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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Resonant Raman-type mixing using coherent population trapping

Vasily G. Arkhipkin, Sergei A. Myslivets, Д. В. Манушкин, A. K. Popov

Published Oct 21, 1998• 0 citations
Publisher

Abstract

We study resonant four-wave mixing process (omega) 4 equals (omega) 1 minus (omega) 2 plus (omega) 3 under conditions of coherent population trapping (CPT) when radiations with frequencies (omega) 1,2 are strong, and (omega) 1 minus (omega) 2 equals (omega) 20 ((omega) 20 is a frequency of electrodipole-forbidden transition). It is shown that under the CPT sufficiently large nonlinear polarization (the same as linear polarization or higher) may be created. We show that in atomic Ba vapor for cw lasers quantum conversion efficiency can be as high as several tens percent.

DOI
10.1117/12.328281

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We study resonant four-wave mixing process (omega) 4 equals (omega) 1 minus (omega) 2 plus (omega) 3 under conditions of coherent population trapping (CPT) when radiations with frequencies (omega) 1,2 are strong, and (omega) 1 minus (omega) 2 equals (omega) 20 ((omega) 20 is a frequency of electrodipole-forbidden transition). It is shown that under the CPT sufficiently large nonlinear polarization (the same as linear polarization or higher) may be created. We show that in atomic Ba vapor for cw lasers quantum conversion efficiency can be as high as several tens percent.
An investigation is reported of resonant four-wave frequency mixing of the type ω 4 =ω 1 —ω 2 +ω 3 under coherent population trapping conditions. Such mixing may appear when radiations of frequencies ω 1,2 are strong and when ω 1 —ω 2 =ω 20 (ω 20 is the frequency of a dipole-forbidden transition). The density matrix method is used to calculate (taking quantum interference into account) the absorption coefficients, the refractive indices, and the nonlinear susceptibilities exactly for the strong fields and in the first order of perturbation theory for the weak fields. A study is made of the dependence of the power of nonlinear optical generation on various characteristics of the transitions and of the radiation, subject to the propagation effects. The cases of homogeneous and Doppler broadening of the resonant transitions are considered. The characteristics of transitions in the barium atom are used in numerical illustrations. It is shown that the efficiency of resonant nonlinear-optical conversion of radiation can be enhanced by utilising interference processes in quantum transitions, which represent coherent population trapping.
An experimental investigation was made of resonant nonlinear four-wave frequency mixing processes involving cw laser radiation in sodium vapor. It was found that, in spite of an increase in absorption, the use of resonant atomic nonlinearities can substantially improve the frequency conversion efficiency in the cw regime. The results of the measurements were compared with the theoretical conclusions. Ultraviolet radiation was generated at the sum frequency ( λ s = 268 nm) with the proportionality factor C = W s / W 1 W 2 W 3 ≈2W −2
We isolate a novel four-wave mixing process, enabled by coherent population trapping (CPT), leading to efficient phase sensitive amplification. This process is permitted by the exploitation of two transitions starting from the same twofold degenerate ground state. One of the transitions is used for CPT, defining bright and dark states from which ultra intense four-wave mixing is obtained via the other transition. This leads to the measurement of a strong phase sensitive gain even for low optical densities and out-of-resonance excitation. The enhancement of four-wave mixing is interpreted in the framework of the dark-state polariton formalism.
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.