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Physical Review A

Effects of cross relaxation and line mixing on third-order nonlinearities of resonant systems

Manoj Kumar, G. S. Agarwal

Published May 1, 1987• 5 citations
Publisher

Abstract

The effect of cross relaxation, i.e., the transfer of coherence between transitions coupled by inelastic collisions, on third-order nonlinear processes, namely, saturated absorption and four-wave mixing, is studied within the context of a model four-level system. Numerical results displaying changes in the resonant structures in four-wave-mixing signals for a range of collisional parameters are presented.

DOI
10.1103/physreva.35.4200

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Physical Review A•Jan 1, 1986•66 citations
The effect of cross relaxation, i.e., the transfer of coherence between transitions coupled by inelastic collisions, on third-order nonlinear processes, namely, saturated absorption and four-wave mixing, is studied within the context of a model four-level system. Numerical results displaying changes in the resonant structures in four-wave-mixing signals for a range of collisional parameters are presented.
A study of the effects of relaxation times on the Four-Wave Mixing (FWM) signal response in frequency space for a two-level system is presented where the collisional effects of the solvent and the presence of the electromagnetic field are considered. The model is a generalization of the conventional two-level approach in that it includes a simplified description of the molecular structure associated with the non-zero permanent dipole moments. Significant changes in both the FWM-intensity and nonlinear optical properties are observed, due mainly to changes in the ratio between the longitudinal and transversal relaxation times.
An influence of nonlinear interference processes at quantum transitions in strong resonance electromagnetic fields on absorption, amplification and refractive indices as well as on four-wave mixing processes is investigated. Doppler broadening of the coupled transitions, incoherent excitation, relaxation processes, as well as power saturation processes associated with the coupled levels are taken into account. Both closed (ground state is involved) and open (only excited states are involved) energy level configurations are considered. Common expressions are obtained which allow to analyze the optical characteristics (including gain without inversion and enhanced refractive index at vanishing absorption) for various V, (Lambda) and H configurations of interfering transitions by a simple substitution of parameters. Similar expressions for resonant four-wave mixing (FWM) in Raman configurations are derived too. Crucial role of Doppler broadening is shown. Theory is applied for numerical analysis of some recent and potential experiments.
We examine the effects of velocity-changing collisions (VCC’s) on nonlinear mixing in a Doppler-broadened vapor. We use a model in which both velocity-changing and phase-interrupting collisions are accounted for. We present explicit calculations and results for four-wave mixing in two-level systems for the case of strong collisions. We give results for both phase-conjugate and forward geometries. We discuss new features and modifications of signal line shapes due to VCC’s. The line shapes reflect the various collisional processes that occur in the system. VCC-induced line narrowing is discussed in detail.
The physics of the degenerate four-wave mixing process for resonant transitions between two degenerate energy levels is investigated by direct numerical integration of the time-dependent density matrix equations. The Zeeman structure of the upper and lower energy levels is included in a multistate formulation of the density matrix equations. The inclusion of the Zeeman structure enables the investigation of the degenerate four-wave mixing process for different polarization configurations of the forward pump, backward pump, and probe beams. Saturation curves and lineshapes are calculated for different polarization configurations and for numerous low-J transitions. At low laser intensity, the results of our calculations are in excellent agreement with perturbation theory in terms of the relative intensities of the degenerate four-wave mixing signal for linear polarization configurations. As the laser intensity increases and the resonance starts to saturate, we find in general that the relative degenerate four-wave mixing reflectivity increases for the crossed polarization configurations compared to the parallel polarization configuration because the saturation intensity is higher. However, for some resonance transitions, some of the crossed polarization configurations saturate at lower laser intensities than the parallel polarization configuration, even though the reflectivity for these crossed polarization configurations is much lower than for the parallel polarization configuration in the perturbative intensity limit. This result is explained in terms of the coupling of the various Zeeman states during the degenerate four-wave mixing interaction for specific polarization configurations. The effect of saturation on the resonance line shapes for the different polarization configurations is also investigated. Finally, a limited number of calculations are performed for resonances that are Doppler broadened as well as collision broadened. The effect of saturation on the reflectivity of the crossed polarization configurations compared to the parallel polarization configuration is even more significant for resonances with comparable Doppler and collisional broadening.
The nonlinear response of a two-level system interacting with two pump beams of different frequencies is studied with a view to examine several recent experiments on nonlinear mixing of high orders, instabilities in homogeneously broadened lasers, and holes in homogeneous lines. Such a nonlinear response is calculated with use of the continued fractions given in our earlier work [J. Opt. Soc. Am. B1, 164 (1984)]. Saturation effects lead to the appearance of many structures at submultiples of the Rabi frequency. The origin of these subharmonics in nonlinear-response functions is explained. It is shown that collisions not only lead to hole burning at the line center for weak fields but can also lead in moderate fields to the appearance of structures at subharmonics of the Rabi frequency. Existence of collision-induced coherences similar to those in four-wave mixing is shown in six-wave mixing. Exact results for the degenerate nonlinear mixing of arbitrary order are presented for arbitrary values of field strengths. Saturating fields create holes at the line center of such nonlinear mixing signals. Gain profiles of two modes symmetrically displaced from line center are also given. Numerical results, with complete account of saturation and collisions, for a variety of nonlinear-response functions are presented.