1458 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 40, NO. 10, OCTOBER 2004 Quantum-Limited Timing Jitter in Actively Modelocked Lasers Matthew E. Grein, Student Member, IEEE, Hermann A. Haus, Life Fellow, IEEE, Y. Chen, and Erich P. Ippen, Fellow, IEEE Abstract—Expressions for the quantum-limited timing jitter in an actively modelocked fiber laser are derived. We identify a set of characteristic constants that govern the timing jitter for the cases using amplitude modulation (AM) and phase modulation (PM) as the active modelocking elements. We find that when using AM, the Gordon–Haus jitter is proportional to the square of the group-ve- locity dispersion and reaches a minimum value for the case of low dispersion. Using PM, the Gordon–Haus jitter increases only lin- early proportional to group-velocity dispersion, and there exists an optimum group-velocity dispersion that minimizes the jitter. We compare the theory to recent experiments of the timing jitter for an active harmonically modelocked fiber laser. Index Terms—Active modelocking, amplitude modulation, phase modulation, quantum noise, timing jitter. I. INTRODUCTION T HE demand for stable, modelocked laser sources with ex- tremely small amplitude and timing jitter has been driven in recent years by the development of high-speed optical com- munications systems and even more recently by the need for precision, high-speed analog-to-digital conversion in which a stream of optical pulses at a high repetition rate is used to set the sampling rate [1]–[4]. Timing jitter degrades bit-error-rate performance in the former, and leads to sampling errors and a limitation on the achievable dynamic range in the latter. The types of laser sources of interest for such applications are ac- tively modelocked lasers in which low-noise, picosecond pulses can be generated and synchronized with an external clock at gi- gahertz repetition rates. There have been a number of theoretical studies of timing jitter in actively modelocked lasers [5]–[10]. A comprehensive analysis of timing jitter in ultrafast modelocked lasers appli- cable to solid-state and other gain media for which the fast gain Manuscript received June 3, 2004. This work was supported by the De- fense Advanced Research Projects Agency under U.S. Air Force Contract F 19628-00-C-0002. M. E. Grein was with the Research Laboratory of Electronics and Depart- ment of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA 02139 USA. He is now with the Lincoln Labo- ratory, MassachusettsInstitute of Technology, Lexington, MA 02420-9108 USA (e-mail: megrein@ll.mit.edu). Y. Chen was with the Research Laboratory of Electronics and Department of Electrical Engineering and Computer Science, Massachusetts Institute of Tech- nology, Cambridge, MA 02139 USA. H. A. Haus, deceased, was with the Research Laboratory of Electronics and Department of Electrical Engineering and Computer Science, Massachusetts In- stitute of Technology, Cambridge, MA 02139 USA. E. P. Ippen is with the Research Laboratory of Electronics, Department of Electrical Engineering and Computer Science, and Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139 USA. Digital Object Identifier 10.1109/JQE.2004.834784 dynamics can be ignored was given in a paper by Haus and Mecozzi [11]. In that paper, the noise was handled with soliton perturbation theory (SPT). In this paper, we extend the anal- ysis to actively modelocked fiber lasers and analyze the achiev- able timing jitter performance for the cases of amplitude and phase modulation. The SPT is useful in analyzing the noise of actively modelocked fiber lasers where solitonic effects play a role in the formation of pulses much shorter than that given by active modelocking alone [12]–[17]. Even in cases where the shortest pulses are not required, there is another reason why soli- tonic or some other kind of nonlinear effect are important in real fiber laser systems. High repetition rates (multi-gigahertz) call for harmonic modelocking where the repetition rate is set at a harmonic of the fundamental cavity frequency, resulting in the formation of supermodes that individually compete for gain, re- sulting in amplitude fluctuations in the laser output. It has been shown that nonlinear effects, including additive-pulse limiting [18], self-phase modulation combined with filtering [19], and two-photon absorption [20] can be exploited to suppress the su- permode noise. At present, there are two basic types of modulation em- ployed in the active modelocking of fiber lasers: amplitude modulation (AM) and phase modulation (PM) [21]. The laser pulse characteristics using either modulator (i.e., pulse shape, pulse duration) are similar [15], [17], [22]. However, it has been shown previously [17] that the characteristics of pulse retiming are qualitatively different for AM and PM. For AM, mis-timed pulses experience loss, leading to a timing restora- tion dependent on the slope of the transmission window and the square of the pulsewidth. For PM, mis-timed pulses are initially frequency-shifted. The frequency shift is converted to a timing shift via group-velocity dispersion (GVD), leading to a timing restoration dependent on depth of modulation, GVD, and filtering. We should expect, then, that the resulting timing jitter for AM and PM are quite different, and we show in this paper that they are. Previous work on passively modelocked soliton [23] and stretched-pulse [24], [25] fiber lasers have shown that the timing jitter is quantum-limited in the sense that the amplified spontaneous emission (ASE) of the gain dominates the timing jitter. Many experiments on actively modelocked soliton fiber lasers (AMFL)–in which the laser is modelocked using an external microwave oscillator-have demonstrated that, at present, the timing jitter is limited by the phase noise of the driving oscillator [26]–[29]. This is a technical limitation of the laser timing jitter. However, just as for the case of the passively modelocked laser, the fundamental limitation is given by the ASE. While there are other quantum-noise sources in the laser 0018-9197/04$20.00 © 2004 IEEE