Mode-locked lasers have an undisputed position in the ultrafast domain, though they are fairly expensive for miscellaneous applications. Thus, laser consumers revert to more cost-effective systems like Q-switched lasers. Here we report on the nonlinear compression of passively Q-switched laser pulses that allows accessing the time domain of sub-10-picoseconds, which has been so far the realm of mode-locked lasers. Laser pulses with an initial duration of 100ps from a passively Q-switched microchip laser are amplified in a photonic crystal fiber and spectrally broadened from 20pm to 0.68nm by self-phase modulation. These pulses are compressed in a grating compressor to a duration of 6ps with a pulse energy of 13µJ.
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Ultrashort laser pulses are currently an indispensable key tool for various applications in fundamental science and the commercial field, including spectroscopy, metrology, communications and material processing. These laser pulses are usually generated by a technique referred to as mode-locking [1,2]. Mode-locked laser oscillators can be divided into two groups depending on the type of the modulator. On the one hand, actively mode-locked lasers use externally driven modulators and are able to achieve pulse durations on the order of a few to several tens of picoseconds . On the other hand, passively mode-locked lasers based on saturable absorbers such as dyes, semiconductors or the Kerr-lens are capable of generating pulse durations from several tens of picoseconds down to a few optical cycles [4,5]. With pulse repetition rates (PRR) typically higher than 10MHz (given by the cavity length) and pulse energies on the nanojoule scale, mode-locked lasers have become a bright solution to various problems.
Nevertheless, without taking any special actions, mode-locked laser systems suffer from many issues e.g. alignment sensitivity, reliability, lack of self-starting and Q-switching instabilities. In addition, the high PRR produced by mode-locked lasers is unsuitable for application such as material processing due to the effect of particle shielding , which requires reduction of PRR. This procedure results in loss of the average power and the pulse energy, and leads to more complex systems in order to regain the loss. Considering the applications that require high peak power  in order to process efficiently (e.g. frequency conversion, wafer dicing and micro machining), Q-switched lasers are the main challengers to mode-locked systems.
An interesting regime for pulse durations is the frontier between the short and the ultrashort pulses, i.e. the region spanning from several tens to a few hundreds of picoseconds. For a long time this region was a terra incognita for Q-switched laser sources. However, in the past years, the trench of pulse duration between mode-locked and Q-Switched lasers was impressively constricted by passively Q-switched microchip lasers. Pulse durations smaller than 500ps have been demonstrated using Cr4+:YAG as the saturable absorber . A further reduction of pulse duration was accomplished by using semiconductor saturable absorber mirrors (SESAM). This led to pulse durations as short as 37ps , since the length of the laser resonator is significantly reduced. Furthermore, microchip lasers based on SESAM and monolithically bonded by means of the spin-on-glass gluing technique show improved stability of laser operation [10,11] delivering pulses of up to 1µJ, ~50ps and PRR up to 2MHz. The PRR provided by these laser sources is optimal for material processing applications. In addition, a simple and passive stabilization technique termed as self-injection seeding has solved the major handicap of passively Q-switched lasers, the intrinsic timing jitter, decreasing the RMS-jitter by three orders of magnitude to ~20ps .
However, the quality of laser-based processing of materials depends strongly on the pulse duration and on the thermal diffusion time of the material, which is of the order of ten picoseconds for materials of potential interest, such as metals and semiconductors . Laser pulses with durations smaller than the thermal diffusion time deposit significantly less heat energy in the material resulting in almost no melt or heat-affected zone . Hence, sub-10ps laser pulses delivered by low-cost laser systems are of immense interest from an industrial point of view.
2. Nonlinear compression of Q-Switched pulses
In the present work, we report on compression of passively Q-switched pulses achieving peak powers in the megawatt regime. Pulse compression of Q-Switched pulses has been reported using soliton compression in a fiber Bragg grating . However, this technique is highly sensitive to the stability of peak power, changes of dispersion and nonlinearity of FBG, and mainly limited to pulses with fairy low pulse energies. In our case, the method used for pulse compression is normally applied to mode-locked pulses chirped by self-phase modulation in optical fiber  and to the first time applied to Q-Switched pulse. In theory, the pulses to be compressed have to satisfy the Fourier-transform limit, i.e. the spectral phase of the pulse is either flat or depends linearly on the frequency. Firstly, the pulses are frequency chirped by self-phase modulation in the optical fiber, which introduces a spectral broadening of the pulse . Often, such pulses experience the effect of chromatic dispersion, which leads to the stretching of pulse duration. This effect is negligible for relatively long pulses and short propagation lengths. Thereafter, a subsequent chirp-removing element temporally compresses the pulses.
