We report on environmentally stable mode-locked Yb-doped all-fiber lasers operating in the wave-breaking-free and stretched-pulse regime. The compact linear cavity is constructed with saturable absorber mirror directly glued to the fibers end-facet as nonlinear mode-locking mechanism and chirped fiber Bragg grating for dispersion management, thus, without any free-space optics. In the wave-breaking-free regime the laser generates positively-chirped pulses with a pulse duration of 15.4 ps. These pulses are compressed to 218 fs in a hollow-core photonic bandgap fiber spliced to the output port. Adaptation of dispersion management has led to operation in the stretched-pulse regime, where a parabolic spectral profile is obtained as well. In this regime pulses are compressible to 213 fs. Numerical simulations are presented which confirm the wave-breaking-free and stretched-pulse evolution inside the fiber laser cavity. Both regimes are compared in terms of pulse quality.
©2007 Optical Society of America
Mode-locked fiber laser systems have been interesting research areas for many years and fiber-based mode-locked lasers have found numerous applications in both research and industry areas. Rare-earth-doped fibers are well-suited for ultra-fast applications as they have a large amplification bandwidth supporting ultra-short pulses and exhibit improved stability and freedom from misalignment. In addition, they offer compact design with inexpensive components and are suitable for high-average-power applications because their geometry leads to efficient heat dissipation. Nonlinear effects are usually quite large in mode-locked fiber lasers, but the interplay between dispersion, gain and nonlinearities can also be used to shape the pulse and pulse dynamics, and hence leads to different regimes of mode-locking.
The design of dispersion-managed passively mode-locked rare-earth-doped step-index fiber lasers is now well controlled and it is possible to generate low- or high-energy femtosecond pulses in the normal or anomalous dispersion regimes. Soliton fiber lasers are built entirely from anomalous group-velocity dispersion (GVD) fiber. The pulse shape and duration are maintained through the combined action of negative GVD and Kerr nonlinearity. The energy achievable in such laser systems is limited by the soliton area theorem to some tens of picojoules [1, 2]. More recently, the possibility of energy scaling of fiber lasers operating in the anomalous net-cavity dispersion has been demonstrated by the employment of low-nonlinearity large-mode-area fibers . A pulse energy as high as 16 nJ has been extracted. In the configuration of stretched-pulse regime, the total-cavity dispersion is close to zero and the pulse width experiences large variations per cavity round trip, with a change in the chirp sign from positive at the end of the normal GVD segment to negative at the end of the anomalous GVD segment. Stretched-pulse lasers with output energies from tens of picojoules to some nanojoules have been reported [4–7]. The most fundamental limitation to pulse energy in a fiber oscillator arises from wave-breaking phenomena because of large nonlinearities. More recently, wave-breaking is suppressed within the cavity by exploiting self-similar pulse propagation, which is resistant to nonlinearity . The generation of parabolic pulses from rare-earth-doped fiber oscillator has been firstly numerical predicted  and subsequently experimentally demonstrated . Self-similar femtosecond lasers with pulse energies above 10 nJ have been recently reported . This new mode-locking regime has been also observed in a polarization-maintaining (PM)-based fiber laser with saturable absorber mirror (SAM)  and in a double-clad fiber laser with using the polarization additive-pulse mode-locking (APM) technique .
In the wave-breaking-free mode-locked fiber laser, the net-cavity dispersion is positive and the nonlinear pulse evolution in the normal GVD fiber segment is monotonic. The pulse accumulates a linear chirp, which is partially compensated at points in the cavity using a linear process (e.g. diffraction gratings). The pulse is always positively chirped inside the cavity with a minimum (but not transform limited) at the entrance of the normal GVD fiber [14, 15]. The direct amplification of the pulse with parabolic spectra allows for the realization of high peak powers without any significant degradation of the recompressed pulse quality . In the specific feature of this regime, so-called similarition laser, the formation of the output pulses is perfectly linearly chirped with parabolic temporal profile [10, 14].
