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Optics Letters

Four-wave mixing in an artificial Kerr medium

P. W. E. Smith, Arthur Ashkin, W. J. Tomlinson

Published Jun 1, 1981• 210 citations
Publisher

Abstract

Degenerate four-wave mixing experiments have been performed using a liquid suspension of 0.234-microm-diameter latex spheres as the nonlinear medium. The measured effective optical Kerr coefficient, n(2), is 3.6 x 10(-3) (MW/cm(2))(-1). This is ~10(5)x the value for CS(2). Measured grating reflectivity, formation, and decay times are in reasonable agreement with a simple model assuming Rayleigh scattering and Brownian diffusion.

DOI
10.1364/ol.6.000284

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Annual Meeting Optical Society of America•Jan 1, 1989•0 citations
Degenerate four-wave mixing experiments have been performed using a liquid suspension of 0.234-microm-diameter latex spheres as the nonlinear medium. The measured effective optical Kerr coefficient, n(2), is 3.6 x 10(-3) (MW/cm(2))(-1). This is ~10(5)x the value for CS(2). Measured grating reflectivity, formation, and decay times are in reasonable agreement with a simple model assuming Rayleigh scattering and Brownian diffusion.
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.
We consider degenerate four-wave mixing in a Kerr medium with a standard noncollinear geometry and the polarization directions of all the beams parallel to one another. The two pump beams, the probe beam, and the phase-conjugate beam are denoted by the subscripts 1,2,4 and 3, respectively. The nonlinear medium is placed between z = 0 and z = 1; the values of the intensities of the beams at z = 0 and 1 are denoted by Ii0 andIi1, where i = 1,2,3,4. Beams 2 and 4 are incident at z = 1; and beam 1 is incident at z = 0. We have determined the dependence of the phase-conjugate reflectivity R = I31/I41 and the pump transmission T = I11/I10 on the following parameters: the probe ratio, q=I41/(I10 + I21); the pump ratio, r = I21/I 1 0; the absorption coefficient–path length product, al; and the coupling constant of the medium, q. In the absence of nonlinear refraction, pump depletion, and linear absorption in the medium, R = tan2q. When all of these effects are taken into account, the maximum value of R is given by Rmax = exp (-2α1)/(q(1 + r)). The minimum value that T can reach is proportional to q for q < 1. Even for small values of q, multistable solutions for R and T are obtained when q is greater than a threshold value, which we denote by qth. We have determined the dependence of qth on the parameters q and r.
The exact theory of degenerate four-wave mixing in a Kerr-like medium in the Bragg scattering regime is used to study the reflectivity of phase-conjugate mirrors pumped by intense laser beams. The analysis takes into account pump depletion, nonlinear phase modulation and the relaxation time of the nonlinearity. The steady-state response exhibits multivalued reflectivity, hysteresis and potential bistability; however, the transient response shows that at most one value of the phase-conjugate reflectivity is stable. Periodic or chaotic pulsations are predicted beyond threshold values of pump intensity. The onset of a natural oscillation in the Kerr-like medium is also predicted in the absence of a continuous probe beam; the resulting field amplitude is stable and weakly sensitive upon the presence of external noise.
Recent interest in degenerate four-wave mixing in artificial Kerr media to produce phase conjugate waves has concentrated on the visible and infrared spectra. Attempts to extend this technique to the millimeter wave and microwave spectral regions encounter severe difficulties arising from the requirements of medium nonlinearity and high beam intensities. The former problem may be solved by the use of artificial Kerr media and the latter by confinement in a waveguide. In a single-mode waveguide, however, wavefront perturbations cannot propagate. Phase conjugation therefore reduces in this case to a 1-D conjugation capable only of correcting for longitudinal phase error. Observation of this conjugate wave with a slow response medium is made possible by using a sequential method. The general concept is to first write the nonlinear refractive index grating using counterpropagating pump and probe waves. Subsequently, both waves are turned off, and a pump wave approaching from the opposite side reads (scatters from) the grating to produce the phase conjugate wave.