Defect-mode waveguide and coupled-mode theory

Defect-mode waveguide (DMWG) is simply constructed by removing every second lattice along a desired path of waves in a 2D artificial crystal, and has a quite efficient transmission with a flat pass-band. Inclusion of bends, branches and crossroads, and also periodic variation in shape and material of the lattices along the waveguide are possible to design a variety of passband characteristics. We developed a new coupled-mode theory which can analyze a chain of an arbitrary number of resonators, namely defects in a crystal, and solved the recursively obtained eigenvalue equations analytically up to seven defects. With more than eight defects, the equations are shown to be numerically solved. The eigenfrequencies were shown to agree well quantitatively with those obtained by simulating the wave propagations by the FDTD method and also with the experimental results obtained for sonic crystal DMWGs. This paper assert that the mode-coupling phenomena between localized modes in adjoining defects is the basic mechanism of the DMWG, and that the coupled-mode theory can investigate analytically the transmission properties of DMWGs in general.