We report here the first demonstration of a mode-locked fiber laser delivering parabolic pulses (similaritons) at 1534 nm. The use of a Raman-based gain medium potentially allows its implementation at any wavelength. The 22nJ output similariton pulses have a true parabolic shape both in the time and spectral domains and a linear chirp. Linear recompression close to Fourier limit is demonstrated allowing us to obtain 6 ps compressed pulses with a compression factor of 75.
©2010 Optical Society of America
Fiber oscillators such as erbium or ytterbium doped fiber lasers as well as Raman lasers are now well developed reliable devices which are used in many different fields such as telecommunications, optical imaging or metrology. Much effort has been dedicated in the past few years to increase the peak power of the pulses delivered by fiber based oscillators since their stability and compact size make them a good alternative to bulk solid-state lasers. The nonlinear phase limit leading to a wave breaking effect has emerged as the main limitation factor . Classical oscillators are based on a dispersion management design along the cavity allowing group velocity (GVD) and self-phase modulation (SPM) induced chirp to interplay . If the nonlinearities in the cavity become too high, these effects cannot be balanced and the cavity becomes unstable. Thus, a new type of waveform involving self-similar propagation has been increasingly adopted in this route towards high energy fiber systems. It has been demonstrated that under normal dispersion, nonlinearity and gain, an initial input pulse will asymptotically evolve into a similariton . These asymptotic solutions of the non-linear Schrödinger equation, also called similaritons, can experience very large non-linearities without suffering from the wave-breaking effect . Their characteristic temporal and spectral parabolic intensity profiles, as well as their linear positive chirp, are conserved during the propagation. Whilst undergoing self-similar propagation the pulse peak power, temporal and spectral widths increase exponentially along the fiber. This specific aspect of similaritons propagation makes them very suitable for high power regime while the linear chirp enables simple pulse compression.
Many works have been devoted in recent years to the study of self-similar propagation. The results of these theoretical, numerical and experimental studies have led to the development of various fiber based systems such as amplifiers or lasers delivering similaritons as presented in [5,6]. Different gain media have been used to obtain the self-similar propagation. Rare-earth doped fibers, especially ytterbium [8–12] and erbium [13,14], have been first implemented in amplifiers schemes and later used in laser oscillators. Good results have also been obtained using Raman gain media but to date only parabolic amplifiers have been built with this method [3–7]. It is however of great interest to develop a similariton laser by exploiting Raman amplification since this technique can be implemented at any wavelength. A great variety of architectures have also been proposed to obtain self-similar propagation. Thus, we can differentiate lasers combining fibres and free-space optics from all-fibre lasers. In references [8–11] the authors have used free-space modules such as grating pairs or saturable absorber mirror to recompress the pulses in the cavity or to mode-lock the laser. Despite their good performance such lasers are not very compact. Furthermore, they suffer from having to couple light in and out of a fiber which can lead to stability problems. Technical progresses in the development of fiber-coupled-elements such as isolators or polarisation beam splitters have allowed for the creation of all-fibre lasers as described herein and in [12,13]. Finally, we can also distinguish two dispersion management methods regarding the presence or absence of a dispersion compensation element in the cavity. To obtain asymptotic self-similar propagation in the shortest length of fiber possible, the input pulse must not have any chirp. For that reason a dispersion compensation element can be placed before the gain medium. As an illustration Ilday et al. have implemented a dispersion delay line that provides anomalous GVD together with negligible nonlinearity to compensate the chirp accumulated by the pulse in a large normal dispersion fiber segment present before amplification . Stable mode-locked operation regime delivering parabolic pulses can however be obtained without a dispersion compensation stage . Indeed, the filtering effect of the gain bandwidth (Yb doped fiber) and of the saturable Bragg-reflector (SBR) used to mode-lock the cavity is reinforced by the strong chirp of the pulses. In this case longer pulse durations of several picoseconds characterises the output of the laser.
