This paper presents an algorithm based on the well-known FDTD numerical method which is adapted for 3D problems of transmission and reflection of photonic crystal waveguides, and which effectively saves memory and computing resources. Specific examples showing its validity and effectiveness are presented. Transmission spectra for double 60-degrees bent waveguides reveal narrow resonant transmission in contrast to the broad spectra observed for straight waveguides. Other groups have also registered this feature in recent experiments. The explanation suggested in this paper is that transmission through sharp bends can occur only with pure diffractively guided modes. The dependence of transmission of a coupled-cavity waveguide on the depths of the etched holes is also investigated.
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