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Soviet Journal of Quantum Electronics

Doppler-free transitions in four-photon parametric resonance processes

A. K. Popov, Vladimir M. Shalaev

Published Jun 30, 1980• 1 citation
Publisher

Abstract

It is shown that the resonance nonlinear susceptibility of four-photon parametric processes in gaseous media can be increased by several orders of magnitude. The increase in the susceptibility is due to suppression of the Doppler broadening of two-photon transitions in strong pump fields when the frequencies of the fields interacting with these transitions can be very different. Under these conditions there is an additional opportunity for increasing the susceptibility by reducing the frequency detuning relative to intermediate levels participating in two-photon transitions.

DOI
10.1070/qe1980v010n06abeh010309

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It is shown that the resonance nonlinear susceptibility of four-photon parametric processes in gaseous media can be increased by several orders of magnitude. The increase in the susceptibility is due to suppression of the Doppler broadening of two-photon transitions in strong pump fields when the frequencies of the fields interacting with these transitions can be very different. Under these conditions there is an additional opportunity for increasing the susceptibility by reducing the frequency detuning relative to intermediate levels participating in two-photon transitions.
The influence of nonlinear interference processes and of changes in populations in strong electromagnetic fields, and also of the Doppler broadening on resonant four-wave frequency mixing is investigated for a system of Raman-type transitions. The case in which a quantum system interacts with one weak field and two strong fields is considered. Each of the energy levels is assumed to be perturbed by just one strong field. It is shown that the Doppler broadening alters drastically the contributions of the populations of the various levels to the investigated process and that this can alter by several orders of magnitude and nonlinear susceptibilities averaged over the velocities and influence significantly the selection of optimal configurations of the transitions and of the experimental conditions for effective resonant four-wave conversion of the radiation frequencies. A numerical analysis of the derived expressions is used to account for the experimentally observed considerable differences between the spectral dependences of the output power and the conclusions drawn from perturbation theory.
A theoretical analysis is made of the influence of the pump intensity on the nonlinear susceptibility of the third harmonic excited under conditions of two-photon resonance between the pump wave and the Doppler-broadened transition. Pumping by both traveling and standing waves is considered. For traveling wave pumping, an expression for the nonlinear harmonic susceptibility in an arbitrary field is derived and analyzed. The optimal detunings of twice the pump frequency relative to the two-photon transition frequency are determined. For standing wave pumping an expression for the nonlinear harmonic susceptibility is obtained from perturbation theory up to and including the third order. It is shown that an important factor in the reduction of the harmonic susceptibility is the saturation of the transition due to Doppler-free two-photon absorption of opposite traveling waves.
An analysis is made of generation of the sum frequency ω3 = 2ω1 + ω2 in the case when the pump frequency coincides with that of a two-photon transition 2ω1 = ω21, and the frequency ω3 is tuned near the resonance line of an atom. Under conditions of resonance with the frequency of the generated field, the parametric process has some characteristic features associated with a strong competition between effects involving increases in the nonlinear susceptibility, absorption, and changes in the phase matching. Moreover, in the presence of a fairly high-intensity field due to a neighboring transition at the frequency ω2, a nonlinear Raman process (which changes the characteristics of the medium at the frequency ω3) begins to play an important part. It is found that the highest parametric oscillation powers over a wide spectral range may be achieved by appropriately varying the intensity of the field due to the neighboring transition, the atom concentration, or the interaction length.
Three-wave frequency mixing is theoretically investigated under simultaneous single- and two-photon resonances; one of the fundamental fields is weak while another one is strong. The influence of field splitting on nonlinear susceptibility is studied for both homogeneously- and Doppler-broadened transitions. We analyzed the role of interference of quantum transitions via quasilevels in absorption and nonlinear generation and its impact on mixing process. The possibility of significant enhancement of nonlinear generation efficiency in optically dense media is demonstrated.
A theoretical investigation is reported of three-wave frequency mixing under simultaneous single-photon and two-photon resonance conditions when one of the fields being mixed is weak and the other is strong. A study is made of the influence of the field splitting on the nonlinear susceptibility in the case of homogeneously and Doppler-broadened transitions. An analysis is made of the role played by interference between quantum transitions via quasilevels in absorption and generation, and of its influence on mixing. It is shown that significant enhancement of the nonlinear generation efficiency is possible in optically dense media.
An analysis is made of the frequency addition processes in the case of a two-frequency double resonance involving vibrational-rotational transitions and their potential applications in nonlinear spectroscopy. A study is made of the influence of the saturation effect and of the frequency detuning from one- and two-photon resonances on the conversion processes and estimates are obtained for a specific molecular gas. It is shown that in the case of two-frequency interaction under double resonance conditions the efficiency of conversion of a probe wave into a wave at the signal frequency increases at least several hundred times, compared with the case of the one-frequency interaction.