1. Introduction

Passively mode-locked rare-earth-doped fiber lasers with their respective emission wavelengths around 1 µm and 1.5µm are increasingly used in different application areas. They are for example utilized as seed sources for fiber based [1] as well as bulk amplifiers [2,3] or for supercontinuum generation [4, 5, 6]. Using fiber oscillators for these applications became possible not until the development of the stretched-pulse [7, 8, 9, 10] and wave breaking-free regime [11, 12, 13] which allowed for scaling the pulse energy to the nJ-range.

Lasers based on thulium-doped fibers (TDF) can extend the accessible wavelengths towards the eye-safe 2 µm-region. However, only very few thulium-doped femtosecond fiber lasers have been demonstrated so far, based on different mode-locking mechanisms. Nelson et al. used a spectral filter and nonlinear polarization evolution (NPE) as mode-locking mechanism [14]. Sharp et al. achieved mode-locking by using a semiconducor saturable absorber [15]. Recently, Solodyankin et al. demonstrated mode-locking in a thulium-doped all-fiber laser by introducing a carbon nanotube absorber into the resonator [16]. All of these three lasers were based on solitonic pulse propagation, whereas fiber dispersion is locally balanced by nonlinearity. An increase of the pulse energy at given dispersion consequently is accompanied by a longer pulse duration. Thus lasers operating in the fundamental soliton regime always imply a tradeoff between achievable pulse energy and pulse duration.

In [17] we demonstrated a TDF laser with internal dispersion compensation based on a grating arrangement. By nearly compensating the group delay dispersion (GDD) of the fiber section to obtain an overall GDD of -0.02 ps², non-solitonic pulse formation could be achieved. This permitted an increase of pulse energy up to 4.3 nJ. The pulses could externally be dechirped to a duration of sub 300 fs, which was less than 10% above the Fourier-limit. Although the pulse energy was increased by nearly two orders of magnitude, the Fourier-limited pulse duration was still longer, than the one previously reported on in [15]. Shorter pulse durations can be achieved either by better matching of dispersion compensation and fiber dispersion or by the generation of additional spectral components via self-phase modulation (SPM). As the latter is a nonlinear effect, its impact strongly relates to the peak intensity of the propagating pulse. In [17] the pulse duration reaches its minimum at the beginning of the fiber section, where the pulse energy is minimal and is increased by dispersion during the amplification. Thus SPM does not contribute to the spectral broadening in a proper way.

In contrast, stretched-pulse lasers are distinguished by a distinct pulse breathing dynamic, where the chirp changes its sign twice during pulse propagation inside the cavity. Consequently the pulse duration reaches its minimum inside the active fiber and a considerable spectral broadening by SPM is expected. Therefore, it is highly desirable to operate the laser in the stretched-pulse regime to increase its performance and to achieve the shortest pulses possible. For an overview on the physical mechanisms, that facilitate this improvements, the reader is referred to [7, 8, 9, 10]. In this paper, we report on stretched-pulse operation of our TDF laser. This is, to the best of our knowledge, the first demonstration of this mode of operation and allowed to decrease the pulse duration significantly while keeping the pulse energy at 4 nJ. The laser generates pulses with a Fourier-limit of 161 fs which could be efficiently dechirped outside the cavity.

 

Fig. 1. Experimental setup. DC: dichroic mirror (HR 1980 nm/AR 793 nm); TFP: thin-film polarizer; FR: Faraday rotator; HWP/QWP: half-/quarter-wave-plate; TDF: thulium-doped fiber.

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2. Setup

The setup of the laser (Fig. 1) is equivalent to the one described in [17]. The laser was based on a ring resonator configuration with a repetition rate of 41.4 MHz. As active fiber, 2.36m double-clad silica fiber with a signal core diameter of 25µm (0.1 numerical aperture (NA)) as well as a cladding diameter of 250µm (0.46 NA) was used. It was doped with 2wt% Tm³⁺ and had an absorption of 5 dB/m at the pumping wavelength of 793nm [18]. As pump source a fiber coupled diode with core diameter of 200µm (0.22 NA) was used. Signal and pump light were seperated by a dichroic mirror (DC). The quantum defect of about 60% between pump and emission wavelength led to a siginificant heat input into the fiber. To avoid performance losses owing to thermal influences we placed the entire length of the active fiber in a water bassin.

The lengths of the passive fiber pigtails were 0.33m and 1.00m at the pump and the out-coupling end of the fiber, respectively. The length at the beginning of the fiber section was minimized in order to introduce only minor anomalous GDD. The fiber pigtail at the end was choosen longer as it contributed significantly to the NPE (due to the higher peak intensity after the TDF), which was used as mode-locking mechanism. Both ends of the fiber section were polished with an angle of 8° to avoid parasitic effects caused by Fresnel reflections, which can inhibit mode-locked operation. The waveplates preceding and following the fiber section were used to manipulate the polarization state for the NPE. A thin-film polarizer (TFP) following the fiber section was used as polarization selective element and its rejection port acted as the output.

With the setup reported on in [19], the GDD of the fiber section was measured to be

-0.31 ps² at 1950 nm. For compensation of the fiber GDD a grating arrangement based on two antiparallel reflection gratings with 600 grooves/mm and a telescope in 4-f-configuration with a focal length of f=100mm was inserted into the cavity. The telescope permits negative effective distances between the grating and consequently provides positive GDD. Dispersion introduced by the free-space optical components was neglegible, as its contribution can be assessed to be an order of magnitude lower than the overall cavity dispersion. The polarization dependent diffraction efficiency of the gratings in combination with the Faraday rotator (FR) and the preceding TFP ensured the unidirectional operation of the laser, which facilitates self-starting of mode-locked operation [20].

