IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 23, NO. 6, MARCH 15, 2011 365 Impact of Zero-Dispersion-Wavelength Distributions on the Noise Figure Nonreciprocity of a Fiber Parametric Amplifier Zhi Tong, Member, IEEE, Carl Lundström, Magnus Karlsson, and Peter A. Andrekson, Fellow, IEEE Abstract—For the first time we both theoretically and experi- mentally show that the zero-dispersion-wavelength (ZDW) vari- ations in highly nonlinear fibers (HNLFs) will modify the output noise figure (NF) of a fiber optical parametric amplifier and make it nonreciprocal, due to the Raman phonon induced excess noise. The results show that a longer ZDW (but still below the pump wave- length) close to fiber input will give a better noise performance. The experimental results agree well with theory. Index Terms—Four-wave mixing, noise measurement, optical parametric amplifier, Raman scattering. I. INTRODUCTION N OISE performance of fiber optical parametric ampli- fiers (FOPAs) has been extensively studied. Besides the intrinsic amplified quantum noise (AQN), three main excess noise sources have been reported to degrade the noise figure of a FOPA [1], which are Raman phonon induced excess noise, pump transferred noise (PTN) and pump residual amplified spontaneous emission (ASE), respectively. However, most of the previous works ignored ZDW fluctuations in FOPAs, which originate from the longitudinal nonuniformity in the gain fibres, and become an important factor limiting the maximum FOPA gain as well as bandwidth [2]. Velanas et al. [3] simulated the NF spectra of FOPAs with random ZDW fluctuations by taking into account both AQN and PTN. They carried out numerous calculations to account for the ZDW statistics and then obtained the average gain and NF, which makes the analysis complicated and time-consuming. When considering the impacts of ZDW distributions on FOPA NF performance, a problem is that different ZDW vari- ations might significantly change the maximum gain as well as the bandwidth, which makes direct NF comparisons unfair (only NF within the gain bandwidth is meaningful). It is better to analyze the NF characteristics with ZDW fluctuations under the same gain spectrum. Marhic et al. [4] have proved that the Manuscript received June 13, 2010; revised December 19, 2010; accepted January 01, 2011. Date of publication January 28, 2011; date of current version March 04, 2011. This work was supported in part by the European Commission STREP project PHASORS (FP7-ICT-2007-2 22457), and by the Air Force Of- fice of Scientific Research, Air Force Material Command, USAF (FA8655-09-1- 3076). The authors are with the Photonics Laboratory, Department of Microtech- nology and Nanoscience, Chalmers University of Technology, SE-412 96 Göte- borg, Sweden (e-mail: zhi.tong@chalmers.se). Color versions of one or more of the figures in this letter are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/LPT.2011.2106202 FOPA gain is reciprocal even in presence of arbitrary ZDW variations. This characteristic makes it possible to directly compare the impacts of ZDW distributions on noise perfor- mance. Thus, more general conclusions can be expected. In this letter, we experimentally verify that the noise performance of a FOPA is nonreciprocal [5], and the measured results are in good agreement with theory. A better NF spectrum can be obtained by placing the fiber with longer ZDW (but still below the pump wavelength) closer to the input end. Raman phonon induced noise leads to this NF nonreciprocity, which does not depend on the phase-mismatching caused by ZDW variations. II. THEORETICAL RESULTS By dividing the gain fiber into small pieces and assuming each piece is uniform, the longitudinal fiber imperfectness like ZDW variations or random birefringence can be modeled in a transfer-matrix fashion (in the un-depleted pump regime) as (1) where represents the complex amplitude, subscripts and denote anti-Stokes and Stokes waves, is the input signal amplitude, and superscript represents the conjugation oper- ation. The uncorrelated vacuum noise fields at the anti-Stokes and Stokes frequencies are denoted as and , respectively. Considering Raman effect, we have [1], [6] (2) where the complex transfer coefficients and depend on the pump power and the phase-matching conditions as well as fiber Raman response, as defined in [1]. is the fiber length, means the fiber segment ranges from to . Each fiber ma- trix can contain different (but constant) ZDW values. Equation (1) applies to both single- and dual-pumped FOPAs. In the fol- lowing we will assume the copolarized, PMD-free case for sim- plicity, due to the fact that contemporary HNLFs exhibit very low PMD coefficients (typically less than 0.05 ps ). According to (1), it can be proved that the signal gain as well as AQN remains identical regardless of the pumping direc- tions, even with Raman effect (Raman gain is independent of the phase-mismatching induced by ZDW variations). Both signal and AQN will experience the same gain in either direction. This is also true after adding the PTN contribution, as PTN is related to the derivative of the FOPA gain with respect to pump power [7], while this derivative remains unchanged when altering the pumping direction. 1041-1135/$26.00 © 2011 IEEE