Theoretical Design and Transmission Analysis of a One-Dimensional Inhomogeneous Photonic Loop Waveguide Network

We present a theoretical design for a photonic structure based on one-dimensional inhomogeneous p-erfect and defect loop waveguide network. The structure is composed of a segment of length d₁ (where d₁ = \(d_{1}^{'} + d_{1}^{{''}}\)) connected to a loop of lengths d₂ and d₃ (where d₂ = \(d_{2}^{'} + d_{2}^{{''}}\) and d₃ = \(d_{3}^{'} + d_{3}^{{''}}\)) and the permittivity of each piece of length d_i (i = 1, 2, 3) is different. We calculate the dispersion relation and transmission coefficient using the Green function method based on the interface response theory. The perfect loop waveguide generates photonic bandgaps depending on the number of cells and the structure parameters. The insertion of a defect in the structure generates defect modes inside the gaps. These defect modes can be precisely controlled in terms of frequency and transmission rate by tuning the length and permittivity of the defective segment. The proposed structure offers promising potential for the development of advanced photonic filters and other photonic devices.