Analytical approximation for photonic array modes in two-dimensional photonic crystal lattices

We presented here a comprehensive analytical approximation, describing array modes (both the modal fields and their associated propagation constants) in 2D photonic lattices (i.e., arrays of identical coupled waveguides/ lasers). Our approximation is a vectorial approach, accounting for the TE and TM polarizations. It is applicable to both the low-contrast and high-contrast photonic devices. The model of standing waves of a membrane was used for analytical evaluation of envelopes of the array modes and the total modal fields. Combination of this model with the coupled-mode formalism for 2D infinite photonic lattices allowed for evaluation of propagation constants of the array modes. Both the computations required only a few seconds. Still, the results, acquired with the analytical approximation, are in close agreement with those acquired with well-established approaches. Moreover, for the first time, analytical expressions for the modal fields and propagation constants become available.