1. Introduction

Applications of ultrafast laser technology outside a laboratory environment rely on compact, stable, maintenance- and alignment-free femtosecond pulse sources. Ultrashort pulse generation in rare-earth-doped fibers is considered to be the most promising approach to fulfill these requirements. Their advantages arise from the light propagation in waveguide-structures, and hence, inherent stability and immunity against thermo-optical issues. Mostly, passive mode-locking is achieved by applying nonlinear polarization rotation or a saturable absorber mirror (SAM) [1]. Indeed, mode-locked single-mode rare-earth-doped fiber lasers are nowadays routinely operated and are entering the market to address real world applications.

However, peak power and pulse energy scaling of mode-locked fiber lasers is not as straightforward as in their bulky counterparts. Mainly, due to the tight confinement of the light over considerably long lengths nonlinear effects, mainly Kerr-nonlinearity [2], avoid self-consistent pulse evolution inside a fiber laser resonator and hinder the pursuit of higher pulse energies from mode-locked fiber lasers. Besides the necessary balance between dispersion and nonlinearity, which can be supported by spectral filtering, the overdriving of the effective saturable absorber can arise as a further energy scaling restriction.

Over the recent decade operation regimes and cavity configurations of fiber oscillators in the 1 µm wavelength region have been developed to obviate this limitation. In the style of conventional mode-locked lasers the canonical approach is the soliton regime (anomalous group velocity dispersion (GVD) regime), however, the energy achievable in such a configuration is limited by the soliton area theorem to some tens of picojoules [3]. An increase of pulse energy from fiber oscillators can be achieved by stretching the pulse during its propagation while reducing the accumulated nonlinear phase. This concept is pursued in operation regimes such as stretched-pulse [4, 5], self-similar [6, 7] or all-normal dispersive [8–10]. Typically, the pulse experiences large spectral and temporal variations during one resonator round trip leading to a reduced average peak power. Pulse energies above 10 nJ have been reported by several groups in a variety of operation regimes [11–13].

Along with the cavity configuration the fiber design determines the amount of accumulated Kerr-nonlinearity. Hence, the employment of low-nonlinearity large-mode-area fibers opens the possibility of energy scaling. This has been demonstrated recently by a femtosecond ytterbium-doped fiber laser operating in the anomalous net-cavity dispersion regime emitting a pulse energy as high as 16 nJ [14].

 

Fig. 1. Schematic representation of the passively mode-locked Yb-doped rod-type photonic crystal large mode area fiber laser. SAM: saturable absorber mirror.

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Fig. 2. Cross section of the 70 µm core rod-type photonic crystal fiber.

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In this contribution, we report on the generation of 265 nJ from a passively mode-locked self-starting fiber laser in a dispersion compensation-free configuration. The pulses are compressed by an external grating pair down to 400 fs. As gain medium a 70 µm core ytterbium-doped photonic crystal fiber is employed. This performance corresponds to a ten fold energy increase in comparison to so far published fiber oscillators. Numerical simulations accurately reflect the experimental results and reveal the mechanisms for self consistent intra-cavity pulse evolution. To our knowledge this is the first time that mode-locked fiber oscillators can compete in terms of pulse energy and peak power with most advanced long-cavity [15–18] or cavity-dumped [19] bulk solid-state femtosecond lasers.

2. Experimental setup

The experimental setup of the passively mode-locked large-mode-area (LMA) fiber laser is shown in Fig. 1. The setup bases on a sigma cavity configuration. As gain medium an ytterbium-doped photonic crystal fiber is employed [20]. A cross section of this fiber is shown in Fig. 2. It possesses a core diameter of 70 µm and is surrounded by hexagonal lattice of air holes with a diameter of 0.9 µm and a hole-to-hole spacing of approximately 12.7 µm. The inner cladding has a diameter of 180 µm and a numerical aperture as high as 0.6 at the pump wavelength. A large outer cladding with 1.4 mm provides high stiffness to avoid losses for the weakly guided fundamental mode due to micro- and macro-bending. The pump light absorption of this fiber is 30 dB/m at 976 nm resulting in a very short fiber length of 51 cm, which is required for efficient operation. The fiber ends are polished at an angle of 8° to eliminate parasitic reflection into the fiber or sub-cavity effects respectively. The fiber laser is pumped from one side by a fiber-coupled (200 µm, NA=0.22) diode laser emitting at 976 nm. A dichroic mirror M1 is used to separate the pump beam from the laser emission, which is centered at about 1035 nm. A second dichroic mirror M2 blocks unabsorbed pump radiation. The ytterbium-doped fiber is placed in the ring section of the cavity. The optical isolator assures the unidirectional propagation of the laser light inside the resonator. The reflected polarization of the polarization beam splitter of the isolator serves as the output. By means of the rotation of a quarter-wave plate between the isolator and the fiber, output coupling ratio is controlled. A mirror array in the linear part of the cavity is used to increase the cavity length resulting in a pulse repetition rate of 10.18 MHz. The total second-order cavity dispersion is about +0.012 ps² at 1032 nm. It is important to note that there is no dispersion compensation element and no additional spectral filter introduced into the setup. Hence, the laser operates in the dispersion compensation free regime.

