Longitudinal Wave Propagation in Dielectric Waveguide Array

Based on the established rigorous theory for two-dimensionally periodic (2DP) medium, Longitudinal propagation in Dielectric Waveguide Array (DWA) was analyzed in detail. Firstly, given longitudinal wave vector (k_z), Brillouin dispersion relations between transversal wave vectors were analyzed. Interactions between space harmonics were also studied. Secondly, on condition that transversal wave vector k_x equaled k_y, dispersion relations between longitudinal and transversal wave vectors were analyzed in detail. Because of interactions between space harmonics increasingly getting stronger with k_z or modulation coefficients increasing, stop-bands could be distinctly displayed and thus longitudinal propagation in DWA could be comprehensively analyzed. The applications about longitudinal propagation in DWA were also discussed.