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Journal of Optics B Quantum and Semiclassical Optics

Raman-effect induced noise limits on (3)parametric amplifiers and wavelength converters

Paul L. Voss, Prem Kumar

Published Jul 28, 2004• 48 citations
Publisher

Abstract

The non-zero response time of the Kerr (χ (3) ) nonlinearity determines the quantum-limited noise figure of χ (3) parametric amplifiers and wavelength converters. This non-zero response time of the nonlinearity requires coupling of the parametric amplification process to a molecular-vibration phonon bath, causing the addition of excess noise through Raman gain or loss. The effect of this excess noise on the noise figure of the amplifier can be significant. We derive analytical expressions for this quantum-limited noise figure in the case of non-degenerate phase-insensitive operation of a χ (3) parametric amplifier and show excellent agreement with experiment without any fitting parameter. We also derive analytical expressions for the quantum limited noise figure for χ (3) -based wavelength converters.

DOI
10.1088/1464-4266/6/8/021

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The non-zero response time of the Kerr (χ (3) ) nonlinearity determines the quantum-limited noise figure of χ (3) parametric amplifiers and wavelength converters. This non-zero response time of the nonlinearity requires coupling of the parametric amplification process to a molecular-vibration phonon bath, causing the addition of excess noise through Raman gain or loss. The effect of this excess noise on the noise figure of the amplifier can be significant. We derive analytical expressions for this quantum-limited noise figure in the case of non-degenerate phase-insensitive operation of a χ (3) parametric amplifier and show excellent agreement with experiment without any fitting parameter. We also derive analytical expressions for the quantum limited noise figure for χ (3) -based wavelength converters.
The nonzero response time of the Kerr [chi(3)] nonlinearity determines the quantum-limited noise figure of chi(3) parametric amplifiers. This nonzero response time of the nonlinearity requires coupling of the parametric amplification process to a molecular-vibration phonon bath, causing the addition of excess noise through Raman gain or loss at temperatures above 0 K. The effect of this excess noise on the noise figure can be surprisingly significant. We derive analytical expressions for this quantum-limited noise figure for phase-insensitive operation of a chi(3) amplifier and show good agreement with published noise-figure measurements.
We present a quantum theory of nondegenerate phase-sensitive parametric amplification in a χ(3) nonlinear medium. The nonzero response time of the Kerr (χ(3)) nonlinearity determines the quantum-limited noise figure of χ(3) parametric amplification, as well as the limit on quadrature squeezing. This nonzero response time of the nonlinearity requires coupling of the parametric process to a molecular vibration phonon bath, causing the addition of excess noise through spontaneous Raman scattering. We present analytical expressions for the quantum-limited noise figure of frequency nondegenerate and frequency degenerate χ(3) parametric amplifiers operated as phase-sensitive amplifiers. We also present results for frequency nondegenerate quadrature squeezing. We show that our nondegenerate squeezing theory agrees with the degenerate squeezing theory of Boivin and Shapiro as degeneracy is approached. We have also included the effect of linear loss on the phase-sensitive process.
We present a quantum theory of nondegenerate phase-sensitive parametric amplification in a chi^3 nonlinear medium. The non-zero response time of the Kerr chi^3 nonlinearity determines the quantum-limited noise figure of chi^3 parametric amplification, as well as the limit on quadrature squeezing. This non-zero response time of the nonlinearity requires coupling of the parametric process to a molecular-vibration phonon bath, causing the addition of excess noise through spontaneous Raman scattering. We present analytical expressions for the quantum-limited noise figure of frequency non-degenerate and frequency degenerate chi^3 parametric amplifiers operated as phase-sensitive amplifiers. We also present results for frequency non-degenerate quadrature squeezing. We show that our non-degenerate squeezing theory agrees with the degenerate squeezing theory of Boivin and Shapiro as degeneracy is approached. We have also included the effect of linear loss on the phase-sensitive process.
Recent theoretical work predicts that the quantum-limited noise figure of a x(3)-based fiber-optical parametric amplifier operating as a phase-insensitive in-line amplifier or as a wavelength converter exceeds the standard 3-dB limit at high gain. The degradation of the noise figure is caused by the excess noise added by the unavoidable Raman gain and loss occurring at the signal and the converted wavelengths. We present detailed experimental evidence in support of this theory through measurements of the gain and noise-figure spectra for phase-insensitive parametric amplification and wavelength conversion in a continuous-wave amplifier made from 4.4 km of dispersion-shifted fiber. The theory is also extended to include the effect of distributed linear loss on the noise figure of such a long-length parametric amplifier and wavelength converter.
The noise figure (NF) of a phase-sensitive parametric amplifier using a nonlinear Mach-Zehnder interferometer (NMZI) with Kerr media is analyzed for amplitude-modulation signals. In the analysis, the distributed loss of the Kerr media and the excess noise of the pump light are taken into account. As for the distributed loss of the Kerr media, the quantum Langevin equation for the NMZI is derived and solved. The results elucidate a simple degradation factor in the NF representation of the amplifier. This factor implies that the NF can be less than the standard quantum limit (SQL) of 3 dB, even if the total loss of the Kerr media exceeds 3 dB. As for the excess noise of the pump light, the semi-classical small signal analysis is utilized. The results clearly indicate that the signal-to-noise ratio of the pump light must be four times higher than that of the input signal in order to realize a low-noise optical amplifier under the SQL of 3 dB.