Hybrid guided modes in uniaxial dielectric planar waveguides

Rigorous electromagnetic methods are applied to calculate the propagation constants and the fields of the allowed guided modes in uniaxial slab waveguides for an arbitrary orientation of the optic axis. In addition to the familiar TE and TM modes, there are hybrid guided modes. These hybrid guided modes can be divided into three distinct types: homogeneous pure guided modes, inhomogeneous pure guided modes, and leaky guided modes. The conditions for the existence of these pure guided and leaky guided modes are derived. A quantitative method of classifying the hybrid modes in terms of the limiting decoupled TE and TM cases within that mode where the ordinary and extraordinary polarizations propagate independently is introduced. For each mode the propagation constant has a continuous band of allowed values as a function of optic axis orientation. Metal-indiffused positive-birefringent (lithium tantalate) and metal-in-diffused and proton-exchange negative-birefringent (lithium niobate) planar waveguides are treated for illustration. This analysis of hybrid guided modes is important, not only for the design and use of anisotropic waveguides, but also suggests a new class of waveguide devices based on material birefringence