In this paper, we report the both numerically and experimentally generation of wave-breaking-free and stretched-pulses from an environmentally stable Yb-doped all-fiber laser. The linear cavity is constructed with polarization-maintaining single-mode fiber allowing environmentally-stable configuration. Nonlinear mode-locking mechanism is obtained by a directly glued SAM and dispersion management of the cavity is assured by chirped fiber Bragg grating (CFBG). Positively-chirped picosecond pulses with parabolic spectra are compressed to femtosecond range by using hollow-core photonic bandgap fiber (HC-PBG). The generation and intra-cavity evolution of wave-breaking-free and stretched-pulses are confirmed by a numerical analysis. To our knowledge, this is the first report of an all-fiber wave-breaking-free Yb-doped fiber oscillator and the generation of pulses with a parabolic spectral shaped in the stretched-pulse regime.
2. Experimental setup
The laser setup in the linear cavity configuration is shown in Fig. 1. A highly ytterbium-doped (~ 300 dB/m absorption @ 976 nm) polarization maintaining (PM) fiber with a mode-field diameter of 4.8 μm and a length of 38 cm is used as gain medium. This fiber is pumped through a thin-film PM-WDM by a single mode diode providing a maximum output power of 400 mW at a wavelength of 976 nm. The passive fibers used in the setup are Panda 980 PM fibers with mode field diameter of 7 μm @ 1035 nm. All PM fibers are fusion spliced with a high polarization extinction ratio and a low loss. Self-starting passive mode-locking has been achieved through the semiconductor saturable absorber mirror. The SAM is based on a non-resonant design, using a GaAs/AlAs Bragg mirror with 27 layer pairs and 26 low temperature molecular beam epitaxy grown InGaAs quantum wells in front of the mirror. AR coated device has low-intensity absorption of 45 %, a modulation depth of ~ 30 %, and a saturation fluence of 100 μJ/cm2. The SAM shows a bi-temporal impulse response with a short relaxation time of < 200 fs and a slower part of 500 fs. The ratio of the fast and slow parts has been determined to 3:2. It is directly glued to the fiber end-facet. A CFBG inscribed in a polarization maintaining fiber is employed for intra cavity dispersion compensation. It possesses a measured peak reflectivity of about 33% centered at 1035 nm with spectral Gaussian bandwidth of 16 nm. Therefore, besides the intra-cavity dispersion compensation the CFBG serves as the output coupler of the linear cavity. The dispersion of the CFBG has been measured by the spectral interferometry to be -0.19 ps2 at 1035 nm.
Additionally, a fiber pig-tailed thin-film isolator is used at the output of the cavity to eliminate parasitic reflection into the cavity or sub-cavity effects. In the two regimes, the pulse is positively chirped at the output of the cavity. Consequently, these pulses have been compressed by a linear process outside the cavity. An air-silica photonic bandgap fiber used (Crystal Fibre AIR-10-1060) for extra-cavity pulse compensation has a core diameter of 10.5 μm and the bandgap ranges from 980 nm to 1080 nm with an attenuation of less than 0.1 dB/m. The dispersion of this fiber is -0.0625 ps2/m at 1035 nm. An adapted length of this HC-PBG fiber has been fusion spliced to output with non optimized losses of 2.3 dB. This setup allows for the generation of femtosecond laser pulses in an all-fiber format. It should be mentioned that the HC-PBG fiber is not polarization-maintaining. Currently available birefringent HC-PBG fibers are unfortunately characterized by a significantly higher transmission loss and a low amount of birefringence not sufficient for polarization-maintaining behavior. However, such fibers are a promising option for future improvements.
3. Experimental results
3.1.1 Wave-breaking-free regime
In the wave-breaking-free operation, the total fiber length inside the cavity is 4.9 m allowing for a second-order cavity dispersion of 0.055 ps2. Hence, the laser operates in the normal dispersion regime. In this operation, the laser started CW operation at lower pump power, by increasing the pump power, the laser started to operate in a Q-switched mode-locking state. At launched pump power of 38 mW, the stable mode-locking threshold is reached and the laser delivers single-pulse trains at about 20.30 MHz. The mode-locking regime is very stable and self-starting with the same characteristic of the operation (spectrally and temporally) for equal pump power. Figure 2 shows the optical power spectrum together with different theoretical fits using sech2, Gaussian and parabolic profiles. The experimental spectrum presents the best agreement with the parabolic profile of 13.9 nm spectral width centered around 1035 nm mainly due to its steep edges. We attribute the residual modulation in the spectrum to interference effects by polarization mode mixing and intra-cavity splice issues. Depending on the pump power, we could observe such a spectral shape for a net-cavity dispersion of 0.048 ps2 to 0.075 ps2 by changing the passive fiber length. Single-pulse operation is proven by using a background-free autocorrelator with a scan range of 150 ps and a 200 ps rise time photo-diode. We measured 7.9 mW average output power for a pump power of 44 mW, which corresponds to 390 pJ energy per pulse.
