Femtosecond laser pulse generation with self-similar amplification of picosecond laser pulses

Huanyu Song; Bowen Liu; Wei Chen; Yuan Li; Youjian Song; Sijia Wang; Lu Chai; Chingyue Wang; Minglie Hu

doi:10.1364/OE.26.026411

1. Introduction

Femtosecond lasers are showing increasing importance in industrial applications and have become pivotal tools in scientific research [1,2]. Based on fiber techniques, femtosecond fiber laser systems deliver high-power pulses with high beam quality. Fiber architectures also provide compactness, robustness, and stability. In femtosecond fiber systems, seed sources have significant impact on system performances, especially on stability. Mode-locked femtosecond fiber lasers are commonly used as seed sources for femtosecond fiber amplification systems. They deliver >10-nm full width at half maximum (FWHM) to support <200-fs dechirped pulse duration [3–5]. In these lasers, saturable absorbers are necessary, such as semiconductor saturable absorber mirrors (SESAM) [6], or artificial saturable absorbers (nonlinear polarization evolution [7] and nonlinear optical loop mirror [8]). Meanwhile, dispersion compensation elements for soliton formation [9] or spectral filters for dissipative-soliton mode locking [10] are needed, but they are usually either expensive fiber elements or free space devices. As a result, they will increase complexity and cost of systems. Compared with femtosecond fiber lasers, picosecond fiber lasers are inherently simpler, cheaper and more stable [11,12]. With rapid development of picosecond laser techniques, picosecond fiber lasers have already been 7 × 24 commercial products in industry.

For taking advantage of picosecond fiber lasers, picosecond pulse compression to femtosecond level, as a developing trend of femtosecond laser technology, had been well studied. Recently, it attracts more and more attention [13–16]. Soliton compression and self-phase modulation (SPM) based nonlinear pulse compression are two common methods. Although soliton compression can provide <100-fs pulse duration [17,18], it is still hard to get high pulse energy with standard single mode fibers. Hollow-core photonic band-gap fibers could increase soliton energy significantly [19], but in turn gas-filled structures make it very complicated. On the contrary, SPM based nonlinear pulse compression does not suffer this problem and is widely used. In 1983, D. Grischkowsky et al. employed SPM to broaden the spectrum in a nonlinear passive fiber, and used a grating pair to dechirp output pulses, which compressed 5.4-ps laser pulses output from a mode-locked dye laser down to 450 fs [20]. In the following research, 100-ps laser pulses were compressed to 90 fs by two-stage pulse compression [21]. In 2011, U. Keller et al. compressed high-power picosecond pulses in a Xenon-filled Kagóme-type hollow-core photonic crystal fiber to <250 fs with 0.7-μJ pulse energy [22]. With the help of SPM, 174-fs pulses were obtained by nonlinearly compressing 100-ps pulses from a Q-switched Nd:YVO₄ microchip laser [15]. To simplify experimental schemes and level up pulse energy, nonlinear spectral broadening is also employed in fiber amplifiers for picosecond-to-femtosecond pulse compression. U. Keller et al. obtained 65-fs pulses in a one-stage fiber amplifier seeded by a picosecond mode-locked thin disk laser [23]. All these results are based on SPM effect for spectrum broadening. However, SPM effect also induces nonlinear chirp on both sides of pulses at the same time, which degrades the temporal quality of dechirped pulses. Recently, F. Wise et al. reported a fiber system using a Mamyshev regenerator and a parabolic pre-shaper to amplify and compress pulses from 10 ps to 140 fs [16]. But, pulse evolution in the pre-shaper should be precisely controlled to promise high-quality parabolic temporal shape.

