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.

Analytical approximation for photonic array modes in 1D photonic crystal superlattices.

We present a comprehensive analytical approximation for array modes (both the modal fields and their associated propagation constants) for 1D photonic crystal superlattices (i.e., large periodic arrays of repeated sequences of different coupled waveguides/lasers). In this class, a regular periodicity of a photonic lattice is supplemented with the additional periodicity of a larger scale. Our approximation is a vectorial approach, accounting for the TE and TM polarizations. It can be applied to both the low- and high-contrast photonic devices. We used the model of standing waves for analytical evaluation of envelopes of array modes in a photonic superlattice. Combination of the model of standing waves with the coupled-mode formalism for infinite photonic superlattices allows evaluation of propagation constants of the array modes. Both the evaluations require only a fraction of a second for computation. Still, the results, acquired with the analytical approximation, are very close to those of well-established approaches. Furthermore, for the first time, analytical expressions for the modal fields and propagation constants become available.

Analytical approximation for photonic array modes in one-dimensional photonic crystal devices.

A new analytical approximation for photonic array modes is presented. We consider the specific class of one-dimensional (1D) photonic crystals (encompassing large arrays of coupled identical planar waveguides, large arrays of identical phase-locked lasers, etc.), in which light propagates along the optical axis of the device. Approximate analytical expressions for the array modes (both spatial distribution and propagation constants) become available. This approach allows a fast, simple, and accurate analytical evaluation of the electromagnetic field in 1D photonic crystal devices.