Inversed design of microstructure for vortex beam generation via perturbative backpropagation neural network

Close attention has been paid to vortex beams recently; designing and constructing artificial microstructures capable of deliberate generation and manipulation of vortex beams are vital for the development of on-chip functionalized optical devices. However, the generation of complex vortex beams often relies on the stacking of metasurfaces, which undoubtedly increases the difficulty of on-chip device design. Therefore, it is of great significance to construct complex vortex beams using a single metasurface. Concurrently, machine learning has emerged as a pivotal research area that has been widely applied to microstructures. This study introduces an innovative approach, which uses a perturbative-backpropagation (PBP) neural network for the inversed design of a multifunctional optical vortex metasurface. We commenced with the derivation of conditions for generating vector beams and scalar vortices from Jones matrices, and then a forward design method incorporating multipole expansion was implemented to refine the design utilizing the structural evaluation function (SEF). To enhance the computational efficiency, an inversed design was conducted using a subset of data from the forward design. This method achieves an impressive accuracy of 98.7% while reducing the computational resources by approximately half compared to the traditional forward design method. Through meticulous design, our metasurface can not only generate conventional scalar vortices when excited by circularly polarized ones but also construct vector beams with linear polarization. This work highlights the potential of machine learning to advance the design of optical metasurfaces.