Forward-Mode Differentiation of Maxwell’s Equations

• DOI: 10.1021/acsphotonics.9b01238
• Publication Date: 2019-10-21T18:03:57Z
• Authors: Tyler W. Hughes; Ian A. D. Williamson; Momchil Minkov; Shanhui Fan
• Keywords: Finite difference

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 popular adjoint variable method, but provides significant improvement both memory speed scaling problems involving several output parameters, as we analyze context finite-difference time-domain (FDTD) simulations. Furthermore, it an alternative numerical derivative methods, based on approximations. To demonstrate usefulness perform analysis two problems. First compute how spatial near-field intensity distribution scatterer changes respect its dielectric constant. Then, spectral power coupling efficiency surface grating coupler fill factor.