1. Introduction

Few-cycle pulses have been subject to intense recent research efforts due to their wide range of applications, for instance in time-resolved studies of fundamental processes in physics, chemistry and biology [1]. High energy few-cycle pulses, typically generated by gas-filled hollow fiber compression (HFC) [2] or optical parametric chirped pulse amplification [3,4], allow for applications such as high harmonic generation and attosecond pulse generation [5].

Although commercial few-cycle Ti:sapphire based oscillators are available, the generation of high quality sub-two cycle pulses is still challenging. An interesting technique is the nonlinear spectral broadening of few-cycle pulses via supercontinuum (SC) generation in optical fibers and subsequent temporal recompression. The shortest pulses (2.6 fs, 1.3 cycles) have been generated using gas-filled hollow core fibers and compression with an active phase shaping device [2], but this generally requires amplified pulses with >100 µJ pulse energy. In contrast, solid core fibers allow for sufficient spectral broadening and potential pulse compression already at nanojoule pulse energies. If a short piece of standard single-mode fiber is employed, pulse energies in the order of 10 nJ can generate spectral broadening sufficient to compress to less than 5 fs duration [6]. However, higher order phase compensation is required and the achievable pulse width is restricted by the material dispersion of silica, which leads to strong dispersive temporal broadening for pulses with 800 nm central wavelength and therefore limits the obtainable spectral width for low energy pulses. In both hollow core fiber and single-mode fiber compression, pumping occurs deep in the normal dispersion regime generating coherent spectra with deterministic phase distribution, which allows reliable recompression.

Photonic crystal fibers (PCF) offer the possibility of dispersion engineering and have been extensively used to generate ultrabroad SC spectra, which are of great interest for few-cycle pulse compression [7]. By using a 5 mm piece of PCF, which exhibits a single zero dispersion wavelength (ZDW) in the vicinity of the pump, compression to 5.5 fs has been demonstrated employing active phase shaping and 2.7 nJ, 15 fs pump pulses [8]. However, pumping close to the single ZDW of a PCF leads to soliton dynamics, which are very sensitive to pump pulse fluctuations, resulting in spectral structure and phase variations from pulse to pulse [9]. These degraded temporal coherence properties ultimately limit the pulse duration and quality achievable by external compression [8–11]. These problems can be avoided by making use of soliton self-compression in PCF, which takes advantage of the initial stage of spectral broadening and temporal compression of higher order soliton propagation, thus obviating the need of post-compression devices [12]. Impressive results down to sub-two cycle durations have been achieved, and the scaling of this concept to the single cycle regime has been theoretically investigated [13]. Input pulse parameters and fiber length are chosen to prevent pulse break-up and maintain coherence, but this usually limits the application of the scheme to subnanojoule pulses. The resulting pulses also typically feature considerable side peaks and pedestals.

In this manuscript we demonstrate that the achievable few-cycle pulse quality and duration in nonlinear compression experiments can be significantly improved by using all-normal dispersion photonic crystal fibers (ANDi PCF) [14]. In such fibers, soliton generation and fission are suppressed and the broadening dynamics are dominated by self-phase modulation and optical wave breaking [15]. More than octave-spanning highly coherent SC spectra have been demonstrated, which preserve a single pulse in the time domain, provide a smooth spectral intensity and phase and are therefore well suited for external recompression [16]. We show that the previously reported limits to few-cycle pulse generation from compression of SC spectra generated in conventional PCFs do not apply for ANDi PCF due to the excellent coherence properties, which are independent of fiber length and input pulse parameters. Hence this concept is applicable to a wide range of possible input pulses. In related work, 400 fs, 20 nJ pulses could be compressed to less than 30 fs using a 4 cm long piece of a similar ANDi PCF and a simple prism compressor [17]. Here we focus on the hard-to-reach sub-two cycle regime and achieve 5.0 fs pulses of excellent quality using linear chirp compensation with a compact chirped mirror compressor. This is the shortest pulse duration achieved to date from the external recompression of SC pulses generated in PCF. In addition, the scalability of the concept to single cycle pulses is numerically investigated.

2. Experimental setup

The experimental setup is shown in Fig. 1(a) . The seed laser is a cavity-dumped Kerr lens mode-locked Ti:sapphire oscillator delivering up to 10 nJ pulse energy at 800 nm central wavelength and 2 MHz repetition rate. An output pulse width of 15 fs is measured using a commercial broadband SPIDER device (VENTEON Laser Technologies GmbH, Germany) with a measurement range from 600 - 1200 nm. The pulses from the oscillator have a small contribution of residual positive linear and higher order chirp, the Fourier limited pulse duration is 12 fs. The pulses are then coupled into a 1.7 mm long piece of ANDi PCF via a 6.5 mm focal length aspheric lens on a piezo-controlled translation stage with up to 40% efficiency (non-optimized). The dispersion of the lens is pre- compensated with chirped mirrors so that pulses of 15 fs duration are expected at the input of the fiber. It has a core diameter of 2.3 μm, pitch Λ = 1.44 μm and relative air hole diameter d/Λ = 0.39. The resulting measured dispersion profile, supplied by the manufacturer NKT Photonics, is displayed in Fig. 1(b) and assumes its maximum of D = −11 ps/(nm km) at a wavelength of 1020 nm [18].

