Pulse propagation in a coupled resonator optical waveguide to all orders of dispersion

In studying the propagation of optical pulses beyond the linear dispersion approximation, the conventional term-by-term Taylor series expansion of the waveguide dispersion relationship fails when applied to the recently introduced family of coupled resonator optical waveguides (CROWs). We have found the surprising result that retaining the complete form of the dispersion relationship in the tight-binding approximation does in fact lead to a closed form analytical solution, clearly highlighting the role of the various phenomenological factors. Such an analysis is usually not possible in the majority of waveguiding structures and is especially useful in the design of photonic crystal CROWs and deep superstructure Bragg gratings.