Accurate and efficient sensitivity analysis using the beam propagation method

We discuss a novel technique for accurately estimating the sensitivities of any desired response based on the finite difference Beam Propagation Method (BPM). Our technique utilizes the central adjoint variable method (CAVM) for estimating the response sensitivities. Using only one simulation of the photonic structure, the response and its sensitivities with respect to all the design parameters are obtained regardless of their number. This approach features accuracy comparable to that of the central finite difference approximation applied at the response level. The effectiveness of our approach is illustrated by using different response functions and different structures. Our approach utilizes virtual perturbations of the system matrices. Central difference scheme is utilized to calculate the sensitivity of these matrices with respect to the assignable parameters. This sensitivity is then utilized to efficiently estimate the sensitivity of the objective function. This technique has been applied first to the scalar 2D BPM. It is also extended to calculate the sensitivities of 3D structures using full vectorial BPM. The proposed approach achieves a significant time saving in calculating the response and its sensitivities. The accuracy of our approach is verified through comparison with the expensive and accurate central finite difference applied directly at the response level. We also utilized the calculated sensitivities in gradient-based optimization algorithms to maximize the power coupling in 3D optical fiber coupler.