A fast hybrid method for the bandgap analysis of 2D photonic crystals based on EMT and AFGSM methods

Fast analysis of photonic crystals is important due to increasing demand in optical systems that utilize photonic crystals as their subblocks. In this paper, we present a hybrid method (HM) to analyze photonic bandgaps of two-dimensional (2D) photonic crystals. The proposed technique allows to evaluate bandgap edges by designing only the parameters of a unit cell. The approach employs effective-medium theory (EMT) to reduce 2D geometry to one-dimensional (1D) multilayer equivalence to avoid the dimensional complexity of the problem. Then, bandgap edges of the equivalent 1D structure are determined by the auxiliary functions of generalized scattering matrix (AFGSM) method. Developed combined technique is applied to square and circular shaped PCs for bandgap analysis. Results show that computation times remarkably shortened, and HM offers an effective usage. We believe findings should make an important contribution to the field of 2D PC bandgap analysis and further design studies.