 

Fig. 1 (a) Schematic experimental pulse compression setup. CM chirped mirrors; L aspheric lens; PM parabolic mirror; T telescope; BCM broadband chirped mirror; P periscope. (b) Dispersion profile and scanning electron microscope picture of the ANDi PCF used in the experiment.

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The SC spectrum generated in the fiber is collimated with a gold-coated 25 mm focal length off-axis parabolic mirror and the resulting large beam diameter is reduced by a telescope consisting of two silver-coated spherical mirrors. The use of mirrors instead of lenses, the short fiber length and the stable SC spectrum allow pulse compression to sub-two cycle durations simply by linear chirp compensation with a compact broadband chirped mirror compressor (UltraFast Innovations GmbH, Germany), designed to provide constant negative GVD of −30 fs² per bounce in the range 650 - 1250 nm. Oscillations of the GVD curves are effectively minimized by using two different incident angles of α = 20° and β = 5°, as indicated in Fig. 1(a). After adaption of the polarization by a periscope, the compressed pulses are characterized using the SPIDER device described above.

3. Compression results

The generated spectrum for 1.7 nJ input pulse energy is depicted in Fig. 2(a) . It spans over more than one octave from 530 nm to 1100 nm and agrees well with numerical simulations. Slight deviations are caused by uncertainties in the phase of the input pulse, which is not known exactly after passing through the focusing lens. The measured spectral phase after compression is flat over the bandwidth of the spectrum, only in the fraction below 650 nm the chirped mirrors are not able to compensate the phase appropriately due to their limited spectral range (650 - 1250 nm).

 

Fig. 2 (a) Measured spectrum at 1.7 nJ pulse energy, comparison with numerical simulation and measured spectral phase after compression. (b) Reconstructed temporal pulse envelope and corresponding simulation result. (c) Measured SPIDER trace of the compressed pulses.

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The simulation assumes a complex chirped sech-shaped temporal input pulse field envelope A(t) = √P₀ sech^(1−iσ)(t/t₀) with full width at half maximum t_FWHM = 2 ln(1 + √2)t₀ = 15 fs duration and P₀ ≈110 kW the input peak power. This definition of the chirp parameter σ introduces a linear chirp over the central part of the pulse with increasing higher order contributions in the wings, which is more realistic for broadband Ti:Sapphire oscillators than a pure linear chirp assumption [19]. We used σ ≈ + 1 for the numerical simulations. The rest of the implementation is identical to the description in [15,20].

Note that the residual chirp parameter of the input pulses is positive. We also conducted experiments in which the chirp was overcompensated before the pulses were coupled into the fiber, i.e. the input pulses had a negative chirp parameter. However, we found that in this case SPM first leads to a spectral compression before spectral broadening occurs. Negative chirp is therefore to be avoided if a broad spectrum and a short pulse are desired.

The reconstructed pulse shape is shown in Fig. 2(b) with a FWHM pulse duration of (5.0 ± 0.3) fs, corresponding to 1.85 ± 0.11 optical cycles. The measurement was stable and repeatable with only minor fluctuations in the reconstructed pulse shape and duration. A SPIDER signal was obtained for the entire bandwidth of the spectrum with good fringe visibility (Fig. 2(c)). Considering that only linear chirp compensation is applied, the pulses exhibit an exceptional quality. The main peak contains more than 80% of the total pulse energy in a ± 5 fs wide temporal window. The measured pulse profile is also in excellent agreement with the simulation, which was obtained from the simulated spectrum in Fig. 2(a) by compensation of quadratic phase only.

The short input pulse width and fiber length were chosen in order to limit the influence of higher order dispersion and reach the sub-two cycle regime with linear compression only. Therefore, the achieved compression ratio is limited to about 3 in this case. However, considerably higher compression ratios are possible with ANDi fibers. This was already theoretically analyzed in [15] for both linear and full chirp compensation and experimentally verified in [17], where compression ratios > 20 were shown to be possible. Since octave spanning coherent SC spectra without significant modulation can be generated in ANDi fibers even with pulses of several hundred femtoseconds duration, only the bandwidth and resolution of the available compression device limit the achievable compressed pulse width and quality, not the SC itself.

Note that a conventional single ZDW PCF pumped in the anomalous dispersion regime cannot be used in our setup, because the resulting spectrum would be positively chirped for wavelengths shorter than the ZDW and negatively chirped for wavelengths longer than the ZDW. ANDi PCF can therefore significantly reduce the complexity of the external recompression compared to conventional PCF, because the entire spectrum can be compressed using a single passive and static device.

The Fourier-limited pulse duration of the measured spectrum is 3.9 fs, which could be obtained by using higher order chirp compensation.

