Light propagation through photonic crystal waveguide bends by eigenmode examinations

Propagation of electromagnetic (EM) waves through sharp bends of photonic crystal waveguides is usually understood using the finite-difference time-domain (FDTD) technique. In this approach, the waveguide arms must be sufficiently long to separate the useful pulses from other parasite pulses. In addition, there is strong fluctuation in the transmission and reflection spectra near the waveguide cutoff frequency. To overcome these difficulties, we propose a frequency-domain approach in which the EM field profile for the guided mode at each single frequency is examined and then taken as a reference to decompose the total field within each waveguide of the bend system into the superposition of two counterpropagating guided modes. A theoretical model describing the multireflection processes within each waveguide is developed to retrieve the transmission and reflection coefficients for the bend from the superposition coefficients of the guided modes. The proposed approach has been applied to two-dimensional photonic crystal waveguide bend structures, with a simulation domain significantly smaller than in the FDTD technique. Good agreement with existing results is achieved, and no apparent fluctuation is found in the spectra even at frequencies close to the waveguide cutoff frequency, indicating the effectiveness and efficiency of the new method.