Figure 3(a) shows the autocorrelation trace obtained directly at the laser output. The positively chirped output pulses have a pulse duration of 15.4 ps (autocorrelation width of 16.4 ps). For comparison, these pulses are compressed in a first step by a grating pair (1250 lines/mm) outside the cavity. An autocorrelation width as short as 328 fs (FWHM) has been obtained, which indicates a compression factor of more than 49. The pulse duration can be calculated from the width of the autocorrelation by assuming a transform-limited wave breaking-free spectrum of the compressed pulse (deconvolution factor 1.5) and is evaluated to be 218 fs.
Subsequently, the output pulses are also compressed by the mentioned HC-PBG fiber outside the cavity allowing for an all-fiber configuration delivering ultra-short pulses. The optimum fiber length has been determined to minimum pulse duration, which corresponds to a dispersion of -0.38 ps2 that is much larger than the negative dispersion given by the CFBG of -0.19 ps2. It proves that the pulses are always positively chirped inside the cavity with only one minimum per round trip located at the end of the anomalous GVD segment. The autocorrelation trace obtained in this case is shown in Fig. 3(b) and presents to the same width of 328 fs (FWHM) as obtained by the grating compressor. The measured average output power after the HC-PBG fiber is 3.8 mW, corresponding to an energy per pulse of 190 pJ.
Additionally, the autocorrelation of the transform-limited pulse calculated from the power spectrum indicates uncompensated nonlinear chirp contributions on the pulse (not shown here). It was shown theoretically that a linear chirp known from self-similar evolution is not always present and that such nonlinear chirp contributions might occur in the wave-breaking free regime . The residual modulation in the spectrum demonstrates that a second polarization mode is not suppressed in our setup. It can be added additional pedestal structure on the compressed pulses.
3.1.2 Intra-cavity pulse evolution
The external compression already proved a positively chirped pulse propagating inside the cavity. To further confirm this statement and get insight into the pulse evolution, a numerical simulation has been performed. Our numerical simulation of the laser is done using a non-distributed model solving every part by the nonlinear Schrödinger equation . The parameters for each element are that of the experimental setup. The simulation started from quantum noise and after convergence, the pulses intra-cavity evolution is calculated. The result is shown in Fig. 4 where the propagation in the single-mode fiber and the gain fiber is scaled to an identical part of the cavity, whereas the saturable absorber and the dispersion compensation by the CFBG is done in a single step. One can clearly see that the pulse spectrum changes only slightly but shows steep edges as measured experimentally. The pulse duration increases until the dispersion compensation, which does not reverse the sign of the chirp meaning that only one minimum in pulse duration is found. The minimum pulse duration located at the end of the anomalous GVD segment is 1.8 ps. The simulation also shows that the pulse duration at output τAC FWHM=7.7 ps. The smaller values compared to the measured autocorrelation width is due to additional passive fiber length of the isolator that are not included in the simulation. With these experimental and numerical results we can conclude that the laser works in a wave-breaking free regime, where the pulse has a positive linear chirp at each position in the cavity.
3.2.1 Stretched-pulse regime
As discussed in the previous section, we obtained close to parabolic intensity spectral profile shape in the wave-breaking-free pulse regime for a large wide of normal net-cavity dispersion. It is now of particular interest to know if similar behavior can be obtained in the close to wave-breaking-free regime. First, to avoid of residual modulation in the spectrum, we used PM-WDM outside of the cavity and the doped fiber is pumped through the CFBG leading to a reduction of the intra-cavity splice issues . The total fiber length inside the cavity is now 4.1 m allowing for a second-order cavity dispersion of 0.016 ps2. Therefore, the laser still operates in the normal dispersion regime as in the above discussed configuration.
