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International Meeting on Instabilities and Dynamics of Lasers and Nonlinear Optical Systems

Nonlinear Mixing and Multi photon Processes in the Field of Two Pumps

G. S. Agarwal, N. Nayak

Published Jan 1, 1985• 0 citations
Publisher

Abstract

A very large number of physical phenomena in the resonant interaction of atomic-molecular systems with the radiation fields can be studied by treating the atomic system as a two level system and by examining its response to the applied fields. Various perturbative results are well known. A number of recent experimental works require the knowledge of the nonperturbative response functions, when both the applied fields are strong. These include a variety of experiments on instabilities(1) in lasers involving the switching from a single mode to for example two mode operation. Similarly recent nonlinear mixing experiments, where not only four wave mixing but also higher mixing in saturating fields has been studied. Pump probe experiments have also been repeated with probes whose intensity could be large. The purpose of this paper is to formulate the general theory and use it to understand the experiments. The formulation we present is also well suited for studying the effect of collisions. Details of various collisional induced coherences in fourwave and six wave mixing etc. can be studied.

DOI
10.1364/idlnos.1985.tha5

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A very large number of physical phenomena in the resonant interaction of atomic-molecular systems with the radiation fields can be studied by treating the atomic system as a two level system and by examining its response to the applied fields. Various perturbative results are well known. A number of recent experimental works require the knowledge of the nonperturbative response functions, when both the applied fields are strong. These include a variety of experiments on instabilities(1) in lasers involving the switching from a single mode to for example two mode operation. Similarly recent nonlinear mixing experiments, where not only four wave mixing but also higher mixing in saturating fields has been studied. Pump probe experiments have also been repeated with probes whose intensity could be large. The purpose of this paper is to formulate the general theory and use it to understand the experiments. The formulation we present is also well suited for studying the effect of collisions. Details of various collisional induced coherences in fourwave and six wave mixing etc. can be studied.
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. 81, 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.
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.
The effect of electromagnetically induced transparency in resonant four-wave-mixing schemes is investigated in an analysis that goes beyond perturbation theory in the coherent driving field. In addition we examine the case where the two-photon pump field is sufficiently strong to necessitate a nonperturbative treatment. This allows us to examine the cases where either one or both of the driving fields are strong. Phase matching is included in a plane-wave propagation treatment that matches the situation most likely to be encountered in actual experiments. The calculations are in part intended to model real experimental situations and thus incorporate driving and pump-field linewidths via the phase-diffusion model and Doppler broadening. With a strong pump-field laser, large enhancements in the efficiency of light generation occur at frequencies corresponding to the Autler-Townes satellites induced by the strong driving field. In this situation gain and high four-wave-mixing efficiency are simultaneously present, resulting in the production of a large intensity of coherent radiation. \textcopyright{} 1996 The American Physical Society.
The nonlinear interaction of two intense optical waves with three energy levels of an atomic system is analyzed theoretically. The frequencies of the applied fields are assumed to be on or near two of the resonances involving the three levels. Particular attention is given to the generation of power at the difference frequency of the two applied fields where their frequency separation lies in the far-infrared range of the spectrum. In the limit of large input fields where atomic transitions are driven to saturation, the generated difference-frequency power is no longer proportional to the product of the two input powers. It is shown that, in this limit, the total rate of emission of photons at the difference frequency may, in principle, approach a value given by rNT\frac{\mathrm{rN}}{T}TrN​, where NNN is the total number of atoms, TTT is the average time of coherent interaction of atoms and the radiation field, and rrr is a factor which in favorable cases approaches unity at low temperatures. Also, a number of additional effects are encountered due to coherent double-quantum transitions among various levels which may be ignored only for weak input powers. These effects are highly dependent on the modes of relaxations of atomic levels and the details of the line shape. The results are applied to several cases, in which the resonance condition yields large efficiency in nonlinear frequency mixing.
A theory of resonantly enhanced degenerate four-wave mixing in two-level systems including the effects of atomic and photon angular momentum is presented in the absence of pump-induced saturation of the transition. It is shown that there exist three distinct quantum-mechanical amplitudes leading to the third-order polarization density. These quantum-mechanical amplitudes are shown to be sensitive to the states of polarization of the incident fields. The quantum-mechanical transport equation in the mmm representation is used to calculate the output signal in the various regimes of laser detuning, atomic linewidth, and polarization states of the radiation field for collinear interaction.
The dynamical behavior of a two-level atom under the influence of two intense pump beams is examined. Exact equations for the nonlinear susceptibilities to all orders in the field strengths are derived. Numerical results for the nonlinear susceptibilities giving the absorption of the radiation from either of the pump beams and the generation of the four-wave mixing signal are given. The susceptibility for four-wave mixing, in addition to showing various saturation peaks, shows a peak at ω1 = ω2 even in the case of radiative relaxation. Higher-order multiphoton peaks in the absorption spectra are found to be extremely sensitive to the temporal fluctuations in the pumps.