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Journal of the Optical Society of America B

Quantum noise spectrum in fiber-based nondegenerate phase-sensitive amplification considering phase mismatch and Raman scattering

Kyo Inoue

Published Nov 8, 2019• 3 citations
Publisher

Abstract

Wavelength dependence of quantum noise in nondegenerate phase-sensitive amplification in an optical fiber, where signal and its phase-conjugated idler lights are incident into a fiber together with pump light, is theoretically investigated. An analytical formula of the quantum-limited noise figure, that takes Raman scattering into account as well as parametric amplification, is derived based on full quantum mechanical treatment. Using the obtained formula, a calculation example of the noise figure spectrum is also presented, where the pump light phase is adjusted so that the signal gain is maximum at a phase-matched wavelength, supposing multichannel amplification.

DOI
10.1364/josab.36.003380

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Journal of the Optical Society of America B•Jul 23, 2018•5 citations
Wavelength dependence of quantum noise in nondegenerate phase-sensitive amplification in an optical fiber, where signal and its phase-conjugated idler lights are incident into a fiber together with pump light, is theoretically investigated. An analytical formula of the quantum-limited noise figure, that takes Raman scattering into account as well as parametric amplification, is derived based on full quantum mechanical treatment. Using the obtained formula, a calculation example of the noise figure spectrum is also presented, where the pump light phase is adjusted so that the signal gain is maximum at a phase-matched wavelength, supposing multichannel amplification.
Phase-sensitive amplification (PSA) can provide low-noise signal amplification, and a quantum-limited noise figure of 0 dB, that is, additional noise-free amplification, is theoretically achievable. However, in fiber-based single-pumped PSA systems, it has been reported that Raman scattering in the fiber degrades the noise figure from the ideal 0 dB. In the present study, the influence of Raman scattering on quantum noise in dual-pumped degenerate PSA in a fiber is investigated. A quantum mechanical treatment starting from the Heisenberg equation of motion is developed, considering the parametric interaction and Raman interaction simultaneously, and an analytical expression for the noise figure is derived. An example of calculation is also presented, which quantitatively indicates the degradation in the noise figure due to Raman scattering.
Phase-sensitive amplification (PSA) based on nonlinear parametric interaction provides low-noise amplification such that the noise figure can be 0 dB in principle. However, when an optical fiber is used as a nonlinear medium for PSA, multiple four-wave-mixing (FWM) processes other than the PSA process are induced, which can degrade the PSA noise performance, especially in dual-pump PSA with a narrow signal-pump wavelength separation. This paper investigates the influence of multiple FWM processes on quantum noise of dual-pump PSA in an optical fiber. The noise figure is calculated using quantum-mechanical operators, considering multiple FWM processes with the PSA process. Calculation examples are also presented, which indicate that the noise figure is degraded by 0.2–0.4 dB from the ideal 0 dB, depending on the signal-pump wavelength separation and fiber parameters.
Phase-sensitive amplification (PSA) is a unique optical amplification scheme, featuring a low-noise property (i.e., quantum limited noise figure of 0 dB) and a phase clamping effect available for phase noise suppression [1]. It is based on optical parametric interaction between signal and pump lights. It is known that the interaction efficiency and then the signal gain depend on the phase matching between those interacting lights. There are typically two frequency arrangements for PSA in an optical fiber: (i) one pump (frequency: fp) with signal (frequency: fs) and conjugated idler (frequency: fi) satisfying fs+ fi= 2fp[Fig. 1(a)], and (ii) two pumps (frequencies: fp1, fp2) with signal (frequency: fs) satisfying fp1+ fp2= 2fs[Fig. 1(b)]. The phase matching condition for the former is well known, which is equivalent to that of phase-insensitive amplification where the signal light is amplified without an idler incident, such that the phase matching is satisfied when the center wavelength of interacting lights is in the normal dispersion region, i.e., a wavelength longer than the zero-dispersion wavelength of a fiber, as indicated in Fig. 1(a) [2]. On the other hand, the phase-matching condition for the latter has not been explicitly investigated, to the author's knowledge. Although several experimental demonstrations of dual-pump fiber PSA have been reported, many of them employed the wavelength allocation of the center wavelength being in the normal dispersion region, without detailed considerations on the phase matching [3-6]. Thereupon, this paper studies the phase matching condition of dual-pump PSA in an optical fiber.
We experimentally investigate the evolution of the direct detection noise figure of a nondegenerate phase-sensitive amplifier based on a nonlinear fiber, as a function of the relative phase between the signal, idler, and pump, all other parameters remaining fixed. The use of a fiber with a high stimulated Brillouin scattering threshold permits us to investigate the full range of phase-sensitive gain and noise figure without pump dithering. Good agreement is found with theory, both for signal only and combined signal and idler direct detections.
We experimentally investigate the evolution of the direct detection noise figure of a nondegenerate phase-sensitive amplifier based on a nonlinear fiber, as a function of the relative phase between the signal, idler, and pump, all other parameters remaining fixed. The use of a fiber with a high stimulated Brillouin scattering threshold permits us to investigate the full range of phase-sensitive gain and noise figure without pump dithering. Good agreement is found with theory, both for signal only and combined signal and idler direct detections.
Phase-sensitive amplification (PSA) is a particular type of optical parametric amplification (OPA) that features a low-noise property such that the quantum-limited noise figure is 0 dB. The PSA operation is typically achieved when the signal and idler spectra are degenerate in optical parametric interactions, i.e., the degenerate OPA condition. However, for a spectrally broadened incident light, these two spectra can be partially degenerate. The present work investigates the noise property of OPA in such conditions in terms of quantum mechanics. The results quantitatively indicate the intermediate properties between PSA and phase-insensitive amplification.