A theory is presented to describe the propagation of a laser pulse with several frequency components ${\omega }_j$=${\omega }_O$+j${\omega }_R$ through a Raman medium, where ${\omega }_0$ is the initial laser frequency and ${\omega }_R$ is the frequency of the Raman transition. We consider primarily the transient regime, where the pulse width is comparable to or less than the relaxation times of the medium. We formulate the Maxwell-Bloch equations in terms of a two-photon Rabi frequency Ω and an overall phase theta. The resulting equations are similar in form to those describing self-induced transparency, and exhibit solutions corresponding to slowly traveling, but ultimately decaying, pulses. Numerical solutions to the equations are presented that include pump depletion, the ac Stark shift, and finite relaxation times. Significant frequency conversion to high-order (j∼8) anti-Stokes modes is observed in the numerical results.

• Received 23 July 1985

DOI:https://doi.org/10.1103/PhysRevA.33.1788