4. Fiber length optimization

In order to minimize the pulse duration achievable by linear compression, the fiber length was optimized by numerical simulation. The generated spectrum was calculated for 1.7 nJ input pulse energy in dependence of the fiber length (Fig. 3(a) ), and the pulse width was determined for linear chirp compensation as well as for full phase compensation (Fig. 3(b)). While the spectrum broadens and consequently the Fourier limited pulse duration decreases with propagation distance, the minimum achievable pulse width of 4.6 fs for linear compression is reached at a fiber length of about 2 mm. For shorter fiber lengths, the spectral bandwidth is not sufficient to support shorter pulses. For longer fibers, the pulse acquires considerable higher order chirp components, which cannot be compensated simply by linear compression. The insets in Fig. 3(b) show that the compressed pulse develops significant side lobes or even broad low level pedestals if the fiber length is chosen too long. The same calculation for higher input pulse energies or shorter input pulse widths leads to shorter compressed pulse durations, but also the optimum fiber length decreases to impractical dimensions. In addition, the range limit of the chirped mirrors needs to be taken into account, so that the combination of 1.7 nJ pulse energy with 1.7 mm fiber length chosen in the experiment are optimum parameters for the presented setup. Hence the measured pulse duration of 5.0 fs is close to the theoretical limit.

 

Fig. 3 (a) Simulated spectral evolution over 10 mm propagation distance in the ANDi PCF for a 1.7 nJ, 15 fs input pulse. (b) Achievable pulse width using linear compression only (black cross) and full phase compensation (red dot). The insets show examples of compressed pulse profiles for linear compression.

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5. Scalability to single cycle pulse compression

Shorter pulse durations approaching the single optical cycle limit can be obtained by using full phase compensation with active phase shaping. In order to demonstrate the scaling potential of the ANDi PCF based compression scheme, we performed numerical simulations with 4 nJ input pulses, which is the highest coupled pulse energy available in the presented experiment. A fiber length of 10 mm is chosen, for which the SC bandwidth is fully developed. Since fluctuations of the spectral phase due to the noise sensitivity of the SC generation process can limit the achievable pulse duration, we follow the procedure outlined in [11] for simulating a realistic compression experiment including input pulse shot noise.

Figure 4(a) shows the calculated degree of coherence |g₁₂⁽¹⁾(λ)| as well as the mean generated spectrum, calculated from an ensemble of 20 independent simulations with random noise seeds. As expected for ANDi PCF, |g₁₂⁽¹⁾(λ)| = 1 over the entire bandwidth, which corresponds to perfect coherence and maximum phase stability. Compensating the median spectral phase results in 2.9 fs pulses of excellent quality, as shown in Fig. 4(b). Due to the high phase stability of the generated SC, the displayed ensemble averages are virtually undistinguishable from single shot simulations.

 

Fig. 4 (a) Mean spectrum and degree of coherence for 4 nJ, 15 fs input pulses and 10 mm fiber length, calculated over the simulation ensemble. (b) Mean compressed pulse obtained using an ideal compressor based on the median spectral phase.

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One could argue that even better results should be expected if a conventional single ZDW PCF pumped in the anomalous dispersion regime is used, because a highly coherent spectrum is generated for 15 fs pump pulses in this case as well and additionally a broader spectral bandwidth would be achieved. However, it was already shown in [8] for a similar setup that even for these extremely short pump pulses and fiber lengths the coherence degradation and the extreme spectral modulation in the anomalous dispersion regime are the limiting factors for external recompression. Even with complete phase control using a spatial light modulator, the resulting pulse quality is poor. Our results therefore show that ANDi PCF deliver significantly increased pulse quality compared to conventional single ZDW PCF for pulse compression applications.

The temporal coherence properties and the relative spectral uniformity of the SC generated in ANDi PCF are distinctly different from SC generated in PCF with single ZDW. Therefore, the fundamental limits to pulse compression outlined in [8–11] do not apply in this case. The achievable pulse duration is not limited by the coherence properties of the generated SC, but only by the capabilities of the employed compression device and pump laser stability.

6. Conclusion

We demonstrated nonlinear pulse compression based on SC generation in ANDi PCF and experimentally obtained high quality sub-two optical cycle pulses of 5.0 fs duration by compensation of linear chirp with a compact chirped mirror compressor. To our knowledge this is the shortest pulse duration obtained from external recompression of SC generated in PCF to date. The results are in excellent agreement with numerical simulations and close to the theoretical limit obtainable using linear compression only. We numerically demonstrated that the SC temporal coherence properties allow the scaling of this pulse compression concept down to the single-cycle regime using an active phase shaping device. These results have high immediacy to the research in the field, because achievable pulse duration and quality in already existing nonlinear pulse compression setups, which often use fibers pumped deep in the normal dispersion regime, can be immediately improved by using an ANDi PCF for spectral broadening, while the rest of the setup can essentially be left unchanged. Note that ANDi fiber designs can be optimized for pumping at any desired wavelength from the ultraviolet to the near-infrared [14]. Therefore, the presented pulse compression concept is not only restricted to Ti:Sapphire pump lasers, but can also be transferred to other ultrashort pulse laser sources, e.g. Yb-doped fiber lasers.