We investigated of the output characteristics of a spectrally filtered stretched-pulse thulium fiber laser in dependence of cavity dispersion and pump power. The experimental results together with corresponding theoretical modeling allow for a deeper insight into the pulse shaping mechanisms.
© 2010 OSA
Since passively mode-locked fiber lasers are capable of delivering pulses with energies in the nJ regime and fs durations, they are increasingly used in many different application areas. Thulium-doped fibers extend the accessible wavelengths towards the eyesafe region of about 2 µm. With their amplification bandwidth of more than 200 nm [1,2] they are excellent candidates for the generation of ultrashort pulses with possible applications in micromachining of transparent materials or laser-induced breakdown spectroscopy [3,4].
Owing to the large spectral width and the short durations, the shape of ultrashort pulses propagating along a fiber is significantly influenced by different parameters. Some of these parameters are intrinsic to the applied components like the amplification bandwidth of the gain medium or distribution of nonlinearity and dispersion, which depend on the wavelength and the fiber’s mode-field diameter. Some others can be adjusted in order to optimize the output parameters like for example overall gain and loss, polarization, spectral filters or the cavity dispersion.
At the wavelength region of 2 µm silica fibers typically exhibit negative group delay dispersion (GDD). Therefore, without dispersion compensation thulium fiber lasers are restricted to soliton operation, which has been demonstrated with different mode-locking schemes, but allows only low pulse energy due to the local compensation of GDD via self phase modulation (SPM) [5–7]. Alternatively, elements for dispersion compensation can be implemented into the cavity, enabling the laser to operate in the stretched-pulse regime. This regime is characterized by breathing dynamics that reduce the total nonlinear phase shift and allow for relatively high pulse energies compared to the fundamental soliton regime, while the pulses can still be compressed to very short durations outside the resonator . Mode-locked operation of dispersion-compensated thulium fiber lasers has also been successfully demonstrated by our group, but has not yet been comprehensively investigated [9,10].
In this paper, we report on results of a spectrally filtered thulium-doped stretched-pulse fiber laser. We investigated the output characteristics at different pump powers with cavity dispersions between −0.0440 ps2 and +0.0495 ps2. Numerical simulations were used to interpret the experimentally observed results.
2. Experimental setup
The experimental setup (Fig. 1 ) was similar to the one we reported on in Ref [9,10]. The laser was arranged in a ring resonator configuration with a repetition rate of 37.6 MHz. The active fiber was a thulium-doped double-clad fiber with a length of 2.5 m, a core diameter of 25 µm (0.1 NA), and a cladding diameter of 250 µm (0.46 NA). Two passive fiber pigtails with a length of 0.5 m at the pump end and 1 m at the outcoupling end were added to enable temperature stabilization in a water basin over the entire length of the active fiber. The active fiber was free-space cladding-pumped by a fiber coupled diode laser at 793 nm. Both ends of the fiber section were angle cleaved to avoid parasitic effects caused by Fresnel reflections, which can inhibit mode-locked operation. The fiber GDD was estimated to be −0.09 ps2/m for both active and passive fibers resulting in an overall GDD of the fiber section of −0.36 ps2 at 1980 nm.
For compensation of the fiber GDD a grating arrangement based on two antiparallel reflection gratings and a telescope in 4-f-configuration was inserted into the cavity. The telescope permits negative effective distances between the gratings and consequently provides positive GDD. To stabilize mode-locked operation, a spectral filter consisting of two razor blades with variable gap was inserted into the dispersion compensation section.
Mode-locking was achieved by nonlinear polarization evolution in the fiber with a thin- fiber polarizer (TFP) following the fiber section as polarization selective element, which also acted as variable output coupler. 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 . The reflected light from the input grating of the dispersion compensation section was used as monitor port to gain some information about the cavity internal spectrum and power. When carrying out spectral measurements at the monitor port some backwards ASE could be observed which could be separated by a TFP. With this configuration also unidirectional operation of the laser could be verified.
3. Numerical model
The numerical simulations were performed with commercial software solving the extended nonlinear Schrödinger equation by the split-step Fourier method . Linear effects included were saturable gain, loss, and dispersion, as to nonlinear effects SPM, Raman response, and self steepening were taken into account. The pulse propagation started from quantum noise and was executed in loop until a steady state was reached. The detailed model (Fig. 2 ) comprised nine elements: The free-space section (FS) consisted of a fast saturable absorber (SAM), a spectral filter and the dispersion compensation section, followed by a lumped loss of 55%, which represented the overall linear loss of the dispersion compensation section. The reflectivity of the SAM is given by where is the linear reflectivity, the saturable reflection coefficient, the instantaneous power, T the time and the absorber saturation power coefficient.
