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A Novel Method for Band Structure Analysis of Photonic Crystal Slabs

We propose a new method to extract the modes of photonic crystal slabs and, thus, obtain their band structures. These slabs, which are 2-D periodic structures with finite thickness, can completely confine light and have the important advantage of simple construction for applications in integrated optic devices. In this paper, reflection pole method (RPM) is utilized to analyze photonic crystal slabs. Modes are poles of reflection and transmission coefficients of multilayered structures. According to this principle, modes can be detected by only pursuing phase variations of transmission coefficients that are equal to rad. Therefore, extraction of modes becomes fast and simple through obtaining these coefficients. Photonic crystal slabs are a kind of crossed gratings, and therefore, we use Fourier modal method (FMM) to obtain their reflection and transmission coefficients. FMM is a popular fast convergence method for the analysis of gratings, which offers ease of implementation. In this paper, slab band structures are calculated for dielectric rods in air and air holes in dielectric. The achieved results are compared with 3-D finite-difference time-domain (FDTD) and plane wave expansion (PWE) methods, demonstrating very good agreement.