1. Introduction

The so-called chirped-pulse oscillator (CPO) concept has been proven to be one of the most successful techniques to generate high-energy femtosecond laser pulses at MHz repetition rates [1, 2]. The basic idea is to insert a Herriot-type multi-pass cell [3] into a standard Ti:Sapphire oscillator. This cell acts as an intra-cavity optical delay line, thus reducing the repetition rate and, at constant average output power, increasing the energy per laser pulse. In order to avoid pulse splitting due to excessive nonlinearities in the gain material, the oscillator is operated at net-positive intra-cavity dispersion. The output pulses are therefore strongly chirped and have to be compressed by a suitable extra-cavity delay line, typically a prism pair or even a suitable Photonic bandgap fibre [4].

Supercontinuum generation is an extremely active research topic, driven by the wide range of potential applications in various fields like frequency metrology, optical coherence tomography or pump-probe spectroscopy [5, 6]. The introduction of microstructured optical fibres or photonic crystal fibres (PCFs) [7] opened the way to generate octave spanning supercontinua by launching femtosecond laser pulses from standard low-energy oscillators into solid core PCFs [8]. However, due to the typically very small core-diameter of these fibres, this approach is limited by the onset of damage on the front facet of the fibre when pulses with several tens of nanojoules (nJ) come into play. One possible solution which has been suggested in the past (albeit using a standard single mode optical fibre) was to negatively pre-chirp the oscillator pulses, using an additional prism pair, and then coupling them into the fibre where they are subsequently spectrally broadened [9]. While the damage problem can be circumvented with this method, the setup is rather complex and the spectral broadening that has been achieved was relatively small.

In this paper we demonstrate the use of a photonic crystal fibre to partially compress the strongly chirped pulses emitted by a chirped-pulse oscillator followed by the generation of an extremely broadband supercontinuum in the same fibre, thus avoiding the need for any additional extra-cavity delay line at all. As the input pulses are almost two picoseconds in duration, damaging the front facet can be avoided up to input energies in excess of 150 nJ.

2. Experimental set up

The laser used in our experiments was a commercially available chirped-pulse oscillator (Femtosource scientific XL 200, Femtolasers GmbH), delivering pulses with an energy of up to 200 nJ and a minimum pulse duration of about 40 fs at a 5 MHz repetition rate. We have extracted the laser light right after the output coupler, i.e. before the inbuilt prism compressor and have fully characterised the pulses using second-harmonic generation frequency-resolved optical gating (SHG-FROG) [10]. As can be seen in Fig. 1(a), due to the net-positive intracavity dispersion the pulses are stretched to almost 2 ps in duration and carry an almost perfectly quadratic phase, i.e. the pulses are linearly chirped as expected from the output of a CPO that is not operating in the vicinity of the zero dispersion point [11].

Using a standard 50 × microscope objective we have coupled these strongly positively chirped laser pulses into a solid core PCF that has a nonlinear coefficient γ = 0.1 (Wm)^-1. A SEM image of the fibre is shown in the inset of Fig. 2. Using multipole simulations [12] we have calculated the dispersion characteristic of the fibre. As can be seen in Fig. 2, the PCF has two zero-dispersion points and the dispersion is highly anomalous at 805 nm, the centre wavelength of the CPO.

 

Fig. 1. Temporal (a) and spectral (b) intensity and phase of the pulses emitted by the CPO (without prism compressor) as measured by FROG.

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Fig. 2. Dispersion of the PCF as calculated by multipole simulations. The inset shows an SEM image of the fibre.

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3. Results and discussion

A range of numerical and a few experimental studies have been carried out in the past investigating the influence an input pulse chirp has on the supercontinuum generation process. It was shown that a linear chirped that is imposed on the input pulse can improve the quality of the supercontinuum obtained [13 – 16]. However, the most obvious advantage of using strongly chirped pulses in our case is certainly the significantly reduced peak intensity at the input facet of the PCF. As the shifted zero-dispersion wavelength in such a fibre is achieved by a microstructured region that surrounds a very small core diameter it was previously assumed that its applicability to supercontinuum generation is limited to low-energy (a few-nJ) pulses [9] with 16 nJ of input energy being the highest reported value to our knowledge [17]. In accordance with the reported dependence of the damage threshold fluence on the laser pulse duration in typical dielectrics [18] we have seen a dramatic increase in the damage threshold of the fibre. Launching the fully compressed output pulses of the CPO (with a duration of 40 fs) into the PCF, we have observed onset of damage at the front facet of the PCF for pulse energies of as little as about 20 nJ while for the uncompressed pulses we did not observe any degradation of the fibre for pulse energies of up to 150 nJ.

