Time-reversed wave mixing in nonlinear optics

Time-reversal symmetry is important to optics. In linear optics, a time-reversed process to laser emission enables total absorption of coherent light fields into an optical cavity of loss by time-reversing the original gain medium. In nonlinear optics, time symmetry exists for some well-known processes such as parametric up/down conversion, sum/difference frequency generation, however, combining exact time-reversal symmetry with nonlinear wave mixings is yet explored till now. Here, we demonstrate time reversed wave mixings for second harmonic generation (SHG) and optical parametric amplification (OPA). This enables us to observe the annihilation of coherent beams under time-reversal symmetry by varying the relative phase of the incident fields. Our study offers new avenues for flexible control in nonlinear optics and potential applications in efficient wavelength conversion, all-optical computing.