Degenerate parametric frequency conversion of phase-modulated femtosecond laser pulses in crystals with a regular and chirped domain structure

A systematic theoretical analysis of the degenerate parametric frequency conversion in a LiNbO₃ crystal with a regular domain structure and a linearly varying domain thickness (chirped crystal) is presented for the pulses of a titanium-sapphire laser with a wavelength of 0.8 μm and durations of 100 and 50 fs in the presence and in the absence of phase modulation. The results are obtained with regard to the difference in the group velocities of interacting pulses and the group velocity dispersion. For an effective frequency conversion of the phase-modulated (PM) pump pulse, it is expedient to employ chirped crystals in which the domain thickness decreases from the entrance to the exit of the crystal. The pump energy is effectively converted into subharmonic energy when the pump carrier frequency decreases with time. It is demonstrated that the efficiency of the energy conversion to a subharmonic of 80% can be realized for PM pumping with a pulse duration of 100 fs in the chirped LiNbO₃ crystal. The efficiency of the parametric frequency conversion depends on the pump intensity as well as on the phase modulation of the pulse and the chirp of the crystal. Note that a variation in one of these parameters causes variations in the remaining parameters needed for the maximum efficiency of the parametric frequency conversion.