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Applied Physics Letters

Light-scattering limitations for phase conjugation in optical Kerr media

Robert M. McGraw, Daniel N. Rogovin, A. Gavrielides

Published Jan 16, 1989• 18 citations
Publisher

Abstract

It is shown that noise from light-scattering fluctuations inherent in an optical Kerr medium sets a lower limit on the incident probe power required to achieve meaningful phase conjugation by four-wave mixing. For visible wavelengths and room temperatures, we determine that about 10 μW of probe power is needed to obtain a signal-to-noise ratio of unity in the conjugate wave for reflectivities that are less than or near the first oscillation condition.

DOI
10.1063/1.101007

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Optics Communications•Dec 1, 1997•3 citations
It is shown that noise from light-scattering fluctuations inherent in an optical Kerr medium sets a lower limit on the incident probe power required to achieve meaningful phase conjugation by four-wave mixing. For visible wavelengths and room temperatures, we determine that about 10 μW of probe power is needed to obtain a signal-to-noise ratio of unity in the conjugate wave for reflectivities that are less than or near the first oscillation condition.
This paper examines thermal (light-scattering) fluctuations as a dominant noise source in nonlinear optical processes. Fundamental limits to conjugate wave fidelity and signal power requirement are obtained through the statistical thermodynamic treatment of light-scattering noise in four-wave mixing based on the fluctuation-dissipation theorem. Several types of nonlinear media are examined including artificial Kerr suspensions, isotropic Kerr media, and fluids near a critical point. Where measurements are available, excellent quantitative agreement is obtained between theory and experiment.
Thermal light-scattering fluctuations are examined as a fundamental noise source inherent in nonlinear optical processes involving Kerr and artificial Kerr media. Stochastic models are introduced to simulate noise in optical phase conjugation via degenerate four-wave mixing, and in signal amplification via nondegenerate two-wave-mixing processes. Significant noise fluctuations in the amplitude and phase components of the processed signals are shown to occur even with incident signal powers in the milliwatt range. For time-dependent processes, including nondegenerate two-wave mixing, the fluctuation-dissipation theorem is shown to generalize a previously derived static susceptibility relation between light-scattering and nonlinear optical response to media exhibiting both power dissipation and nonlocal interaction.
The connection between light scattering and nonlinear optical response is examined quantitatively for Kerr media and is generalized to include isotropic materials with nonlocal interactions near a critical point. A number of important quantities, including the nonlinear refractive index (n2{\mathit{n}}_{2}n2​) and the four-wave-mixing coefficient, are shown to acquire increasing grating wave-vector (q) dependence as the critical point is approached. This dependence is identical to the q dependence obtained for light scattering in the Ornstein-Zernike theory. Illustrative calculations are presented for near-critical xenon using the Redlich-Kwong equation of state and parameters obtained from independent measurements. These results indicate n2{\mathit{n}}_{2}n2​ values of ${10}^{\mathrm{\ensuremath{-}}15}$--${10}^{\mathrm{\ensuremath{-}}14}$ m2{\mathrm{m}}^{2}m2/W and response times in the 1--10-\ensuremath{\mu}sec range. Calculations are presented for the phase-conjugate reflectivity in degenerate four-wave mixing that include both nonsaturable background loss and light-scattering noise. Reflectivities in excess of unity are predicted for 1.06-\ensuremath{\mu}m wavelength and cw pump intensities in the 10-kW/cm2{\mathrm{cm}}^{2}cm2 range.
We describe the steady-state enhancement of the phase-conjugate reflectivity that occurs with linear absorption near self-oscillation in four-wave mixing systems. Using a simplified general model, we show that this effect can arise in a variety of phase conjugators including those based on photorefractive and Kerr media. A new expression is introduced for the optimal reflectivity condition, which occurs if the transfer of energy from the strong forward pump to the weak probe is maximized at the entrance to the nonlinear medium.