The role of coherent interactions in pulse shaping in passively mode-locked lasers

Abstract

As the duration of pulses generated by passively mode-locked lasers decreases, the pulse bandwidth becomes a significant fraction of the avalable gain bandwidth. When this occurs, it is necessarily true that the response of the polarization of the gain medium does not follow the electric field of the pulse adiabatically. Thus, one cannot use the Franz-Nodvik model1 for the amplification (or absorption) portions of the pulse shaping. The study of the coherent amplification of short pulses is well developed,2 but most schemes require a numerical solution to the Maxwell-Bloch equations that is both complicated and time consuming and is therefore unsuitable for a model of a mode locked laser, in which the pulse must be propagated through several cavity elements many times. Thus we have developed an approximate solution to the Bloch equations that accounts for the coherent parts of the interaction, at least to first order, so that we may assess the importance of coherent amplification on the shaping of ultrashort pulses in mode-locked lasers. We compare the results of our numerical model with the measured pulse shapes from a colliding-pulse mode-locked dye laser and discuss some of the implications of the coherent part of the light-matter interaction in setting a lower bound for the pulse duration.