The fiber section consisted of five elements. With the gain being homogenously distributed along the complete active fiber, the experimentally observed output characteristics could not be reproduced. As rate equations were not included in the simulation software, the spectral and longitudinal gain distribution was calculated with a model by Pfeiffer et al. based on cross sections measured with the actually used fiber [13,14]. According to these calculations, the active fiber section was sub-divided into three elements. The amplification was restricted to the first part with a length of 1.5 m, while the following elements, each with a length of 0.5 m, were estimated to be passive and introducing a minor exponential reabsorption loss (loss coefficient αL = 0.1/m), respectively. The spectral gain function was approximated by a Gaussian shape with a full width at half maximum (FWHM) of 80 nm at a center wavelength of 1980 nm, the saturation energy was set to 1 nJ. Mode field diameters of the active and passive fiber were estimated to be 22 µm and 28 µm, respectively, referring to . The nonlinearity parameter was set to
4. Experimental and numerical results
Corresponding to the results from Ref [9,10], with the waveplates position and the spectral filter set appropriately, mode-locked operation was self starting, when the pump power reached a factor of 1.5 to 2 above lasing threshold, resulting in multiple pulse operation. When the pump power was reduced from that point, the number of circulating pulses decreased until single pulse operation with a continuous wave (CW) background was reached. The CW background could be suppressed by further reduction of pump power to about 6.6 W, resulting in clean, stable single pulse operation which was confirmed by measurements of the optical spectrum, the autocorrelation, a fast detector signal and the radio frequency (RF) spectrum.
With increasing positive cavity dispersion, the laser showed a tendency to q-switched mode-locking at low pump powers revealed by a low-frequency modulation of the pulse train and sidebands in the RF-spectrum. Q-switching could be eliminated after start of mode-locked operation by adjusting the spectral filter to reduce the intracavity losses. Thus, for larger positive cavity dispersion stable CW mode-locking was not completely self-starting, but nevertheless could still be achieved easily.
Starting with a dispersion of + 0.0495 ps2 the cavity dispersion was reduced stepwise to −0.0440 ps2 by adaptation of the grating distance while maintaining the waveplates and filter position and only adjusting the pump power for maximum single pulse output power at each step. Comparable to the experimental condition, the gain and the saturable absorption coefficient were the only simulation parameters that were adapted for the respective dispersion compensation to match the experimentally observed characteristics. This will be discussed later. The remaining SAM parameters were set to, and The filter transmission with a FWHM of 20.5 nm was estimated from measurements of the amplified spontaneous emission of the weakly pumped active fiber with and without blocking the backcoupling path.
In Fig. 3 the resulting parameters of the laser output and the simulated pulses as well as the respective simulation parameters are plotted versus cavity dispersion. Figure 3(a) shows pulse energy and autocorrelation (AC) FWHM. As collinear autocorrelations were measured, the AC width was estimated by applying a low pass filter onto the interferometric AC trace. Figure 3(b) shows the spectral FWHM and the bandwidth-limited pulse duration. In Fig. 3(c), the gain and the reflection parameter of the saturable absorber as well as resulting outcoupling ratio in simulation and experiment are plotted. Concerning the outcoupling ratio one has to take into account that the intracavity power was evaluated from power measurements with a thermal sensor at the monitor port at sub mW power level. Therefore, the absolute values are not to be regarded as overaccurate. Nevertheless, the measurement should reflect the actual development qualitatively well.
For cavity dispersion between −0.044 ps2 and + 0.035 ps2 the resulting pulse energy and bandwidth-limited pulse duration was in qualitatively good agreement with theoretical predictions as well as with previously reported experimental results [16,17]. Both of them reveal a minimum at about zero dispersion and increase with deviation. The pulse energy in simulation and experiment increased only slightly with negative dispersion, but considerably with positive dispersion. A maximum pulse energy of 5.4 nJ was achieved at 0.0385 ps2 of cavity dispersion. The internal and the externally measured pulse energy evolve in the same way, which is revealed by power measurements at the output and the monitor port and is in agreement with the simulations.
Above 0.015 ps2 of cavity dispersion the experimentally observed and the simulated pulse parameters increasingly diverged. Simultaneously, the shape of the spectrum and the AC both underwent significant changes, as opposed to the negative dispersion regime, where only slight changes were observed. This development is shown in Fig. 4 by means of selected spectra and AC traces. The modulations of the spectra and of the spectral filter originate from a wavelength-dependent transmission of the splices between the doped fiber and the passive pigtails, which could be verified by spectral measurements with and without the fiber pigtails.
Above a cavity dispersion of + 0.035 ps2 the spectrum broadened significantly and a sidepeak at the short wavelength side developed resulting in shorter bandwidth-limited pulse duration. Simultaneously the pulse energy decreased and the AC trace revealed a pedestal and sidelobes which also maintained when the pulse was dechirped externally. For this dispersion region, the characteristics of the experimentally observed pulses could not be reproduced by the numerical simulations.
We attribute the deformation of the spectral shape and the increasing deviation of the experimentally observed characteristics from the simulations to polarization effects as there are polarization mode dispersion (PMD) and particularly cross phase modulation (XPM). A number of arguments support this explanation to be the most reasonable. As polarization effects are not included in the simulation software, this could explain deviations of simulation and experiment, especially in terms of the spectral asymmetry. Nevertheless, the simulations offer good insight into the evolution of the pulse propagating inside the cavity.