Furthermore, a positive input chirp has also significant effects on the dynamic pulse evolution inside the PCF [19]. Firstly, the highly anomalous dispersion of the PCF at the centre wavelength of the pulse spectrum linearly compresses the pulses thus enhancing their peak intensity inside the fibre. Secondly, the initial chirp adds to the chirp that is created by self-phase modulation (SPM) during propagation along the fibre and thus enhances also the nonlinear, soliton-like pulse compression that eventually initiates the generation of the supercontinuum [20]. To study these effects in more detail, we have performed numerical simulations by solving the generalised nonlinear Schrödinger equation (GNLSE) [21] using the split-step Fourier method [22]. Our model includes the dispersion of the nonlinearity (associated with self-steepening and optical shock formation), the nonlinear Raman response (both instantaneous electronic and delayed Raman contributions) and dispersive terms up to sixth order (the coefficients were obtained by expanding the calculated dispersion curve (Fig. 2) into a Taylor series). As the input pulse shape we have used the data that we have obtained by the FROG measurements.

For low input energy levels the laser pulses undergo purely linear compression in the fibre due to its anomalous dispersion. Figure 3 shows the measured (black) and simulated (red) pulse shape for a 1 nJ pulse after a propagation distance of 15 mm. The spectral intensity is virtually unchanged, but in the time domain, the pulses have been compressed from 2 ps down to about 650 fs.

 

Fig. 3. Temporal shape of low energy (1 nJ) pulses after a propagation distance of 15 mm. Black: Measured by FROG. Red: Numerical Simulation.

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At higher input energy levels, the pulses also initially start to compress. However, once the peak intensity becomes sufficiently high, nonlinear processes begin to dominate the pulse propagation inside the fibre. The pulses become spectrally broadened by self-phase modulation (SPM) and then higher-order soliton fission dynamics (induced by Raman scattering and higher-order dispersion) lead to the formation of an extremely broadband supercontinuum. Depending on the initial peak power of the pulses that are coupled into the fibre, these nonlinear processes become predominant after a certain propagation distance z. The higher the input power, the sooner inside the fibre the supercontinuum is generated. Figure 4 shows the result of numerical simulations of the temporal evolution inside the fibre for laser pulses with an energy of 0.1 nJ (left) and 6 nJ (right), respectively. In the low power case nonlinear effects are too weak to have an influence on the pulse propagation. The pulses undergo linear compression until after about 35 mm of propagation inside the fibre the pulse duration has reached its minimum, i.e. the pulses are nearly transform-limited. Further propagation dispersively broadens the pulses again. Note that the slight asymmetry in the pulse shape is a result of higher-order dispersion terms, most notably the relatively high third-order dispersion (TOD).

 

Fig. 4. Computed temporal evolution inside the PCF for a 0.1 nJ pulse (left) and a 6 nJ pulse (right).

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In the 6 nJ case, the temporal pulse evolution within the fibre is very similar to the low-energy case discussed above, but only for roughly the first 20 mm of propagation within the fibre. In this initial stage, the pulse duration continuously decreases as the pulses travel along the PCF and the spectrum broadens only moderately under the influence of SPM. At this point however, the peak intensity has been increased such that higher order nonlinear processes begin to dominate the pulse dynamics: A high-order soliton is formed that, under the influence of Raman scattering and higher-order dispersion breaks up into a series of lower-amplitude sub-pulses (soliton fission) accompanied by a simultaneous generation of dispersive waves [23]. The spectral position of this dispersive radiation can be obtained by phase-matching considerations that can be written as [24]:

with β being the well known mode-propagation constant, v_g the group velocity of the corresponding (fundamental) soliton and P₀ its peak power. For the given dispersive properties of our PCF and for pulse parameter as discussed below we thus expect to generate dispersive waves within the wavelength range of about 400 nm – 550 nm.

Coupled with intrapulse Raman scattering and four-wave mixing of the individual solitons with the dispersive waves this leads to a subsequent dramatic increase in the spectral width of the radiation [25]. In order to examine these effects more closely, we have numerically calculated the spectral and temporal evolution of pulses propagating inside the PCF for pulse energies ranging from 0.1 nJ to 25 nJ. Due to the relative short fibre lengths involved, we assume the pulse propagation to be virtually lossless, i.e. the difference between the pulse energy before the microscope objective that is used to couple the pulses into the fibre and the energy measured at the output of the PCF is assumed to be purely caused by coupling losses.

