Bandgap analysis of 2D photonic crystals with Auxiliary Functions of Generalized Scattering Matrix (AFGSM) method

In this paper, an accurate and rapid method is presented to characterize bandgaps of photonic crystals (PCs) constituted by two-dimensional (2D) arrays of dielectric rods with rectangular and circular cross sections. The transmittance and reflectance spectrums of finitely periodic 2D PCs are analyzed using the combination of Rigorous Coupled Wave Analysis (RCWA) and Generalized Scattering Matrix (GSM) methods. In the proposed method, band-edge frequencies of infinitely periodic 2D PCs are determined via Auxiliary Functions of Generalized Scattering Matrix (AFGSM) method using RCWA as a sub-block code. Numerical investigations show that estimating the band-edge frequencies of ideal 2D PCs via AFGSM method is identical with determining the bandgaps of the finite periodic global structure. The high convergence rate of the proposed technique also allows us to perform a bandgap characterization including the higher order Floquet modes without solving the eigenvalue equations for each cascaded layer. Furthermore, the variation of bandgaps when modifying the incidence angle, physical and geometrical parameters are presented for both TE and TM polarizations. The effect of introducing defect in 2D PC structure and resulting band natures are outlined. Our results are in excellent agreement with both theoretical and experimental results in the literature.