Topology optimization of a photonic crystal waveguide termination to maximize directional emission

Topology optimization based on nonlinear programming techniques and design sensitivity analysis are used to maximize directional emission from a waveguide termination in a two-dimensional square lattice rods-in-air photonic crystal. Maximizing directional emission from a photonic crystal waveguide termination is desirable since a horn antenna style termination of comparable functionality is very large, while small simple terminations show strong angular spread. The optimized waveguide termination designed here is compact and exhibits a fivefold increase in power incident upon the target area over the simple termination. This improvement is achieved by creating surface modes that interfere to produce highly directional emission.