Analytical theory of coupled-waveguide Bragg reflectors and resonant transmission filters

A simple coupled-mode theory (CMT) is presented for the analysis of coupled waveguide Bragg reflectors and phase-shifted resonant transmission filters for dense wavelength division multiplexing (WDM) applications. This theory combines the normal mode-based orthogonal CMT for the mode coupling and the waveguide mode-based nonorthogonal CMT for the mode excitation at the input/output junctions. Analytical solutions are obtained for the power reflected and transmitted in different waveguides under different conditions. The salient features of the interplay among the mutual coupling between the two coupled waveguides, the phase-shifting between two Bragg reflectors and different types of Bragg reflections are revealed and discussed. Our analytical solutions agree with other numerical results and can be reduced to the well known results for some special cases