We report in the present article a laser combining several of the previously discussed features. Our objective in this study is to develop an all-fibre similariton laser running potentially at any wavelength by using Raman gain. This mode-locked laser has a dispersion compensation free design and can be considered all-normal dispersion since the length of the SMF patch-cords between the elements is negligible compared to the length of the DCF serving as Raman gain medium (SMF length is < 0.5% of total cavity length). In the following we will show both numerically and experimentally that the output similariton pulses have a parabolic shape. Additionally, we report in section 4 the observation of a self-similar behavior of the laser output with the increase of pump power. The pulses have an energy of 22 nJ, an average power of 1.25 mW and a bandwidth of 2.4 nm. This simple design offers interesting performance and can lead to a stable compact source after improvement of the pulse to pulse intensity fluctuation which is in the herein under 15%. Finally, linear recompression close to the Fourier limit is also demonstrated allowing us to confirm the linear chirp of the similaritons and obtain pulses as short as 6 ps.
2. Numerical study of the laser
The laser has been designed using a numerical model based on direct simulation of the generalised nonlinear Schrödinger equation (GNLSE). Each fiber section of the ring laser is described with appropriate parameters based on commercially available component. We use for our simulation the well known split-step Fourier method for a very large number of round trips, N, of the propagating field . The laser is seeded with an initial pulse and stable operation regime with a parabolic output is obtained after a large number of round trips N. In this case (N>>1) the energy of the initial pulse in the round trip with number N is equal to the energy of the pulse at the end of the roundtrip.
However, our simulations show that for the parabolic (similariton) regime of the laser, the last term in Eq. (1) is very small compared with the amplification term and hence can be neglected.
The different components of the laser such as the coupler and the isolator are taken into account by integrating their respective loss in the code. The Gaussian filters are defined by the frequency function where is the filter width . A weak parabolic pulse is used as a seed in the laser leading to robust parabolic regime after propagation over a large number of roundtrip. During its propagation in the Raman fiber, the pulse reaches the parabolic asymptotic solution described by Eqs. (2) to (5) :
Using the manufacturer data of the different parameters we have calculated the optimal length lS of the fiber amplifier necessary to reach the self-similar propagation. The simulated spectra and temporal intensities at different places in the cavity are shown in Fig. 1 .
Four characterisation points have been defined throughout the cavity (cf. Fig. 2 ). The output of the laser, point A, is described in the top line of Fig. 1. As can be seen, both the temporal and the spectral domains have a parabolic shape. When varying the input parameters, we have identified two different stable operation regimes for this mode-locked ring laser. They respectively correspond to a period of one or two roundtrips in the cavity. The regime under which the laser is self-stabilizing mainly depends on the bandwidth of the first BPF in combination with other parameters of the laser. For these simulations we have neglected the impact of the single mode fiber patch cord used to link the different elements of the laser since their cumulated length is around 15 m for a total cavity length of more than 3100 m.
3. Cavity design
The simulation code used to obtain this original cavity design (cf. Fig. 2) gives us the opportunity to determine precisely the best characteristics of each component, and thus, to obtain a stable mode operation. As a result, the cavity is built around a 2.4 km long Raman amplifier using a dispersion compensating fiber (DCF) with a dispersion of DDCF = −111.3 ps/nm/km at 1535 nm. The amplifier is pumped with a continuous wave Raman pump set at a wavelength of 1435 nm. The amplifier is divided in 2 parts separated by an optical isolator (ISO) to limit the double Rayleigh-Bragg scattering and to select only one lasing direction.
The NOLM  is constituted by a 45/55 coupler whose two ends (3 and 4 in Fig. 2) are looped together with 727 m of highly nonlinear fiber (HNLF) from Sumitomo Electric with a dispersion of −0.21 ps/nm/km at 1550 nm, a core diameter of 3.2 μm and a nonlinear coefficient of 0.0132 W−1m−1. Only the central part of the pulses, which are more intense and thus accumulate a higher nonlinear phase than the wings, interfere constructively and exit the coupler via the port 2. This temporal selection enables the mode-locking operation. In the spectral domain, pulses have experienced spectral broadening at the output of the NOLM due to self-phase modulation in the HNLF. This SPM-induced spectral broadening is accompanied by the accumulation by the pulse of a temporal positive chirp which must be removed before reentering the Raman amplifier. Indeed the smaller the chirp of the input pulse, the faster the waveform reaches the asymptotic solution and experiences a self-similar propagation. This is the reason why a second band-pass filter is placed between the NOLM and the Raman fiber. By removing most of the pulse spectrum, the Raman fiber input pulse has very low residual chirp.
