Analytical and numerical studies of waveguiding and coupling in periodic dielectric materials

Abstract

Using both analytical approaches and finite difference time domain simulations, we investigate different types of waveguiding and coupling mechanisms, including direct coupling between the optical resonators, waveguide-resonator coupling, indirect resonator coupling via waveguide modes, and Bragg reflection in cylindrically symmetric geometries. By coupling an array of high Q optical resonators together, we form a new type of waveguide, coupled resonator optical waveguide (CROW), where photons propagate by hopping from one resonator to its nearest neighbors. Using tight-binding approximation, we find that the CROW band dispersion can be simply characterized by a coupling coefficient [kappa]. The tight-binding results are confirmed by using the finite difference time domain algorithms to analyze two examples of CROW’s: one is composed of coupled defect cavities in a two-dimensional triangular lattice photonic crystal, while the other is formed by coupling an array of dielectric microdisk cavities. By coupling a resonator to a waveguide, we significantly change the reflection and transmission characteristics of the waveguide. The waveguide dispersion can also be drastically modified by coupling an array of resonators to the waveguide, due to indirect coupling between the resonators via waveguide modes. Using a formalism based on the quantum scattering theory, we investigate how the waveguide-resonator coupling, resonator gain (loss), degeneracy and symmetries of the resonator modes influence the optical properties of such coupled waveguide-resonator systems. Bragg guiding can be achieved in cylindrically symmetric geometries by using cladding media with alternating high and low refractive indices. Examples include Bragg fibers and dielectric coaxial fibers. An asymptotic formalism is developed to study the dispersion, propagation loss, and field distribution of guided modes in such fibers. The results are compared with those obtained from numerical calculations, where excellent agreement is found between the two approaches.