Optimizing the trajectories of freeform waveguides using a modal theory

Freeform dielectric waveguides connect optical chips made of different materials in fully integrated photonic devices. With a spatial extent in the order of hundred micrometers, they constitute a computational challenge and make Maxwell full-wave solvers unhandy for the accelerated design. Therefore, we need tools for the fast prediction of waveguide transmission to enable the rapid optimization of waveguide trajectories. Previously developed methods relied on the assumption that only a fundamental mode propagates in the waveguide. However, the propagation of higher-order modes is not just unavoidable due to the geometry of the waveguides but also, sometimes, beneficial as it increases the number of channels to transmit information. We present approximation methods for the fast calculation of transmission that accommodates the presence of higher-order waveguide modes. We also show the application of the approximation methods to optimize waveguide trajectories given their input and output ports, and the obstacles to be avoided.