It has to be mentioned that its non perfect temporal shape, due to the cut in the spectrum, is not of concern since the important parameters on an input pulse to obtain a self-similar propagation are its chirp and its energy [3,4]. The total length of the cavity determines the repetition rate of 64 kHz. We typically obtain 22 nJ output pulses for a pump power PP = 1.5 W. As mentioned in section 2 several similariton regimes can exist. We observe here the most stable of them which has a period of one round-trip.
The output parabolic pulses are externally recompressed using 12.8 km of Corning single mode fiber SMF-28E(R) with a dispersion parameter DSMF of 15.3ps/nm/km. With this simple setup we have linearly recompressed the output pulses to a duration of 6 ps close to the Fourier limit (FL) which is about 3 ps. This factor of two between the FL and the recompressed pulse duration can be attributed to the non-compensated third order of dispersion and imperfections in the linear chirp of the similaritons.
4. Experimental results and comparison with theory
Figure 3 describes the output power with respect to the pump power. The laser threshold is quite high due to the design of the cavity itself. A small fraction of the total energy exiting the amplifier arrives to the NOLM due to the presence of the BPF. Therefore the pump power must be increased to a high power before self mode-locking is initiated. For a pump power below 1.35 W the laser becomes unstable and high pulse-to-pulse fluctuations lead to a breaking down of the mode-locking. If pump power is increased above 2W, the similariton’s temporal and spectral intensity distributions become strongly structured and multiple pulse operation is observed.
By varying the pump power across the power range described above, we have been able to identify the region where the interplay between the dispersion, the nonlinearity and the gain is optimal for similariton generation (see Fig. 3 and 4 ).
Figures 4(a) and 4(b) respectively represent the experimental spectral density and temporal profile of the pulses, for a pump power of 1.5W. At this operation point, the output pulses have an energy of 22 nJ (64 kHz repetition rate), a bandwidth of 2.4 nm and a duration of 450ps (measured with a fast photodiode having a rising time of 12ps). As the pump power is increased from laser threshold to 2W, an increase of the bandwidth is observed. This behavior is characteristic of the self-similar propagation regime taking place in the Raman fiber.
Good agreement can be observed between the simulated curves and the experimental results as well as with the parabolic fit. To obtain the set of green curves in Fig. 4(a) and 4(b), we have seeded the laser in our simulations with a very weak parabolic pulse with characteristics close to the experimental results. In order to compare our numerical prediction of the laser behaviour shown in Fig. 1 with the experiment, we have inserted a 1% output coupler at each of the four characteristic points defined earlier. These measurements are presented in Fig. 5 thereafter.
While a good agreement is generally observed between experimental results and simulations, one difference can be noticed on the spectral density of U3 taken after the NOLM. The constructive interferences in the coupler lead to an asymmetric spectrum. Different factors can cause such behaviour. Firstly, as shown at the end of section 4, the polarisation mode dispersion (PMD) in the Raman fiber becomes non negligible in our experiment. PMD is the source of the creation of two co-propagating pulses with different polarisations which can affect the final interference pattern of the NOLM. On the second hand, our simulations have shown that the strong spectral cut done by the first band-pass filter is a source of temporal distortion of the pulse which we believe also affects the interference of the waves at the output of the NOLM. We have studied the influence of this parameter on the final steady state regime by changing the bandwidth of this first filter. We have observed numerically that it is a key parameter of the laser since it can lead to tremendous changes in the similariton regime of the laser . A part of this noise at the output of the first BPF originates from the Raman fiber itself. Here again, the very long gain medium leads to a large amount of Rayleigh noise  despite the presence of two isolators in the laser. The addition of the noise due to the gain and of the noise from the BPF destabilizes the mode-locking regime provided by the NOLM and leads experimentally to a pulse to pulse intensity fluctuation under 15%. A final source of intensity fluctuation on the pulse train can also be attributed to the environmental stress since the fibers in our setup are simply lying on the table without packaging or protection against air flow and mechanical vibrations.
