Discontinuous Galerkin Method to Model Light Propagation in Photonic Crystals of Any Size

Abstract

The study of photonic crystals has strongly benefited from computational methods see, e.g., [1], [2], which are generally more accessible than laboratory experiments. Such calculations enable the study of idealized structures free of fabrication defects and provide insight into physical phenomena that would be difficult to isolate in experiments. Due to their predictive power, computations are also used to optimize the structures prior to performing the cost- and time-expensive fabrication. Nevertheless, computational modelling of realistic photonic crystals, consisting of hundreds of unit cells, is notoriously difficult due to their multiscale character, requiring very fine discretization of each unit cell. This leads to tremendous computational complexity, basically untractable for a realistic-size crystal, even on powerful supercomputers.