Reconfiguring structured light beams using nonlinear metasurfaces

Ultra-compact, low-loss, fast, and reconfigurable optical components, enabling manipulation of light by light, could open numerous opportunities for controlling light on the nanoscale. Nanostructured all-dielectric metasurfaces have been shown to enable extensive control of amplitude and phase of light in the linear optical regime. Among other functionalities, they offer unique opportunities for shaping the wave front of light to introduce the orbital angular momentum (OAM) to a beam. Such structured light beams bring a new degree of freedom for applications ranging from spectroscopy and micromanipulation to classical and quantum optical communications. To date, reconfigurability or tuning of the optical properties of all-dielectric metasurfaces have been achieved mechanically, thermally, electrically or optically, using phase-change or nonlinear optical materials. However, a majority of demonstrated tuning approaches are either slow or require high optical powers. Arsenic trisulfide (As$_2$S$_3$) chalcogenide glass offering ultra-fast and large $\chi^{(3)}$ nonlinearity as well as a low two-photon absorption coefficient in the near and mid-wave infrared spectral range, could provide a new platform for the realization of fast and relatively low-intensity reconfigurable metasurfaces. Here, we design and experimentally demonstrate an As$_2$S$_3$ chalcogenide glass based metasurface that enables reshaping of a conventional Hermite-Gaussian beam with no OAM into an OAM beam at low-intensity levels, while preserves the original beam's amplitude and phase characteristics at high-intensity levels. The proposed metasurface could find applications for a new generation of optical communication systems and optical signal processing.

