Geometry projection method for optimizing photonic nanostructures.

A geometry projection method for the design of photonic nanostructures is demonstrated and compared with a topology optimization method. By using a higher-dimensional surface to delineate the material interfaces, the projection method restricts the regions of intermediate dielectric properties to a narrow user-defined band and gives some implicit control over feature size. Topology optimization addresses these issues by using a penalization to avoid areas of intermediate dielectric and a filter to obtain implicit control over feature size. The directional emission from a photonic crystal waveguide termination is improved by both methods by generating a series of irregularly shaped dielectric posts. Results are presented, and the relative merits of each method are discussed.