Nonlinear pulse propagation near a two-photon resonance.

The propagation of light pulses whose spectra are in the vicinity of a material two-photon resonance is studied. We derive the appropriate form for the nonlinear polarization. In the limit of fast material response (as compared to the pulse duration) we obtain a wave equation that includes a new term that reflects the nonlinearly dispersive nature of the propagation. We find that nonlinear dispersion leads to self-steepening, and asymmetric spectral modulation, which in the absence of linear dispersion eventually leads to an optical shock formation. However, second-order linear dispersion is eventually able to stop the steepening and we show that a new set of solitons are supported by the system, resulting from the interplay of linear dispersion, intensity dependent refractive-index, and nonlinear dispersion. We assess the effects of third-order linear dispersion on these pulses and show that for realistic values of the parameters and not too large propagation distances they remain relatively stable. We study also the evolution of ultra-short pulses in a medium whose relaxation time is comparable to the pulses duration, and apply those results to the study of femtosecond pulse propagation in quantum dot doped waveguides