In this paper, we demonstrate self-similar amplification (SSA) of picosecond laser pulses in a short gain fiber, allowing delivery of <100-fs nearly transform-limited (TL) laser pulses. SSA simultaneously provides nonlinear spectral broadening and power amplification in a gain fiber. Meanwhile, pulses obtain a linear chirp after evolution. Consequently, high-quality and short dechirped pulses are warranted. Furthermore, the narrow bandwidth of picosecond laser pulses can avoid gain shaping effect during self-similar evolution,

To obtain optimum results, we first numerically study self-similar amplification of picosecond pulses (SSA-PS), demonstrating the duration and energy of picosecond seed pulses mainly dominate the SSA process. Furthermore, the initial chirp of seed pulses does not play a key role on the evolution, which is proven to be the obvious difference from self-similar amplification of femtosecond pulses (SSA-FS). Based on simulation results, we can predict the optimum energy and duration of seed pulses for faster convergence to parabolic pulse in a short gain fiber. In the following, these numerical results are validated by systematic experiments. Finally, we developed a compact picosecond pulse self-similar amplification system seeded by a homemade all-fiber picosecond mode-locked laser. This system successfully generates 66-fs nearly TL pulses with 6.1-W average power at a 30-MHz repetition rate.

2. Numerical simulation

SSA-FS has been deeply studied since 2000 [24–30], indicating that seed pulse and gain parameters have great impacts on pulse evolution. However, there are few researches on SSA-PS. In this paper, we systematically simulate SSA process and analyze the impact of picosecond seed pulse parameters on SSA evolution and output laser performance. In the simulation, amplification process is modeled by coupling nonlinear Schrödinger equation (NLSE) and steady-state propagation-rate equations [31]. The NLSE describes nonlinear propagation of laser pulses in fibers and is solved by split-step Fourier algorithm. The steady-state propagation-rate equations which describe pump laser absorption and gain of signal laser along the gain fiber are calculated with fourth-order Runger-Kutta formula. Both equations are coupled and solved by an iterative procedure under boundary conditions set by an initial pump power and an initial signal pulse spectral power distribution.

To quantitatively estimate self-similar evolution process and output results, we employ a misfit parameter between the intensity profiles of an amplified pulse |A|² and a parabolic pulse |A_pa|² with the same pulse energy and peak power [29]:

M^{2} = \frac{\int {({| A |}^{2} - {| A_{p a} |}^{2})}^{2} d t}{\int {| A |}^{4} d t}

According to the definition, a smaller M means the amplified pulse profile has a higher degree of similarity to parabolic shape, i.e., a better self-similar evolution. When an M-factor is around 0.04, the amplification can be considered as a self-similar process. Furthermore, Strehl-ratio [32], as described below, is applied to evaluate the temporal quality of pulses after compression.

S R = \frac{1 / \int {| A |}^{2} d t}{1 / \int {| A_{T L} |}^{2} d t}

Here, |A|² is the dechirped pulse profile, while |A_TL|² is the corresponding TL pulse. Strehl-ratio reaching 1 indicates that the dechirped pulse is approaching TL pulse. This means that the pulse acquires an almost linear chirp in amplification, which is another feature of self-similar evolution.

On the basis of SSA theory, self-similar evolution is decided by pulse energy and temporal properties of seed pulses, especially pulse duration which play an important role on evolution speed in gain fibers [25,27,30,33]. Firstly, we numerically investigate the impact of pre-chirp and duration of picosecond Gaussian seed pulses on SSA. In the simulation, a 2-m-long Yb³⁺-doped double-cladding (DC) gain fiber, with a 10-μm core diameter and a 125-μm inner cladding diameter, is used. The emission and absorption cross sections of the gain fiber are derived from Ref [34], which makes gain process realistically performed. Energy of seed pulses and output pulses are fixed at 3.3 nJ (200-mW average power) and 83.3 nJ (5-W average power), respectively. The Gaussian seed pulse is described by spectral bandwidth and chirp parameter. After amplification, output pulses are evaluated by the M-factor. M-factors with respect to bandwidth and pre-chirping group delay dispersion (GDD) of seed pulses are summarized in Fig. 1. In this paper, we use pre-chirping GDD imposed on TL seed pulses to quantify pre-chirp. As shown in Fig. 1, M-factors have a symmetric pattern about zero pre-chirping GDD. The pulse duration contours are calculated from spectral bandwidth and pre-chirping GDD, as displayed with dash lines in the figure. The pulse duration contours are nearly the same as M-factor distribution. Regardless of bandwidth and pre-chirping GDD, seed pulse duration almost determines the self-similar evolution process. When seed pulse duration ranges from 1.7 ps to 2.3 ps, the pulses can evolve to asymptotic solution in a 2-m gain fiber, with different pre-chirp and bandwidth.

