We demonstrate increased peak power from an Yb fiber CPA system operating with strong self-phase modulation by shaping the spectral-phase of the input pulses. An adaptive control loop used feedback from the output autocorrelation. We investigated pre-compensation of both SPM phase distortion at high energies, and residual dispersion from mismatched stretcher/compressor technologies at low energies. Phase shaping resulted in improved pulse quality. When using a bulk grating stretcher, shaping increased the autocorrelation peak by a factor of 2.9, and with a fiber stretcher, shaping increased the autocorrelation peak by a factor of 3.4. High-quality 800 fs, 65 µJ recompressed pulses were produced. This technique could benefit a wide variety of fiber amplifier systems and is self-optimising for operation at both low and high pulse energies.
©2008 Optical Society of America
High-energy femtosecond pulses are required for a wide range of industrial and scientific applications. The traditional industrial laser sources based on glass and crystal gain media have found many applications, and Ti:Sapphire CPA systems provide sub-50 fs pulses for the most demanding scientific applications. However, with the advantages of direct diode-pumping, high gain, compact, and good thermo-optical properties, Ytterbium (Yb)-fiber systems have advanced rapidly during the past decade such that they are attractive high-power sources particularly suited for industrial applications. State of the art Yb-fiber chirped pulse amplification (CPA) systems using large-mode-area Photonic Crystal Fiber (PCF) technology can produce >1 mJ pulses [1–3]. However, nonlinear effects such as self-phase modulation (SPM) in the amplifier fibers can degrade the output pulse peak power and hence limit the maximum useful pulse energy from femtosecond sources. Achieving higher energies will require new fiber components and more complex amplification techniques.
Femtosecond pulse-shaping methods have become popular within the Ti:Sapphire ultrafast laser community for overcoming the residual stretcher/compressor dispersion mismatch and SPM induced distortions in lasers and CPA systems [4–12]. There have been several reports of the use of computer optimization routines coupled directly with a femtosecond pulse-shaper for either minimizing pulse duration or for generating waveforms of arbitrary temporal shape. This approach has been useful because the adaptive learning optimization algorithms rapidly search through the large parameter space for the required pulse shape. Recently, the ultrafast fiber laser community has reported the first demonstrations of the use of adaptive technology in such systems. The key goal for fiber systems has been to maximize the output pulse peak power when operating with significant accumulated nonlinear phase (B-integral). Compared to bulk CPA implementations, the long fiber path also introduces much greater material dispersion between stretcher and compressor. Spectral amplitude shaping  has been demonstrated at low energies, creating parabolic pulses that maintain a linear chirp in the presence of SPM (B-integral values up to 16 radians). Phase modulation using a LiNbO3 electro-optic phase modulator has also been demonstrated  for low energy pulses.
In this paper we report, for the first time to our knowledge, results from an Yb-fiber CPA system, incorporating a computer controlled phase only pulse shaper. The system used large-mode-area PCF amplifiers and a dielectric grating compressor, to produce high quality 800 fs 65 µJ pulses. We report two variants of the system. First, we used a bulk stretcher which had second and third order dispersion matched to the compressor. We also show results from a 5km fiber pulse-stretcher, which resulted in substantial mismatched third order dispersion after the compressor. For the bulk stretcher variant, shaping the pulses increased the autocorrelation peak by a factor of 2.9 compared to unshaped pulses, and for the fiber stretcher variant, shaping increased the autocorrelation peak by a factor of 3.4 compared to unshaped pulses.
We used a liquid crystal spatial light modulator (SLM) based pulse shaper to enable operation at any chosen repetition rate. This is important because by appropriate time-gating of the seed pulses, Yb-fiber CPA systems can use CW pumping to operate at repetition rates from kHz to GHz to enable power scaling to >100 W average power. Phase shaping is able to offset the pulse broadening effect of SPM in the amplifiers , and to compensate for mismatched dispersion between different stretcher and compressor technologies. In contrast, spectral amplitude shaping alone is not able to compensate for dispersion mismatches when the SPM is low. Furthemore, phase only shaping requires a single mask SLM whereas combined phase and amplitude shaping requires a more costly dual mask SLM.
The computer control loop varied a reduced set of Taylor coefficients for the shaper phase profile, and enabled the autocorrelation peak to be improved substantially in approximately two minutes. While a pixel by pixel optimization approach may enable further fine tuning of the results it would require longer for the optimization algorithm to run. Our adaptive learning loop target was to maximise the autocorrelation absolute peak to pedestal difference measured and output from our oscilloscope. For many applications where the peak power of the pulse is the critical parameter this would be a useful target. More complex pulse-measurement techniques may be required to achieve other pulse shapes or objective functions. We used a generalised simulated annealing (GSA) control algorithm in these experiments which is easy to implement computationally. We note that both simulated annealing [10, 12] and genetic algorithms have been used for CPA system optimization in prior work [6, 8].
