Improved broadband performance of an adjoint shape optimized waveguide crossing using a Levenberg-Marquardt update

We derive an adjoint shape optimization algorithm with a compound figure of merit and demonstrate its use with both gradient descent and Levenberg-Marquart updates for the case of SiO₂-buried SOI coplanar waveguide crossings. We show that a smoothing parameter, basis function width, can be used to eliminate small feature sizes with a small cost to device performance. The Levenberg-Marquardt update produces devices with larger bandwidth. A waveguide crossing with simulated performance values of > 60 dB cross power extinction ratio and > -0.08 dB through power over the 1500-1600 nm band is presented. A fabricated device is measured to have a maximum of -0.06 dB through power and a 50 dB cross power extinction ratio.