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Journal of the Optical Society of America B

Investigation of intensity noise transfer during four-wave mixing in nonlinear optical media

Aravind P. Anthur, Seán Ó Dúill, Liam P. Barry

Published Jan 13, 2017• 4 citations
Publisher

Abstract

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.

DOI
10.1364/josab.34.000389

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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.
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.
Nondegenerate four-wave-mixing (fwm) is a process by which one or two pump fields generate two signal beams, with conservation of the total photon energy and momentum. The signal beams can be distinguished by their frequency, or by their wave vector, or by their polarization. When the nonlinear medium which creates the fwm process is contained in a resonant cavity, the signal generation is caused by an instability, because the signal fields experience gain (fwm gain), and when this gain overcomes the cavity losses the signal beams build up. This chapter discusses several static and dynamical instabilities which arise from nondegenerate fwm. It considers a cavity with plane mirrors and examines the properties of quantum noise reduction which arise in the intensity difference between the signal beams generated by the fwm process. The chapter illustrates the problem of Gauss-Laguerre transverse modes in a ring cavity with spherical mirrors.
The noise-transformation properties of competing four-wave-mixing processes in an optical fiber are numerically investigated for an input signal with two frequency components, ${\mathrm{\ensuremath{\omega}}}_{1}$ and ${\mathrm{\ensuremath{\omega}}}_{2}$. When pulses from such a source propagate through a single-mode optical fiber, the two input frequency components can mix to form symmetric pairs of sidebands at ${\mathrm{\ensuremath{\omega}}}_{3}$=2${\mathrm{\ensuremath{\omega}}}_{1}$-${\mathrm{\ensuremath{\omega}}}_{2}$, ${\mathrm{\ensuremath{\omega}}}_{4}$=2${\mathrm{\ensuremath{\omega}}}_{2}$-${\mathrm{\ensuremath{\omega}}}_{1}$, ${\mathrm{\ensuremath{\omega}}}_{5}$=2${\mathrm{\ensuremath{\omega}}}_{3}$-${\mathrm{\ensuremath{\omega}}}_{1}$, and ${\mathrm{\ensuremath{\omega}}}_{6}$=2${\mathrm{\ensuremath{\omega}}}_{4}$-${\mathrm{\ensuremath{\omega}}}_{2}$. Noise that was initially confined to the input frequencies ${\mathrm{\ensuremath{\omega}}}_{1}$ and ${\mathrm{\ensuremath{\omega}}}_{2}$ is redistributed to the sidebands in a way that reduces the relative intensity fluctuations of the input frequencies, when the fiber length is judiciously chosen.
The noise properties of propagation through optical fiber are of interest in optical communications. In recent years much attention has been focused on reducing the quantum fluctuations in one of two complementary field variables below the limit associated with coherent states. Nonlinear optical processes have played a key role in the realization of such behavior. We numerically investigate the noise properties associated with competing four-wave mixing (FWM) processes in optical fiber from a classical perspective. The nonlinear interaction of two pump waves at frequencies ω1 and ω2, which produce sidebands at 2ω2–ω1 and 2ω1–ω2 by multiple FWM, is considered. By introducing known classical fluctuations at the fiber input, one can trace the evolution of the noise in the different frequency components of the FWM spectrum by generating histograms at different fiber lengths and for different input pump powers and frequency separations. Classical behavior resembling squeezing is observed under appropriate conditions.
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.