Ultrashort Laser Pulse Phenomena, 2nd Edition

190 Light–Matter Interaction

The description of the various processes in Fig. 3.15 by Eqs. (3.127)–(3.129) dif-

fers only in the initial conditions, that is the field amplitudes at the crystal input.

This system of equations is analogous to the ones encountered for SHG. For

relatively weak pulses, conversion efficiencies are low, and the group velocity

dispersion contributes to a broadening of the generated radiation.

As in the case of SHG, there is a particularly interesting regime which

combines the complexities of short pulses, high intensity, and long interaction

lengths. The pulses have to be sufficiently short that simultaneous phase match-

ing cannot be achieved over the pulse bandwidth. The crystal length and pulse

intensities are sufficiently