Forward-Mode Differentiation of Maxwell's Equations

Abstract: We present a previously unexplored forward-mode differentiation method for Maxwell's equations, with applications in the field of sensitivity analysis. This approach yields exact gradients and is similar to the popular adjoint variable method, but provides a significant improvement in both memory and speed scaling for problems involving several output parameters, as we analyze in the context of finite-difference time-domain (FDTD) simulations. Furthermore, it provides an exact alternative to numerical derivative methods, based on finite-difference approximations. To demonstrate the usefulness of the method, we perform sensitivity analysis of two problems. First we compute how the spatial near-field intensity distribution of a scatterer changes with respect to its dielectric constant. Then, we compute how the spectral power and coupling efficiency of a surface grating coupler changes with respect to its fill factor.