1. Introduction

The performance of passively mode-locked fiber lasers in terms of pulse energy has been increased drastically in the last years so that they became comparable to their solid-state counter-parts. This made this type of ultrafast lasers suitable for more and more applications. Nearly all of the work has been done on ytterbium-doped fiber (YDF) lasers emitting at 1µm where the pulse shaping in normal dispersive fibers facilitates the generation of parabolic or more general wave breaking-free pulses [1, 2]. This opened new perspectives for energy scaling so that pulse energies of more than 20 nJ have been demonstrated in a single-mode fiber laser [3]. As the pulses propagate highly chirped inside the cavity the peak power is drastically reduced. This results in decreased nonlinear influences particularly from self-phase modulation (SPM) and the pulses can maintain an almost linear frequency chirp.

These lasers can be operated at large cavity dispersion as the phase behaviour of normal group-verlocity dispersion (GVD) and SPM is inherently cumulative. In contrast to the stretched-pulse regime, the balance of phase contributions is not possible but also not necessary to establish the stable steady-state. It is achieved by amplitude modulation namely by the saturable absorber mechanism and the bandwidth filtering in the gain fiber [4]. As long as the amplitude modulation is sufficient, there is no upper limit for the cavity dispersion deepening the potential for energy scaling [1].

YDFs offer great potential as gain saturation and gain bandwidth limitation is detrimental for the parabolic pulse evolution [1]. In erbium-doped fibers (EDF) gain saturation occurs at lower power and the gain bandwidth is proportionately smaller so the transfer of the parabolic pulse regime to the important telecom-wavelength is debatable. Most of the fs-EDF-lasers previously reported on has been operated in the vicinity of zero cavity dispersion where pulse energies up to 6 nJ has been demonstrated [5]. Nevertheless, EDF-lasers can also be operated in the normal dispersion regime but not only the interplay between GVD and SPM has to be taken into account [6, 7]. In the so called gain-guided soliton regime, a weakly chirped solitary wave was found whose pulse duration is related to the gain bandwidth as gain-guiding is necessary to sustain the pulse [8]. In this regime, an improvement of the obtainable pulse energy compared to the soliton regime of anomalous dispersive fibers has not been demonstrated.

In this paper we report on an EDF-laser passively mode-locked by nonlinear polarization rotation (NPE) operating in the large normal dispersion regime. We demonstrate that although generic features of the parabolic pulse regime are present, the spectral output characteristic differs from the ones reported on so far. The main difference is an energy redistribution within the pulse from the gain maximum of the EDF to longer wavelengths via intrapulse Raman-scattering (IRS). However, owing to the large positive chirp inside the cavity, the main advantage concerning energy scaling is present. Pulse energies of more than 10 nJ could be achieved which are, to the best of our knowledge, the highest reported on for fs-EDF-lasers.

2. Experimental setup

In order to realize high-power fs-pulses we designed the oscillator as sketched in Fig. 1. A unidirectional ring geometry facilitated self-starting mode-locking and was based on 4.95m custom made normal dispersive EDF (2.7µm core diameter with 0.28NA) with an Er ³⁺-concentration of 0.23 mol-%. The length of the gain fiber was chosen for a pump light absorption of >99% measured without cavity feedback. Additionally, we integrated 17 cm of anomalous dipersive SMF1528 standard fiber which was the minimum length required for the wavelength-division multiplexer (WDM) coupler for pump light delivery. Heat generation at the splice between the two fibers owing to a slight imperfect mode-matching necessitated water cooling of this connection. The end faces of the fibers were polished at an angle of 8° to avoid parasitic lasing. The gain fiber was core-pumped along the propagation direction of the oscillator. As a high-power diffraction limited pump source we used a Raman pump fiber assembly delivering 3.7W at 1.48µm. It consisted of a cladding pumped YDF laser followed by a cascaded Raman fiber laser. All fibers in the EDF-cavity were single-mode for the pump- and laser wavelength. Based on measurements with a white-light interferometer [9], the group-delay dispersion (GDD) of the fiber section was estimated to β ₂=0.104 ps² at the operating wavelength of 1.64µm. Beside the short piece of SMF (β ₂=-0.003 ps²) no additional dispersion compensation was present in the resonator. The dispersion contributions of the free-space components is negligible.

