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Physical Review Letters

Bifurcation in Degenerate Four-Wave Mixing in Liquid Suspensions of Microspheres

Daniel N. Rogovin, P. McGrath

Published May 20, 1985• 8 citations
Publisher

Abstract

We examine phase conjugation in liquid suspensions of microparticles in the saturation limit. If the polarizations of the pump waves are orthogonal, new states should appear discontinuously in a pairwise fashion which are stable at the bifurcation point. These states correspond to different intensities of the conjugate and amplified probe waves. Analysis indicates that this effect should be experimentally accessible in the microwave region utilizing 10-\ensuremath{\mu}m microspheres.

DOI
10.1103/physrevlett.54.2222

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We examine phase conjugation in liquid suspensions of microparticles in the saturation limit. If the polarizations of the pump waves are orthogonal, new states should appear discontinuously in a pairwise fashion which are stable at the bifurcation point. These states correspond to different intensities of the conjugate and amplified probe waves. Analysis indicates that this effect should be experimentally accessible in the microwave region utilizing 10-\ensuremath{\mu}m microspheres.
We examine phase conjugation via degenerate four-wave mixing in liquid suspensions of microspheres in the small-field limit, where saturation effects can be ignored. For these media, electro- strictive forces modulate the microparticle density in such a way that two orthogonal spatial gratings are created. Coherent scattering of the pump radiation from these two gratings gives rise to the formation of a conjugate wave, as well as amplification of the probe wave. We discuss the steady-state and transient characteristics of the probe and conjugate waves in this regime where the dynamics of the microparticles is governed by diffusion.
We examine phase conjugation via degenerate four-wave mixing in liquid suspensions of microellipsoids in the small-field limit, where saturation effects can be ignored. For these media, electro- strictive torques rotate the microellipsoids in such a way that two orthogonal orientational gratings are created. Furthermore, electrostrictive forces modulate the microparticle density, which gives rise to the formation of two orthogonal spatial gratings that are superimposed on the orientational ones. Coherent scattering of pump radiation from these four gratings generates the conjugate wave and, in the low-loss limit, amplifies the probe wave. We discuss the steady-state and transient characteristics of the probe and conjugate waves in this limit where microparticle dynamics are governed by diffusion.
Transient phase conjugation by degenerate four-wave mixing in saturable dyes is investigated theoretically and experimentally. Two special cases are examined: (1) the case in which two pump waves and a probe wave are simultaneously turned on and (2) the case in which the pump waves are turned on well before the incidence of the probe wave. For case (1) a peak appears in the transient reflectivity for high pump intensity, while for case (2) the reflectivity increases monotonically with time up to the steady-state value irrespective of the value of the pump intensity.
Measurements of optical phase-conjugation signals by degenerate four-wave mixing in an isotropic Kerr-like suspension of polystyrene spheres are reported. Polarization discrimination through orthogonally polarized pump beams was used to measure separately the coarse-grating and the fine-grating contributions. Autocorrelation techniques permitted measurement at low power levels. The coarse-grating contribution to χ(3) for a suspension of 0.05-μm-diameter polystyrene spheres in water yielded an effective χ(3) = 2.4 × 10−15 (m/V)2, in good agreement with theory, whereas the fine-grating contribution for the same solution yielded χ(3) = 0.56 × 10−15 (m/V)2, a value 10 times smaller than predicted by theory. Limitations of the theory are discussed.
Rigidly held molecules display nonlinear optical properties which differ substantially from the properties of isotropic absorbers.1 In particular, the absorption of a collection of randomly oriented, rigidly held molecules saturates differently for different polarization states. We show that the polarization properties of degenerate four-wave mixing in such a medium are dramatically modified by this polarization-dependent saturation. We predict theoretically that for linearly polarized pump waves and for an input intensity near the saturation intensity, degenerate four-wave mixing in this material system can lead directly to vector phase conjugation; that is, to the simultaneous reversal of the optical wavefront and conjugation of the polarization state of the incident optical field.2 We confirm these theoretical predictions through phase conjugation experiments using fluorescein doped boric acid glass as the material system, and we find that degenerate four-wave mixing leads to nearly perfect vector phase conjugation when pumped by linearly polarized pump waves for field strengths near the saturation intensity.