DEGENERATE 2-PHOTON PROPAGATION AND THE OSCILLATING 2-STREAM INSTABILITY - THE GENERAL-SOLUTION FOR AMPLITUDE-MODULATED PULSES

Coherent propagation of an optical pulse in a medium with a second-ord er resonance is investigated when we include both the dynamical Stark effect and a population-dependent refraction index. We show how to obt ain the general solution when the incident pulse has no phase-modulati on. The amplitude-modulation of the incident pulse can be arbitrary as can be the initial state of the medium. This general solution is redu ced to obtaining the solution of an ordinary differential equation and quadratures. For an initially de-excited medium, the solution reduces to that given by Poluektov et al. {I. A. Poluektov, YU. M. Popov and V. S. Roitberg, 1975, Kvant. Elektron. (Moscow), 2, 1147 [1975, Sov. J . Quant. Electron., 5, 620]}. We give some illustrative examples of so lutions for various initial profiles. It is also shown that the oscill ating two-stream instability (OTSI) from plasma physics is equivalent to the Maxwell-Bloch equations for degenerate two-photon propagation. We give a solution for the OTSI which contains five arbitrary real fun ctions.