Nonlinear adiabatic evolution and emission of coherent Bloch waves in optical lattices

We investigate energy propagation in a perturbed optical lattice, studying the nonlinear adiabatic evolution of a light beam. Through an asymptotic model, we demonstrate that: (i) energy propagating in the adiabatic regime visualizes the dispersion relation of the unperturbed lattice; (ii) the adiabatic evolution can be broken by nonlinearity, giving rise to tunneling between Bloch bands; (iii) the tunneling is accompanied by nonlinear emission of one - or more - coherent Bloch waves, the properties of which can be completely controlled by linear and/or nonlinear parameters. We verify the analytical results against numerical simulations and indicate possible experimental implementations.