An Adjoint Variable Method for Wideband Second-Order Sensitivity Analysis Through FDTD

We propose an efficient adjoint variable method (AVM) for estimating wideband second-order response sensitivities using the finite-difference time-domain (FDTD) approach. Our AVM approach reduces the number of required simulations for computing the Hessian matrix of the desired objective function from $O(n^{2})$ to only $n + 1$ where $n$ is the number of designable parameters. All first-order sensitivities are also estimated as a by-product. Our sensitivity technique is illustrated through 1-D, 2-D, and 3-D electromagnetic examples involving both dispersive and nondispersive materials. The accuracy of our AVM approach is verified through comparison with analytical sensitivity results or sensitivities estimated using the accurate but computationally intensive central finite-difference (CFD) approximations.