Passive mode-locking is achieved employing a SAM placed at the end of the linear section of the sigma cavity. The SAM bases on a multi-layer GaAs/AlAs Bragg mirror and a low-temperature molecular beam epitaxy grown InGaAs quantum well structure in front of the mirror. The low-intensity absorption of the SAM at around 1035 nm is ~45 %, the modulation depth ~30 % and the saturation fluence as high as 100 µJ/cm². The bi-temporal impulse response possesses a short relaxation time of <200 fs and a slower part of ~500 fs.

3. Experimental results

An optimization of the saturation criteria of the saturable absorber in terms of spot size resulted in stable mode-locked operation. However, when mode-locking is achieved, the wave-plate inside the laser have been optimized to extract higher energies. It is important to note that due to the low-nonlinearity of the employed fiber, passive mode-locking can not be achieved by nonlinear polarization rotation alone. Even after initiation of mode-locking by the saturable absorber no polarization effects on the emitted pulses have been observed. A rotation of the intra-cavity wave-plate does affect the intra-cavity power and hence the spectral and temporal width. However, the spectral and temporal pulse profile is not affected.

 

Fig. 3. Optical spectrum of the output signal. Inset shows the optical spectrum on a logarithmic scale.

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Above the mode-locking threshold (at about 2 W average output power) the laser delivers a single-pulse train with a repetition rate of 10.18 MHz. The highest possible average output power in the presented configuration is as high as 2.7 W, corresponding to a pulse energy of 265 nJ. The operation of mode-locking is self-starting independent of the orientation of the wave-plate. The emission spectrum at the highest pulse energy, which is characterized by steep edges, is shown in Fig. 3. The center wavelength is 1031.7 nm and the spectral bandwidth (FWHM) is 8.4 nm. Figure 4(a) shows a measured autocorrelation trace obtained directly at the laser output. The positively chirped output pulses have an autocorrelation width (FWHM) of 4 ps. These pulses are externally compressed by a transmission-grating pair, each grating possessing a grating period of 800 nm [21]. The measured autocorrelation trace is presented in Fig. 4(b) with an autocorrelation width of 546 fs. Assuming a deconvolution factor of 1.36 a pulse duration as short as 400 fs has been obtained, indicating a compression factor of more than 7.3. Additionally, the autocorrelation width of the transform-limited pulse calculated from the power spectrum is 431 fs which indicates that the pulses can be compressed down to near transform-limited pulse duration. The deconvolution factor is motivated by numerical simulations described in the next section of the manuscript. The pulses do not present any pedestal indicating clean pulse generation. A compressor efficiency of 75% results in an energy per compressed pulse as high as 200 nJ, corresponding to a 500 kW pulse peak power. To prove single-pulse operation a backgroundfree autocorrelator with a scanning range of 150 ps and a 200 ps rise time photo-diode are used. It should be mentioned that the reported performance is limited by overdriving of the saturable absorber in the present configuration. We believe that this overdriving can be at least partly attributed to thermal loading of the SAM structure.

 

Fig. 4. (a) Autocorrelation trace of the output chirped pulses and (b) after extra-cavity compressed pulses.

