Dissipative soliton resonance in an all-normaldispersion erbium-doped fiber laser

Dissipative soliton resonance in an all-normaldispersion erbium-doped fiber laser X. Wu, D. Y. Tang*, H. Zhang and L. M. Zhao School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798 * Corresponding author: edytang@ntu.edu.sg Abstract: We report on the generation of 281.2 nj mode locked pulses directly from an erbium-doped fiber laser mode-locked with the nonlinear polarization rotation technique. We show that apart from the conventional dissipative soliton operation, an all-normal-dispersion fiber laser can also emit square-profile dissipative solitons whose energy could increase to a very large value without pulse breaking. 2009 Optical Society of America OCIS codes: (140.3500) Lasers, erbium; (060.5530) Pulse propagation and temporal solitons; (140.4050) Mode-locked lasers. References and links 1. L. M. Zhao, D. Y. Tang and J. Wu, Gain-guided soliton in a positive group-dispersion fiber laser, Opt. Lett. 31, 1788-1790 (2006). 2. A. Chong, J. Buckley, W. Renninger and F. Wise, All-normal-dispersion femtosecond fiber laser, Opt. Express 14, 10095-10100 (2006). 3. A. Chong, J. Buckley, W. Renninger and F. Wise, All-normal-dispersion femtosecond fiber laser with pulse energy above 20 nj, Opt. Lett. 32, 2408-2410 (2007). 4. N. Akhmediev and A. Ankiewicz, Dissipative Solitons in the Complex Ginzburg-Landau and Swift- Hohenberg Equations, in Dissipative Solitons, N. Akhmediev and A. Ankiewicz, ed., (Springer, Berlin, 2005). 5. N. N. Akhmediev, V. V. Afanasjev and J. M. Soto-Crespo, Singularities and special soliton solutions of the cubic-quintic complex Ginzburg-Landau equation, Phys. Rev. E 53, 1190-1201 (1996). 6. B. A. Malomed and A. A. Nepomnyashchy, Kinks and solitons in the generalized Ginzburg-Landau equation, Phys. Rev. A 42, 6009-6014 (1990). 7. J. M. Soto-Crespo, N. N. Akhmediev, V. V. Afanasjev and S. Wabnitz, Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion, Phys. Rev. E 55, 4783-4796 (1997). 8. N. N. Akhmediev, J. M. Soto-Crespo and Ph. Grelu, Roadmap to ultra-short record high-energy pulses out of laser oscillators, Phys. Lett. A 372, 3124-3128 (2008). 9. W. Chang, A. Ankiewicz, J. M. Soto-Crespo and N. Akhmediev, Dissipative soliton resonances, Phys. Rev. A 78, 023830 (2008). 10. H. Zhang, D. Y. Tang, X. Wu and L. M. Zhao, School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798, are preparing a manuscript to be called Dark soliton fiber laser. 11. L. M. Zhao, D. Y. Tang, T. H. Cheng and C. Lu, Nanosecond square pulse generation in fiber lasers with normal dispersion, Opt. Commun. 272, 431-434 (2007). 12. P. Kolodner, D. Bensimon and C. M. Surko, Traveling-wave convection in an annulus, Phys. Rev. Lett. 60, 1723-1726 (1988). 13. V. J. Matsas, T. P. newson and M. N. Zervas, Self-starting passively mode-locked fiber ring laser exploiting nonlinear polarization switching, Opt. Commun. 92, 61-66 (1992). Recent studies on the passively mode locked fiber lasers have revealed solitary wave emission in the all-normal-dispersion fiber lasers [1, 2]. Different from the anomalous dispersion fiber lasers, where the soliton formation is mainly due to the interplay between the anomalous cavity dispersion and the fiber nonlinear optical Kerr effect, in the normal dispersion fiber lasers the soliton formation is a result of the mutual interaction among the normal cavity dispersion, fiber nonlinear Kerr effect, laser gain, losses, and gain dispersion. In particular, the effective laser gain bandwidth filtering has played an important role [1-3]. Determined by their different soliton shaping mechanisms, the solitons obtained have distinctive features: while the solitons observed in the anomalous dispersion fiber lasers have an optical spectrum with clear sidebands, the solitons formed in the normal dispersion fiber lasers have an (C) 2009 OSA 30 March 2009 / Vol. 17, No. 7 / OPTICS EXPRESS 5580

