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Optics Letters

Doppleron-induced stimulated reflection

Harry Friedmann, A. D. Wilson‐Gordon

Published Jul 15, 1989• 2 citations
Publisher

Abstract

In a gaseous system, energy can be transferred from an intense incoming beam to a counterpropagating probe beam at the same frequency. The effect may be interpreted in terms of Doppleron processes and arises because the medium undergoes interaction with beams of different effective frequencies owing to the Doppler effect.
DOI
10.1364/ol.14.000737

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Dopplerons are the signature of the nonlinear response of moving atoms driven by a continuous standing-wave laser beam. They display maxima on the velocity-dependent atomic population difference at velocities nearly equal to ±(c/ω)[(δ(ω2 + 2Ω2)1/2/(2p + 1)], where Ω is the Rabi frequency associated with an individual beam field and δω is the detuning between the driving frequency and the center of the Doppler linewidth. Probing the device with a weak signal yields gain for Doppler broadenings of the magnitude of the detuning, exclusively on the atomic-resonance-frequency side, with a maximum shifted from the driving frequency by the generalized Rabi frequency associated with a standing wave, defined by (δω2 + 4Ω2)1/2. The existence of dopplerons is demonstrated by peaks occurring at frequencies shifted from the driving frequency by even harmonics of doppleron frequencies. The intensity of the peaks is shown to depend on the Doppler width, and the complexity of the gain curve is shown to increase as the pump intensity does.
We present a theoretical study of phase-conjugate (PC) emission by backward degenerate four-wave mixing (DFWM) processes in a resonant gas medium. In this study, high-intensity (pump) saturation and Doppler broadening are simultaneously taken into account. We develop a general formalism to deal with the saturation effects in the case of a three-level atom (with degenerate frequencies) and obtain analytical expressions of the PC field amplitude (after integration over the velocity distribution) under the following conditions: (1) the probe beam and one of the pump beams have intensities weak enough to be treated at the lowest perturbation order, whereas the other pump intensity is arbitrarily high; (2) the probe crosses the standing pump wave at grazing incidence. It is shown that the saturation induced by the forward pump (copropagating with the probe beam) leads to entirely different behavior of the nonlinear susceptibility from that induced by the backward pump (counterpropagating with the probe beam). This saturation anisotropy is specific to the inhomogeneous broadening of the gas medium, which is also responsible for the frequency splitting experimentally observed in the intensity line shape of the PC emission for large pump intensities. At saturation, this splitting is theoretically shown to be proportional to the Rabi frequency, with a proportionality coefficient critically dependent on the relaxation processes; in the case of a single-relaxation model, the splitting is equal to 1.5 times the Rabi frequency. The PC intensity line shape is demonstrated to be of dispersive origin in the case of backward saturation, whereas for forward saturation, narrow structures are predicted in both real and imaginary parts of the nonlinear susceptibility, also leading to the intensity line-shape splitting. One also finds that the reflectivity of PC mirrors based on resonant DFWM strongly depends on the origin of the saturation. For a saturating forward pump, the PC emission intensity tends toward zero with increasing pump intensities, and it reaches a finite (nonzero) limit in the case of backward saturation. Most of these predictions have been observed experimentally [ BlochD., Phys. Rev. Lett.49, 719 ( 1982)].