 

Fig. 1. Experimental setup. EDF: erbium-doped fiber; QWP: quarter wave-plate; HWP: half wave-plate; PBS: polarizing beam splitter; ISO: Faraday isolator; SMF: single-mode fiber; WDM: wavelength-division multiplexer.

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The total cavity length was 6m resulting in a repetition rate of 37.1 MHz. Mode-locking was initiated and stabilized by NPE and the rejection port of a polarizing beam splitter was used as the output. To manipulate the polarization state for the NPE we applied a half- and a quarter wave-plate in front of as well as behind the fiber section. Although in principle not necessary, it turned out that the half wave-plate in front of the fiber section was needed to avoid q-switch mode-locking. Without the half wave-plate applied it was not possible to achieve stable cw mode-locking. For all free-space components equivalent fiber-based devices are available, so an all-fiber version of the setup seems feasible.

3. Results and discussion

Above a pumping power of 1.1W self-starting mode-locked operation of the laser was observed. Once mode-locking was achieved, the output power increased linearly with a slope efficiency of 7.5% as can be seen from Fig. 2 (a). Above a pump power of 2.8W double pulses and above 3.2W triple pulses were formed equally spaced. The pulse train was observed by a long range autocorrelator (150 ps scanning range) and a fast photodiode (70 ps rise-time)/oscilloscope (70GHz resolution). The strong hysteresis regions between the regimes suggest that the formation of multi-pulse operation is caused by an overdriven NPE [10]. Before entering the double pulse regime the laser undergoes a small region of quasi-periodicity and chaotic pulsation, respectively. Also these phenomena are usually caused by excessive nonlinearities triggering these dynamic instabilities [11]. Further increase of the pump power led to a second window of regular behaviour but with two pulses circulating in the cavity. The situation qualitatively recured between the double- and triple pulse regime. To handle the excessive nonlinearities which are most likely responsible for the limitation of the pulse energy, the use of a shorter gain fiber is considered for future experiments. The disadvantage of an inefficient pump light conversion should be compensated (indirectly) by an optimized nonlinear phase shift. Another option to stabilize the pulse train at high energy is the implementation of additional spectral filters as reported in [12]. However, in the single pulse regime we achieved a maximum output power of 380mW corresponding to a pulse energy of 10.3 nJ.

It is to mention that we observed a small satellit pulse at a distance of 35 ps from the main pulse. It contained about 2% of the pulse energy and was always present independent of wave-plate settings or other adjustable parameters. Neither the energy content nor the position changed substantially when the pump power was increased. We attribute it to spurious reflections inside the cavity. As all coatings were designed for 1.55 µm we believe that this problem can be solved with optimized components.

 

Fig. 2. (a) Output power and single pulse energy in respect to the pump power (the lines are just to guide the eye). (b) Optical spectrum at the maximum single pulse output power on logarithmic and linear scale, respectively.

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The optical spectrum at the maximum single pulse output power is displayed in Fig. 2 (b) on a logarithmic as well as on a linear scale. The spectral peak intensity is located at 1640nm with a 3-dB width of 15.7nm but at -20dB the spectral width exceeds 130 nm. The intensity of nonabsorbed pump light was 40 dB below the one of the pulse. On the long wavelength side the optical spectrum has a sharp decay around 1645nm which corresponds to the end of the gain spectrum of the EDF. In addition, the WDM-coupler limited the spectrum as it had significant signal suppression for wavelength above 1615 nm. The spectral components above that wavelength must therefore be generated with marginal feedback. Surprisingly not even the full gain bandwidth is used as the spectrum drops down at the gain maximum at 1545 nm. This can be explained by ground state absorption in the long gain fiber [13]. Hence, the whole optical spectrum is generated in the four-level system of the EDF. Owing to the combined effect of reabsorption at the short and attenuation in the WDM-coupler at the long wavelength side, a spectral filter is formed. This provides some amplitude modulation supporting the pulse train as reported in Ref. [3, 12].

