Modes of a symmetric slab optical waveguide in birefringent media - Part I: Optical axis not in plane of slab

We derive the eigenvalue equation and the expressions for the field distribution for the TM modes of an anisotropic symmetric slab waveguide; the TE modes are identical to the isotropic case. It is assumed that the field components do not depend on the coordinate and that the axis of the uniaxial crystal lies in the plane. We find that, in spite of the symmetry of the waveguide, even and odd modes do not exist because the phase fronts of the modes are tilted with respect to the waveguide axis. However, the absolute magnitude of the Hycomponent of the field has even or odd symmetry. The interesting case of an anisotropic slab waveguide with the optical axis located in the plane of the slab will be presented in Part II of this paper.