Nonlinear pulse compression based on the generation of ultra-broadband supercontinuum (SC) in an all-normal dispersion photonic crystal fiber (ANDi PCF) is demonstrated. The highly coherent and smooth octave-spanning SC spectra are generated using 6 fs, 3 nJ pulses from a Ti:Sapphire oscillator for pumping a 13 mm piece of ANDi PCF. Applying active phase control has enabled the generation of 4.5 fs pulses. Additional spectral amplitude shaping has increased the bandwidth of the SC spectra further leading to nearly transform-limited pulses with a duration of 3.64 fs, which corresponds to only 1.3 optical cycles at a central wavelength of 810 nm. This is the shortest pulse duration achieved via compression of SC spectra generated in PCF to date. Due to the high stability and the smooth spectral intensity and phase distribution of the generated SC, an excellent temporal pulse quality exhibiting a pulse contrast of 14 dB with respect to the pre- and post-pulses is achieved.
© 2011 OSA
Few-cycle laser pulses are indispensable for a wide range of applications such as time-resolved studies of fundamental processes in physics, chemistry and biology  due to their unique temporal and spectral properties. The usage of high energy few-cycle pulses, which can be generated via techniques like gas-filled hollow fiber compression [2,3] or optical parametric chirped pulse amplification (OPCPA) [4,5] enables high harmonics generation (HHG) and even the generation of attosecond pulses [6,7]. This leads to new applications, such as studies of processes that take place on an attosecond timescale  or the investigation of band structures of semiconductors via photo electron spectroscopy .
The near infrared few-cycle regime is already commercially covered by Ti:Sapphire oscillators. However, the spectral bandwidth delivered by these oscillators is ultimately limited by the gain bandwidth of Ti:Sapphire. Nevertheless, shorter pulses can be achieved by shaping of the spectral amplitude, which unfortunately leads to significant power losses and a reduction of temporal pulse quality. With this technique pulses as short as 3.6 fs (1.3 optical cycles) have been generated . However, the temporal pulse quality is rather poor with a severe amount of energy in pre- and post-pulses and a pulse contrast with respect to the first pre-pulse of less than 5 dB.
In order to overcome these limitations, several interesting pulse compression schemes exploiting spectral broadening of few-cycle pulses in optical fibers have been subject of recent research. The shortest pulses with a duration of 2.6 fs (1.3 optical cycles) have been generated via supercontinuum (SC) generation in a gas-filled hollow core fiber and subsequent temporal recompression with an active phase shaping device . Unfortunately, this technique requires very high pulse energies of several hundreds of microjoules. In contrast, optical fibers with a solid core can produce sufficient spectral broadening for few-cycle pulse generation even at nanojoule pulse energies. Using a short piece of single mode fiber and a chirped mirror compressor it was possible to achieve pulse durations of 4 fs (1.7 optical cycles) . However, this scheme is limited by the material dispersion of bulk silica, which introduces strong temporal pulse broadening, which leads to a limitation of achievable spectral bandwidth. Especially photonic crystal fibers (PCF) are well suited for generation of ultra-broad SC spectra due to the possibility to tailor their dispersion properties. Pulse compression to 5.5 fs (2.4 optical cycles) has been demonstrated employing active phase shaping of SC generated in a PCF with one zero dispersion wavelength (ZDW) close to the pump wavelength . However, the broadening process in such fibers is dominated by soliton dynamics, which are very sensitive to pump pulse fluctuations, causing variations of the spectral shape and phase from pulse to pulse . These pulse to pulse fluctuations limit the temporal coherence properties and hence the achievable pulse duration [12–15]. In order to overcome this problem soliton self-compression can be pursued, whereby higher order solitons are spectrally broadened and temporally compressed during the propagation through a PCF, thus eliminating the need for post compression devices. With this approach pulses with a duration of 4.6 fs (1.6 optical cycles) have already been demonstrated . Nevertheless, pulse energy and fiber length have to be precisely chosen to prevent pulse break-up, thus limiting the applicability and scalability of the concept. Furthermore, these pulses feature significant pre- and post-pulses as well as pedestals.
