The scattering matrix method was applied to the analysis of finite two-dimensional photonic crystals and lightwave devices. Results indicated that 1) the light transmission at the photonic band gap (PBG) is suppressed to less than 30 dB in the densely packed and honeycomb crystals, both of which are composed of only four rows of unit cells of semiconductor columns and 2) this PBG effect is weakened to half when the nonuniformity from 10 to 30% is brought to the diameter of columns. Also, the light propagation in defect waveguides with abrupt bends, a branch and a directional coupler was demonstrated by this method. It was found that the coupling loss at the input end of the waveguide is drastically changed by the shape of the input end. The reflection loss at 60 bends was estimated to be less than 1 dB, and the excess loss at an abrupt Y-branch was estimated to be 0-4.6 dB, depending on the frequency of the input wave. The demultiplexing and power dividing functions were expected in a directional coupler with a submicron coupling length, which is considered to be due to antiguide characteristics of the waveguides.
Jun Yonekura, Mitsutaka Ikeda, and Toshihiko Baba, "Analysis of Finite 2-D Photonic Crystals of Columns and Lightwave Devices Using the Scattering Matrix Method," J. Lightwave Technol. 17, 1500- (1999)