Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Suppression of classical intensity fluctuations via competing nonlinear processes in an optical fiber

John R. Thompson

Published Oct 1, 1993• 1 citation
Publisher

Abstract

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.

DOI
10.1103/physreva.48.3152

Related papers

The influence of multiple four-wave mixing in optical fiber on noise propagation

John R. Thompson

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.

Annual Meeting Optical Society of America•Jan 1, 1992•0 citations

Squeezing of classical noise by nondegenerate four-wave mixing in an optical fiber

M. D. Levenson, Robert M. Shelby, Stephen H. Perlmutter

Nondegenerate four-wave mixing in an optical fiber is shown to attenuate one quadrature of random sideband fluctuations created by external modulators. A theory of the nonlinear interaction that includes nonlinear dispersion fits the results. Analogous experiments on quantum noise inputs should prove successful.

Optics Letters•Oct 1, 1985•103 citations

Squeezing of classical and quantum noise in an optical fiber

M. D. Levenson, Robert M. Shelby

Near-degenerate four-wave parametric mixing in an optical fiber couples fluctuations in signal and idler frequency bands in such a way that the noise at a particular optical phase is reduced while that in an orthogonal phase quadrature is amplified. We have performed experiments on this effect and explained our results in terms of a theory which incorporates a nonlinear dispersion effect. The nonlinear dispersion alters the mathematical character of the solutions and limits the effective interaction length. For relatively low frequency shifts (<100 GHz) and 100 m of fiber, the heterodyne detected optical noise can be reduced by 5 dB in the squeezed quadrature. Theory predicts that this parametric interaction should reduce the noise level below the standard quantum limit. In a realistic fiber, phase noise due to guided acoustic wave Brillouin scattering (GAWBS) dominates the quanturn noise and cannot be reduced by four-wave mixing. Narrow gaps in the GAWBS noise can be engineered into special fibers. At the frequencies of these gaps, the noise level indeed can be squeezed below the quantum limit.

Annual Meeting Optical Society of America•Jan 1, 1985•0 citations

Signal Processing using Nonlinear Optical Eects in Single- and Few-Mode Fibers

Søren Friis

The stagnating increase in data transmission capacity in optical communication systems combined with the ever growing demand of transmission bandwidth is leading to an impending capacity crunch, referring to the point in time after which the available bandwidth of the individual user starts to decrease. To postpone this point in time, existing technologies in terms of data transmission through optical fibers must be optimized and new degrees of freedom must be introduced to continue the exponential increase in available bandwidth; space-division multiplexing is believed to be the strongest candidate for another degree of freedom in transmission fibers. This thesis is two-fold: firstly, starting at Maxwell’s equations and basic principles of quantum mechanics, a semi-classical model of the noise properties of fiber optical parametric amplifiers and frequency converters is presented. The model accounts for multiple effects present in nonlinear fibers such as four-wave mixing, Raman scattering, distributed loss, and dispersion, and it is valid in the depleted pump regime. After validating the model against well-known results of quantum models, the model is used to predict the impacts of Raman noise, loss, and pump depletion on the noise properties of parametric frequency conversion and phase-insensitive and phase-sensitive parametric amplification. An important part of realizing space-division multiplexing is the ability of optical signal processing so the second part of this thesis addresses few-mode Raman fiber amplifiers and parametric amplifiers and frequency converters. A model of weak random linear mode coupling in the pump of a two-mode distributed Raman fiber amplifier is presented and it is shown that an amplification noise figure induced by mode coupling increases with the degree of mode coupling and that this tendency increases as the pump depletes. Also, a very low mode-dependent gain of 0.25 dB per 10 dB gain is experimentally demonstrated in a two-mode distributed Raman fiber amplifier by exciting the pump in a combination of two modes. A comprehensive model of four-wave mixing in two-mode fibers acvi counting for six simultaneous processes is derived, and the conversion efficiency from signal to idler in the four-wave mixing processes of phase conjugation and Bragg scattering in two two-mode fibers with different phase matching properties are experimentally investigated. A conversion efficiency of > −2.70 dB is demonstrated for Bragg scattering in the conversion of a signal in the LP01-mode to the idler in the LP11-mode; the signal-to-idler separation is ∼ 25 nm. Good qualitative agreement between experiments and theory is found for both processes in both fibers.

•Jan 1, 2016•0 citations

Translation of quantum states by four-wave mixing in fibers

Colin J. McKinstrie, J.D. Harvey, Stojan Radic +1 more

Optical frequency conversion by four-wave mixing (Bragg scattering) in a fiber is considered. If the frequencies and polarizations of the waves are chosen judiciously, Bragg scattering enables the translation of individual and entangled states, without the noise pollution associated with parametric amplification (modulation instability or phase conjugation), and with reduced noise pollution associated with stimulated Raman scattering.

Optics Express•Jan 1, 2005•194 citations

Coherent control of ultrafast optical four-wave mixing with two-color ω−3ω laser pulses

Carles Serrat

A theoretical investigation on the coherent control of optical transient four-wave mixing interactions in two-level systems with two intense few-cycle propagating laser pulses of central angular frequencies $\ensuremath{\omega}$ and $3\ensuremath{\omega}$ is reported. By numerically solving the full Maxwell-Bloch equations beyond the slowly varying envelope and rotating-wave approximations in the time domain, the nonlinear coupling to the optical field at frequency $5\ensuremath{\omega}$ is found to depend critically on the initial relative phase $\ensuremath{\phi}$ of the propagating pulses: the coupling is enhanced when the pulses interfere constructively in the center $(\ensuremath{\phi}=0)$, while it is nearly suppressed when they are out of phase $(\ensuremath{\phi}=\ensuremath{\pi})$.

