A formalism is developed for the numerical calculation of mode behavior in thin-film optical waveguides where the substrate, film, and cover materials are isotropic, uniaxial, or biaxial single crystals, each with its own arbitrary orientation and used in any combination. A digital plotter is utilized to illustrate the evolving magnetic and electric fields inside waveguides for which the field profiles are not simple standing-wave patterns but which demonstrate complicated distributions, such as elliptic polarizations and twisting spirals. An effort is also made to relate the results of the present approach to those obtained by others, e.g., TE–TM mode conversion manifests itself in the present theory as an interference phenomenon between two oppositely rotating, roughly circularly polarized waveguide modes, a behavior similar to that found in the rotation of a linear polarization within optically active crystals.
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