Fig. 1 M-factors versus pre-chirping GDD and bandwidth of seed pulses. The dash lines represent pulse duration contours.

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To figure out the decisive effect of pulse duration on SSA-PS, self-similar evolution along the gain fiber is studied. As illustrated in Fig. 2, pre-chirp shows less impact on SSA-PS. Firstly, based on Fourier transform theory, pre-chirping GDD of picosecond seed pulses with narrow bandwidth has negligible effect on seed pulse duration, especially when bandwidth is less than 1 nm. Furthermore, the self-similar evolution in gain fibers is also insensitive to pre-chirp of seed pulses. In Fig. 2(a) and 2(b), the evolution of both bandwidth and pulse duration along the gain fiber is depicted, with fixed seed pulse duration and different pre-chirping GDD. When pre-chirping GDD of seed pulses is altered from −7.0 ps² to 7.0 ps², bandwidth is adjusted for a constant pulse duration of 2 ps. Bandwidth and duration varied along the gain fiber are nearly the same, although pre-chirping GDD is different. In the pulse evolution, low peak power induces less spectral broadening process in the first half of gain fiber, and the narrow bandwidth will reduce gain shaping effect during amplification. The narrow bandwidth of picosecond pulses also limits spectral breathing process, as shown in the inset of Fig. 2(a). As a result, all the pulses with different pre-chirping GDD nearly converge to the same bandwidth and pulse duration, indicating pre-chirp of seed pulses with narrow spectral bandwidth almost does not change SSA-PS process. The same conclusion can be drawn from Fig. 2(c) and 2(d). With varied pre-chirping GDD from −0.5 ps² to 0.5 ps², M-factors for 1.8 ps, 2.0 ps, and 2.2 ps pulse duration remain ~0.04, and the corresponding Strehl-ratios are higher than 0.8. The temporal and spectral intensity profiles of output pulses for 2-ps seed pulses with different bandwidth, i.e., different pre-chirping GDD (0 ps², ± 0.43 ps², ± 0.52 ps² and ± 0.70 ps²) are shown in Fig. 2(d). All the pulses evolve to parabolic shape after amplification. The spectra are strongly broadened and can support sub-100-fs pulses. By using a grating pair to dechirp pulses to TL, all of them show similar compressed pulse profile.

Fig. 2 Evolution of (a) bandwidth and (b) pulse duration, along the gain fiber; (c) M-factor and Strehl-ratio versus chirp with fixed pulse duration of 1.8 ps, 2.0 ps and 2.2 ps; (d) Pulse profiles after compression with fixed seed pulse duration of 2 ps and different pre-chirping GDD; insets: pulse profiles (left) and spectra (right) at the output of amplifier.

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The impact of seed pulse energy on picosecond pulse self-similar evolution is also studied in the simulation. The changes of M-factor versus seed pulse duration and energy are illustrated in Fig. 3. For a fixed seed pulse duration (T₀), there exists a range of seed pulse energy (E₀) to promise self-similar evolution (M~0.04) in the gain fiber. In Fig. 3, black diamonds present optimum seed pulse energy for SSA with respect to different seed pulse durations. These optimum points can be well fitted by an expression $U_{0} = 0.59 \times T_{0}^{3}$ . This expression gives a relationship between optimum seed pulse energy and pulse duration for the fastest convergence to parabolic pulse. In analytical theory of SSA, the optimum seed pulse energy, which gives the fastest convergence to parabolic pulse, is proportional to $T_{0}^{3}$ [29]

U_{0} = \frac{g^{2} T_{0}^{3}}{27 γ β_{2} \sqrt{2}}

As a result, the numerical simulation results show a good agreement with the theoretical prediction, which confirms our numerical model and results. More importantly, this equation can easily predict the optimum pulse energy for a given pulse duration in SSA-PS.