In this work we use an all-normal dispersion PCF (ANDi PCF) for SC generation. This fiber does not possess any ZDW and exhibits only normal dispersion across the spectral region of interest (500 nm to 1500 nm) and therefore does not suffer from noise sensitive soliton dynamics. The process is governed by self-phase modulation (SPM) and optical wave breaking only , which results in very smooth and highly coherent ultra-broad SC spectra. Such spectra are well suited for temporal recompression and it has already been shown that the sub-two cycle regime (5.0 fs, 1.9 optical cycles) is easily accessible via linear chirp removal . However, to take advantage of the full potential of the ultra-broad SC spectra it is necessary to compensate not only for the linear chirp, but all occurring dispersion effects. In this manuscript we report on the generation of nearly transform-limited pulses with high quality and contrast by applying active spectral phase control in order to compensate for higher-order dispersion effects. Using a 13 mm long piece of ANDi PCF pulse durations down to 4.5 fs have been reached with excellent pulse quality. The pulses exhibit a pulse contrast of 19 dB with respect to the strongest pre- and post-pulses, which is to our knowledge superior to any other technique with similar pulse durations reported so far. Additional spectral amplitude shaping increases the bandwidth of the octave spanning SC spectra even more and allows compression of the pulses down to 3.64 fs (1.3 optical cycles), which is the shortest pulse duration achieved with recompression of SC spectra generated in PCF to date. The temporal pulse quality is still superb with a pulse contrast of 14 dB. In addition, the stability of the generated pulses and the spatial beam profile are investigated, revealing very good stability with respect to energy fluctuations of the pump pulses and superb beam quality, respectively.
2. Experimental setup
The experimental setup is shown in Fig. 1 . The seed laser is a Kerr-lens mode locked Ti:Sapphire oscillator delivering 3 nJ, nearly transform-limited 6 fs pulses (5.6 fs Fourier-limited pulse duration) with 800 nm central wavelength at a repetition rate of 76 MHz. These pulses pass a chirped mirror compressor which provides a negative GVD of −60 fs2 per bounce to pre-compensate for the positive dispersion that is introduced by the lens for the coupling into the ANDi PCF. The coupling lens is aspheric and has a focal length of 6 mm. The second order dispersion of this lens is pre-compensated with three bounces on the chirped mirror compressor. It has been possible to couple 1 nJ pulses into the 13 mm long piece of ANDi PCF, which is commercially available (NKT Photonics NL-1050 NEG 1). It has a core diameter of 2.3 μm, a pitch Λ of 1.44 μm and a relative air hole size d/Λ of 0.39. The dispersion parameter of this fiber is negative all over the entire wavelength range of interest, having a maximum value of −11 ps/(nm·km) at a wavelength of 1020 nm .
To minimize temporal pulse distortion and chromatic aberrations, and hence to improve the compressibility of the spectral broadened pulses, the ANDi PCF is followed by an all-reflective optical setup. The beam is collimated by a gold-coated off-axis parabolic mirror with a focal length of 25 mm, which is followed by a telescope consisting of two spherical mirrors to reduce the beam diameter by a factor of five. The pulses then pass the active phase shaping device, which consists of a spatial light modulator (SLM) in the Fourier-plane of a grating based 4f-setup. The 128 pixel SLM can influence the spectral phase of the pulses and therefore compress them close to their transform-limit. The second order dispersion is removed by a chirped-mirror compressor (8 bounces, −30 fs2 per bounce) suitable for the whole spectral range from 600 nm to 1200 nm, whereas fine tuning of the GVD is realized by a pair of fused silica wedges. The throughput of the whole compression device is 30%, decreasing the energy of the compressed pulses to 0.3 nJ. After rotating the polarization with a periscope, the pulses are characterized using an ultra-broadband SPIDER device. The measured spectral phase is then loaded onto the SLM of the active phase shaping device to iteratively compress the pulses close to their Fourier-limit.
