Optical pulse deformation in second order nonlinear media

The deformation of optical pulses in one dimensional lossless second order nonlinear media is considered. Using a KdV-type of equation, with dispersion determined by the material properties, the deformation of a bichromatic initial signal is studied. An explicit expression for a third order approximation is used and the maximal temporal amplitude MTA is investigated. This MTA is obtained by looking at the maximum over time of the amplitude at each position. It is shown that modulations of the carrier waves and of the envelopes of the bound and free third order terms determine respectively the oscillations and the recurrence of the MTA curve. We will illustrate the explicit formula with numerical displays for the characteristic cases.