We present the first demonstration of sub-3 cycle optical pulses at 3.1 μm central wavelength generated through self-compression in the anomalous dispersion regime in a dielectric. The pulses emerging from this compact and efficient self-compression setup could be focused to intensities exceeding 1014 W/cm2, a suitable range for high field physics experiments. Numerical simulations performed with a 3D nonlinear propagation code, provide theoretical insight on the processes involved and support our experimental findings.
© 2013 Optical Society of America
Intense few-cycle pulses are challenging to obtain directly from a laser system due to limitations in amplification bandwidth, spectral reshaping and dispersion management. A remedy to this problem is nonlinear propagation in gaseous media in capillaries  or free-space (filamentation) [2,3] and subsequent compression with chirped mirrors  or bulk material . These techniques can reduce pulse durations from the typical 30 fs at 800 nm to below two-cycles but depending on implementation, efficiencies and pulse durations across the output beam may vary . To be useful, nonlinear propagation has to avoid chaotic pulse splitting, which sets an upper limit to usable pulse peak power . Self-compression to the few-cycle regime, i.e. without any need for dispersion compensation, was predicted  and achieved at 800 nm and 1500 nm wavelengths , but was limited to gaseous media, i.e. relatively low nonlinearity, to prevent the before-mentioned rapid and chaotic pulse splitting [6,9]. A lesser-known method to compress transform-limited pulses, with potentially large energy scalability, is based on group-velocity mismatch and fast amplitude modulation during three-wave-mixing in a nonlinear crystal . The technique was demonstrated at Nd:YAG wavelength and allowed compression from 10 ps duration to 310 fs while doubling the frequency .
The current upsurge in activity to generate intense few-cycle pulses in the mid-IR motivates revisiting nonlinear propagation and pulse compression in this wavelength range. Mid-IR pulses experience anomalous dispersion upon propagation which opens enticing new possibilities for nonlinear pulse propagation, self-compression or to investigate self-similar propagation. Moreover, the typically lower pulse energies of mid-IR systems – as compared to well-established 800 nm systems - prevent using gaseous media to investigate such possibilities. Bulk dielectric media, with their typically higher nonlinearities, could provide a solution; nonetheless stable nonlinear propagation without chaotic pulse splitting has not been reported to date.
Here we show that stable and efficient self-compression in bulk material is possible via filamentation of mid-IR pulses in the anomalous dispersion regime. The spectro-temporal properties of the pulses resulting from such highly nonlinear interaction have been investigated and we demonstrate pulse durations of sub-3 optical cycles with energy throughput as high as 65% using uncoated optics; 80% should be feasible by preventing Fresnel losses with coated optics or operation under Brewster’s angle.
2. Experimental setup
The mid-IR seed pulses used for the experiment were generated by a home-built optical parametric chirped pulse amplifier (OPCPA) system . The system delivered 20 μJ energy, 70-fs (6.8 cycle) pulses at 3100 nm center wavelength at 160 kHz repetition rate; the excellent output spatial profile was measured to M2 of 1.8 and power stability was typically better than 1% rms over 30 min. Figure 1 shows the simple experimental setup used in this experiment, consisting of an uncoated 10 cm focal length CaF2 lens and a 3-mm thick uncoated, single crystal, Yttrium Aluminum garnet (YAG) plate which was moved 6 mm along the beam across the focal plane in steps of 0.5 mm to initiate nonlinear propagation inside the plate at different peak intensities; the confocal parameter was 5 mm. YAG was chosen as a nonlinear medium for its availability, high nonlinear coefficient n2 and extended IR transparency. The medium therefore permitted generating spectra supporting few-cycle pulses in the mid-IR spectral range at the absence of any noticeable thermal effects.
The emerging beam was collimated with a silver-coated, 15 cm focal length mirror and the pulse was characterized with frequency-resolved optical gating (FROG). Our FROG device was specifically designed to handle ultrabroad bandwidths in the mid-IR spectral region  with its time axis calibrated; mid-IR spectra were measured using a Fourier transform infrared spectrometer with a liquid nitrogen cooled MCT detector.
