PHYSICAL REVIEW A 81, 023815 (2010) All-fiber ring Raman laser generating parabolic pulses V. I. Kruglov, D. M´ echin, * and J. D. Harvey Physics Department, The University of Auckland, Private Bag 92019, Auckland, New Zealand (Received 23 July 2009; published 16 February 2010) We present theoretical and numerical results for an all-fiber laser using self-similar parabolic pulses (“similaritons”) designed to operate using self-similar propagation regimes. The similariton laser features a frequency filter and a Sagnac loop which operate together to generate an integrated all-fiber mode-locked laser. Numerical studies show that this laser generates parabolic pulses with linear chirp in good agreement with analytical predictions. The period for propagating similariton pulses in stable regimes can vary from one to two round trips for different laser parameters. Two-round-trip-period operation in the mode-locked laser appears at bifurcation points for certain cavity parameters. The stability of the similariton regimes has been confirmed by numerical simulations for large numbers of round trips. DOI: 10.1103/PhysRevA.81.023815 PACS number(s): 42.60.Fc, 42.65.Jx, 42.81.Dp, 42.25.Fx I. INTRODUCTION Pulse formation in modern femtosecond lasers is generally mediated by the interplay between dispersion and nonlinearity. In these cases, a self-focusing nonlinearity is balanced by anomalous group velocity dispersion (GVD) [1,2]. Such lasers have segments of normal and anomalous GVD and the net or path-averaged cavity dispersion can be normal, zero, or anomalous. In the cases when the net GVD approaches zero, stretched-pulses can occur [3], described by breathing solutions. Such fiber lasers can have pulse energies an order of magnitude higher than soliton lasers. More complex pulse formation and pulse evolution occurs when the cavity GVD approaches zero and finally becomes normal. It has been demonstrated [4] that the resulting lengthy pulses are highly chirped, in agreement with the theory [2]. Pulse shaping in such a laser is based on spectral filtering of the chirped pulse, which cuts off the temporal wings of the pulse. Mode-locked laser operation with large net normal GVD is expected to lead to stable high-energy pulses [5]. Self-similar parabolic pulses (“similaritons”) with a lin- ear chirp generated in optical-fiber amplifiers with normal GVD have generated considerable interest in recent years. Asymptotically exact similaritons have been found and exper- imentally observed for propagation in optical-fiber amplifiers [6–9]. The results of these theoretical, experimental and numerical studies have recently found increasing practical application in high-power amplifier systems, efficient temporal compressors [10–16], and similariton lasers. The similariton solution also has been found in the growth of trapped Bose- Einstein condensates (BECs) [17] and for trapped BECs in 3 + 1 dimensions [18]. Recently, the self-similar laser [19] and so-called chirped-pulse oscillator (CPO) [20] have been investigated for large net normal GVD to achieve higher pulse energies [21,22]. Both self-similar and CPO lasers generate high pulse energies with femtosecond dechirped pulse durations [23–25]. The pulses propagating in self-similar lasers are parabolic and highly chirped. * Present address: PERFOS, 11 Rue de Broglie, 22300 Lannion, France. The stability of the pulse generation from one round trip to another in a laser is an important quantity for applications in optics and telecommunications [26–28]. Pulse evolution with periodic changes of the pulse energy from one round trip to another can also yield stable [29] and useful devices. The impact of amplified spontaneous emission noise and Raman- induced imperfections in amplification where calculated for optical-fiber communication systems in Refs. [30–32]. We report here theoretical and numerical predictions for the generation of parabolic pulses in an all-fiber ring laser with Raman amplification. These similariton pulses tend toward a parabolic shape and accumulate a linear chirp, in agreement with theoretical predictions. We have observed that the frequency filter and Sagnac loop operating as one integrated unit can yield mode-locked laser operation for this similariton laser. The all-fiber similariton laser presented here (Fig. 1), supported by a full analytical model, is designed to operate using self-similar propagation regimes. For appropriate laser parameters, it demonstrates stable operating regimes with period-one and period-two round-trip operation. We call such stable regimes similariton period-one (SP1) and similariton period-two (SP2). The new period-two operation in the mode- locked laser regime appears at bifurcation points for certain lengths of the second compression segment of the cavity. We have confirmed the stability of the similariton regimes by direct numerical simulations for large numbers of round trips. II. DESIGN AND THEORY OF A SIMILARITON LASER WITH RAMAN GAIN The schematic diagram of the laser is shown in Fig. 1. The operating wavelength of the laser has been chosen to be close to 1535 nm so that a pump at a wavelength close to 1445 nm can be used. The pump is launched and extracted from the cavity using wavelength division multiplexor (WDM) couplers. A backward pumping scheme is used to avoid pump depletion and linear loss is neglected in the gain fiber, so g s is considered constant along the similariton stage. The first stage where the similariton propagation takes place is constructed using a dispersion-compensating fiber (DCF) in order to have positive GVD around 1535 nm. The length of the fiber has been chosen to be long enough to generate a parabolic pulse; that is, the asymptotic regime is reached at point A. Then 1050-2947/2010/81(2)/023815(11) 023815-1 ©2010 The American Physical Society