Generation of a pure phase-modulated pulse by the cascading effect: a theoretical approach

New techniques to produce spatiotemporal phase modulation without the use of electro-optic devices are proposed and discussed. By using the nonlinear second-order effect in crystal it is possible to change the amplitude modulation of a pump wave into the phase of a signal wave. To that end, we propose the use of a well-known cascading configuration for which the phase mismatch is high. Analytical results of spatial and temporal incoherent phase modulation are developed with the correlation function formalisms. Furthermore, highly accurate expansions of signal phase and intensity are derived. The effects of group-velocity difference, group-velocity dispersion, and diffraction on the change of amplitude into phase modulation are studied. Finally, an experimental demonstration of a KDP crystal with a sinusoidal pump modulation that creates sinusoidal phase modulation is proposed.