In our case, the pulses from a passively Q-Switched microchip laser (Fig. 1a-c ) can be considered as nearly transform-limited. Since on the one hand, the active Fabry-Perot-resonator determines the spectral bandwidth of the emitted pulses due to its high finesse and large longitudinal mode spacing (due to the short cavity length). In fact, as a consequence of the latter, this laser oscillates on a single longitudinal mode. On the other hand, the shape and duration of the pulse are determined by the characteristics of the Q-Switched laser, i.e. gain, cavity round-trip time and modulation contrast of the saturable absorber. The pulse duration in this laser can be estimated using following formula :Fig. 1d). The spectral bandwidth emitted from the single-axial mode is measured to be ~20pm (Fig. 1e) and expected to be slightly smaller due to limited spectral resolution of the optical spectrum analyzer. According to the time-bandwidth-product, the spectral width of a 100ps, transform-limited Gaussian pulse equals to 16.6pm, which conforms to the measurements.
Conventional Q-Switched lasers are able to produce transform-limited pulses when taking a special effort such as injection-seeding or injection-locking of longitudinal modes of a slave-laser by a weak master-oscillator [18–20]. However, nonlinear effects, such as stimulated Raman scattering (SRS), stimulated Brillouin scattering (SBS) and degenerated four-wave mixing (DFWM) in optical fibers impose limits to the amount of SPM-broadening achievable in practice. The strength of these nonlinear effects depends on the parameters of the optical pulse and the fiber . SBS becomes limiting to pulses with durations >1ns, which are produced by most conventional Q-Switched lasers. However, for shorter pulses SRS is the most limiting effect and acts not only as a loss mechanism but also distorts the linear nature of the frequency chirp. For a given fiber length, the SPM-broadening is proportional to the peak power of the pulse over the pulse duration, while SRS is only proportional to the peak power. Hence, the initial duration and shape of the pulse have immense consequences on acquirable nonlinear phase in the optical fiber and, therefore, on the pulse compressibility. The upper limit of pulse duration suitable for nonlinear compression is on the order of a few hundred picoseconds, which is fulfilled by our microchip laser. Nevertheless, DFWM can still restrict the extent of SPM-broadening in an optical fiber independently of its pulse duration provided that conditions are met for phase-matching .
In this experiment, the SPM-induced spectral broadening is acquired during the amplification process in a 3.8m long, ytterbium-doped photonic-crystal fiber (Fig. 2 ), which allows extracting high average powers  (>100W). The pulse energy (EP) of the 100ps-pulses is boosted from initially 200nJ up to 17µJ and thereby spectrally broadened from ~20pm to 0.68nm at the central wavelength of 1064nm (Fig. 3a ). These pulses are compressed in a diffraction grating compressor based on a pair of transmission gratings (Fig. 2) with 1740lines/mm. An overall efficiency of 80% is achieved after passing through the compressor. The grating separation is adjusted with respect to the broadened spectrum and the optimal compression.
After the compressor stage, the pulse duration is measured by means of a background-free autocorrelator. Figure 3b shows the results of the optical pulse compression for different pulse energies and spectral widths. The spectral width of the pulse grows with the pulse energy and equals to 0.68nm at EP=17µJ, where compression has been performed resulting in the width of AC-trace of 8.2ps. A numerical simulation based on a standard split-step Fourier method solving the nonlinear Schrödinger equation, shows the comparison of theory and experiment (Fig. 4 ). In such a way, a de-convolution factor of 0.735 has been retrieved. The simulation shows slightly shorter compressed durations than obtained in the experiment. Further, the autocorrelation traces of compressed pulses obtained from the experiment have stronger pedestals. These disagreements can be attributed to the slightly asymmetrical shape of the initial Q-Switched pulses, whereas the numerical simulation is computed with an ideal Gaussian-pulse. The exact estimation of the energy contained under the main peak of compressed pulses is complicated and currently a subject of further investigations. In addition, an autocorrelation trace shows a distorted view of the temporal pulse shape, which has to be considered for such an estimation (compare simulation data of Fig. 4a and Fig. 4b). Considering the temporal shape of compressed pulse obtained from numerical simulation, approximately 80% of the pulse energy is contained under the main peak. However, the pedestal of compressed pulses can be removed by simple techniques based on the dependence of the peak power e.g. saturable absorber cleaner, nonlinear polarization rotation, and second-harmonic generation. Considering the compressor efficiency and the de-convolution factor, the recalculation leads to pulses with a duration as short as 6ps, a pulse energy of up to 13µJ and a peak powers of ~1.7MW.
In conclusion, we have demonstrated the first realization of nonlinear compression of Q-switched pulses and obtained a pulse duration of 6ps. The results reveal the feasibility of operating laser systems based on Q-switched sources in the realm of mode-locked laser concerning their pulse duration. The requirements for a sufficient nonlinear compression of Q-Switched pulses appear to be the Fourier-transform-limit and initial pulse duration of a few 100ps. Design considerations show that a passively Q-Switched microchip laser combined with a fiber amplifier and a compact compressor based on chirped volume-Bragg-gratings can reach >100W average power, >100µJ pulse energy and <10ps pulse duration with diffraction-limited beam quality. Even sub-picoseconds pulses are achievable starting with shorter initial pulses or using a cascaded nonlinear compression. Such cost-effective systems have a great potential for applications with requirements on sub-10ps durations, high pulse energy and PRR in the range from kHz to MHz.
This research was partly supported by the German Federal Ministry of Education and Research (BMBF) under contract 13N9722.
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