Circuit theory for a class of anisotropic and gyrotropic thin-film optical waveguides and design of nonreciprocal devices for integrated optics

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.