3. Experimental results
3.1 Numerical investigations
The spectral broadening in the ANDi PCF has been numerically investigated by applying the split-step Fourier method solving the extended nonlinear Schrödinger equation . For this simulation the chromatic aberration of the coupling lens is taken into account. This aberration causes a different focal position for each wavelength, thus reducing the coupling efficiency for the spectral wings of the input pulses. For this reason the simulation has been carried out using the measured spectrum from the Ti:Sapphire oscillator with its wings cut off. This spectrum, which leads to the best agreement with the measurements, is plotted in Fig. 2 (grey). Additionally, it is assumed that the pulses are not perfectly compressed by adding a variable amount of second order dispersion onto the input pulses. The best agreement between
simulation and experimental measured output spectrum has been achieved with −25 fs2 residual dispersion. Both effects increase the duration of the Ti:Sapphire input pulses from 6 fs to 11 fs. Nevertheless, spectral broadening to more than one optical octave is achieved, as depicted in Fig. 2 (red curve), where also the simulated spectrum (black curve) and the input spectrum (grey curve) are shown. Please notice that the spectra are shown with a linear scale, revealing a more than octave spanning bandwidth corresponding to a transform-limited pulse duration as short as 3.6 fs. The measured spectrum is very smooth with only minor sharp features mainly resulting from similar features from the input spectrum. Unfortunately the spectral bandwidth of the output pulses is cut down to one optical octave spanning from 600 nm to 1200 nm due to the bandpass of the grating based phase shaping device, increasing the transform-limited pulse duration to 4.38 fs.
3.2 Spectral phase shaping
After compensating the spectral phase of the pulses with the active phase shaping device the stability of the residual spectral phase of the compressed pulses in presence of energy fluctuations of the input pulses of the ANDi PCF is investigated. The input pulse energy exhibits root mean square (RMS) fluctuations of 0.3% due to oscillator instabilities, which slightly increase to 0.5% RMS fluctuations of the output pulse energy due to beam pointing and coupling instabilities. These values are retrieved by measuring the pulse energy of each pulse of the 76 MHz pulse train for 68 s, using a photodiode (17 ps rise time) and a real-time oscilloscope (30 GHz bandwidth), leading to a measurement bandwidth reaching from 15 mHz to 76 MHz. Using the SPIDER device multiple spectral phase measurements are carried out and statistically evaluated. Figure 3(a) shows the spectrum and the averaged spectral phase with the vertical error bars indicating the RMS of the phase. The phase is very stable with only small deviations mostly in the wings of the spectrum, which especially arise from the low SPIDER-signal at the extreme spectral wings. For each of the measured phases a temporal pulse shape is calculated. These different pulse shapes are averaged and the resulting pulse is plotted in Fig. 3(b). The mean pulse full width at half maximum (FWHM) duration is 4.50 fs with only 0.05 fs of RMS fluctuations, which is less than 3% above the transform-limit. This shows that the spectral broadening in ANDi PCF delivers pulses with excellent temporal coherence and therefore nearly perfect compressibility even in presence of energy instabilities of the driving laser system. Please notice that the pulse is plotted in a logarithmic scale. The pulse is of excellent shape and the contrast to the first pre-pulse is approximately 19 dB and even better to the post-pulses, whereas 89% of the total pulse energy is contained within the main pulse. Such pulses are very well suited for amplification to high pulse energies and subsequent high intensity laser-matter-interactions, such as HHG, since the pre-pulse will have only minor influence on the investigated system before the main pulse arrives.
The important contrast to the pre-pulse can be improved even further by simply adding a precise amount of third-order dispersion to shift the energy into post-pulses while affecting the pulse duration only insignificantly, which will be subject to future experiments.
