Symmetry-breaking instabilities in perturbed optical lattices: Nonlinear nonreciprocity and macroscopic self-trapping

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 nonreciprocal oscillations; beyond that, symmetry breaking yields an 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.