A TRANSFER-MATRIX APPROACH BASED ON LOCAL NORMAL-MODES FOR COUPLED WAVE-GUIDES WITH PERIODIC PERTURBATIONS

A simple transfer matrix method is applied for the analysis of power coupling and scattering in optical waveguide structures with periodic index perturbations. The transfer matrix is determined by a mode-matching technique for the local normal modes of the structures. This approach accounts for the change in the field patterns along the waveguide axis and is more rigorous than the coupled-mode theory based on the ideal modes. The distinct advantages of the transfer matrix method based on the local normal modes are that 1) it can be applied to structures with relatively strong index perturbations caused by large grating height and/or large index difference; 2) the TM modes whose transverse electric field is perpendicular to the index interface can be properly treated; and 3) the radiation loss due to scattering at the index discontinuities along the waveguide axis can be estimated. New analytical expressions for the power coupling in a grating-assisted codirectional coupler are derived and numerical results are shown for some typical structures. Comparisons with the coupled-mode analysis based on the ideal modes are made and discussed.