Fig. 3 M-factors versus energy and duration of seed pulses. Black diamonds present optimum seed pulse energy for different seed pulse duration. The yellow line is a fit of the black diamonds.

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Based on the numerical analysis above, we can conclude that duration and energy of seed pulses are the two most important factors that dominate the process of SSA-PS, which is indicated by theoretical analysis. However, different from SSA-FS, pulse evolution of SSA-PS is insensitive to pre-chirp. These conclusions provide an efficient route to optimize the asymptotic process of SSA-PS.

3. Systematic verification

According to the simulation above, bandwidth and pre-chirping GDD of seed pulses can negligibly affect self-similar evolution of picosecond pulse, when pulse duration and energy are optimized. In the experiment, a fiber SSA system is built to verify simulation results. The experimental scheme is shown in Fig. 4. To obtain picosecond pulses with adjustable bandwidth, a femtosecond laser system is used as the front end, and delivers chirped ultrashort laser pulse with ~20-nm spectral bandwidth centered at 1038 nm, as shown in the inset of Fig. 4. Then, a spectral filter, consisting of a 1200-lines/mm grating and a fiber collimator, is utilized to extract a small spectral fragment from the femtosecond laser source. With this configuration, the central wavelength and bandwidth of picosecond pulses can be adjusted. After that, the picosecond pulses propagate through a 1000-lines/mm grating pre-chirper, which is used to tune the pre-chirp of picosecond pulses. And the pulse energy is changed by a half wave plate and a polarization beam splitter. A 2-m Yb-doped polarization-maintaining (PM) DC fiber with a 10-μm core diameter and a 125-μm inner cladding diameter (PLMA-YDF-10/125-M, Nufern) is applied as the gain media of self-similar amplifier. The fiber is backward-pumped by a 976-nm diode laser with a pigtail fiber. The pulses are dechirped by a 1000-lines/mm grating pair after the amplifier.

Fig. 4 Experimental setup for verification, and the spectrum of femtosecond laser system (inset). PBS: Polarization Beam Splitter, HWP: Half Wave Plate, DM: Dichroic Mirror and LD: Laser Diode.

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Due to intense spectral broadening process in amplification, self-similar evolution is sensitive to gain shaping effect which can lead to serious deformation from ideal self-similar parabolic solution. As a result, it is important to match the central wavelength of seed pulses to that of the gain spectrum. In the experiment, coupling position of the fiber collimator is tuned to alter the central wavelength of picosecond seed pulses, through which the central wavelength of gain spectrum and seed pulses could be matched well. Consequently, gain shaping effect can be suppressed, benefitting the self-similar evolution. By changing the distance between collimator and grating, we can also obtain pulses with different bandwidths from the femtosecond laser system. Figure 5(a) shows 1.1-nm, 2.0-nm and 2.5-nm bandwidths obtained for the following amplifier, respectively.

Fig. 5 (a) Spectra and auto-correlation traces (inset) of seed pulses with fixed pulse duration of 2 ps and different bandwidth; (b) Retrieved pulse profiles and auto-correlation traces after compression.

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By adjusting the distance between gratings of pre-chirper, seed pulse duration can be kept constant with different bandwidth. According to the optimization approach in simulation, seed pulse duration and energy are fixed at ~2 ps and 3.3 nJ, respectively. The gain of self-similar amplifier is 14 dB. After amplification, the pulses are dechirped to nearly TL pulses, meaning that the pulses with different bandwidth and pre-chirping GDD are all evolved to parabolic profiles with linear chirps. As shown in the inset of Fig. 5(b), three autocorrelation traces overlap very well. As what we discussed before, these picosecond pulses should have almost the same evolution process. Temporal intensity profiles are retrieved with the measured autocorrelation traces and spectra by applying the phase and intensity from correlation and spectrum only (PICASO) algorithm [35]. The retrieved pulses [Fig. 5(b)] have ~100 fs pulse duration, but show slightly different oscillations on trailing edges, which is caused by a small nonlinear chirp accumulated in the amplifier. Thus, SSA-PS insensitive to bandwidth and pre-chirp in a certain range is confirmed experimentally.