effective gain bandwidth limited spectral width with characteristic steep spectral edges. To distinguish the solitons and to highlight the effect of the effective gain filtering on the soliton formation, the solitons formed in the normal dispersion fiber lasers were called the gainguided solitons. We note that the formation and dynamics of the gain-guided solitons are fully governed by the extended complex Ginzburg-Landau equation (CGLE) [1]. Therefore, they are in essence a type of dissipative solitons [4]. Formation of dissipative solitons in a fiber laser is theoretically independent of the sign of cavity dispersion. However, in the anomalous dispersion fiber lasers, because of the existence of the intrinsic soliton shaping mechanism caused by the interplay between the cavity dispersion and fiber nonlinear optical Kerr effect, and the fact that its formed solitons have normally a far narrower spectral width than that of the laser gain, the function of the laser gain is to simply balance the cavity losses, and no gain filtering actually occurs. Consequently the formed solitons display dominantly the nonlinear Schrödinger equation soliton features rather than the dissipative soliton features. An all-normal-dispersion fiber laser is an ideal test-bed for the experimental study on the dissipative soliton features. Theoretical studies on the extended CGLE have revealed a large variety of solitary wave solutions. Apart from the well-known sech 2 -profile solitons, flat-top solitons were also predicted [5-7]. Very recently, Chang et al. have also predicted a novel dissipative soliton resonance effect [8, 9]. In the case of dissipative soliton formation in a fiber laser, it was theoretically shown that with certain laser parameter selections, the energy of the formed dissipative solitons could increase indefinitely, characterized as that the solitons increase their width indefinitely while keeping their amplitude constant. However, to our knowledge, neither the flat-top dissipative solitons nor the dissipative soliton resonance effect has been reported experimentally for the fiber lasers. In this paper we report on the experimental observation of large energy square pulse emission of an erbium-doped fiber laser mode locked with the nonlinear polarization rotation (NPR) technique. We point out that the stable nonlinear square-pulse emission of the laser manifests the flat-top dissipative soliton operation predicted. Furthermore, we found experimentally that the square pulse width increased linearly with the pump strength while the pulse intensity kept almost constant. Single pulse energy as large as 281.2 nj has been achieved in our experiment without the appearance of pulse breaking, which is a clear qualitative evidence of the existence of dissipative soliton resonance. Fig. 1. Schematic of the experimental setup. WDM, wavelength-division-multiplexing coupler; EDF, erbium-doped fiber; PDISO, polarization-dependent isolator; PC, polarization controllers. The fiber laser used in our experiments is schematically shown in Fig. 1. It has a ring cavity of 163.2 m long. A segment of 3.7-m EDF with doping concentration of 2880 ppm and group velocity dispersion (GVD) parameter of about -32 (ps/nm)/km was used as the gain fiber; dispersion compensation fibers (DCFs) with GVD of about -4 (ps/nm)/km constituted (C) 2009 OSA 30 March 2009 / Vol. 17, No. 7 / OPTICS EXPRESS 5581

the rest of the ring. The NPR technique was adopted for achieving the mode locking. Therefore, a fiber pigtailed polarization dependent isolator together with an inline polarization controller was employed to control the polarization of light in the cavity. The polarizationdependent isolator also ensured the unidirectional operation of the ring. The laser was pumped by a 1480 nm high power Raman fiber laser (KPS-BT2-RFL-1480-60-FA) through a wavelength-division-multiplexing (WDM) coupler. The backward pump scheme was exploited to eliminate the influence of the residual pump power. A 50% fiber coupler was used to output the laser emission. All the components (isolator, WDM and fiber output coupler) were specially made with the DCF. The laser is an all-normal-dispersion, all-fiber laser. An optical spectrum analyzer (YOKOGAWA AQ6370) and a 50 GHz high-speed oscilloscope (Tektronix CSA 8000) together with a 45 GHz photodetector (New Focus 1014) were used to simultaneously monitor the spectrum and output pulse train of the laser. Spectral Intensity (db) -20-30 -40-50 -60 (b) Power pump=427mw Power pump=851mw Power pump=1380mw -70 1550 1560 1570 1580 1590 1600 1610 1620 1630 Wavelength (nm) Fig. 2. Square pulse emission of the laser. (a) Zoom-in high speed oscilloscope traces under different pump power; inset: oscilloscope trace of a square pulse train. (b) Optical spectra of the square pulses under different pump power. A major difference of the current fiber laser from those reported previously [1, 2] is that a long cavity was used, which increases the total normal cavity dispersion. Mode locking of the laser is always self-started, and depending on the linear cavity phase delay bias setting and the pump strength, various modes of laser operation were observed, including the conventional (C) 2009 OSA 30 March 2009 / Vol. 17, No. 7 / OPTICS EXPRESS 5582