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4. Intra-cavity pulse evolution

As discussed above the generation of the mode-locked high-energy pulses from Yb-doped short-length large-mode-area fiber without intra-cavity dispersion management is experimentally demonstrated. The following discussion is devoted to confirm these results by numerical simulation of the intra-cavity pulse evolution. The simulation of the laser is based on a non-distributed model solving all parts described by the nonlinear Schrödinger equation with the split-step algorithm [22]. One cavity round trip includes the action of the output coupler, the saturable absorber and the active fiber. The parameters for each cavity element are identical to those described in the experimental part of the manuscript. It is important to note that there is no higher-order dispersion considered in the numerical simulation. The gain in the active fiber is modeled according to g=g ₀/(1+E/E_sat), where g0 is the small signal gain (assuming 30 dB) and E is the pulse energy. A gain bandwidth of 20 nm is assumed. E_sat denotes the saturation energy due to limited pumping and is set to 67 nJ leading to an extracted energy of 270 nJ at an high out-coupling ratio of 90 %. For the given cavity configuration and power level the simulation has started from quantum noise and converged into a stable solution after approximately 400 round trips, as shown by transient spectral evolution in Fig. 5. Note that the stable solution did not depend on the initial quantum noise condition and it is obtained even at higher temporal and spectral resolution.

 

Fig. 5. Transient evolution in the spectral domain from quantum noise to steady state solution for E_sat=67 nJ. (Logarithmic scale: -30 dB 0 dB (max))

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To gain insight into the intra-cavity pulse evolution, the spectral and temporal characteristics of one cavity round trip of the converged pulse are shown in Fig. 6. The effects of the saturable absorber mirror and output coupling is done in a single step. As shown, the pulse duration and spectral bandwidth changes only slightly during the intra-cavity propagation. This behavior is in contrast to other operation regimes, well know from dispersion-managed mode-locked fiber lasers (e. g. stretched-pulse regime) where temporal and spectral breathing is significantly more pronounced. The minimum pulse duration occurs directly after the SAM resulting from the nonlinear absorbing mechanism. The pulse duration monotonically increases during the amplification in the gain fiber. As revealed by the simulation the pulses are always positively chirped inside the cavity with only one minimum per round trip located at the entrance of the fiber. Hence, the fiber oscillator operates in the wave-breaking free regime. The simulation shows a pulse duration of 5.25 ps (FWHM) at the output for an extracted pulse energy of 270 nJ, which is in good agreement with the experiment. Due to the linear chirp of the pulses the SAM causes a slight decrease of spectral width as well. In addition the gain bandwidth of the fiber is causing a spectral narrowing before sufficient peak power leads to spectral broadening due to self-phase-modulation (SPM) in the gain fiber. Finally, the balance between bandwidth filtering by SAM, the gain and the broadening by SPM leads to a self-consistent intra-cavity pulse evolution.

 

Fig. 6. Simulation of the intra-cavity pulse evolution of the dispersion compensation free mode-locked fiber laser in the temporal and spectral domain. (OC- Output coupling, SAM-saturable absorber mirror. Logarithmic scale: -30 dB 0 dB (max))

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Figure 7 discusses the results of the numerical simulation obtained at the output port. The spectrogram as shown in Fig. 7(a) presents a positively chirped pulse. The linear chirp is dominating, however, contributions from higher order phases are observable as well. The power spectrum, shown in Fig. 7(b), possesses the same characteristics as the measured spectrum. It has step edges and a bandwidth (FWHM) of 11 nm. We believe that the asymmetric spectral behavior can be attributed to the temporal behavior of SAM. The calculated autocorrelation trace obtained by optimal de-chirping with 800 nm period grating pair used in a Littrow configuration is shown in Fig. 7(c). The autocorrelation width is 385 fs corresponding to a pulse duration of 283 fs. The autocorrelation has a small wing structure due to the uncompensated nonlinear chirp.

 

Fig. 7. (a) Spectrogram of the steady state solution for the dispersion compensation free mode-locked fiber laser at the output of the fiber (Spectrogram resolution: 600 fs, linear scale: 0 max). (b) Spectrum at the output. (c) Autocorrelation of the transform-limited pulse calculated from the spectrum.

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5. Conclusion

In conclusion, we have demonstrated for the first time to our knowledge the generation of 265 nJ ultra-short pulses from a mode-locked Ytterbium-doped short-length large-mode-area fiber laser operating in the dispersion compensation free regime. The self-starting oscillator emits 2.7 W of average power at a pulse repetition rate of 10.18 MHz. The pulses have been compressed down to 400 fs, corresponding to 500 kW peak power. Numerical simulations confirm the stable solution and reveal the mechanisms for self-consistent intra-cavity pulse evolution. The pulse energy is one order of magnitude higher than so far reported for fiber oscillators in the 1 µm wavelength region. We are convinced that a performance above the µJ barrier will be possible with the presented approach and a revised SAM structure.