Three-wave nonlinear optical interactions in dispersive media

Three-wave optical interactions in homogeneous nonlinear dispersive media are studied with a complementary use of analytic and numerical methods. The main emphasis of the study is to investigate the effects of dispersion in the generation of picosecond substructure in optical parametric processes. In a three-wave interaction at optical frequencies
\omega_{1}, \omega_{2}, \omega_{3}
satisfying the resonance condition (i.e.,
\omega_{3} = \omega_{1} + \omega_{2}
), it is shown that the presence of dispersion in the medium leads to the generation of picosecond multipulsed substructure in the pulse profiles. Both the degenerate (
\omega_{1} = \omega_{2} = \omega_{3}/2
) as well as the nondegenerate (
\omega_{1} \neq \omega_{2}
) parametric amplification processes are studied. For all the cases, a specific and realistic situation involving a LiNbO
3
crystal illuminated by a pulsed laser of intensity 10
¹⁴
W/m
²
is considered. The time envelopes of the initial pulses are chosen to be Gaussian with a full width at the half-maximum intensity of 21 ps. The existence of the picosecond substructure in the pulse profiles, predicted by the present study, is in good agreement with the experimental observations of Kryukov et al. Experiments are proposed for the generation and detection of such picosecond substructures.