from one charge to another or from the OAM beam to a beam not carrying an OAM. More recently, electrically tunable q-plates [29] as well as mechanically, electrically, thermally and optically tunable metasurfaces have been demonstrated [30][31][32][33][34][35][36][37][38][39]. Nevertheless, a majority of the tuning approaches demonstrated to date were not able to simultaneously realize ultra-fast speed and high efficiency.
Nonlinear optical interactions offer a promising way for ultra-fast, picosecond scale, and efficient optical switching, tuning and reconfiguration [40][41][42][43][44]. Recently, several material platforms, including silicon [39,40,43] and GaAs, have been used to realize nonlinear light-matter interactions in optical metasurfaces [44][45][46]. However, while silicon and GaAs have both high linear refractive indices and Kerr nonlinearities, and low linear losses in the telecommunication range, their two-photon absorption (TPA) coefficients are large, resulting in a low figure of merit.
On the contrary, As2S3 chalcogenide (ChG) glass displays a very good nonlinear figure of merit [47] in both the near-infrared and the mid-wave infrared spectral bands [48,49]. Moreover, its excellent nano-structuring properties, which enable patterning with resolution superior to polymer photoresists, enable a resist-free approach that simplifies fabrication of the As2S3-based devices to a single-step process [50]. Therefore, we choose the ChG-glass platform to realize a reconfigurable metasurface. In this work, we design, fabricate, and experimentally demonstrate an As2S3 metasurface capable of reshaping a conventional Hermite-Gaussian beam with no OAM into an OAM beam at low intensity levels, while preserving the original beam's amplitude and phase characteristics at high intensity levels. Such intensity dependent performance is enabled by the Kerr nonlinearity of ChG glass and carefully designed metasurface that relies on guided resonances of the nanoholes made in the ChG thin film. The basic principle of operation of the proposed metasurface device is illustrated in Fig. 1. The input Hermite-Gaussian beam is transmitted through the metasurface and acquires different phase 5 distribution depending on the input-light intensity. We design our metasurface such that, in the low-intensity regime, the phase acquired in the even quadrants (II and IV) is larger than for the odd quadrants (I and III). The phase distribution directly after the metasurface has a stepwise profile with the values given in row 2 in Table. 1. After propagation, this step-wise phase change smoothens and becomes a continuously varying phase that characterizes OAM-carrying beams.
Therefore, in the low-intensity regime, the HG beam, upon transmission through our metasurface, is transformed into a beam that carries OAM. For a high intensity input beam, the phase introduced by the metasurface is uniform, and the input HG beam maintains its phase and intensity distribution and does not acquire the OAM. The output beam reconfigurability is enabled by the design of the metasurface described in detail below, that uses highly nonlinear ChG glass. Switching between low-and high-intensity regimes allows for dynamic introduction of the OAM in the beam.   [51], as only for these modes the symmetry of the in-plane electric field components allows for coupling with the incident plane wave [52]. The electric and magnetic field distributions in the metasurface for the light interacting As illustrated in Fig. 1, our metasurface design requires the relative phase shift between the odd and even quadrants to be 90 in the low-intensity regime, and 0 in the high-intensity regime.
Based on the result shown in Fig  In order to confirm that the predictions based on uniform linear index changes give us a correct design, we performed nonlinear simulations for the hole arrays with the chosen hole sizes o d and e d . The results shown in Fig. 3b confirm that for the low intensity (intensity of the incident plane wave equal to 2.4 MW/cm 2 , which corresponds to the intensity used in the experiment), the phase difference between the odd and even quadrants is equal to 88°. When the intensity is increased to 1.2 GW/ cm 2 , the waves transmitted through both structures are in phase, as illustrated in Fig. 3c.
The maps of the nonlinear refractive index modification n  indicate that in the case of the non-   To realize the functionality described in Fig. 1 14 Once the 90° phase difference between the odd and even quadrants was confirmed in the lowintensity regime, a phase plate was added to the path of the main beam to produce a HG beam.
The beam was next focused on the sample using a lens, as shown in the dashed rectangle in Fig. 5a, yielding a beam size of 60 µm. A near-infrared camera was used to capture the main beam transmitted through the metasurface and the interferograms of the main and reference beams. In the low-intensity regime, when the incident beam has the average power of 5 nW, which is not enough to induce a significant nonlinear index change, odd and even quadrants maintain the 90° phase difference as shown in Figs. 2f, 2g. Upon transmission through such metasurface with two quadrants introducing a 90° phase difference, the HG beam acquires an OAM. The transverse intensity distribution of the main beam transmitted through the metasurface is shown in Fig. 6a, and the pattern resulting from the interference of the main beam and the reference Gaussian beam is shown in Fig 6b. The interference pattern reveals has spiral shape, typical for the OAM beams, due to the helical geometry of the phase front. In the nonlinear regime, when the incident beam has the average power of 2 µW (peak intensity around 1.1 GW/cm2), the 90° phase shift in the even quadrants is removed due to the nonlinear response of the metasurface. Therefore, the phase distribution across the entire metasurface becomes uniform and does not affect the phase of the transmitted HG beam. The transverse intensity distribution of the high-intenity main beam transmitted through the metasurface is shown in Fig. 6c, and the corresponding interference pattern with the reference beam is shown in Fig. 6d. The interferogram features semi-circular shapes characteristic for interference of a HG and a Gaussain beams. This result clearly demonstrates the possibility of dynamic introduction of an OAM into a HG beam that can be controlled by the intensity of the input radiation. The transmittance of the metasurface sample in the low and high intensity regimes were measured to be 50% and 53%, respectively. 15 The simulation results corresponding to the linear and nonlinear regimes are shown in Figs. 6eg and Figs. 6h-j, respectively. In Fig. 6e-f, we observe a dark beam center and spiral phase characteristic for the beams carrying an OAM. The spiral fringe in Fig. 6g matches the interference experiment shown in Fig. 6b. When the refractive index is increased by 0.04, the beam maintains its HG profile as shown in Fig. 6h-i. The interference pattern in Fig. 6j is corresponding to Fig. 6d.

Experiment.
To characterize the fabricated metasurface, we built a Mach-Zehnder interferometer with a delay line as shown in Figure 5a. To generate a Hermite-Gaussian mode, a phase plate was inserted in the main beam path. The phase plate was a glass substrate spin-coated with a layer of S1813 photoresist to delay the beam path for half wavelength. The photoresist on half of the substrate was removed by 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 pass the Hermite-Gaussian mode.

Supplementary information
In Fig. 2d, e in the main text, we showed the electric and magnetic field distributions corresponding to two spectrally separated resonances supported by the structure with the hole diameter 320 d  nm. To illustrate the origin of the guided resonances and characterize them, in  For a single-unit-cell calculations, the frequency-domain results presented in Fig. 2 in the main text and in Figs. S1c-d are obtained using the CST frequency-domain solver with convergencebased mesh refinement [3]. For these simulations, the mesh was refined in the subsequent steps until the difference in calculated transmittance in the two consecutive steps is smaller than 1%.
This refinement process allows us to precisely determine the position of the resonances of the structure.
Finally, we found that the size of the simulation domain necessary to model the actual metasurface