Analytical expressions for the resonant frequencies and modal fields of finite coupled optical cavity chains

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 tight binding formalism is applied in a finite chain of optical cavities of arbitrary length. 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 two-dimensional photonic crystal chain of coupled resonators and an excellent agreement is observed.