Application of the tight binding formalism in the analysis of finite coupled optical resonator chains

Coupled optical resonators are constantly attracting increased attention in telecommunication applications. For an infinite chain of optical resonators, 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 tight binding formalism is applied in a finite chain of optical resonators for the first time. This allows the derivation of simple analytical formulas for the resonant frequencies and the corresponding modal fields. The analytical results are compared with the numerical results of the plane wave expansion method in the case of a finite 2D photonic crystal chain of coupled resonators and excellent agreement is observed.