The theoretical model used in this work was described elsewhere  and computes nonlinear propagation of the frequency components of the mid-infrared pulse in the YAG plate using a radially symmetric carrier resolving model in the form of the forward Maxwell equation coupled with an evolution equation for the electron-hole and electron-ion plasma. In the model, diffraction is described in the paraxial approximation, dispersion is described by a Sellmeier relation , self-steepening and nonlinear chromatic dispersion are included as well as optical field ionization rates  and avalanche ionization via the Drude model. The zoom-out inset in Fig. 1 shows the simulated spatio-temporal evolution of the input pulse.
3. Experimental results
We have previously investigated and reported  the spatio-spectral behavior of supercontinuum generation in a setting similar to that shown in Fig. 1 and simulations had predicted that self-compression would occur depending on the input energy, seed pulse duration, focal beam size and YAG plate thickness. In order to experimentally map such wide parameter space, a few conditions were fixed based on preliminary simulations: the pulse duration was set to the shortest duration directly achievable at the output of the OPCPA system (70 fs equivalent to 6.8-cycle duration), the YAG plate thickness was set to 3 mm and the focal length of the focusing lens was set to 10 cm. Focal lengths of 5 and 7.5 cm have also been tested and led to longer self-compressed pulse durations, the latter being attributed to non-optimum interaction length in the crystal. Both the impinging energy and the location of the YAG plate in the focus were left as free parameters: tuning of the YAG plate position allowed tuning of the peak intensity and of the length of filamentary propagation in the YAG plate while modifying the energy allowed fine adjustment of the peak intensity.
In order to map the parameter space to corroborate the experimental feasibility of self-compression, the YAG plate was scanned through the focus of the 10 cm focal length lens in steps of 0.5 mm over a 6 mm distance. For each position of the YAG plate (where position refers to the entrance face of the plate) a FROG trace was recorded along with the corresponding spectrum and the pulse duration was retrieved. Figures 2 and 3 show experimental results from these scans with simulation data overlaid. Our investigation initially started with 3 μJ pulse energy with the origin in Fig. 3 of the position of the YAG plate being the focal plane, which we determined by measuring the caustic of the beam through the linear focus in air. The YAG plate position indicated on Fig. 2 is the distance between the front of the YAG plate and that of the linear focus; negative values are located closer to the focusing lens. The evolution of the seed pulse intensity, as the YAG plate is scanned through focus, shows qualitatively that self-compression to 32 fs (2.9 cycle) does occur and that no pulse splitting is observed even though weak splitting dynamics can be seen for positions around −1 mm (Fig. 2 (a)). The highest intensity at the entrance face of the YAG plate was ~2 TW/cm2 at the focus for a pulse energy of 3 μJ; without plate, no filamentation in air was observed. Note that no damage of the YAG plate was noticeable even after operating for several days. The well-defined retrieved intensity profiles showed in Fig. 2 (a) allowed extracting FWHM duration of the pulse without ambiguity and these values are overlaid at the bottom of the figure with the durations extracted from our numerical simulations.
Nonlinear propagation and filamentation inside the YAG plate was described by pur numerical model by taking into account the transient change of refractive index induced by plasma generation as well as plasma absorption. The electron-hole plasma in the dielectric medium was described through optical field ionization and avalanche ionization. The plasma density reaches a maximum density in the range of 1018-1019 cm−3, quickly decreasing after a few hundreds of fs due to recombination; these effects are taken into account in our model [14,18]. We find striking agreement with experiment for a Kerr coefficient n2 = 6x10−16 cm2/W with 50% contribution of a delayed Raman-Kerr effect, a collision time of 20 fs in the Drude model and an optical field ionization rate W(I) lower than its multi-photon asymptote σ17I17 with coefficient σ17 = 2x10−203 cm34/s.W17. The intensity distribution was radially averaged over a 50 μm radius which is always at least twice as large as the filament radius. Pulse durations, extracted from the simulation, are also calculated for a radius of only 25 μm to check against radial inhomogeneity. We find that these values vary by only a few percent, indicating that the high intensity filament and its periphery were homogeneously self-compressed.
Based on the found excellent match with experiment, simulations reveal the mechanism for optimal compression: while the beam diameter is maintained approximately constant throughout the YAG plate, the pulse duration shortens due to the interplay between self-phase modulation and strong anomalous dispersion (k’ = −4082 fs2/cm1) in addition to steepening of the pulse tail by the self-generated electron-hole plasma. We find that while anomalous material dispersion largely compensates self-phase-modulation induced chirp thereby shortening the pulse duration, the temporal profile is freed from its background mainly due to the strong spatio-temporal reshaping (also depicted in Fig. 1 in the zoom-out).
