Analysis of three-dimensional dielectric structures using an orthonormal-basis method: thin film photonic crystal waveguides

This paper gives the theoretical basis for the development of a novel modal method to describe 3D dielectric structure modes. To this end, the vector wave equation, which determines the magnetic field, is written in terms of a linear operator, whose eigenvectors satisfy orthonormality relation. The key of our method is to obtain a matrix representation of the wave equation in a basis that is defined by the modes of an auxiliary system. Our proposed technique can be applied to systems with arbitrary 3D real or complex refractive-index distributions. In this work we have focused on thin-film photonic crystal waveguides with an asymmetrical core.