Colliding-pulse phase modulation and chirping of ultrashort optical pulses in thin slabs of nonresonant and of saturable media

Abstract

The time dependence of the frequency shift (δω) due to colliding-pulse phase modulation (CPPM) is computed, for collision of femtosecond optical pulses, both in nonresonant and in saturable media. In particular, thin material slabs (up to several pulse widths τ) are considered, and although the results are more generally applicable, special attention is given to a typical saturable-absorber jet in a colliding-pulse mode-locked laser. Results show that CPPM in nonresonant media causes noticeable effects on the chirp, both for thin slabs with L ≈ laser wavelength, where the coherence of the pulses leads to interference effects, and for thicker slabs with L ≈ cτ. Complications to CPPM by saturable media are discussed, and it is shown that the consequences of dispersion by the ground-state population, and finite phase-relaxation time, may be important for short, low-energy pulses. The results show, for parameters typical of contemporary colliding-pulse mode-locked lasers, what conditions are favorable for short, stable pulse formation in solitonlike pulse shaping. It is also shown that there are conditions for which the pulses produced would be spread by any sign of group-velocity dispersion.