The strongest hint on an increasing impact of XPM with positive dispersion is the decrease of the outcoupling ratio with increasing cavity dispersion. As the polarization at the beginning of the fiber section was kept constant during the whole experiment, variation of the outcoupling ratio is caused by varying nonlinear polarization rotation. The lower outcoupling ratio therefore is a result of higher saturation of the absorber owing to stronger nonlinear polarization rotation that is induced by XPM. This stronger polarization rotation requires an increase of the saturable reflection parameter to match the simulation to the experiment.
Regarding the evolution of pulse energy and duration as well as outcoupling ratio versus cavity dispersion we estimate the pulse energy to be limited by nonlinear chirp contributions. Similar to optical wave-breaking with positive fiber GDD, excessive nonlinear phase contributions at negative GDD can cause a non-monotonic pulse chirp leading to a pulse breakup . The other possible limiting effect, an overdriving of the saturable absorber mechanism, can be ruled out as it contradicts the decrease of outcoupling ratio with increasing accumulated nonlinearity over most of the investigated range.
Merely at major positive cavity dispersion, overdriving of the saturable absorber mechanism might be the limiting effect as indicated by the pulse energy, minimum duration as well as the outcoupling ratio remaining nearly constant.
Negative cavity dispersion
In Fig. 5 , the spectral and temporal evolution versus propagation distance for a single cavity roundtrip (a) as well as the measured and simulated single pulse spectrum (b) and AC trace (c) with a cavity dispersion of −0.0275 ps2 are displayed. The transmission of the spectral filter with a FWHM of 15.2 nm at a central wavelength of about 1986 nm here was estimated by spectral measurements before and after the dispersion compensation section. To match the experimental observed parameters, the saturable absorber parameters for this configuration were set to, and and the gain was set to Figure 5(b) and 5(c) show the very good spectral and temporal agreement of simulation and experiment. The simulated pulse energy was 4.2 nJ which was a little higher than the measured energy of 3.2 nJ. The simulated pulse duration at the end of the fiber section was about 700 fs. The pulses could externally be dechirped to 277 fs duration, which was 5% above bandwidth limit.
Both in experiment and simulation, the spectral width at the end of the fiber section increased, when the pump power and accordingly the gain parameter was reduced. This was caused by the pulse duration minimum shifting towards the end of the fiber section resulting in a broader spectrum at the end of the fiber owing to reduced reconversion of spectral components. The shape of the spectrum and the AC trace remained basically unchanged.
Positive cavity dispersion
In contrast to the negative dispersion region, at positive cavity dispersion the output pulse characteristics significantly depended on the pump power which corresponds to the results reported on in Ref . In Fig. 6 , pulse parameters with varying pump power at + 0.0385 ps2 cavity dispersion are displayed. Similar to an increase of cavity dispersion, decreasing the pump power led to an increasing side peak at the shorter wavelengths side [Fig. 6(a)], accompanied by a pedestal and side lobes occurring in the AC trace [Fig. 6(c)]. The pulse power varied almost linearly with the pump power, while the bandwidth-limited and compressed pulse duration remained nearly unchanged for lower pump powers and slightly increased with higher pump power [Fig. 6(b)]. The dispersion of the external compression unit was kept constant during variation of pump power; therefore a shift of the minimum pulse duration position inside the resonator resulted in maladjustment of pulse chirp and external dispersion compensation. The insets in Fig. 6(c) show the AC traces after compression. The minimum pulse duration of 216 fs was achieved at 7.09 W of launched pump power.
The evolution of the spectral shape and the AC trace suggests that according to the negative dispersion regime increasing the pump power causes the position of minimum pulse duration shifting towards the pump end of the fiber. This is mainly indicated by the position of the spectral side peak suggesting that higher pulse energy corresponded to generation of a broader spectrum. However, owing to the shift of the pulse minimum position, most of the generated spectral components were reconverted resulting in a narrower spectrum at the end of the fiber.
We investigated a spectrally filtered, passively mode-locked thulium fiber laser with variable dispersion compensation. Cavity dispersion was varied between −0.0440 ps2 and + 0.0495 ps2. The output characteristics of the laser could be reproduced very well by numerical simulations for a wide parameter range offering good insight into evolution of the pulse propagating along the fiber.
The highest pulse energies could be achieved with positive cavity dispersion while still very short pulse durations could be maintained. For the positive cavity dispersion regime the output characteristics strongly varied with pump power which could be attributed to a shift of the position of minimum pulse duration inside the resonator.
We achieved a minimum pulse duration of 216 fs and a maximum energy of 5.4 nJ. This is to best of our knowledge the highest pulse energy from an ultrashort pulse thulium-doped laser. The pulse energy was estimated to be limited by the onset of a nonlinear chirp.
The authors thank the German Research Foundation (DFG) for funding the Cluster of Excellence Centre for Quantum Engineering and Space-Time Research QUEST.
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