By rotating the half wave plate, seed pulse energy can be adjusted from 0.7 nJ to 6 nJ. All the pulses are amplified to ~70 nJ with different energies, but other parameters of seed pulses are kept as the same (~2-ps duration and ~0.9-nm bandwidth). As shown in the inset of Fig. 6(a), autocorrelation traces of the dechirped pulses have similar pulse profiles and pulse duration. Intensity profiles retrieved by PICASO are also depicted in Fig. 6(a). The dechirped pulses with seed pulse energies of 3.3 nJ and 6.0 nJ overlap well. As the only exception, slightly different pulse duration and intensity profile is shown with 0.7-nJ seed pulse energy. The dechirped pulse durations are 130 fs, 111 fs and 109 fs for seed pulse energies of 0.7 nJ, 3.3 nJ and 6.0 nJ, respectively. According to our simulation results shown in Fig. 3, for 2-ps seed pulse, the optimum pulse energy ranges from ~2 nJ to ~6 nJ, where the pulses can evolve to parabolic shape and be compressed to high-quality pulses. In general, we can predict a probable range of seed pulse energy with known seed pulse duration according to the theory. With such a large range, it is much easier to get SSA-PS.

Fig. 6 Retrieved pulse profiles and auto-correlation traces (inset) of (a) different seed pulse energy and (b) different seed pulse duration.

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Besides, the impact of pulse duration on SSA-PS is also verified by this experiment. All seed pulses have the same pulse energy of 3.3 nJ and bandwidth of ~0.9 nm. With pre-chirper, the pulse duration can be easily changed to 1.8 ps, 2.3 ps and 2.7 ps. The amplified pulses with ~70-nJ pulse energy are compressed by a grating pair. The inset of Fig. 6(b) shows dechirped autocorrelation traces after amplification, and the intensity profiles retrieved by PICASO are shown in Fig. 6(b). At this time, the dechirped pulses have remarkable difference in pulse durations (114 fs, 131 fs and 171 fs, for 1.8-ps, 2.3-ps and 2.7-ps seed pulse duration) and intensity profiles. With 2.7-ps seed pulse duration, the dechirped pulse has a larger pedestal and degraded temporal quality, while with 1.8-ps and 2.3-ps seed pulse they shows shorter dechirped pulse duration with better temporal quality. The reason is that 1.8-ps and 2.3-ps seed pulses with 3.3-nJ pulse energy are located in the optimum range of self-similar evolution, as shown in Fig. 3.

In summary, for SSA-PS, pulse duration and energy have significant impacts on the evolution of picosecond pulse, while pre-chirp has negligible effect. This provides a way to obtain <100 fs pulses with TL temporal quality from picosecond laser with SSA.

4. Experiment and results

Based on the simulation results and the experiment verification, we developed a compact picosecond pulse self-similar amplification system with a homemade all-fiber picosecond mode-locked laser used as the seed source. The system can deliver <100-fs nearly TL pulses. The picosecond laser source consists of an oscillator and a pre-amplifier. The oscillator is an all PM fiber laser and mode-locked with a SESAM [as shown in Fig. 7(a)]. Yb³⁺-doped PM single-mode fiber (PM-YSF-HI-HP, Nufern), which is the same gain fiber of oscillator, is applied as the gain media of pre-amplifier. The picosecond laser source directly outputs ~6-ps pulses at a 30-MHz repetition rate with up to 200-mW average power. The spectrum is centered at 1064.2 nm with 0.9-nm bandwidth [Fig. 7(b)]. According to the results we discussed above, 6-ps pulse duration is too long to achieve self-similar evolution in the gain fiber of self-similar amplifier. To this end, a grating pair with 1600 lines/mm is equipped to compress the pulses from picosecond laser source to ~2.6 ps [inset of Fig. 7(b)]. To get better SSA, the seed pulse energy is optimized to ~3.2 nJ before it is coupled into the gain fiber.

