Output control of dissipative nonlinear multimode amplifiers using spacetime symmetry mapping

Abstract

In many linear and nonlinear systems, time-reversal symmetry makes it possible to control the output waves by appropriately shaping the input waves. However, time-reversal symmetry is broken in systems with energy dissipation, necessitating a different approach for relating the input and output fields. We theoretically consider a saturated multimode fibre amplifier in which light generates a heat flow and suffers thermo-optical nonlinearity, thus breaking time-reversal symmetry. We identify a spacetime symmetry that maps the target output back to an input field. This spacetime symmetry mapping applies phase conjugation, gain and absorption substitution but not time reversal, and it holds in a steady state and for slowly varying inputs. Our approach enables coherent wavefront control of nonlinear dissipative systems.