JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 25, NO. 9,SEPTEMBER 2007 2837 Noise in Dual-Pumped Fiber-Optical Parametric Ampliﬁers: Theory and Experiments Per Kylemark, Jian Ren, Magnus Karlsson, Stojan Radic, Member,IEEE, Colin J. McKinstrie, and Peter A. Andrekson, Fellow,IEEE Abstract—The noise ﬁgure (NF) of a dual-pumped parametric ampliﬁer with copolarized pumps is quantiﬁed for the ﬁrst time to our knowledge. It is shown that the NF is increased by the noise on the pump sources, in agreement with theory, and that it gives a uniform NF degradation due to a uniform gain spectrum. The magnitude of the NF degradation increases with increasing input-signal power. Various aspects of the NF are studied, such as the effects of three idlers generated by the four-sideband in- teraction, and Raman-induced losses and excess noise caused by the population of thermal phonons. It is shown that the use of unequal pump powers only affects the low-power NF to a minimal degree. Also, the gain dependence of the NF is studied, as are the wavelength and signal power dependences of the NF. It is shown that at high gain, the NF saturates even when pump noise is an issue. Also, unequal pump powers with ﬁxed gain have a minor impact on the noise performance of the ampliﬁer. Theory and experiments agree well with each other. Index Terms—Four-wave mixing (FWM), modulation inter- action (MI), noise ﬁgure (NF), parametric ampliﬁcation, phase conjugation (PC). I. I NTRODUCTION T HE ﬁber-optical parametric ampliﬁer (FOPA) is unique in many ways [1], [2]. It not only provides gain but also simultaneously acts as a wavelength converter through the gen- eration of phase-conjugated signal copies, which are also called idlers. Phase conjugation (PC) can be used to counteract ﬁber dispersion [3]. Also, the idlers can be used for signal-quality monitoring [4], [5]. The FOPA is a multipurpose device with applications [6] to wavelength conversion [1], optical pulse generation (return to zero and nonreturn to zero) [7], optical sampling at very high bit rates [8], optical demultiplexing [9], packet switching [10], optical-level equalization [11], and op- tical regeneration [12], [13]. Although it enables many current applications and has the potential to enable many more, it is still a relatively immature ampliﬁer and is the subject of much ongoing research. What makes the FOPA special compared to other ampliﬁers is the requirement of phase matching between the ampliﬁed signal and the pumps [1], [14]. This puts the Manuscript received September 14, 2006; revised March 16, 2007. This work was supported in part by the Swedish Foundation for Strategic Research and by the U.S. National Science Foundation under Grant ECS-0406379. P. Kylemark, M. Karlsson, and P. A. Andrekson are with the Photonics Laboratory, Department of Microtechnology and Nanoscience, Chalmers Uni- versity of Technology, 412 96 Göteborg, Sweden (e-mail: per@gnulix.org; Magnus.karlsson@mc2.chalmers.se; Peter.andrekson@mc2.chalmers.se). J. Ren and S. Radic are with the Department Electrical and Computer Engineering, University of California at San Diego, La Jolla, CA 92093 USA. C. J. McKinstrie is with Bell Laboratories, Alcatel-Lucent, Holmdel, NJ 07733 USA. Digital Object Identiﬁer 10.1109/JLT.2007.902098 demands of small dispersion and dispersion slope on the ﬁbers that are utilized. The dispersion dependence of the gain might in the future realize optical ampliﬁers with extremely broad bandwidths [15]. Also, the response time of the parametric ampliﬁer (PA) is extremely short, i.e., only a few femtoseconds, as it is based on the Kerr effect. This property is one of the main reasons that it can be used for diverse applications, because any change in pump power immediately affects the gain. The PA was long thought to be a perfect ampliﬁer in terms of its noise performance with only a minimal amount of noise added that is dictated by the Heisenberg uncertainty principle. The noise performance is quantiﬁed by the noise ﬁgure (NF), and an optical ampliﬁer is said to be quantum limited when the NF approaches 3 dB [16], [17]. However, it was shown that the PA suffers from additional noise caused by the optical pump source due to the pump-power dependence of the gain [18], [19]. The FOPA’s ultrafast response, together with the require- ment of good phase matching, might make this source of noise particularly large compared with other ampliﬁers that do not require good phase matching to provide gain, for example, the Raman ampliﬁer [20]. The reason is that a large walk-off (WO) between the signal and the pump imposes a bandwidth limitation on the pump-induced noise, which consequently reduces the NF for ampliﬁers with large WOs [21]. Raman ampliﬁers can also be implemented with counter-propagating pumps, in which case, the WO is maximal, and the pump- induced noise is minimal. The presence of pump noise in a PA results in an NF that increases linearly with input power of the optical signal. At low input-signal powers, the quantum-limited NF is approached. As is well known, the FOPA can be implemented with one or with many pumps. The NF of the single-pumped PA (1-pump PA) has been studied both theoretically [18], [19] and experimentally [22]–[24], with very good agreement, whereas the dual-pumped PA (2-pump PA) has been primarily studied theoretically [25], [26]. The 2-pump PA [27] has advantages compared with the 1-pump PA due to its uniform gain spectrum [28], [29], which also affects its noise performance [26]. In principle, the 2-pump PA is based on a four-sideband (FS) interaction between the two pumps, the signal, and three generated idlers. However, it can be treated approximately as a two-sideband (TS) PA when the two pumps are placed symmet- rically relative to the zero-dispersion frequency (ZDF), and the gain bandwidth is maximized simultaneously. This is fortunate, since at present there only exist theoretical expressions for the FS interaction in limiting cases [25], [28], [29]. The TS process is called PC [28], [29]. The dominance of this TS process 0733-8724/$25.00 © 2007 IEEE