Abstract

Bragg reflection waveguides (BRWs), consisting of a guiding layer (core) surrounded by periodic media (claddings), exhibit a unique dispersion relation, resulting in a forbidden and allowed band structure.¹ We recently proposed a novel directional coupler consisting of two such BRWs in close proximity.² Here we analyze the coupling properties of the BRW directional coupler. To obtain the modal profiles of the proposed structure, we first derive its characteristic equation and solve for the propagation constant β± for the two fundamental modes. Proceeding with a perturbation analysis we find an explicit analytic expression for the coupling constant κ. The coupling constant decreases exponentially with the separation of the guides (similar to that of conventional couplers), with a decay constant characteristic of the dispersion relation of the periodic medium in the coupling region. Comparing the expression for κ in a conventional directional coupler to the one we derived, we find some novel properties: (i) The effective width of the core (accounted by the Goos-Haenschen shift) may be smaller than the physical width; (ii) for the same core separation the coupling constant is much larger; this can be viewed as effective shrinking of the optical path by the periodic coupling section; and (iii) since the decay constant is a function of both refractive indices of the periodic medium, the coupling constant may be tuned electrooptically or even detuned (with consequent destruction of the confined guiding).

© 1989 Optical Society of America