Coupled-mode theory for non-periodic structured waveguides

In this work a new generalization of the theory of coupled modes for non-periodic structured waveguide is presented. Based on a set of eigen waves of a homogeneous periodic waveguide, a new basis of vector functions is introduced that takes into account the non-periodicity of the waveguide. Representing the total field as the sum of these functions with unknown scalar coefficients, a system of coupled equations that determines the dependence of these coefficients on the longitudinal coordinate has been obtained. It was shown that the single-wave equation has an additional phase term. In the frame of proposed approach, the z-dependent series impedance and local wave vector were introduced for structured waveguides.