Controlled supercontinuum generation for optimal pulse compression:a time-warp analysis of nonlinear propagation of ultra-broad-band pulses

We describe the virtues of the pump-probe approach for controlled supercontinuum generation in nonlinear media, using the example of pulse compression by cross-phase modulation in dielectrics. Optimization of a strong (pump) pulse and a weak (probe) pulse at the input into the medium opens the route to effective control of the supercontinuum phases at the output. We present an approximate semi-analytical approach which describes nonlinear transformation of the input pulse into the output pulse. It shows how the input and the output chirps are connected via a time-warp transformation which is almost independent of the shape of the probe pulse. We then show how this transformation can be used to optimize the supercontinuum generation to produce nearly single-cycle pulses tunable from mid-infrared to ultraviolet.