Amir Sagiv: Reversibility loss and phase loss in nonlinear optics

The reversibility of light propagation in nonlinear media has recently received experimental attention, as it may lead to improvements in holography and imaging. This leads to a fundamental question – is the governing Nonlinear Schrodinger equation (NLS) reversible? We demonstrate that even though the NLS has a time-reversal symmetry, reversibility can become highly unlikely under noise or perturbations. Loss of reversibility in the NLS and other dynamical systems reveals the emergence of a preferred "arrow of time”, reminiscent of the thermodynamical one.

This “arrow of time” is also revealed by loss of phase – we show that as an ensemble of NLS solutions propagates, its phase information is lost in a statistical sense. An implication of this phenomena is that interactions between laser beams become chaotic and impossible to predict, contrary to the widespread belief. Not all is lost, however. Even though each interaction is unpredictable, the statistics of many interactions are predictable and follow a universal model.