When increasing the pump power additional spectral components were generated as can be seen from Fig. 3 (a) where we displayed the central wavelength as well as the decay of the optical spectrum at -10dB and -20 dB, respectively. For increasing pump power the spectrum broadened on both sides until the plateau around 1660nm was separated above 1.5W. Above that value broadening occured mainly on the long wavelength side of the spectrum. Also for the main peak of the spectrum there is a shift of 26nm to longer wavelengths when pump power is increased. The spectral shape depended basically on the energy per pulse independent on the number of pulses circulating in the cavity as this behaviour qualitatively recured in the double and triple pulse regime, respectively. This indicates that nonlinear effects are responsible for the spectral broadening. Owing to the enhancement of the red part of the optical spectrum, we conclude that IRS strongly affects the pulse formation.

 

Fig. 3. (a) Main peak (circles) and decay of the optical spectrum at -10 dB (open triangles) and -20,dB (closed triangles) in respect to the pump power. (b) Normalized optical spectra measured at 1.3W (gray solid line) and 2.6W (black solid line) launched pump power together with the normalized Raman-gain spectrum assuming a pump wavelength of 1540 nm (dotted line).

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To elucidate this, the normalized spectra measured at 1.1W and 2.8W launched pump power are displayed in Fig. 3 (b). The shifted spectral components are located within the main peak of the Raman-gain spectrum. Its location is based on the assumption that the short wavelength side of the spectrum around 1540nm serves as the pump for the IRS process. For the Raman-gain spectrum shown, the data achieved by Stolen and Ippen were applied [14]. The energy redistribution within the pulse compensates the depletion of the ground state absorption for increasing pump power. As a consequence the short wavelength side remained unaffected when the pum power was increased. The impact of IRS makes the output characteristic different from the parabolic and wave breaking-free regime, respectively. Furthermore, the pulses can also not be refered to as gain-guided solitons [8] as the energy tranfer via IRS causes significant broadening beyond the gain bandwidth.

 

Fig. 4. (a) Autocorrelation trace of the chirped pulse (solid line) and Gaussian fit (dotted line). (b) Temporal profile (solid line) together with Gaussian fit (dotted line) and temporal phase, respectively measured by frequency resolved optical gating.

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As already mentioned the pulses are highly chirped inside the cavity. The autocorrelation width at the output was measured to 5.6 ps as can be seen from Fig. 4 (a). We compressed the pulse outside the cavity with a transmission grating based compressor (670 grooves/mm) and measured the pulse duration by frequency resolved optical gating. The GDD of the compressor was β ₂=-0.08 ps² at 1.64 µm. This is much larger than the GDD provided intracavity by the short piece of SMF which was only β ₂=-0.003 ps². Therefore the pulse is always positively chirped in the cavity with a minimum but not Fourier-limited pulse duration at the beginning of the EDF. This monotonic dynamic was also found for the parabolic and wave-breaking free pulse regime, respectively [1, 2, 4]. The retrieved temporal profile together with the temporal phase is displayed in Fig. 4 (b). The dechirped pulses had a duration of 74 fs which is 6% above the Fourier-limit calculated to 70 fs by a fast Fourier transformation assuming a zero phase. With the compressor efficiency of 75% taken into account this corresponds to a peak power of >100kW. The measured temporal phase shows only fractional deviation from the ideal constant phase. Similar results were also achieved with a compressor based on reflection gratings and SMF1528, respectively. The chirp can be deduced from this measurements to a value of 53. The autocorrelation trace as well as the temporal profile shows an almost perfect overlap with a Gaussian (represented by the dotted lines in Fig. 4). This is also in agreement with the parabolic pulse regime of passively mode-locked YDF-lasers [4, 15]. From the dechirped pulse duration and the measured optical spectrum we estimated a time-bandwidth product of 0.69 which is between 0.44 known for stretched-pulse operation and 0.93 calculated for the parabolic pulse regime [15].

4. Conclusion

In summary we presented a passively mode-locked fiber oscillator delivering highly chirped fs-pulses with energies up to 10 nJ at 1.64 µm. To the best of our knowledge, this is the highest pulse energy reported on for ultrafast erbium-doped fiber oscillators. The pulses were highly stretched with an autocorrelation width of 5.6 ps inside the laser but could be externally dechirped to <75 fs. This is within 6% of the Fourier-limit pointing out the linearity of the chirp. Although the spectral output characteristic differs from the well-known wave-breaking free pulses owing to the impact of intrapulse Raman-scattering, our results demonstrate the potential of operating passively mode-locked erbium-doped fiber oscillators in the large normal dispersion regime.