IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 3, NO. 4, AUGUST 1997 1065 Short Cavity Erbium/Ytterbium Fiber Lasers Mode-Locked with a Saturable Bragg Reflector Brandon C. Collings, Keren Bergman, Member, IEEE, S. T. Cundiff, Sergio Tsuda, J. Nathan Kutz, Member, IEEE, J. E. Cunningham, W. Y. Jan, M. Koch, and W. H. Knox Abstract— We present short cavity erbium/ytterbium fiber lasers that are passively mode-locked with a saturable Bragg reflector. The lasers produce sub-500-fs pulses at fundamental cavity repetition rates as high as 300 MHz. Stable passive har- monic operation increases the repetition rate to 2.0 GHz. The mode-locking mechanism in both the normal and anomalous group velocity dispersion regimes is investigated using complete analytical and numerical models and direct comparison with the experimental results. A simple technique for accurately measur- ing the total cavity dispersion is presented. Index Terms— Mode-locked lasers, optical fiber communica- tion, optical fiber lasers, optical pulse generation, optical solitons, quantum-well devices, rare-earth materials/devices, ultrafast op- tics. I. INTRODUCTION H IGH-SPEED optical networks require sources producing ultrashort pulses at ever increasing repetition rates and average output powers. The 1550-nm wavelength region in silica fiber represents the lowest attenuation window where efficient, nearly quantum limited amplification is provided by Er-doped fiber amplifiers and soliton pulse propagation is supported. To be practical, these sources must be compact, reliable and require minimal power consumption. Mode-locked Er-doped fiber lasers, currently the subject of much research, provide potentially attractive short pulse sources possessing some key advantages over modulated continuous-wave (CW) sources including large optical bandwidths, high intensities and powers, short coherence lengths and high timing stabil- ity. The spectral bandwidth generated from a single mode- locked source can be partitioned to form a large number of wavelength-division multiplexed (WDM) channels, which may be economically advantageous over employment of multiple, individually selected distributed-feedback (DFB) lasers [1]. For applications in practical communication systems, mode- locked fiber lasers must demonstrate reliability and preferably Manuscript received April 15, 1997. This work was supported by the National Science Foundation under Grant DMS-9508634 and Grant ECS- 9502491, and by the Brazilian Conselho Nacional de Desenvolvimento Cient´ ıfico e Tecnol´ ogico. B. C. Collings and K. Bergman are with Electrical Engineering, Princeton University, Princeton, NJ 08544 USA. S. T. Cundiff, S. Tsuda, J. E. Cunningham, W. Y. Jan, and W. H. Knox are with Bell Laboratories, Lucent Technologies, Holmdel, NJ 07733 USA. J. N. Kutz is with Bell Laboratories, Lucent Technologies, Holmdel, NJ 07733 USA. He is also with the Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544 USA. M. Koch is with the Physics Department, Ludwig–Maximilians-University, Munich, Germany. Publisher Item Identifier S 1077-260X(97)09017-5. be composed entirely of standard telecommunications certified components. The mode-locking mechanism is central to the development of a competitive source. Several groups have successfully demonstrated passively mode-locked fiber lasers employing additive-pulse mode-locking (APM) which converts nonlinear self-phase modulation (SPM) into ultrafast amplitude modula- tion via an interferometer, as in the figure eight laser [2]–[8]. Another technique employs nonlinear polarization evolution in conjunction with a polarizer which also provides ultrafast amplitude modulation [9]. These mode-locking mechanisms are analogous to a fast saturable absorber and have typi- cally been demonstrated in long length cavities (4–100 m), which can suffer from amplitude and timing jitter induced by environmental instabilities [10]. Fiber lasers have also been passively mode-locked in linear cavity configurations employ- ing a semiconductor structure as the fast saturable absorber [11], [12]. The recently demonstrated saturable Bragg reflector (SBR) provides a self-starting mode-locking mechanism with minimal loss enabling efficient femtosecond mode-locking of low-gain lasers [13]–[16]. Because of this efficient mode- locking mechanism, a minimal amount of gain fiber and intracavity power is required. This allows the construction of shorter fiber laser cavities with higher fundamental repetition rates capable of generating subpicosecond pulses. This is the motivation behind the short (30–200 cm) fiber lasers discussed in this paper, which produce stable, self-starting high repetition rate pulse trains with wide optical bandwidths providing promising sources for high-speed TDM/WDM networks. In this paper, we present several fiber lasers of various lengths mode-locked with SBR’s with cavity dispersions in both the normal and anomalous (soliton) regimes. We also demonstrate passive harmonic mode-locking which produces stable, multigigabit femtosecond pulse trains. We study the dynamics of the SBR and mode-locking mechanism both experimentally and theoretically for several cavity configu- rations. Our model accounts for the formation dynamics of the pulse and its interaction with the SBR. Three separate time constants are used to model the SBR: an instantaneous response, a slow saturated response and a relaxation time. The overall temporal response of the SBR model closely matches experimental measurements obtained with pump- probe experiments. Our general mode-locking model predicts both the temporal and spectral pulse profiles with remarkable accuracy. We also present a simple method for accurately measuring the total group velocity dispersion of a complete 1077–260X/97$10.00  1997 IEEE