Full Vectorial 3-D Sensitivity Analysis and Design Optimization Using BPM

We present a novel approach to the sensitivity analysis of 3D structures using the full vectorial beam propagation method (FVBPM). Using no extra simulations, the sensitivities of the response with respect to all design parameters are obtained regardless of their number. Our approach is exploited to calculate the sensitivities of the propagation constants of multimode waveguides. It is also applied to the 3D imaginary distance FVBPM (ID-FVBPM) and utilized to extract the sensitivities of the mode parameters. The calculated sensitivities are then utilized within a gradient-based optimization algorithm to illustrate the application of the obtained sensitivities. The accuracy of our approach is verified through a comparison with the expensive central finite difference applied directly at the response level.