Analytical expressions for photonic band structure of periodic large arrays of identical waveguides for photonic crystals applications

Abstract The Extended Coupled-Mode Theory, developed for infinite two-dimensional periodic arrays of identical coupled waveguides (photonic crystal lattices), has proven to be an effective numerical approach for the analysis of the photonic band structure of finite yet large photonic components (such as arrays of identical parallel waveguides, photonic crystal fibers, and arrays of identical coupled microcavities). In this work, we present a further development of this approach, leading to a full analytical coupled-mode description of the photonic band structure of two-dimensional photonic lattices. This comprehensive formalism is applicable to both step-index and graded-index waveguide arrays. It provides a fast, accurate and numerically stable analytical tool for the efficient analysis of the optical properties of complex photonic crystal systems.