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A circuit-theoretic treatment is presented for thin-film optical waveguides using a class of real anisotropic and gyrotropic materials. The analysis is based on the two-mode approximation in normal-mode theory. The terminal behavior of those guides is described by the 2 × 2 transmission matrix and expressions for matrix elements of six systems that are introduced as canonical elements in circuit synthesis are derived. Properties of canonical elements are discussed with particular attention on their reciprocity. Using the transmission matrix, we can treat the design of thin-film optical devices by a simple matrix operation familiar in conventional transmission-line circuit synthesis. As a typical application the design of various nonreciprocal integrated-optical devices is treated in detail. The desired response is synthesized by cascading selected canonical elements in an appropriate order. Examples include the gyrator, unidirectional mode converter, differential phase shifter, isolator, and circulator.

This paper is concerned with thin-film optical waveguides using anisotropic and gyrotropic materials, which may play an important role in the field of integrated optics. As a fundamental problem on such waveguides, normal (propagating) modes are analyzed here by the Rayleigh-Ritz variational technique. The analysis can be interpreted directly in terms of coupling of normal modes of the basic guide with simpler material parameters. Results are placed in the form of a matrix eigenvalue problem suitable for computer calculation, whose eigenvalues and eigenvectors lead to propagation constants and field expansion coefficients, respectively. Characteristics of anisotropic guides are discussed and compared with those of conventional isotropic guides. As a typical application TE↔TM mode converters are analyzed in some detail and numerical examples are presented.

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