The laser output pulses shown in Fig. 4 are 450 ps long and strongly chirped. As we have seen earlier, according to the self-similar propagation theory, this chirp is linear and positive. Due to an experimental limitation in the scanning range of our Frequency Resolved Optical Gating (FROG) device no direct measurement of the chirped pulse and thus no characterisation of its chirp could be done. In consequence, to verify the linearity of the chirp of our pulses, we have propagated them in a single mode fiber operating in the anomalous dispersion regime. This propagation allows the pulse to accumulate a negative linear phase which can compensate the initial positive chirp. In order to accumulate a linear phase in the single mode fiber, propagation must be purely linear and no nonlinear effect (ie. spectral broadening) must be observed at the output. To respect that condition the pulse power is adjusted by a variable attenuator before the SMF. This external recompression system allowed us to recompress the pulses down to 6 ps using 12.8 km of SMF28(e). Figure 6 shows the FROG measurement of the recompressed pulses . As can be observed, this strong recompression influences the pulse profile which is not parabolic anymore. By examining now the temporal phase on the recompressed pulse, blue curve in Fig. 6, we can see that it has been very well compensated and that it is close to zero for a large portion of the pulse.
Several reasons explain the lack of full compressibility of our pulses. Firstly, the overall shape of the remaining phase shows that a small fraction of the chirp of the similariton has not been perfectly compensated. This is due to the length of the fiber which cannot be precisely adjusted. Furthermore, the non compensation of the third order dispersion terms leads to a remaining phase term present after compression.
Indeed, parabolic pulses experience third order dispersion inside the cavity which cannot be compensated by the third order dispersion of the single mode fiber used for the recompression. Finally, in addition to this imperfect phase compensation, the effect of the polarisation mode dispersion, in the Raman gain fiber itself, start to be non negligible. Based on the available literature we estimate a value of the polarisation mode dispersion for the DCF fiber of about 0.7 ps.km−1/2. Therefore after propagation in the 2.4 km long amplifier, the PMD cause about 1ps increase in the pulse duration. These factors are responsible for the difference between the minimum compressed pulse duration of 6 ps we have obtained and the Fourier limit of 3 ps. Despite these imperfections and the pedestal present on one edge of the pulse, the compressed pulses are still of good quality since more than 85% of the energy is contained in the main pulse. This overall good phase compensation by linear compression allows us to be confident that our pulses are positively linearly chirped as expected from self-similar propagation.
The evolution of a pulse throughout the cavity of a mode-locked parabolic Raman laser has been studied numerically and realised experimentally for the first time. Stable pulses exist with very good parabolic profiles. An initial numerical study allowed us to choose the optimal components of our setup and to obtain experimentally a parabolic pulse source whose behaviour is in good agreement with our predictions.
The current system delivers 22 nJ pulses at a repetition rate of 64 kHz. Pulses have been dechirped from 450 ps to 6 ps by linear recompression. This simple all-fiber design already offers interesting performances and can be considered as a proof of principle towards the realisation of a compact and stable similariton source implementable at any wavelength therefore being potentially interesting for wide range of applications.
Further improvements, including increasing the output pulse bandwidth, the implementation of a linear recompression stage inside the cavity and a reduction of the pulse fluctuation can be expected to lead to sub-picosecond duration and a substantial increase in peak power and pulse stability.
References and links
1. W. J. Tomlinson, R. H. Stolen, and A. M. Johnson, “Optical wave breaking of pulses in nonlinear optical fibers,” Opt. Lett. 10(9), 457–459 (1985), http://www.opticsinfobase.org/ol/abstract.cfm?uri=ol-10-9-457. [CrossRef] [PubMed]
2. M. E. Fermann, “Ultrafast Fiber Oscillators,” in Ultrafast Lasers, M. E. Fermann, A. Galvanauskas and G. Sucha, ed. (Marcel Dekker, New York Basel, 2003) pp. 89–154.
