In the following section, experiments of the fibre CPA system run at full repetition rate of 48.7 MHz are reported. The average power was relatively high and the pulse energies low compared to the contents of section6.4. The experiments were performed
Chapter 6. Energy-scalable femtosecond pulse shaping in a fibre-based CPA system 148 to investigate the capability of the pulse shaper in combination with the CPA system to generate short and clean femtosecond pulses.
6.3.1 Stretcher and compressor design
The fibre stretcher, chosen instead of a grating-based stretcher for reasons of practicality and costs, was placed directly after the oscillator and the grating-based compressor was located after the final amplifier as can be seen from figure6.1. As described in section
2.2.5, the group delay dispersions of stretcher (GDDS), amplifier (GDDA) and compres-
sor (GDDC) have to be balanced. The GDDA was neglected in the design calculations
for two reasons: Firstly, GDDAis much smaller than GDDSand GDDC, because ampli-
fying fibres with lengths shorter than 2 m are used, and secondly, fine tuning to balance the total GDD can be carried out by careful alignment of the compressor grating sepa- ration after coarse values for fibre stretcher length and compressor grating separation have been found. Thus, equation (2.18) simplifies to GDDS + GDDC = 0. This can
be fulfilled, because a grating compressor has negative GDD, whereas a standard fibre has positive GDD in the spectral region below approximately 1.3 µm. The compressor gratings were set-up as close as possible to Littrow configuration (angle of incidence = angle of diffraction), however taking into account clipping of the beams at the edges. Another constraint was the limited width of the second grating in conjunction with the dispersed beam from the first grating [14,15]. If the separation becomes too large, the spectrum on the second grating will exceed the width of 130 mm leading to a truncation of the spectrum. Trigonometric considerations of the physical setup for near-Littrow configuration lead to an angle of incidence to the first grating of θin = 53.5◦, a diffrac-
tion angle of θd = 49.2◦ and a perpendicular grating separation of G = 804 mm (with
centre wavelength 1040 nm and grating period 1500 mm−1). The grating slant distance
b = G/ cos θdwas 1230 mm. With equation (2.15) for a double-pass setup, which effec-
tively doubles the accumulated GDD per round-trip, the value of the compressor GDD becomes−2.574 · 10−23s2. An HI 1060 standard SMF acted as pulse stretcher. The GVD
of this fibre type is +2.568· 10−26s2/m at a wavelength of 1040 nm. Therefore, with equation (2.16), a fibre with a length of 1002 m was required. A 1 km-long piece of HI 1060 was inserted into the setup.
6.3.2 Pulse shaping results
The conventional DE algorithm with the trigonometric mutation operator (see section
2.3.4) was used in this experiment. The TPA signal of a gallium arsenide phosphide (GaAsP) detector taken at the output of the compressor is directly related to the pulse peak intensity and therefore to the pulse width. Thus, by using the peak TPA signal
Chapter 6. Energy-scalable femtosecond pulse shaping in a fibre-based CPA system 149 as feedback parameter for ff it, the DE optimisation algorithm searched for the mini-
mum pulse width. The optimisation progress of the TPA signal during 400 iterations is shown in figure 6.3. The optimisation yielded a 9× improved signal. The results of this adaptive optimisation experiment are shown in figures6.4(b),6.4(d)and6.4(f)
alongside the graphs for the unshaped pulses in figures6.4(a), 6.4(c)and6.4(e). The DE parameters were set to F = 0.9 and CR = 0.9 and phase and amplitude shaping was enabled. Every 8thpixel from pixel 12 to 116 (including) was actively controlled at each iteration, therefore Nc = 14. This was increased to every 4th pixel during the
optimisation to get improved convergence. The phase profile was then interpolated over all pixels [16].
0 100 200 300 400 0 2 4 6 8 10 Algorithm Iterations
Relative TPA Intensity
FIGURE6.3: Optimisation progress of the TPA signal during 400 iterations of the DE algorithm.
