Comparative Study of Photonic Defective Comb-Like Structure by the Green Function and the Transfer Matrix Method

In this paper, we investigate the propagation of electromagnetic waves in periodic comblike waveguides structure made of dangling side branches (resonators) and finite waveguides. We introduce two defective resonators inserted in two different sites inside the perfect periodic system. This kind of system has been studied theoretically using Green’s function method (GFM), the main objective of this work is to make a comparative study between the results found in the literature and the results found by the Transfer Matrix Method (TMM) for the first time in such photonic defective comb-like system. Noted that the calculations made by the transfer matrix method (based on Maxwell’s equation and the continuity conditions) are simpler compared to the calculations when applying the Green function method. The results founding in this paper either at the level of the transmission and reflection rates are in agreement with the results found by the Green function method, which gives an idea of the effectiveness of this simple method and their agreement with the experience.