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Physical Review A

Quantitative characteristics of pressure-induced four-wave mixing signals observed with cw laser beams

A. Bogdan, M. C. Downer, N. Bloembergen

Published Jul 1, 1981• 58 citations
Publisher

Abstract

We report observation of a pressure-induced extra resonance in four-wave mixing (PIER4 signal) using single-mode continuous-wave dye lasers. The narrow laser linewidth permits for the first time a quantitative verification of the frequency, intensity, and pressure dependence of the PIER4 signal predicted by the theory of the nonlinear susceptibility ${\ensuremath{\chi}}^{(3)}$.

DOI
10.1103/physreva.24.623

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Theory and interpretation of pressure-induced resonances

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Using both a bare-atom and dressed-atom picture of atom-field interactions, we present a theory of the pressure-induced resonances that can arise when four radiation fields interact with a three-level quantum system. The four fields drive two coupled atomic transitions which share a common level, the levels being arranged in a ``ladder'' scheme. As the field frequencies are varied, certain resonant structures in the excitation spectrum of the upper state population appear only in the presence of collisions. The resonant structures result from processes that have been referred to in the past as collisionally aided radiative excitation (CARE) and pressure-induced extra resonances in four-wave mixing (PIER4). We show that both CARE- and PIER4-type resonances have a common origin, which can be linked to conservation of energy. In contrast to conventional PIER4 signals, line shapes calculated in this work result from a ``single atom'' rather than a collective emission. Moreover, the signals vanish unless the applied fields are relatively coherent, again in contrast to conventional PIER4.

Physical Review A•Jan 1, 1989•16 citations
We report observation of a pressure-induced extra resonance in four-wave mixing (PIER4 signal) using single-mode continuous-wave dye lasers. The narrow laser linewidth permits for the first time a quantitative verification of the frequency, intensity, and pressure dependence of the PIER4 signal predicted by the theory of the nonlinear susceptibility \ensuremathχ(3){\ensuremath{\chi}}^{(3)}\ensuremathχ(3).
The effect of pump fluctuations on various coherent processes that arise in three-level systems interacting with two external fields is examined. Such coherent processes include the forward Hanle effect and various four-wave mixing effects such as the generation of phase-conjugate signals. A general formulation that enables one to calculate the influence of laser linewidth on the coherent signals produced in various directions is presented. Ensemble averages, over laser temporal fluctuations, of various physical quantities, such as atomic polarization, are calculated. The spectrum of polarization fluctuations is shown to consist of several new features which lead to coherent radiation in different directions depending on the resonant frequencies in the polarization fluctuations. The influence of pump linewidth on pressure-induced extra resonance (PIER) is treated in detail. The possibility of producing a laser-fluctuation-induced coherent signal at one of the atomic frequencies is examined. This new signal, which is produced in a direction different from that of the PIER signal, but has the same type of resonant character as PIER, is found to have significantly different pressure dependence than the PIER signal. The results of our numerical computations are qualitatively explained in terms of the convolutions of products of third-order susceptibilities and pump field-correlation functions.
By using the Schenzle-Brewer model, in which the ground state of a two-level system also has a finite lifetime, it is shown that two pressure-induced extraresonant degenerate four-wave mixing signals are obtained. The first extra resonance is similar to that predicted and observed by Bogdan et al. [Opt. Lett. 6, 82, 348 (1981)]. It is characterized by a linewidth equal to the inverse lifetime of the upper state and appears only in the presence of collisional redistribution. The second extra resonance is characterized by a linewidth equal to the inverse lifetime of the ground state and does not depend on collisional redistribution for its appearance.
Continuous wave (cw) phase conjugation of a HF laser beam has been observed using resonant degenerate four-wave mixing in a HF gas absorption cell. A HF laser was operated in the P1(8) transition to provide total (forward plus backward) pump beam and probe beam intensities of about 400 and 30 W/cm2, respectively, in the cell. Conjugate reflectivities were measured as a function of HF pressure and frequency detuning from line center. Reflectivities of the order of 10−4 were measured at HF gas pressures of the order of 2 Torr when the laser frequency was tuned near line center.
Using both a bare-atom and dressed-atom picture of atom-field interactions, we present a theory of the pressure-induced resonances that can arise when four radiation fields interact with a three-level quantum system. The four fields drive two coupled atomic transitions which share a common level, the levels being arranged in a ``ladder'' scheme. As the field frequencies are varied, certain resonant structures in the excitation spectrum of the upper state population appear only in the presence of collisions. The resonant structures result from processes that have been referred to in the past as collisionally aided radiative excitation (CARE) and pressure-induced extra resonances in four-wave mixing (PIER4). We show that both CARE- and PIER4-type resonances have a common origin, which can be linked to conservation of energy. In contrast to conventional PIER4 signals, line shapes calculated in this work result from a ``single atom'' rather than a collective emission. Moreover, the signals vanish unless the applied fields are relatively coherent, again in contrast to conventional PIER4.