Modes in anisotropic optical waveguides formed by diffusion

Solutions of the wave equation are obtained for planar guides whose dielectric constant ε is anisotropic and decreases exponentially in the direction perpendicular to that of wave propagation. Although for TE modes the solutions are quite similar to those obtained earlier for exponentially varying but isotropic ε, there are some singificant differences for TM modes. The condition for single-mode operation and the number of modes of such guides are given in terms of the exponential decay rate, the difference between the surface and bulk values of ε, and the wavelength. The results are illustrated for the cases of Se-diffused CdS and out-diffused LiNbO3.