3.3 Spectral amplitude shaping
In order to further increase the bandwidth of the spectrum, and hence decrease the achievable pulse duration, the spectral amplitude of the pulses has been shaped. The shaping has been realized in the Fourier-plane of the active phase shaping device in front of the SLM, where a small piece of tissue is placed to decrease the intensity of the central part of the spectrum and achieve a nearly flat-top spectrum. By this means the Fourier-limited pulse duration was decreased from 4.38 fs to 3.49 fs. The amplitude shaping decreases the pulse energy by 85%, however the remaining pulse energy of 45 pJ is still sufficient to seed an ultra-broadband OPCPA system (for example ). Nevertheless, the pulse energy of the spectrally broadened pulses can be further scaled without damaging the fiber by pre-chirping the pulses and using end-caps to keep the peak power and the fluence on the surface constant, respectively. Again, the spectral phase is measured multiple times for statistical evaluation. The result is shown in Fig. 4(a) . The spectrum now exhibits sharper features, which are due to the fabric nature of the tissue for the amplitude shaping. The measured spectral phase is still very flat and has an excellent stability. Figure 4(b) shows the pulse shape, which has been retrieved from averaging the temporal pulse shapes of every measurement. The mean pulse FWHM duration is 3.64 fs with 0.06 fs of RMS fluctuations, which is only 4% above the transform-limit. These are the shortest pulses achieved via temporal compression of SC spectra generated in PFC to date, containing only 1.3 optical cycles at the central wavelength of 810 nm. Due to the shaping of the spectral amplitude the pulse contrast to pre- and post-pulses decreased to 14 dB. However, this is still an outstanding value, whereas 81% of the total energy is contained within the main pulse. This is to our knowledge the best temporal quality reported in this pulse duration regime. The pulse quality could be improved significantly by employing a dual-mask SLM, which is able to shape the spectral phase as well as the spectral amplitude, thus will not suffer from the fabric structure of the tissue used in this experiment. Actually the pulse quality can be even improved beyond the quality of the unshaped pulses shown here, since a completely smooth spectrum can be shaped by removing all remaining sharp features from the spectrum shown in Fig. 3(a). The presented pulse duration can also be improved, since the spectral broadening within the ANDi PCF can be sufficient to support single-cycle pulse durations . However, the presented setup is limited because of the usage of a grating
based phase shaping device, which cannot support more than one optical octave of spectral bandwidth because the different diffraction orders start to overlap. A prism based setup and chirped mirrors designed to support more than one optical octave could provide access to the sub-cycle regime.
3.4 Beam profile measurements
For high intensity experiments the quality of the beam profile plays an important role, since it limits the focusability and therefore the achievable intensity. Especially ultra-broadband Ti:Sapphire oscillators suffer from poor beam quality. It has been shown that the beam quality and divergence are wavelength dependent, whereas mainly the spectral wings exhibit degraded beam quality . In contrast, the method presented in this manuscript delivers very good spatial beam quality independently of the wavelength due to the guiding nature of the ANDi PCF. Figure 5(a) shows the measured focal spot after a spherical mirror with a focal length of 500 mm, which is placed directly behind the collimating off-axis parabola. In order to investigate the beam quality with respect to the wavelength, spectral components are filtered out and the corresponding focal spot is measured, as can be seen in Figs. 5(b)–5(e). The slight increase (15% from Fig. 5(b) to Fig. 5(e)) of the focal spot size with increasing wavelength is caused by the wavelength dependence of the mode field diameter in the ANDi PCF, which increases from 2.1 μm at 600 nm to 2.4 μm at 1000 nm. This small wavelength-dependent divergence has only minor influence on the focusability of the pulses.
4. Conclusion and outlook
In conclusion, we have demonstrated the generation of very smooth and highly coherent octave-spanning SC spectra in an all-normal dispersion PCF. The ultra-broadband pulses have been compressed close to their Fourier-limit with an active phase shaping device. Pulse durations (FWHM) of 4.50 fs have been reached. Additional spectral amplitude shaping increased the spectral bandwidth and pulse durations of 3.64 fs (1.3 optical cycles) are generated, which is the shortest pulse duration achieved via temporal compression of SC spectra generated in PCF to date. The temporal pulse shape is highly stable even in presence of input pulse fluctuations in front of the ANDi PCF, confirming the superb temporal coherence properties of the generated SC spectra. The temporal pulse quality is excellent due to the smoothness of the generated SC spectra, leading to a pulse contrast of up to 19 dB, which is to our knowledge superior to any other results in this parameter regime reported so far. Also the spatial beam profile has been shown to be excellent, which makes the pulses suitable for high intensity experiments due to their good focusability. In summary, the presented approach appears superior to ultra-broadband Ti:Sapphire oscillators [10,21] with respect to temporal pulse quality and spatial beam quality. The generated pulses will be implemented as a seed source of an ultra-broadband OPCPA system soon .
The presented superb temporal pulse quality can be even further increased, if an adequate spectral amplitude shaping device is employed. The proposed concept can be extended towards even shorter pulse durations, since coherent spectra covering more than one optical octave can be generated in ANDi PCF . If a suitable phase shaping device covering more than one optical octave is implemented, single-cycle or even sub-cycle pulses can be achieved.
We especially thank Igor Pastirk from Biophotonic Solutions Inc. for fruitful discussions and support concerning the active phase shaping device. This work has been partly supported by the German Federal Ministry of Education and Research (BMBF) with project 03ZIK455 ‘onCOOPtics’, the Helmholtz Institute Jena and the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC Grant agreement no .
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