3D Adjoint Optimization for Designing Inhomogeneous Dielectric Materials with Specified Performance Objectives

In this work, we present an adjoint-based optimization method for the 3D volume integral equation aimed at optimizing inhomogeneous dielectric materials. The material is discretized into voxels, with the permittivity <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(\epsilon)$</tex> in each voxel adjusted to maximize a specified objective function. Using this approach, we design flat, inhomogeneous lenses with tailored focal lengths, lenses that achieve distinct focal points at different frequencies, and lenses that split the power between two focal points. The optimization is formulated using the 3D acoustic wave equation and validated against full-wave electromagnetic simulations using commercial solvers.