At launched pump power of 20 mW, the laser delivers self-starting and stable single-pulse trains at about 24.6 MHz. We could indeed generate clean optical spectrum with very low residual modulation. Figure 5 shows the optical power spectrum of output signal. For comparison, we also present the three different theoretical fits. The optical spectrum shows that the spectral profile of this regime fits well with a parabolic intensity profile near the peak over more than one decade of intensity. The optical spectrum has a width of 12.3 nm centered around 1035 nm. Also in the stretched-pulse regime single pulse operation has been verified. We measured 4 mW average output power for a pump power of 25 mW, which corresponds to 160 pJ energy per pulse.
Figure 6 (a) shows the autocorrelation trace directly obtained at the laser output. The positively chirped output pulses have a pulse duration of 6.3 ps (autocorrelation width of 7.4 ps). The autocorrelation trace of the compressed pulses using a HC-PBG fiber and the transmission bulk grating compression shows the same autocorrelation width of 310 fs (FWHM). It indicates a compression factor of more than 23. The measured autocorrelation traces are shown in Fig. 6(b). The pulse duration can be calculated from the width of the autocorrelation by applying the deconvolution factor of 1.46 of the transform-limited pulse corresponding to the optical spectrum and is evaluated to be 213 fs.
The optimum HC-PBG fiber length has been determined to minimum pulse duration, which corresponds to a dispersion of -0.17 ps2 that is very close but smaller than the negative dispersion given by the CFBG of -0.19 ps2. It indicates that the pulses change the chirp sign from positive at the end of the normal GVD segment to negative at the end of the anomalous GVD segment. The measured average output power after the HC-PBG fiber is 2 mW, corresponding to an energy per pulse of 80 pJ. Additionally, the autocorrelation of the transform-limited pulse calculated from the power spectrum as well as the measured autocorrelation traces are free from pedestal structures, what can be attributed to the weak residual modulation and the spectral shape in general (no steep edges). Consequently, due to the significantly cleaner compressed pulses this spectral shape of the pulses might be more attractive than the spectral shape obtained in the wave-breaking-free regime.
3.2.2 Intra-cavity pulse evolution
The intra-cavity pulse evolution could be inferred from the magnitude of anomalous GVD required to dechirp the pulse outside the cavity. To study of the intra-cavity pulse evolution, the numerical simulation has been repeated with the parameters of experimental setup in the second configuration. The simulation also started from quantum noise and after convergence, the pulses intra-cavity evolution is calculated. The result is shown in Fig. 7 where the propagation in the single-mode fiber and the gain fiber is scaled to an identical part of the cavity, whereas the saturable absorber and the dispersion compensation by the CFBG is done in a single step. This regime presents different temporal and spectral evolution of the pulses inside the cavity than in the previous regime. We can see clearly that the pulse spectrum changes dramatically during one roundtrip compared to the wave-breaking-free regime but also shows steep edges as observed experimentally. Two minima of the pulse duration are found located at the anomalous GVD segment and at the normal GVD segment, which indicates that the sign of the chirp reserve during one roundtrip. The minimum pulse duration is 371 fs. The simulation also shows that the pulse duration at output τAC FWHM=3.3 ps, which is in good agreement with the experiment. With these experimental and numerical results we can conclude that the laser works in a stretched-pulse regime with a parabolic spectral intensity profile, where the pulse has two minimum inside the cavity with negative and positive chirp.
In conclusion, we have developed a passively mode-locked environmentally stable Yb-doped all-fiber laser operating in the wave-breaking-free regime. The fiber laser directly generates positively-chirped picosecond pulses at a repetition rate of 20.30 MHz. These pulses can be compressed to 218 fs in a HC-PBG providing a femtosecond all-fiber laser system. Furthermore, we confirmed the wave-breaking-free regime experimentally and by numerical simulations. We have also demonstrated chirped pulses with parabolic spectral profile in the stretched-pulse regime. These pulses have been compressed to 213 fs with significantly reduced pedestal structures. This completely alignment-free, ultra-compact and low cost femtosecond laser source has great potential for several applications, such as nonlinear microscopy, but can also serve as an ultra-short seed source for a variety of short pulse amplifiers at the one micron wavelength region.
The authors would like to thank T.V. Andersen (NKT Research) for dispersion measurement of CFBG. This work was partly supported by the German Federal Ministry of Education and Research (BMBF) under contract 13N8721 as well as the support by the Deutsche Forschungsgemeinschaft (Research Group ”Nonlinear spatial-temporal dynamics in dissipative and discrete optical systems”, FG 532).
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