Vector variational analysis of the guided modes in the three‐dimensional anisotropic optical waveguides

Abstract

AbstractThe guided wave characteristics in a three‐dimensional dielectric optical waveguide containing anisotropic materials must be investigated by vectorial analysis. Such analyses are extremely complicated if non‐diagonal terms are contained in the dielectric tensor or more than two anisotropic materials are involved. In this paper the guided modes are analyzed by a variational method in the case where the dielectric tensor contains nondiagonal elements of the transverse components. First, a new variational expression and trial functions suitable for analysis of the guided mode in these waveguides are derived. Next, numerical calculations are performed for a rectangular dielectric waveguide in which both the core and the substrate are made of anisotropic materials. With these calculations, we investigate the effects of the directions of the multiple principal axes on accuracy of the propagation constant near the lower limit, coupling of the guided modes and directions of the electromagnetic vectors. It is found that there are tight hybrid modes and weak hybrid modes. In the case of weak hybrid modes the electromagnetic vectors are straight and almost parallel to the principal axes. On the other hand, in tight hybrid modes the electromagnetic vectors bend significantly and the vector direction is rotated as the normalized frequency is varied.