# Nonlinear Metasurface for Structured Light with Tunable Orbital Angular Momentum
## 2 Results
### Simulations and Experiments  
In order to demonstrate the proposed OAM beam-converter, a metasurface was fabricated with two sizes of the blocks \(l=400\) nm and \(l=700\) nm. The arrays of nano-blocks were patterned in ChG thin film using electron-beam lithography, as shown in Figure 4a. First, chromium windows were prepared on a glass substrate. Then, a ChG film was deposited on top of the chromium windows with thermal deposition. The linear refractive index of the film was measured using spectroscopic ellipsometry to be \(n_{0}=2.43\). Finally, after the exposure to electron beam, a solution of diluted MF-319 was used to develop the sample. The resulting ChG structure with a thickness of 400 nm is shown Figure 4b. The fabricated sample contains four quadrants where diagonal quadrants contain blocks with the same side-length. The total size of the fabricated metasurface was 93 \(\upmu\)m \(\times\) 93 \(\upmu\)m.  
The simulation of a whole metasurface consisting of four quadrants is performed with CST Microwave Studio. Then we simulate the propagation of the near-field result from CST in free space for 4 mm with the beam propagation method [38]. Figure 4c shows the normalized intensity and Figure 4d illustrates the phase of transmitted light. The spiral-shaped phase in Figure 4d proves that the wavefront of the transmitted beam is helical.  
The fabricated metasurface was characterized using the interferometry setup shown in Figure 4e. The beam from a photodiode laser at the wavelength of 1550 nm was split by a beam splitter. The main beam was focused on the sample by a lens and collimated by a second lens placed after the sample. Then the main beam was combined with the reference beam using a beam splitter and the resulting interference patterns were captured by a camera. The experimental measurement of the main beam  
Figure 3: Spectral dependencies of **(a)** the transmittance and **(b)** the phase of the transmitted light as a function of the side-length, revealing the presence of Mie resonances. The dashed line indicates the operation wavelength \(\lambda_{0}=1550\) nm. The two black crosses indicate the parameters used for the metasurface beam converter design.  
transmitted through the metasurface is shown in Figure 4f. The intensity profile with a dark singularity at the center suggests that the beam carries an OAM. In order to prove the presence of the helical wavefront, we performed two experiments on the interference of the main beam and the reference Gaussian beam. In the first experiment, after the two beams were combined, the propagating directions and centers of the Gaussian beam and main OAM beam were overlapped. The resulting interference pattern reveals spiral-shaped fringes as shown in Figure 4g. In the second experiment, a small angle was introduced between the two beams, and the interference pattern contained fork-like fringes indicating the presence of the OAM, as shown in Figure 4h.  
In our previous work, the ChG hole metasurface converts an HG beam into an OAM beam by utilizing the guided resonances in a photonic crystal structure and overlapping two guided resonances to realize the desired phase shift in the even quadrants [32]. In contrast, in this experiment, the phase different between different quadrants of the fabricated metasurface is introduced by a single Mie-resonance and according to Figure 2, the resonance close to the wavelength of 1550 nm is the magnetic resonance.