Symmetry breaking instabilities in perturbed optical lattices: nonlinear non-reciprocity and "macroscopic" self-trapping

A. Fratalocchi and G. Assanto

Phys. Rev. A 75, 063828 (2007)


We develop an asymptotic analysis of nonlinear energy propagation in lattices subject to slowly varying perturbations, investigating symmetry breaking and its effects. We derive a general set of evolution equations and study them by using catastrophe theory, revealing a wealth of system dynamics. Below a power threshold, symmetry breaking drives non-reciprocal oscillations; beyond that, symmetry breaking yields a novel effect of "macroscopic" self-trapping, which supports a self-maintained energy imbalance between Bloch bands. We numerically verify the theoretical results and discuss their possible implementation in waveguide arrays.