3. M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, “Self-similar propagation and amplification of parabolic pulses in optical fibers,” Phys. Rev. Lett. 84(26), 6010–6013 (2000). [CrossRef] [PubMed]
4. C. Finot, G. Millot, C. Billet, and J. M. Dudley, “Experimental generation of parabolic pulses via Raman amplification in optical fiber,” Opt. Express 11(13), 1547–1552 (2003), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-11-13-1547. [CrossRef] [PubMed]
5. F. W. Wise, A. Chong, and W. H. Renninger, “High-energy femtosecond fiber lasers based on pulse propagation at normal dispersion,” Laser Photon. Rev. 2(1-2), 58–73 (2008). [CrossRef]
6. J. M. Dudley, C. Finot, D. J. Richardson, and G. Millot, “Self-similarity in ultrafast nonlinear optics,” Nat. Phys. 3(9), 597–603 (2007). [CrossRef]
7. C. Finot, F. Parmigiani, P. Petropoulos, and D. J. Richardson, “Parabolic pulse evolution in normally dispersive fiber amplifiers preceding the similariton formation regime,” Opt. Express 14(8), 3161–3170 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-14-8-3161. [CrossRef] [PubMed]
9. A. Chong, J. Buckley, W. Renninger, and F. Wise, “All-normal-dispersion femtosecond fiber laser,” Opt. Express 14(21), 10095–10100 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-14-21-10095. [CrossRef] [PubMed]
10. C. K. Nielsen, B. Ortaç, T. Schreiber, J. Limpert, R. Hohmuth, W. Richter, and A. Tünnermann, “Self-starting self-similar all-polarization maintaining Yb-doped fiber laser,” Opt. Express 13(23), 9346–9351 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-13-23-9346. [CrossRef] [PubMed]
11. A. Ruehl, O. Prochnow, D. Wandt, D. Kracht, B. Burgoyne, N. Godbout, and S. Lacroix, Parabolic Pulse Regime of an Ultrafast Fiber Laser,” in Advanced Solid-State Photonics, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper TuB2. http://www.opticsinfobase.org/abstract.cfm?URI=ASSP-2007-TuB2
12. O. Prochnow, A. Ruehl, M. Schultz, D. Wandt, and D. Kracht, “All-fiber similariton laser at 1 mum without dispersion compensation,” Opt. Express 15(11), 6889–6893 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-11-6889. [CrossRef] [PubMed]
13. B. Oktem, C. Ülgüdür, and F. Ö. Ilday, “Soliton–similariton fibre laser,” Nat. Photonics (2010), doi:. [CrossRef]
14. J. Dudley, A. C. Peacock, V. I. Kruglov, B. C. Thomsen, J. D. Harvey, M. E. Fermann, G. Sucha, and D. Harter, “Generation and interaction of parabolic pulses in high gain fiber amplifiers and oscillators,” in Optical Fiber Communication Conference, 2001 OSA Technical Digest Series (Optical Society of America, 2001), paper WP4.
15. V. I. Kruglov, D. Mechin, and J. D. Harvey, “All-fiber ring Raman laser generating parabolic pulses,” Phys. Rev. A 81(2Issue 2), 023815 (2010). [CrossRef]
16. G. P. Agrawal, Nonlinear Fibre Optics, Elsevier Ed. (Academic Press, Inc., San Diego, CA, 2001).
17. V. I. Kruglov and J. D. Harvey, “Asymptotically exact parabolic solutions of the generalized nonlinear Schrödinger equation with varying parameters,” J. Opt. Soc. Am. B 23(12), 2541–2550 (2006), http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-23-12-2541. [CrossRef]
18. N. J. Doran and D. Wood, “Nonlinear-optical loop mirror,” Opt. Lett. 13(1), 56–58 (1988), http://www.opticsinfobase.org/abstract.cfm?URI=ol-13-1-56. [CrossRef] [PubMed]
19. K. W. DeLong, R. Trebino, J. Hunter, and W. E. White, “Frequency-resolved optical gating with the use of second-harmonic generation,” J. Opt. Soc. Am. B 11(11), 2206–2215 (1994), http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-11-11-2206. [CrossRef]