The mode classes and the propagation constants are determined for hybr
id guided modes in biaxial slab waveguides of arbitrary orientation, T
he properties of the biaxial media are presented in a coordinate-free
manner; therefore, any orientation of the biaxial cover, film, and sub
strate media relative to the waveguide can be analyzed, With this rigo
rous electromagnetic analysis technique the following information of p
ropagating modes in these structures can be obtained: the mode class (
TE, TM, or hybrid) can be identified; the propagation constants can be
calculated as a function of the orientation of the cover, film, and s
ubstrate regions; and each mode can be uniquely labeled based on decou
pled orientations of the waveguide.