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AIP conference proceedings

Four-wave mixing and thermal noise

Robert M. McGraw, Daniel N. Rogovin

Published Jan 1, 1988• 0 citations
Publisher

Abstract

In this paper, we present a statistical thermodynamic analysis of thermal noise in four‐wave mixing. For degenerate four‐wave mixing, we obtain a static susceptibility relation between the Kerr coefficient ε2 (related to the signal strength) and light scattering thermal fluctuations (related to the noise). The signal‐to‐noise power ratio (SNR) is given in the weak coupling limit.

DOI
10.1063/1.37366

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In this paper, we present a statistical thermodynamic analysis of thermal noise in four‐wave mixing. For degenerate four‐wave mixing, we obtain a static susceptibility relation between the Kerr coefficient ε2 (related to the signal strength) and light scattering thermal fluctuations (related to the noise). The signal‐to‐noise power ratio (SNR) is given in the weak coupling limit.
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.
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.
This paper presents an examination of power dissipation in a nonlinear optical medium during the coherent transfer of energy from a pump to a signal beam, and quantitatively relates this dissipation (through the fluctuation-dissipation theorem) to the spectrum of thermal fluctuations that give rise to light-scattering noise. Calculations are presented for two-wave mixing in an artificial Kerr media using a powerful stochastic model for computer simulation of amplitude, phase, and intensity fluctuations due to light-scattering noise.
We give the analytical expressions for the transfer of amplitude noise from the mixing frequencies to the generated frequencies during a nondegenerate and partially degenerate four-wave mixing (FWM) process and verify them by comparing with the numerical simulation results. We use these analytical expressions to study the amplitude noise relationships between the mixing frequencies and the generated frequencies during an FWM process, for various conditions. We also study the variance, relative intensity noise (RIN), and signal-to-noise ratio (SNR) of the generated frequencies as a function of the power, RIN, and SNR of the input signal.