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Annual Meeting Optical Society of America

Spatial pattern formation in multiwave mixing

G. Grynberg

Published Jan 1, 1989• 0 citations
Publisher

Abstract

A nonlinear medium interacting with two counterpropagating pump beams is potentially unstable. This instability is related to a mirrorless four-wave mixing oscillation.1 Recent experiments done in vapors2 show that the behavior is strongly different according to the sign of the frequency detuning from resonance. When the laser frequency ω is larger than the atomic resonance frequency ω0, the oscillation appears as a sharp conical emission, the oscillation frequency being ω. In some cases the cone is fragmented into a hexagon. When ω < ω0, the oscillation is more difficult to achieve and appears as a very broad cone.

DOI
10.1364/oam.1989.ff2

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A nonlinear medium interacting with two counterpropagating pump beams is potentially unstable. This instability is related to a mirrorless four-wave mixing oscillation.1 Recent experiments done in vapors2 show that the behavior is strongly different according to the sign of the frequency detuning from resonance. When the laser frequency ω is larger than the atomic resonance frequency ω0, the oscillation appears as a sharp conical emission, the oscillation frequency being ω. In some cases the cone is fragmented into a hexagon. When ω < ω0, the oscillation is more difficult to achieve and appears as a very broad cone.
The use of a cw laser beam detuned from resonance by only a few gigahertz to observe conical emission1 makes the computational problem tractable (2 CRAY CPU hours per spectrum), leading to a simple physical model of this spatio-temporal instability. From the excellent qualitative agreement between computations and experimental observations, one understands the physics of conical emission as follows: self-trapping2 of A1, probe generation by resonance fluorescence, Raman-gain amplification3,4 of this probe which produces A3(ω3), four-wave mixing3 between A1(ω1) and A3(ω3) which generates A4(ω4 = 2ω1 - ω3) and transfers energy back and forth between A3 and A4, division of A4 into A4L and A4R by optical-Stark-shifted absorption, division of A3 into A3L and A3R by four-wave-mixing coupling, and formation of the cone from A4L (and sometimes from the low-energy shoulder of A4R) by propagation through the spatially-dependent index of refraction prepared by A1(x,y,z). We both observe and compute that light A4(ω4) of a particular frequency may appear both in the cone and in the center, ruling out phase matching as the determinant of the cone angle, unlike many other cones, e.g., two-wavelength conical emission.5
Experimentally observed near-field and far-field spatial profiles, frequency spectra, and cone angles are in good agreement with numerical computations of a theory that includes Doppler-broadened Raman-gain amplification of Doppler-broadened resonance fluorescence, four-wave mixing, propagational coupling, self-trapping of the pump beam, and diffraction and pump-induced refraction of the new frequencies. The use of a cw laser beam detuned from resonance by only a few gigahertz makes the computational problem tractable, leading to a simple physical model of this spatiotemporal instability.
Pattern formation in nonlinear systems is a very active subject in many areas of physics. For example, in hydrodynamics the arrangement of the convective cells of the Rayleigh-Bernard instability [1] constitutes a model problem for pattern formation. In optics, important advances have been recently obtained in the case of lasers [2]. In contrast, transverse pattern formation in mirrorless optical passive systems [3] is no so wellknown because of the intrinsic complexity of a system without cavity and of the fact that the first experiments were done with pulsed lasers [4], We present here results obtained with c.w. lasers and rubidium atoms. In particular, we show some interesting relationship with the hydrodynamics observations.
We describe one of the possible ways of development of a spatial instability of counterpropagating strong light beams in resonant media. The interplay between self-focusing and saturation effects results in a formation of counterpropagating stable filaments. The nondegenerate four-photon scattering in these waveguiding structures leads to a far-field multiconical emission with the cones' frequencies shifted to both red and blue sides of the resonant transition. \textcopyright{} 1996 The American Physical Society.
Nondegenerate four-wave mixing (FWM) has been used for wavelength conversion of optical information.1 In such experiments, two beams F-P (frequency ω1) intersect in a nonlinear medium with a small crossing angle θ (≈ 10 mrad), while a third beam B {frequency ω2) is nearly counterpro- pagating to F [Fig. 1(a)]. This can be viewed as real-time holography with frequency conversion.1 However, the physics differ considerably when the medium is transparent at frequency ω1, as there is no optically induced grating. This occurs when FWM is based on resonant two-photon, ω1 + ω2, absorption (frequencies ω1 and ω2 being resonant with a cascade three-level system and ω1 coupling unpopulated excited states). One interesting feature is that the two-photon coherence is nearly Doppler-free and does not depend much on the θ angle.