 

Fig. 2. Spectral width at FWHM(squares) and pulse energy (circles) in respect to the group-delay dispersion for the mode of operation reported on in [17]. The lines are just to guide the eye.

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3. Results

Starting from the mode of operation reported on in [17] taken at a GDD of -0.02 ps ², we varied the GDD in order to find a better operation point to obtain shorter pulse durations. The dependence of the achievable spectral bandwidth in respect to the GDD is displayed in Fig. 3. The spectral bandwidth increased from 16.5nm at -0.0² ps 2 to 23nm at slightly positive GDD. On the other hand, the achievable pulse energy (also displayed in Fig. 3) exhibited a minimum at -0.002 ps². At the value for maximum spectral bandwidth, it did not exceed 3.5 nJ. As a good compromise between spectral bandwidth and pulse energy we operated the laser at a GDD of 0.01 ps². Although the variation of the GDD already resulted in a distinct increase of the spectral bandwidth, a further optimization was possible as we achieved another, which could be attributed to the stretched-pulse regime.

The output power versus pump power of the laser is shown in Fig. 3(a), which is constrained to the relevant part due to a better facility of inspection. When increasing the pump power to 7W-8W, the laser was self-starting resulting in an arbitrary, unreproducable multiple pulse emission. With reduction of pump power, the number of circulating pulses decreased until single pulse operation without a cw-background was reached at a pump power of 5.7W. Above 5.6W of pump power, the power spectrum and the shape of the autocorrelation trace were quite similar to the negative overall cavity GDD regime (see [17]), which is denoted as SPO in Fig. 3(a). Below 5.6W of pump power, stretched-pulse operation was obtained, revealing in an increased spectral width and a significant change of the shape of the autocorrelation trace. According to the average output power of 167mW the pulse energy was 4 nJ.

The power spectrum, depicted in Fig. 3(b), with 35nm FWHM at a center wavelength of 1974nm corresponds to a Fourier-limited pulse duration of 161 fs. The time-bandwidth-product of the calculated Fourier-limited and the dechirped pulse was 0.44 and 0.46, respectively. This indicates a Gaussian pulse shape which is found for stretched-pulse operation [7, 8, 9, 10]. The origin of the asymmetric shape and the unequally spaced modulations at the shorter wavelength side is not clear yet. It might be attributed to passive properties from the applied components as well as higher order dispersion or interference effects due to polarization-mode dispersion [21]. Interference caused by double pulses can be ruled out as in this case the modulations would be equally spaced.

 

Fig. 3. (a) Extract from output power and pulse characteristics versus pump power and (b) power spectrum at stretched-pulse operation; SPO: Single pulse operation reported on in [17].

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Fig. 4. Autocorrelation traces of the (a) uncompressed and (b) compressed pulse. The intensity autocorrelation of the compressed pulse was generated from the interferometric one via applying a mathematical low-pass filter. The measured autocorrelation width of 240 fs corresponds to a pulse duration of 173 fs. Inset: Calculated autocorrelation traces of the bandwidth-limited pulse.

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Figure 4(a) shows the interferometric autocorrelation trace at the output port indicating a strong chirp. The autocorrelation width corresponds to a pulse duration of several picoseconds. With a grating arrangement similar to the internal one, the pulses could be externally dechirped to an autocorrelation width of 240 fs (displayed in Fig. 4(b)). Assuming the Gaussian pulse shape, this corresponds to a pulse duration of 173 fs, which is only 7% above the Fourier-limit. The small wings in the measured autocorrelation trace of the dechirped pulse, which did not occur in the calculated one (inset of Fig. 4(b)), are a further indication for a stretched-pulse operation. They can be explained by an uncompressed pedestal below the pulse caused by the onset of a non-monotonic chirp at negative fiber GDD [22].

The GDD of 0.2 ps² applied for optimum dechirping was significantly smaller, than the one provided by the grating arrangement implemented for dispersion control. This implies that the chirp at the end of the fiber section is overcompensated by the internal dispersion compensation. Hence, the chirp changes its sign twice per roundtrip and there are two points of minimal pulse duration inside the cavity. This is a typical feature of the pulse dynamics in the stretched-pulse regime [9, 10].

The ratio of external GDD applied for optimum pulse compression to the GDD of the fiber was 65%. Therefore, the points of minimal pulse duration are shifted from the center of the dispersion sections (as expected for zero GDD) towards the beginning of the TDF. This is in agreement with earlier studies on the stretched-pulse regime [10]. Compared to the mode of operation reported on in [17], the pulses exhibit a more distinct SPM induced spectral broadening. Utilization of this fact allowed us to decrease the Fourier-limited as well as the dechirped pulse duration to 60% compared to our former results.

4. Conclusion

To the best of our knowledge, we presented the first thulium-doped stretched-pulse fiber laser, capable of generating the shortest pulses from a thulium-doped oscillator reported on so far. The mode of operation was verified by the ratio of external applied dispersion to fiber dispersion and supported by the shape of the autocorrelation trace and the time-bandwidth product. It was facilitated by introducing positive GDD into the cavity to compensate the GDD of the fiber section resulting in a positive GDD of 0.01 ps². The laser emitted pulses with an energy of 4 nJ at a center wavelength of 1974nm which could dechirped outside the cavity to a duration of 173 fs.