The paper is organized as follows. In Sect. 2 we discuss the experimental techniques and the implementation of adaptive control. The optimization results are presented in Sect. 3, where the pulse autocorrelations are shown for the bulk stretcher setup, and then for the fiber stretcher setup. Section 3 also discusses possible strategies for future optimization of the system. We conclude in Sect. 4.
2. Experimental setup
The schematic of our phase controlled Yb fiber CPA system is shown in Fig. 1. The seed laser pulses (~500 fs, λ 0=1053 nm, Δλ~2.5 nm) were first phase-shaped then stretched in duration using either a bulk grating stretcher with design similar to that in Ref.  or a 5 km length of Corning SMF28e fiber. With the shaper turned off, the pulse duration at the output of the stretcher was measured using a 40 GHz photodiode and sampling scope to be 1 ns for the bulk stretcher and 0.8 ns for the fiber stretcher. For the high energy results, an electro-optic modulator reduced the repetition rate from 80 MHz to 100 kHz. Core-pumped Yb-fiber pre-amplifiers increased the average power to ~0.1 W, then two cladding-pumped amplifiers were used to achieve high pulse energies and average powers. The pre-amplifiers described in Ref.  were optimized to preserve the bandwidth of the input pulse by using modelling tools. The cladding-pumped amplifiers comprised 2 m lengths of single-polarization air-clad Yb-doped photonic crystal fiber (core diameter 40µm, NA 0.03; inner cladding diameter 170 µm, NA 0.6) pumped by fiberised 975 nm diodes. The maximum diode powers were 6 W and 20 W respectively, and we estimated that the pump-coupling efficiencies were 75% for both amplifiers. Using both bulk and fiber stretcher setups we estimated that the launched pump power was 3 W into the final amplifier and the launched energy at the input and output of the final amplifier were 2 µJ and 100 µJ, respectively, for the 65 µJ recompressed pulses. For the high energy results, acousto-optic modulators prevented ASE build-up, and reduced the final repetition rate to 16.67 kHz. A dielectric grating compressor with 65% overall transmission efficiency recompressed the pulses. The gratings in the stretcher and compressor both had 1740 gr/mm.
The pulse shaper included a telescope to expand input beam to a dimension of 6 mm (1/e 2 intensity half-width) in the plane of incidence of the grating. The grating groove density was 1100 lines/mm and it was oriented at a 10 degree incidence angle. A cylindrical lens (f=200 mm) focussed the beam and a 128-pixel, 12.8 mm wide, single-mask phase-only liquid crystal spatial light modulator (SLM) (model number: SLM-128-MIR from CRI) was placed at the Fourier plane of the folded 4f setup . We calculated the optical resolution of the 4f setup to be 0.04 nm . The pixel separation of the shaper implies that the spectrum could be manipulated in blocks of width 0.078 nm. The transmission window of the shaper was 10 nm.
The control loop was approached as a global optimisation problem, using the Generalised Simulated Annealing (GSA) algorithm . Simulated annealing algorithms are stochastic based, whereby worse solutions have a probability to be accepted to avoid local minima. In GSA, next solutions evolve in random directions according to the Tsallis-Stariolo distribution/generator. The search parameters of the algorithm were the coefficients of the spectral phase, β n, whilst the return value was the absolute difference from autocorrelation peak to pedestal-minimum across the viewable time-range that was output from our oscilloscope. Although SA algorithms normally start at random initial values, we started our GSA algorithm from β n=0, because we expect that the amount of the necessary phase correction will be small. Furthermore, we applied a reflective boundary condition within our search space. For the bulk stretcher configuration, the β 2…β 6 terms were optimised. For the fiber stretcher, we found that including β 1…β 4 dispersion terms improved results, whereas adding β 5 and β 6 terms led to minimal improvements so these terms were finally omitted. Following initial trials, the search algorithm typically ran for 150 iterations and took ~2 minutes to optimise the autocorrelation peak.
3.1 Bulk stretcher setup:
The design of the bulk grating stretcher was carefully optimised to match both the β 2 and β 3 dispersion terms of the compressor, so the recompressed pulses at low energy were of high quality as shown by the autocorrelation traces in Fig. 2(a). The results in Fig. 2 also demonstrate the limits imposed by strong SPM because 65 µJ pulses without shaping are severely distorted (estimated B-integral~2.5π). The 65 µJ autocorrelation FWHM has increased from ~1.2 ps to ~1.4 ps and there is a pedestal which could not be removed by optimising the grating separation in the compressor to maximise the autocorrelation peak. The corresponding pulses had bandwidth of 2.5 nm at the final amplifier input, and had bandwidth of 2.6 nm at the output.
