Recent Advances in Spatial Analog Optical Computing

Traditional analog computers that perform mathematical operations electronically or mechanically suffer from their relatively large size and slow response. Recently, the idea of spatial analog optical computing has overcome these restrictions. The different techniques to implement spatial analog optical computation can be categorized into two fundamental approaches: (I) metasurface (MS) approach and (II) Green's function (GF) approach. In the first approach, a metasurface is designed to implement the Green's function of the desired operator in the spatial domain. This means that this approach needs two sub-blocks to perform Fourier and inverse Fourier transform. On the other hand, in the second approach, the optical field is modified while it travels through an appropriately designed structure such that the desired operator is directly implemented in the spatial Fourier domain. GF approach takes advantage of the nonlocal (k-dependent) response of properly tailored optical metamaterials and metasurfaces. But it imposes another restriction that only transfer functions with even symmetry can be realized unless symmetry is broken. In this review, after explaining the mentioned approaches, we classify the operators designed by the GF method in two groups based on their resonant or non-resonant nature. The resonant designs such as those that are based on surface mode excitation possess a high-gain response in a relatively narrow bandwidth. On the contrary, the non-resonant designs such as those that use photonic spin Hall effect provide higher bandwidth with a low gain. Next, we review a rich set of the applications of spatial analog optical computing e.g., edge detection, image smoothing, periodic noise suppression, Grovers quantum search algorithm, solving integro-differential equations, etc. which have emerged from different mathematical operations e.g., spatial differentiation, spatial integration, hig/low pass filtering, Laplace operator, etc. implemented optically. Most of these ideas have been investigated numerically although experimental demonstrations have been presented in some cases.