Inverse design of ultrawideband one-dimensional metamaterial photonic filters using Riccati equation constrained gradient descent

Abstract

One-dimensional photonic wave devices exhibit a pivotal role in wave engineering. Despite their relative simplicity, designing 1D wave devices that implement complex functionalities over a broad frequency range is challenging and requires careful sculpting and multiple optimizations. This paper theoretically and experimentally demonstrates a new inverse design paradigm to achieve a desired broadband frequency response efficiently. Specifically, we calculate the required dielectric profile along the device using constrained gradient descent optimization to minimize the L2 norm between the desired and actual responses. In each optimization step, we avoid the need to solve the complete set of Maxwell equations by using Riccati’s equation or its discrete ancestor as the optimization constraint for calculating the local reflection coefficient. Using this approach, we design several unorthodox filters, such as dual-band narrowband bandpass filters located within a wideband bandstop and ultrawideband first and second-order differentiators. The technique produces excellent results for ultrawideband frequency ranges, with very low computational complexity and, remarkably, with a single trivial guess for the optimization starting point. We experimentally implemented the two differentiator designs in radio frequencies using electronic circuit elements that comprise a metamaterial transmission line structure.