Nonlinear pulse propagation near a two-photon resonance.

Guram T. Adamashvili

D. Grischkowsky, M. M. T. Loy, P. F. Liao

Two-photon resonantly enhanced parametric generation processes have generally been described using time-dependent perturbation theory. In this paper we show that a theory of two-photon coherent effects can be used to derive and explain these nonlinear mixing processes. Our technique makes use of the adiabatic following (AF) approximation to obtain solutions to a vector model describing the two-photon resonance. We show that the usual results for the nonlinear susceptibilities correspond to the $\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}}$ vector of Feynman, Vernon, and Hellwarth adiabatically following the $\stackrel{\ensuremath{\rightarrow}}{\mathrm{\ensuremath{\gamma}}}$ vector in the small-angle limit. Consequently, the theory allows a natural extension to large angles, and power-dependent nonlinear susceptibilities are obtained. We then use these AF results for the polarization to study the propagation of pulses nearly resonant with a two-photon transition, and we demonstrate that the pulse reshaping is due to the two related effects of a nonlinear pulse velocity and self-phase modulation.

S. O. Elyutin, Andrei I. Maimistov, Edward A. Manykin

Anatoli V. Andreev

Abstract : The mathematical algorithms and programs for the study of the resonant light-matter interactions in the multi-component and multilevel media and photonic bandgap structures have been developed. The optimal component distribution in the two-component media have been found to get a pulse of a superradiative emission of the highest intensity. The mathematical algorithms and programs for the study of the femtosecond pulse propagation in an extended medium of the two-level atoms have developed. The regime of the inversionless superradiance in the two-component superradiative medium has been investigated. The theory of the superradiance by an ensemble of the two-level atoms embedded in the dielectric host was developed. It was shown that the near dipole-dipole interaction of dense collection of two-level atoms is enhanced by the presence of the host material, decreasing the pulse temporal width and increasing the peak pulse intensity of superradiative emission. The theory of nonlinear light-matter interaction in multidimensional resonant photonic crystals under Bragg diffraction condition has been developed. It was obtained the analytical and numerical solutions describing the novel kinds of nonlinear solitary waves: the Laue soliton, O-field, propagating and standing gap solitary waves. It has been described the spatio-temporal nonlinear dynamics of coherent field in periodic resonant structures with arbitrary modulation of atomic density and gain gratings.

J.-Y. Bigot, B. Hönerlage

We study the evolution in time and in one space coordinate of picosecond laser pulses interacting with a nonlinear medium modeled by three quantum states. This is done by solving numerically the equation of evolution of the density matrix elements together with the Maxwell equation. The nonperturbative treatment of the density matrix allows us to understand the contribution of the different optical transitions and populations to the pulse deformation during its propagation. We apply the model to CuCl where the quantum levels are the fundamental, the excitonic, and the biexcitonic states. Near the two-photon resonance, the pulse is strongly altered and the excitonic and biexcitonic levels show a population inversion. A modulation of the amplitude and a superbroadening of the phase occur during the propagation.

R. Tanaś, S. Kielich