Title: Inverse Design for Waveguide Dispersion with a Differentiable Mode Solver

Abstract: Inverse design of optical components based on adjoint sensitivity analysis has the potential to address the most challenging photonic engineering problems. However existing inverse design tools based on finite-difference-time-domain (FDTD) models are poorly suited for optimizing waveguide modes for adiabatic transformation or perturbative coupling, which lies at the heart of many important photonic devices. Among these, dispersion engineering of optical waveguides is especially challenging in ultrafast and nonlinear optical applications involving broad optical bandwidths and frequency-dependent anisotropic dielectric material response. In this work we develop gradient back-propagation through a general purpose electromagnetic eigenmode solver and use it to demonstrate waveguide dispersion optimization for second harmonic generation with maximized phase-matching bandwidth. This optimization of three design parameters converges in eight steps, reducing the computational cost of optimization by ~100x compared to exhaustive search and identifies new designs for broadband optical frequency doubling of laser sources in the 1.3-1.4 micron wavelength range.Furthermore we demonstrate that the computational cost of gradient back-propagation is independent of the number of parameters, as required for optimization of complex geometries. This technique enables practical inverse design for a broad range of previously intractable photonic devices.