the linear regime, described in Section 2.1. Finally, in Section 2.3, we present a design of a nonlinear metasurface capable of switching between the positive and negative OAM. The functionality described in Figure 1 is enabled by a ChG-based metasurface illustrated in Figure 2a, which is an array of ChG nano-blocks fabricated on a substrate. The size of the array was assumed to be infinite in the \(x\)- and \(y\)-directions, and the incident light was a plane wave propagating along the \(z\)-axis with electric and magnetic fields polarized along the \(x\)- and \(y\)-directions, respectively. For the wavelength of interest around 1550 nm, the numerical simulations were performed by CST Microwave Studio with the following geometric parameter: the height of the blocks \(h=400\) nm, the lattice constant \(a=930\) nm, and the side-length of the blocks \(l=700\) nm. The refractive index of ChG was \(n_{0}=2.4\) measured using spectroscopic ellipsometry and the refractive index of the glass substrate \(n_{g}=1.5\). Two dips located at wavelengths 1464 nm and 1510 nm corresponding to resonant interaction with the metasurfaces were indicated on the transmittance spectrum shown in Figure 2b. The near-zero transmittance resulted from a near-unity reflectance, as the materials were assumed to be lossless in the simulations. The distributions of the electric and magnetic fields in the unit cell cross-section are shown in Figure 2c,d. At the wavelength of 1464 nm, the magnetic field formed a vortex around the electric field revealing an electric resonance. At the wavelength of 1510 nm, the vortex-like electric field distribution was a signature of a magnetic resonance.