Accuracy of the tight binding approximation for the description of the photonic crystal coupled cavities

Abstract

Coupled optical cavities are constantly attracting increased attention in telecommunication applications. For an infinite chain of optical cavities, also known as the coupled resonator optical waveguide (CROW), the tight binding approximation has been used in order to evaluate its dispersion characteristics and the modal fields. In this paper, the accuracy of the tight binding formalism is investigated for a finite chain of optical cavities of arbitrary length. This approximation allows the derivation of simple analytical formulas for the resonant frequencies and the corresponding modal fields, which involve only the resonant frequency of the isolated cavity and the coupling coefficients between two consecutive coupled cavities. The equations for the modal fields involve an expansion in terms of displaced versions of the field distribution of the mode of the isolated cavity and simple trigonometric functions. These analytical results are compared with the numerical results of the plane wave expansion method in the case of a finite photonic crystal chain of coupled resonators and an excellent agreement is observed even if the cavities are placed close together. The results clearly indicate the usefulness and accuracy of the tight binding formalism for the description of coupled optical resonators.