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Optics Express

Dependence of the amplification performance of unsaturated degenerate phase-sensitive amplification on wavelength allocation

Kyo Inoue

Published Nov 14, 2017• 4 citations
Publisher

Abstract

This paper theoretically investigates the dependence of the performance of dual-pump degenerate phase-sensitive amplification (PSA) on wavelength allocation. A fiber-based PSA under unsaturated-gain conditions is considered. Phase mismatch is formalized in terms of incident light frequencies, taking the nonlinear phase shift into account, based on which PSA performances, such as signal gain, noise figure, and phase-clamping effect, are evaluated as a function of the signal wavelength. The results quantitatively indicate that these PSA properties are degraded as the signal wavelength is detuned from the phase-matched condition.

DOI
10.1364/oe.25.029724

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This paper theoretically investigates the dependence of the performance of dual-pump degenerate phase-sensitive amplification (PSA) on wavelength allocation. A fiber-based PSA under unsaturated-gain conditions is considered. Phase mismatch is formalized in terms of incident light frequencies, taking the nonlinear phase shift into account, based on which PSA performances, such as signal gain, noise figure, and phase-clamping effect, are evaluated as a function of the signal wavelength. The results quantitatively indicate that these PSA properties are degraded as the signal wavelength is detuned from the phase-matched condition.
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.
Dual-pump fiber optical parametric amplifiers offer wide, flat gain spectra across arbitrary wavelengths, often outperforming the use of single-pump designs. However, gain flatness depends on the pump frequencies’ center of gravity relative to the nonlinear fiber’s zero-dispersion wavelength. This study experimentally investigated the gain, gain flatness, and noise figure of degenerate dual-pump fiber-optic phase-sensitive amplification at various separations between these points. We demonstrated 38 dB gain with 1.5 dB gain flatness variation over a 30 nm bandwidth as well as a noise figure below the conventional 3 dB quantum limit for a degenerate signal.
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) 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 amplifiers (PSAs) offer numerous advantages over phase-insensitive amplifiers in optical communications. Squeezing of optical phase through PSA can remove accumulated phase jitter, which is a critical functionality for an all- optical, phase-shift keyed network. In recent experiments, reviewed in this report, different implementations of PSA were used for phase regeneration of both return-to-zero differential phase-shift keying and nonreturn-to-zero differential phase-shift keying data. The first demonstration explored the properties and performance of PSA that occurs in nonlinear interferometers. Experiments confirmed that a PSA operating in the depleted pump regime provides simultaneous reduction of amplitude and phase noise (PN). Phase regeneration performance limit was reached as a consequence of pump-wave imperfections, which can be significantly reduced through proper design. PSA that occurs directly in fiber in a traveling-wave configuration through partially degenerate four-wave mixing was also studied. The latter implementation offers stronger phase-matched gain and suppression of amplitude-to-phase noise conversion. Technical issues that remain to be addressed are identified for each implementation. Results characterized using coherent detection offer direct measurements of the phase-regenerative behavior.