JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 20, NO. 3, MARCH 2002 469 Narrow-Linewidth Idler Generation in Fiber Four-Wave Mixing and Parametric Amplification by Dithering Two Pumps in Opposition of Phase Min-Chen Ho, Member, IEEE, Michel E. Marhic, Senior Member, IEEE, Member, OSA, K. Y. Kenneth Wong, Student Member, IEEE, and Leonid G. Kazovsky, Fellow, IEEE, Fellow, OSA Abstract—Wide-bandwidth and high-gain fiber optical para- metric amplifiers (OPAs) have been demonstrated recently. Their application as all-optical wavelength converters has been ham- pered by pump-induced converted-signal spectrum broadening, due to the required pump phase modulation. In this paper, we the- oretically investigate and experimentally demonstrate a technique to cancel the converted-signal broadening by using four-wave mixing (FWM) or parametric amplification with two pumps phase-modulated 180 out of phase. The resulting converted- signal quality is comparable to that of the output signal. Index Terms—Brillouin scattering, optical frequency conver- sion, optical parametric amplifiers (OPAs), phase modulation. I. INTRODUCTION W AVELENGTH converters are important building blocks in wavelength division multiplexing (WDM) networks. They allow nonblocking wavelength routing and de-entralized wavelength management [1], [2]. Although wavelength converters based on optical-to-electrical (O/E) and electrical-to-optical (E/O) techniques provide good signal quality, all-optical wavelength converters have the advantages of modulation format and bit rate transparency, and can provide multiwavelength conversion simultaneously. Several all-optical wavelength conversion techniques have been proposed and demonstrated [3]–[6]. Fiber optical parametric amplifiers (OPAs) have been demonstrated recently to have potential wide bandwidth [7]. A high-gain continuous wave (CW)-OPA has also been demonstrated [8], showing the practical use of fiber OPAs as both amplifiers and wavelength converters. However, the performance of fiber OPAs as wavelength converters is lim- ited by the degradation of converted-signal quality. Specifically, the spectrum of the converted signal (idler) is broadened by the dithering of the pump, which is required to avoid stimulated Brillouin scattering (SBS). In a one-pump fiber OPA, the idler spectral broadening can reach several gigahertz, which is too large for many practical applications. Manuscript received January 31, 2001; revised October 30, 2001. This work was supported by the National Science Foundation (NSF) under Grant ECS- 9821026-001. M.-C. Ho was with with the Optical Communication Research Laboratory (OCRL), Department of Electrical Engineering, Stanford University, Stanford, CA 94305 USA. She is now with Onetta, Inc., San Jose, CA 94089 USA. M. E. Marhic, K. Y. K. Wong, and L. Kazovsky are with the Optical Commu- nication Research Laboratory (OCRL), Department of Electrical Engineering, Stanford University, Stanford, CA 94305 USA. Publisher Item Identifier S 0733-8724(02)01477-9. In [9], we proposed a technique using opposite dithering of two pumps to solve the idler broadening problem, and reported preliminary experimental results in [10]. It relies on the use of two pumps, phase-modulated 180 out of phase, to cancel out the broadening of the converted signal. In this paper, we present a theoretical model and additional results for this tech- nique. We have performed four-wave mixing (FWM) and OPA experiments to demonstrate the principle. We demonstrated two separate pump dithering techniques, and in each case, we ob- tained very effective linewidth broadening reduction of the con- verted signal. A technique based on dithering of one pump and the signal was presented in [11]. II. THEORY:IDLER BROADENING IN FWM AND TWO-PUMP OPA Fiber OPAs are based on the nonlinearity in the fiber. When a single strong pump propagates with a relatively weak signal in the fiber, energy is transferred from pump to signal and idler (converted signal) through nonlinear interactions. The pump, signal, and idler angular frequencies satisfy the relation . The efficiency and gain bandwidth of fiber OPAs strongly depend on the pump power. Pump power levels over hundreds of milliwatts are currently necessary to achieve reasonable performance. Unfortunately, at this high power level, another nonlinear phenomenon, stimulated Brillouin scattering (SBS) also occurs. It causes reflection of most pump power and, thus, reduces the pump power going through the fiber. SBS has been studied widely, and techniques have been proposed and demonstrated to suppress it. Because SBS has only a very narrow bandwidth, a common technique to suppress it is to ar- tificially broaden the pump linewidth by modulating the pump. This process is called pump dithering. Amplitude modulation (AM), frequency modulation (FM), or phase modulation (PM) can be used to achieve this goal. At high pump powers, pump broadening of several gigahertz is required. Although pump dithering suppresses SBS, it creates another problem, shown in Fig. 1(a). If is shifted by , then is shifted by . As a result, the pump frequency dithering is transferred to the idler, multiplied by a factor of two. This leads to idler spectrum broadening of several gigahertz at high pump power. To solve the idler linewidth broadening problem, a technique was proposed in [9]. The principle is shown in Fig. 1(b). Instead 0733-8724/02$17.00 © 2002 IEEE