As can be clearly seen in Fig. 5, for all pulse energies we can distinguish between a quasi-linear pulse compression phase (quasi-linear because the pulses are, depending on the peak intensity, already moderately spectrally broadened due to SPM) followed by the sudden generation of an ultrabroadband supercontinuum spectrum. In the case of a pulse energy of 6 nJ it is very informative to compare the spectral evolution shown in Fig. 5 with the temporal evolution that is shown in Fig. 4 (right). After a propagation distance of 20 mm, Fig. 5 shows that the spectrum undergoes dramatic broadening while in Fig. 4 the ejection of multiple solitons can clearly be seen at this point. Because the dispersive radiation is split into a series of long (and thus low-intensity) pulses their signature is only evident in the spectral domain. Similar correspondences can also be observed for all other simulated pulse energies. However, as the temporal evolution does only provide limited information, we will concentrate on the spectral domain picture.

The higher the initial pulse energy, the earlier inside the fibre the actual supercontinuum is formed. The arrow in each of the sub-plots in Fig. 5 marks the transition between these two phases. It is important to note that while the pulse energy inside the fibre varies by a factor of >6 (4 nJ to 25 nJ), the actual peak power at the position of the arrow is equal to 12kW ± 30%. It can also be seen that after a long enough propagation distance, e.g. at the output of a 10 cm long piece of PCF, the generated spectrum is remarkably independent of the input energy. We therefore conclude that the initial pulse compression phase effectively adjusts the peak intensity of the pulses to a level for efficient supercontinuum generation. In addition, the phase matching conditions for the formation of dispersive waves (as given by Eq. 1) is responsible for the drop in intensity that can be observed for wavelengths below about 400 nm.

 

Fig. 5. Evolution of the spectral intensity inside the fibre for different pulse energies. The arrow marks the onset of a dramatic spectral broadening caused by soliton fission.

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Fig. 6. (a). Supercontinuum spectra for different pulse energies. The laser spectrum is shown in black as a comparison (b). Energy of the supercontinuum pulses versus energy of the uncompressed oscillator pulses.

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In Fig. 6(a), the measured supercontinuum spectra for different pulse energies for a fibre length of 10 cm are shown. In the wavelength range from 350 nm to 1000 nm an Ocean Optics USB 4000 spectrometer was used to measure the spectral intensity while for the low-frequency components an optical spectrum analyser from Anritsu was used. As can be seen, spectral components have been generated at wavelengths down to below 350 nm (the limit of the measurement range of our spectrometers), and are extending up to above 1600 nm. Due to an efficient coupling of energy from the individual solitons into dispersive waves as discussed above, the highest spectral intensities within the supercontinuum are located around the original pump wavelength (800 nm) as well as in the wavelength range between 400 nm and 550 nm. In accordance with our simulations, the supercontinuum spectra for output energies ranging from 5 nJ up to 25 nJ are similar in terms of spectral extent and shape. This implies that fluctuations in power caused by a change in the coupling conditions or by the laser itself will only have a small impact on the properties of the generated white-light spectrum. Figure 6(b) shows the energy of the supercontinuum pulses versus the energy of the uncompressed laser pulses measured in front of the microscope objective. The conversion respectively coupling efficiency is ranging from about 30% for low input power levels to about 20% for high input powers. We attribute this deterioration in coupling efficiency with respect to input power to thermal heating and subsequent movement in the fibre alignment stages. Finally, damage of the front facet of the PCF became visible for input energies in excess of 150 nJ.

4. Conclusions

In conclusion, we have demonstrated the generation of an ultrabroadband supercontinuum spectrum by coupling the uncompressed and highly positively chirped pulses from a chirped-pulse oscillator into a photonic crystal fibre that features anomalous dispersion at the CPO’s centre wavelength. Depending on the input energy, the pulses are partly compressed inside the fibre followed by the onset of a sudden spectral broadening due to soliton fission and dispersive wave generation. The generated spectra cover a wavelength range from < 350 nm to > 1600 nm and are remarkably independent on pulse energy. Due to the long pulse duration at the input facet of the fibre, damage can be avoided up to very high energy levels.