The improvement in pulse quality achieved by phase shaping with strong SPM is shown for E=65 µJ in Fig. 2(b). The grating separation in the compressor was adjusted to maximise the autocorrelation peak of the unshaped 65 µJ pulses and then held constant while the feedback loop found the optimum shaped pulse. The unshaped-pulses were severely distorted, but shaping increased the autocorrelation peak by a factor of 2.9, reduced the pedestal, and decreased the autocorrelation FWHM from 1.4 ps to 1.1 ps (~800 fs deconvolved Gaussian pulse; ΔνΔτ~0.45). The Fourier transform of the output spectrum with a flat phase is a reasonable match to the shaped-pulse autocorrelation.
Figure 2(c) shows the spectra at the input and output of the of pulse shaper at 65 µJ, which confirms that the spectral amplitude is not significantly shaped or distorted. Figure 2(c) also shows the applied phase for the optimised 65 µJ pulses. Figure 2(d) shows the spectra at the output of the system for different pulse energies. The spectra without shaping at low energy, and with shaping at high energy are generally of similar shape. The modulation depth of the ripples on the high energy spectra was minimized by adjusting the half-wave plate at the input to the final large-mode area polarizing-fiber amplifier, but it was not possible to eliminate these features. We measured that 90% of the output power from that amplifier was along one polarisation axis. The spectral modulations increased sharply with increased output pulse energy, so we believe that the modulation was due to a combination of polarization and nonlinear interactions in the final amplifier fiber.
3.2 Fiber stretcher setup:
With the fiber stretcher, the third order dispersion adds to that of the compressor and even without SPM the resultant third order dispersion gives rise to a pedestal as shown by the autocorrelation traces in Fig. 3(a). A further complication was that we observed strong spectral broadening after the stretcher fiber because the high peak powers of the ~500 fs unstretched input pulses led to SPM. Although SPM in the stretcher fiber could be avoided by attenuating the seed pulse energy, in order to obtain high energies at the system output we found it was necessary to launch increased seed pulse energies through the stretcher to minimise noise in the amplifiers. Therefore the shaper was required to compensate three effects: the stretcher/compressor third order dispersion mismatch, the SPM spectral broadening of the initially unchirped pulses in the 5 km of Corning fiber, and the SPM acting on the strongly chirped pulses in the amplifier fiber. In the first experiment with low SPM in both the stretcher and the amplifier fibers we first adjusted the bulk compressor grating separation to optimise the pulse without shaping and we then fixed the grating separation while the search algorithm operated to increase the autocorrelation peak. With high SPM in the stretcher fiber, shaping experiments were performed with the compressor grating offset from this starting position by up to ±2%. When there was low SPM in the amplifier fibers, reducing the grating separation by 1% (30 mm) enabled the largest improvement in the autocorrelation when the shaper operated. For high pulse energies, reducing the compressor grating separation by 0.7% (20 mm) enabled the largest improvement in the autocorrelation when the shaper operated.
As shown by the autocorrelation traces in Figs. 3(a), 3(c), and 3(e), shaping produced a significant increase in the autocorrelation peaks in all cases. For the low energy pulses either with or without SPM in the stretcher fiber, the pedestal was also reduced. For the 65 µJ pulses, the autocorrelation pedestal was reduced somewhat, but not as much as for the low energy pulses. The Fourier transforms of the output spectra with a flat phase generally show a narrower pulse than was obtained experimentally, even at low pulse energies. Further work is being undertaken to understand this result, but it is thought to be due to the limitations of the pixelated shaper trying to correct for the large uncompensated third order dispersion in the case of the fibre stretcher.
Figures 3(b), 3(d), and 3(f), show the spectra at the system output and the phase profiles applied by the shaper. The spectra measured on a dB scale (not shown) demonstrated that in all cases the signal was more than 20 dB above the amplified spontaneous emission (ASE) noise level. The spectrum is not significantly changed by pre-shaping when there is no SPM in the stretcher. With SPM in the stretcher, the spectrum was modified by the shaper both at the system output (shown) and immediately after the stretcher fiber (not shown). The spectrum from the stretcher fiber varies because the SPM is sensitive to the chirp of the input pulse set by the shaper. The variations in spectral bandwidth at the stretcher output would have led to different stretched pulse durations depending on the position along the fiber where the new spectral components were generated, and hence on the amount of dispersion those broadened spectral components experienced. For the 65 µJ results, the pulse energy launched into the stretcher fiber was ~150 pJ, and the energy was ~25 pJ at the output. The pulse durations at the input and output of the stretcher fiber were not measured when the shaper was active so it is not straightforward to estimate that B-integral without nonlinear numerical modeling.