A contour plot of the square root of the FROG trace is displayed in figures6.4(a)and
6.4(b). The square root was applied to the raw FROG data to point out details at lower intensity. The contour levels indicate [0.05 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9]. The tem- poral wing structure of the shaped pulses only extends out to approximately ±2 ps. Note the different scales for the delay in the two plots. The lowest contour line level is 0.0025 (without square root) corresponding to a peak-to-pedestal ratio of 26 dB. Thus, there is no significant pulse pedestal indicating good higher-order dispersion compen- sation. After pulse retrieval from the FROG data, the temporal intensity profile and the instantaneous linear frequency −1/2π · dϕ (t) /dt as well as the spectral intensity and the group delay dφ (ω) /dω were calculated. Only a low-intensity pedestal and no side lobes are present in the temporal intensity profile in figure6.4(f), which indicates a good compensation of TOD introduced in the individual stages of the setup. The flattened profile of the group delay curve in figure6.4(d) compared to the unshaped case confirms this. The temporal oscillations and the quadratic group delay profile of the unshaped pulses are due to this uncompensated TOD (figures6.4(c)and6.4(e)) [13,17]. The poor agreement of the retrieved and the measured spectra suggests an in- sufficient calibration of the SHG FROG setup leading to a systematic error, which could not be clarified. A comparison of the autoconvolution of the measured spectrum with
Chapter 6. Energy-scalable femtosecond pulse shaping in a fibre-based CPA system 150 Delay [ps] Frequency Detuning [THz] −20 −10 0 10 20 −5 0 5 (a) Unshaped Delay [ps] −3 −2 −1 0 1 2 3 −5 0 5 (b) Shaped −40 −2 0 2 4 0.2 0.4 0.6 0.8 1 Frequency Detuning [THz] Intensity [a.u.] −25 0 25 retrieved measured (c) Unshaped −40 −2 0 2 4 0.2 0.4 0.6 0.8 1 Frequency Detuning [THz] −5 0 5 Group Delay [ps] retrieved measured (d) Shaped −50 0 5 10 15 20 0.2 0.4 0.6 0.8 1 Time [ps] Intensity [a.u.] −10 0 10 (e) Unshaped −1.50 −1 −0.5 0 0.5 1 1.5 0.2 0.4 0.6 0.8 1 Time [ps] −10 0 10 Inst. Frequency [THz] (f) Shaped
FIGURE6.4: Initial pulse shaping results of experimental setup with 1 km fibre stretcher. The results for unshaped pulses are shown for comparison.(a),(b)Contour plot of the square root of the FROG trace (contour levels indicate [0.05 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9], Fourier grid size 128 × 128).(c),(d)Spectral intensity and group delay vs. frequency,(e),(f)Temporal pulse profile and instantaneous frequency vs. time. See text for details.
Chapter 6. Energy-scalable femtosecond pulse shaping in a fibre-based CPA system 151 the frequency marginal (integration of the FROG trace over the delay) could have been used to reveal an inconsistency of the FROG data and hence such a systematic error [13]. However, this was not carried out at the time of the experiments.
In this preliminary experiment, with an estimated 2 W of average power after the com- pressor and the repetition rate of 48.7 MHz, the pulse energy was calculated to be 41 nJ. The FWHM pulse width was 340 fs giving a pulse peak power of 113.4 kW (assum- ing a Gaussian temporal profile). Higher pulse energies could readily be obtained by increasing the pump power of the power amplifier.
6.3.3 Discussion
The measured spectrum after shaping had a FWHM bandwidth of 5.5 nm. The the- oretical FWHM pulse width for a transform-limited pulse that can be supported by this bandwidth is 289 fs assuming a Gaussian temporal profile with a time-bandwidth product of 0.441. The discrepancy between the measured 340 fs and the transform-limit 289 fs can be attributed to some remaining higher-order dispersion. For instance, the signs of the TOD term β3 for stretcher and compressor are both positive, therefore the
pulse shaper has to compensate for this large amount of TOD. The maximum TOD value that can be imposed on the pulse is±0.076 ps3as calculated from equation (2.35) with λ0 = 1040 nm, Npix= 97, c = 3 · 108m/s, ∆λpix = 0.237 nm and taking the folded
pulse shaper configuration (reflection mode) into account. This would be sufficient for a compensation of the TOD contribution of the 1 km of HI 1060 fibre alone, which is 0.039 ps3 [12]. But the TOD contribution from the grating compressor of 0.16 ps3 as calculated from equation (2.17) can not be fully compensated by the pulse shaper. A potential improvement would be the application of an SLM with more LC-pixels. The frequency span per pixel would then be reduced leading to a finer phase control over the entire spectrum and an increased compensation capability of the pulse shaper. An- other possibility would be the use of a grating stretcher (with a 1-to-1 telescope) instead of the fibre. The TODs of grating stretcher and grating compressor have opposite signs and would cancel each other.
The presented results show that the configuration of stretcher and compressor as de- scribed above was capable of producing high-quality pulses in the femtosecond regime without significant pulse pedestal or side lobes.
Chapter 6. Energy-scalable femtosecond pulse shaping in a fibre-based CPA system 152