Analysis of photonic band-gap structures in stratified medium

Abstract

Purpose - To demonstrate the flexibility and advantages of a non-uniform pseudo-spectral time domain (nu-PSTD) method through studies of the wave propagation characteristics on photonic band-gap (PBG) structures in stratified medium Design/methodology/approach - A nu-PSTD method is proposed in solving the Maxwell's equations numerically. It expands the temporal derivatives using the finite differences, while it adopts the Fourier transform (FT) properties to expand the spatial derivatives in Maxwell's equations. In addition, the method makes use of the chain-rule property in calculus together with the transformed space technique in order to make the algorithm flexible in terms of non-uniform spatial sampling. Findings - Through the studies of the wave propagation characteristics on PBG structures in stratified medium, it has been found that the proposed method retains excellent accuracy in the occasions where the spatial distributions contain step of up to five times larger than the original size, while simultaneously the flexibility of non-uniform sampling offers further savings on computational storage. Research limitations/implications - Research has been mainly limited to the simple one-dimensional (1D) periodic and defective cases of PBG structures. Nevertheless, the findings reveal strong implications that flexibility of sampling and memory savings can be realized in multi-dimensional structures. Practical implications - The proposed method can be applied to various practical structures in electromagnetic and microwave applications once the Maxwell's equations are appropriately modeled. Originality/value - The method validates its values and properties through extensive studies on regular and defective 1D PBG structures in stratified medium, and it can be further extended to solving more complicated structures.