In theory, a pulse that is stretched by a large factor with mainly linear dispersion, as in the bulk stretcher, evolves into the Fourier transform of the initial pulse , such that the effect of SPM on the spectral phase of the stretched pulse can be compensated by spectral phase shaping. However, that theory requires a constant spectrum as the pulse is subject to SPM, whereas in a fiber CPA system the spectrum is altered by gain-shaping as demonstrated by comparison of the spectra in Figs. 2(c) and 2(d). Therefore the improvement in the autocorrelation peak using the bulk-stretcher demonstrates the ability of the computer controlled learning loop to operate with the complex interaction of gain-narrowing and SPM in the fiber amplifiers.
In the fiber stretcher, SPM acts on a very weakly chirped pulse which is qualitatively different from the action of SPM on the strongly chirped pulse in the amplifier fiber. In this case the adaptive approach could be perhaps used as a tool to investigate the pulse evolution in the stretcher and amplifier fibers since it enables the optimum input phase to be determined for a given target pulse profile. That knowledge could assist, for example, in determining the required parameters for a numerical model of the system. We note that other authors have considered pulse delivery through short fiber lengths by phase pre-compensation for the effects of both SPM and dispersion[19, 20], but that work was not a close match to our 5 km stretcher fiber and the subsequent pulse amplification system.
When considering possible improvements to the system, we first note that at pulse energies above 65 µJ the autocorrelation pedestal was not eliminated by the shaper. The increase of the autocorrelation pedestal in the time domain was accompanied by the increased spectral modulations. It is possible that the SPM has induced a similarly rapid variation in the spectral phase of the pulses. This could explain the observation that although the Taylor coefficients applied by phase shaping enabled substantial improvement in the autocorrelation the approach did not enable complete removal of the pedestal because the limited number of dispersion coefficients controlled by our algorithm also implies a maximum complexity of the shaped phase. Ultimately, a pixel by pixel optimization algorithm may provide the highest degree of pulse clean-up. Other limitations are imposed by the pixellated shaping device, such as the resolution limit which controls the maximum time-span, the limited number of pixels which controls the maximum complexity of the shaped pulse , and a known variety of pulse imperfections as described in detail by Vaughan et al. . An improved system could therefore include an SLM with more pixels and a pixel by pixel optimization algorithm. Furthermore, switching to a combined phase and amplitude modulator could, for example, enable investigations with pre-shaped spectra to compensate for gain narrowing effects.
We have demonstrated that spectral-phase pre-shaping controlled by an adaptive feedback loop improved the pulse quality from an Yb fiber CPA system operated with strong SPM and residual third-order dispersion dispersion from mismatched stretcher/compressor technologies. High-quality 65 µJ recompressed pulses with a duration of 800 fs were produced, and the autocorrelation peak of the shaped pulses was 2.9 and 3.4 times higher for grating and fiber stretchers, respectively, compared to the unshaped pulses. Using a reduced set of Taylor coefficients for the shaper phase profile enabled the autocorrelation peak to be improved substantially in approximately two minutes. We have suggested further technical improvements to the shaper that may enable the system to operate with higher pulse energies and to further reduce the residual autocorrelation pedestal.
We suggest that the results shown here demonstrate the possibility of power-scaling ultrashort pulse fiber systems by enabling the production of high quality, high energy pulses when there is significant SPM in the amplifier fiber. In future, combined spectral amplitude and phase pre-shaping could enable improved results at even higher pulse energies, and may allow optimum operation when there is SPM in the stretcher fiber. Scaling the average power from ~1.1 W of these experiments to >100 W should be possible by increasing the pulse repetition rate and using higher power pump laser-diodes.
Phase shaping enables the possibility of switching from the bulk grating stretchers often used for ultrashort pulse systems to more compact technologies because phase shaping can compensate for the dispersion mismatches that arise. For example, compact and relatively inexpensive fiber stretchers, or linearly-chirped fiber-bragg-grating stretchers could be used. Phase shaping can also optimize the pulse duration when using novel compressor technologies that have complex dispersion profiles, such as hollow core photonic bandgap fibers. Furthermore, the phase-shaper can create complex target-pulse shapes for use in areas such as pumping mid-IR OPOs for applications in coherent control [22, 23].
We are grateful to J. Mills (ORC) for assistance with pulse characterisation. H. S. S. Hung, N. K. Daga, and N. Naz acknowledge the support of EPSRC studentships. J. Price is supported by a Royal Academy of Engineering/EPSRC research fellowship, and the research is funded by EPSRC, UK. This work was supported, in part, by EPSRC instrument grant EP/C009479/1 and Research Councils UK GR87307.
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