A computational design of cylindrically symmetric 2D dielectric grating meta-lens with optical limiting effect based on saturable absorption by FDTD simulation

Meta-surface materials can shape the amplitude and phase with high spatial resolution and exhibit properties not occurring in natural materials, receiving considerable attention nowadays. Many exotic phenomena have been successfully demonstrated in linear optics. However, to meet the growing demand for the integration of more functionalities into a single optoelectronic circuit, the tailorable nonlinear optical properties of meta-surfaces will also need to be exploited. Here, by carefully tailoring meta-atoms' dimensions using FDTD simulation, we manage to design an optical limiting cylindrically symmetric 2D grating meta-lens with GaAs meta-atoms on SiO₂ substrate. The nonlinearity based on saturable absorption is obtained by embedding quantum dots inside meta-atoms. Each quantum dot is treated as a two-level quantum system and optical Bloch equations are used for refractive index calculations and meta-lens simulations. Good focusing and optical limiting effect is observed and analyzed.