Optimization of planar self-collimating photonic crystals.

Self-collimation in photonic crystals has received a lot of attention in the literature, partly due to recent interest in silicon photonics, yet no performance metrics have been proposed. This paper proposes a figure of merit (FOM) for self-collimation and outlines a methodical approach for calculating it. Performance metrics include bandwidth, angular acceptance, strength, and an overall FOM. Two key contributions of this work include the performance metrics and identifying that the optimum frequency for self-collimation is not at the inflection point. The FOM is used to optimize a planar photonic crystal composed of a square array of cylinders. Conclusions are drawn about how the refractive indices and fill fraction of the lattice impact each of the performance metrics. The optimization is demonstrated by simulating two spatially variant self-collimating photonic crystals, where one has a high FOM and the other has a low FOM. This work gives optical designers tremendous insight into how to design and optimize robust self-collimating photonic crystals, which promises many applications in silicon photonics and integrated optics.