arXiv:physics/0410192•Physical Review A•Aug 9, 2005•17 citations
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, \ensuremathω1{\mathrm{\ensuremath{\omega}}}_{1}\ensuremathω1​ and \ensuremathω2{\mathrm{\ensuremath{\omega}}}_{2}\ensuremathω2​. 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 \ensuremathω3{\mathrm{\ensuremath{\omega}}}_{3}\ensuremathω3​=2\ensuremathω1{\mathrm{\ensuremath{\omega}}}_{1}\ensuremathω1​-\ensuremathω2{\mathrm{\ensuremath{\omega}}}_{2}\ensuremathω2​, \ensuremathω4{\mathrm{\ensuremath{\omega}}}_{4}\ensuremathω4​=2\ensuremathω2{\mathrm{\ensuremath{\omega}}}_{2}\ensuremathω2​-\ensuremathω1{\mathrm{\ensuremath{\omega}}}_{1}\ensuremathω1​, \ensuremathω5{\mathrm{\ensuremath{\omega}}}_{5}\ensuremathω5​=2\ensuremathω3{\mathrm{\ensuremath{\omega}}}_{3}\ensuremathω3​-\ensuremathω1{\mathrm{\ensuremath{\omega}}}_{1}\ensuremathω1​, and \ensuremathω6{\mathrm{\ensuremath{\omega}}}_{6}\ensuremathω6​=2\ensuremathω4{\mathrm{\ensuremath{\omega}}}_{4}\ensuremathω4​-\ensuremathω2{\mathrm{\ensuremath{\omega}}}_{2}\ensuremathω2​. Noise that was initially confined to the input frequencies \ensuremathω1{\mathrm{\ensuremath{\omega}}}_{1}\ensuremathω1​ and \ensuremathω2{\mathrm{\ensuremath{\omega}}}_{2}\ensuremathω2​ 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.
Near-degenerate four-wave parametric mixing in an optical fiber couples fluctuations in signal and idler frequency bands in such a way that the noise at a particular optical phase is reduced while that in an orthogonal phase quadrature is amplified. We have performed experiments on this effect and explained our results in terms of a theory which incorporates a nonlinear dispersion effect. The nonlinear dispersion alters the mathematical character of the solutions and limits the effective interaction length. For relatively low frequency shifts (<100 GHz) and 100 m of fiber, the heterodyne detected optical noise can be reduced by 5 dB in the squeezed quadrature. Theory predicts that this parametric interaction should reduce the noise level below the standard quantum limit. In a realistic fiber, phase noise due to guided acoustic wave Brillouin scattering (GAWBS) dominates the quanturn noise and cannot be reduced by four-wave mixing. Narrow gaps in the GAWBS noise can be engineered into special fibers. At the frequencies of these gaps, the noise level indeed can be squeezed below the quantum limit.
The stagnating increase in data transmission capacity in optical communication systems combined with the ever growing demand of transmission bandwidth is leading to an impending capacity crunch, referring to the point in time after which the available bandwidth of the individual user starts to decrease. To postpone this point in time, existing technologies in terms of data transmission through optical fibers must be optimized and new degrees of freedom must be introduced to continue the exponential increase in available bandwidth; space-division multiplexing is believed to be the strongest candidate for another degree of freedom in transmission fibers. This thesis is two-fold: firstly, starting at Maxwell’s equations and basic principles of quantum mechanics, a semi-classical model of the noise properties of fiber optical parametric amplifiers and frequency converters is presented. The model accounts for multiple effects present in nonlinear fibers such as four-wave mixing, Raman scattering, distributed loss, and dispersion, and it is valid in the depleted pump regime. After validating the model against well-known results of quantum models, the model is used to predict the impacts of Raman noise, loss, and pump depletion on the noise properties of parametric frequency conversion and phase-insensitive and phase-sensitive parametric amplification. An important part of realizing space-division multiplexing is the ability of optical signal processing so the second part of this thesis addresses few-mode Raman fiber amplifiers and parametric amplifiers and frequency converters. A model of weak random linear mode coupling in the pump of a two-mode distributed Raman fiber amplifier is presented and it is shown that an amplification noise figure induced by mode coupling increases with the degree of mode coupling and that this tendency increases as the pump depletes. Also, a very low mode-dependent gain of 0.25 dB per 10 dB gain is experimentally demonstrated in a two-mode distributed Raman fiber amplifier by exciting the pump in a combination of two modes. A comprehensive model of four-wave mixing in two-mode fibers acvi counting for six simultaneous processes is derived, and the conversion efficiency from signal to idler in the four-wave mixing processes of phase conjugation and Bragg scattering in two two-mode fibers with different phase matching properties are experimentally investigated. A conversion efficiency of > −2.70 dB is demonstrated for Bragg scattering in the conversion of a signal in the LP01-mode to the idler in the LP11-mode; the signal-to-idler separation is ∼ 25 nm. Good qualitative agreement between experiments and theory is found for both processes in both fibers.
A theoretical investigation on the coherent control of optical transient four-wave mixing interactions in two-level systems with two intense few-cycle propagating laser pulses of central angular frequencies $\ensuremath{\omega}$ and $3\ensuremath{\omega}$ is reported. By numerically solving the full Maxwell-Bloch equations beyond the slowly varying envelope and rotating-wave approximations in the time domain, the nonlinear coupling to the optical field at frequency $5\ensuremath{\omega}$ is found to depend critically on the initial relative phase $\ensuremath{\phi}$ of the propagating pulses: the coupling is enhanced when the pulses interfere constructively in the center $(\ensuremath{\phi}=0)$, while it is nearly suppressed when they are out of phase $(\ensuremath{\phi}=\ensuremath{\pi})$.