Fig. 7 (a) Experimental setup of picosecond pulse self-similar amplification system; WDM: Wavelength Division Multiplexer, ISO: Isolator and FBG: Fiber Chirped Grating; (b) Spectrum and compressed auto-correlation trace (inset) of the picosecond laser source; retrieved pulse profiles, spectra (inset) and auto-correlation traces (inset) at output powers of (c) 4.6 W and (d) 6.1 W.

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During SSA, SPM effect dominates spectral evolution process and strongly broadens spectrum. As output power increases, the output spectrum is getting wider, leading to shorter dechirped pulses. When the output powers are 4.6 W and 6.1 W, 10-dB bandwidth of the spectra are 39 nm and 49 nm, respectively [as shown in upper insets of Fig. 7(c) and 7(d)]. Due to the linear chirp accumulated during SSA, amplified pulses can be easily dechirped by a grating pair. The dechirped auto-correlation traces of these two different output powers are depicted in lower insets of Fig. 7(c) and 7(d). Temporal intensity profiles retrieved by PICASO algorithm have 82-fs and 66-fs pulse duration, respectively. Meanwhile, the corresponding TL pulses are displayed by dash lines [Fig. 7(c) and 7(d)]. When the output power is 4.6 W, the retrieved temporal intensity profile of dechirped pulse coincides well with that of TL pulse, except for a small pedestal beside the main pulse [Fig. 7(c)]. The calculated Strehl ratio is 0.87, indicating an almost linear chirp of amplified pulse. The pit at the center of seed spectrum causes the irregular oscillation under the action of nonlinearity, leading to a small pedestal of dechirped pulses. When output power rises to 6.1 W, the output pulse has a much broader spectrum and is compressed to 66 fs [Fig. 7(d)], but the Strehl-ratio drops to 0.79 due to high nonlinearity.

5. Conclusion

In this paper, SSA-PS is discussed systematically by numerical simulations and experiments. We first numerically studied the impact of parameters of picosecond seed pulses on asymptotic process and amplification results. Different from SSA-FS which is sensitive to bandwidth, pre-chirp, pulse duration and energy, self-similar amplification of picosecond seed pulses is only determined by pulse duration and pulse energy. Especially, optimum energy of different seed pulse duration in the simulation matches the prediction of analytical solution. This demonstrates the accuracy of our simulation and experiment results, providing an efficient way to optimize the evolution process of SSA-PS. To further verify the viewpoints given by our simulation, we implemented systematic experiments which demonstrate that duration and energy of seed pulses are the most important parameters in SSA-PS. Nearly the same dechirped temporal intensity profiles at the output are obtained when seed pulses have the same duration but different bandwidth and pre-chirping GDD. In the simulation, although the pulse duration is limited below ~3 ps, longer seed pulses with enough energy can also evolve to parabolic pulse according our prediction.

Encouraged by the above conclusions, we developed a compact SSA-PS system which used a homemade picosecond fiber laser as the seed source. With the help of SSA, our system delivers 66-fs pulses with 6.1-W average power. The compressed pulses show nearly TL temporal quality. In the system, the core diameter of gain fiber is only 10 μm, which limits the output energy. In the future, we can use gain fibers with larger core diameters to scale up output pulse energy to 1 μJ. Although the gratings and the fiber coupling system are not all-fiber configurations, we believe that chirped fiber Bragg grating and fiber combiner techniques could make a system fusion spliced from oscillator to output port. Furthermore, our work shows a great potential of generating femtosecond laser pulses based on picosecond laser sources, which can even be gain-switched diodes without mode-locking [16]. Under this circumstance, high power short pulses (several tens of femtosecond) can be obtained in a more simplified manner, which will be very useful for industrial applications or scientific researches outside labs.

Funding

National Natural Science Foundation of China (NSFC) (U1730115, 61535009, and 11527808).

Acknowledgements

We thank Yong Wang at Electrical and Computer Engineering Department of Colorado State University for useful discussions.

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Femtosecond laser pulse generation with self-similar amplification of picosecond laser pulses

Abstract

1. Introduction

2. Numerical simulation

3. Systematic verification

4. Experiment and results

5. Conclusion

Funding

Acknowledgements

References

Cited By

Figures (7)

Equations (3)

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