Calculation of propagation loss in photonic crystal waveguides by FDTD technique and Padé approximation

The propagation losses in single-line defect waveguides in a two-dimensional (2D) square-lattice photonic crystal (PC) consisted of infinite dielectric rods and a triangular-lattice photonic crystal slab with air holes are studied by finite-difference time-domain (FDTD) technique and a Padé approximation. The decaying constant β of the fundamental guided mode is calculated from the mode frequency, the quality factor (Q-factor) and the group velocity vg as β = ω/(2Qvg). In the 2D square-lattice photonic crystal waveguide (PCW), the decaying rate ranged from 103 to 10−4 cm−1 can be reliably obtained from 8 × 103-item FDTD output with the FDTD computing time of 0.386 ps. And at most 1 ps is required for the mode with the Q-factor of 4 × 1011 and the decaying rate of 10−7 cm−1. In the triangular-lattice photonic crystal slab, a 104-item FDTD output is required to obtain a reliable spectrum with the Q-factor of 2.5 × 108 and the decaying rate of 0.05 cm−1.