Dielectric profile variations in high-index-contrast waveguides, coupled mode theory, and perturbation expansions.

Perturbation theory formulation of Maxwell's equations gives a theoretically elegant and computationally efficient way of describing small imperfections and weak interactions in electromagnetic systems. It is generally appreciated that due to the discontinuous field boundary conditions in the systems employing high dielectric contrast profiles standard perturbation formulations fails when applied to the problem of shifted material boundaries. In this paper we developed coupled mode and perturbation theory formulations for treating generic perturbations of a waveguide cross section based on Hamiltonian formulation of Maxwell equations in curvilinear coordinates. We show that our formulation is accurate beyond the first order and rapidly converges to an exact result when used in a coupled mode theory framework even for the high-index-contrast discontinuous dielectric profiles. Among others, our formulation allows for an efficient numerical evaluation of such quantities as deterministic PMD and change in the GV and GVD of a mode due to generic profile distortion in a waveguide of arbitrary cross section. To our knowledge, this is the first time perturbation and coupled mode theories are developed to deal with arbitrary profile variations in high-index-contrast waveguides.