Electromagnetic Sensitivity Analysis of Scattering Parameters Based on the FDFD Method

We propose a novel technique to compute response gradients (Jacobians) from frequency-domain field solutions provided by high-frequency electromagnetic (EM) simulations. It is based on our recently developed self-adjoint sensitivity-analysis (SASA) approach where only one EM simulation suffices to obtain both the responses and their gradients in the optimizable-parameter space. Our novel technique exploits the computational efficiency of the SASA while adapting it to the system equations of the frequency-domain finite-difference (FDFD) method. There are three major advantages to this development: (a) the Jacobian computation is completely independent of the simulation engine, its grid and its system equations; (b) the implementation is straightforward and in the form of a post-processing algorithm operating on the exported field solution; (c) it is computationally very efficient-memory and computer-time requirements are negligible compared to those of the simulation itself. The proposed technique drastically reduces the overall time required by field-based optimization processes arising in design and inverse problems as compared to response Jacobians computed via response-level finite differences or parameter sweeps. Its accuracy is verified by comparisons with response-level central finite-difference derivative estimates.