Envelope time reversal of optical pulses using accelerating quasi-phase matching

In this work we set upon showing theoretically that the use of accelerating spatiotemporal Quasi-Phase-Matching (QPM) in media with parametric optical interactions makes it possible to generate a time-reversed replica of the pump pulse envelope in a frequency converted component. We construct the geometrical form for the modulation that will lead to an up-converted envelope-time-reversed replica of the pump pulse. The conversion relies on group-velocity mismatch between the fundamental and the up-converted harmonic, and is controlled by the acceleration rate (chirp) of the QPM pattern. Without loss of generality we develop this concept for the prototypical nonlinear frequency conversion of second harmonic generation (SHG). The modulation pattern can also support other phase-matched up-conversion processes other than the desired envelope-time-reversed replica. We analyze the condition under which such replicas occur. The analytical results are corroborated with numerical simulations for the case of SHG in a nonlinear crystal.