dissipative solitons [1] and dark solitons [10]. In particular, under strong pumping a stable square pulse emission mode was also observed. Figure 2(a) shows the typical oscilloscope traces of the observed square pulse emission. We note that the rising and falling edges of the measured square pulses are limited by the response time of our measurement systems. The square pulse duration increases with the pump strength, while the peak of the pulse almost remains constant as the pump power varies. Figure 2(b) is the optical spectrum of these square pulses. Their spectrum has no characteristic sharp spectral edges as that of the dissipative solitons, but resembles that of the amplified spontaneous emission (ASE) of the EDF with the spectral center shifted to the longer wavelength side. Figure 3 shows the experimentally measured square pulse width and output power variation with the pump power. The narrowest stable square pulse experimentally obtained was about 632 ps, while the longest pulse width could become as long as tens of ns, which was limited by the available pump power injected into the cavity. In our experiment the highest laser output power attained 344.5 mw under the pump power of 1186 mw. No output power saturation was observed. As we had burned a WDM coupler at a slightly higher pump power, we had kept our maximum pump strength at the current level. At the maximum pump power the square pulses also reached the maximum duration of 18.5 ns. Associated with the pulse width increase the spectral bandwidth of the pulses also slightly increased, as shown in Fig. 2(b). The square pulse laser emission was stable, as shown in the inset of Fig. 2(a). The pulse train has a repetition rate of 1.225 MHz (corresponding to a pulse interval of 816.3 ns) as determined by the cavity length. 20 400 18 Pulse width Output power 350 Pulse width (ns) 16 14 12 10 8 6 4 300 250 200 150 100 Output power (mw) 2 50 0 0 500 1000 Pump power (mw) 0 Fig. 3. The experimentally measured average output power and pulse width versus the pump power injected into the cavity. A remarkable feature of the square pulses is that their pulse energy could increase to a very large value without pulse breaking and pulse shape distortion. In our experiment the maximum pulse energy was as large as 281.2 nj, which was limited by the pump power injected into the cavity. At the maximum pulse energy the pulse still has a square shape, with almost the same peak power it has before but with pulse duration increased to 18.5 ns. We have also experimentally investigated the square pulses with our high-speed oscilloscope combined with a commercial autocorrelator (FR-103MN). No internal fine structures were observed within the pulses. We note that the dissipative solitons, characterized by their sharp spectral edges, were also observed in our laser. Comparatively, the dissipative solitons have not only much narrower (C) 2009 OSA 30 March 2009 / Vol. 17, No. 7 / OPTICS EXPRESS 5583

pulse width (maximum duration about 36 ps) but also much smaller maximum pulse energy (~8.2 nj). The maximum dissipative soliton pulse energy was limited by the effective gain bandwidth of the laser rather than the available pump power. In our experiment as the energy of a dissipative soliton increased beyond the above maximum value, it broke into two solitons. Multiple dissipative solitons were always obtained under strong pumping. In a previous paper we have already reported the square pulse operation of an all-normal-dispersion erbium-doped fiber laser [11]. However, in our previous laser due to that a large output coupling (90%) coupler and a fiber bench with free space waveplates were used, the laser cavity had very large linear losses. Therefore, with our available pump power (700 mw) only very low energy square pulses could be obtained. Based on the pulse parameters measured, we estimate that the peak power of the square pulse inside the cavity was about 30 W. Obviously the pulse propagation in the fiber cavity is strongly nonlinear. Therefore, the stable square pulse emission of the laser suggests that the observed square pulse could be another solitary wave formed in the laser. Indeed, flat-top solitons were theoretically predicted to exist in the extended CGLE [5, 6], formed as the kinkantikink bound state. Such a soliton was previously observed in a binary fluid convection experiment [12]. To further support that the observed square pulse is a dissipative soliton formed in the laser, we note that recently Chang et al. have theoretically predicted a novel resonance effect of the dissipative solitons [9]. It was shown that near resonance a rectangular dissipative soliton increased its pulse width and energy indefinitely while keeping its amplitude constant. The square pulse obtained in our laser displayed exactly this resonance feature. However, different from the theoretical prediction, the observed square pulse width and pulse energy increase with pump power didn t show clear exponential dependence but a line one. We believe this discrepancy could be due to that with our current laser parameter selection, at the maximum experimentally available pump power just a weak resonance was reached. This explanation is further supported by the experimentally observed soliton spectral profiles. No steep spectral edges with sharp side peaks were observed on the spectral profiles. It is to note that as the pump power was increased, the experimentally observed soliton spectral profile did exhibit the tendency of edge steepening. Therefore, it is expected that if even higher pump power would be allowed, stronger resonance would be further achieved, and a closer agreement with those of the theoretical predictions would be obtained. Finally, we note that square pulse emission had also been observed in the anomalous dispersion fiber lasers [13], indicating that its formation is independent on the sign of the cavity dispersion. Nevertheless, in the anomalous dispersion fiber lasers due to the intrinsic soliton formation, fine internal structures could also appear in the square pulses and complicate the phenomenon. In conclusion, we have experimentally observed large energy, square pulse emission of an all-normal-dispersion erbium-doped fiber laser mode locked with NPR technique. The stable nonlinear propagation of the pulses in the laser cavity manifests a new type of the theoretically predicted dissipative solitons, namely the flat-top soliton of the laser. Experimentally we found that both the pulse width and pulse energy of the square pulses were scalable with the pump strength, which confirms the existence of the so-called dissipative soliton resonance effect. The large energy square shape soliton of the laser could be used for large pulse energy ns level mode-locked pulse generation, which could be potentially used for laser targeting and lidar systems. Acknowledgments This project is supported by the National Research Foundation Singapore under the contract NRF-G-CRP 2007-01. (C) 2009 OSA 30 March 2009 / Vol. 17, No. 7 / OPTICS EXPRESS 5584