The spectral behavior was simultaneously investigated and revealed a dramatic spectral broadening as the pulse experienced maximum self-compression accompanied by a large red-shift of the peak spectral intensity (Fig. 3). The seed spectrum was found to broaden from ~600 nm width at 1/e2 of the peak intensity outside the focus to almost 1000 nm at 1/e2 of the peak intensity in the focal region while the center wavelength shifted by almost 300 nm, from 3100 nm to 3400 nm. The spatial homogeneity of the broadened spectrum was investigated in a previous study . Investigating the evolution of the spectral phase through focus revealed that the self-compressed pulses exhibited residual uncompensated phase attributed to self-phase modulation, suggesting the potential for further compression. Even though the simulation and experimental traces show qualitative agreement – spectral broadening and red-shifting – the magnitude of the red-shift is larger experimentally than theoretically expected. Several attempts have been made to investigate this discrepancy – the main challenge laying in the absence of data for the Raman-Kerr response of our crystal – particularly by adjusting the Raman contribution. Numerically increasing the Raman-Kerr contribution from 20% to 90% of the total Kerr index in the nonlinear propagation or modifying step by step the frequency shift from 0.05 to 0.3 PHz in the Raman response did result in a moderate increase in the magnitude of the observed red-shift, while the pulse duration retrieved by simulations was not significantly affected by these changes. The discrepancy indicates that the observed redshift may not be related to the Raman-Kerr response of the crystal and is not prevalent for reaching the optimal pulse compression.
Based on the simulation results and careful mapping of pulse duration after propagation, optimum self-compression conditions for 3 μJ seed pulses were identified and the optimally self-compressed pulses were carefully characterized by sampling the inner part of the beam. Figure 4(e) and 4(f) show measured and retrieved FROG traces with a maximum 0.5% error. The input pulse and its spectrum are shown in the top row of Fig. 4 while the middle row shows the optimally self-compressed pulse. The measured spectrum for the optimally self-compressed pulse shows an extent of over 1000 nm and the retrieved spectrum from the FROG measurement is in good agreement with the measured spectrum confirming again the consistency of the measurement. We retrieve a FWHM pulse duration of 32 fs which corresponds to 2.9-cycles of electric field at the slightly red-shifted output of 3200 nm. Note the residual up-chirp that could be further compensated by transmission through a small amount of glass leading to pulse duration of 29 fs (2.7 cycle). The spatial profile of the beam after self-compression was measured using a knife-edge technique and showed that the process left the seed spatial profile undisturbed. Focusability and homogeneity of the beam was confirmed by successfully achieving ionization in a low density Ar gas jet confirming intensities in the 1014 W/cm2 range.
All nonlinear propagation techniques for generating ultrashort pulses, whether hollow fiber or filamentation, are ultimately limited by the necessity to avoid chaotic pulse splitting or spatial breakup. We therefore scaled our mid-IR OPCPA system from 3 to 15 μJ  and investigated scaling of self-compression in dielectrics to our maximum available pulse energy. We find that the 5 times higher input energy leads to equally stable self-compression to a slightly longer duration of 3.7 cycles and with the YAG plate positioned behind the focal plane. Spectral broadening of similar magnitude as in the low energy case was observed and the spatial profile shows no alteration from the input profile. Based on our simulations we find that optimal pulse compression at the higher energy would require a slightly different YAG plate length, thereby explaining the slight increase in pulse duration.
Another important aspect for a new compression technique is the efficiency of the process compared to established techniques such as gas-filled hollow fibers and filamentation typically exhibiting 60% throughput at best. We experimentally determine the throughput by first placing the YAG plate far out of focus thereby cancelling contributions from ionization. We find the total throughput to be 85% with the 15% losses matching Fresnel losses from our uncoated plate. Moving the YAG plate into the position of optimum self-compression, the throughput reduces to 65% for both the low energy and high energy case; Fig. 5 shows the measurements for various positions through the focus. We overlay results from our simulation which predict the overall efficiency (Fig. 5(a)) and the origin of the losses (Fig. 5(b)). Quantitatively, ionization and plasma absorption highly depend on simulation parameters but the filament intensity self-adjusts so as to maintain overall losses at the same level, mainly determined by the plate thickness and focusing geometry. While the ionization and plasma absorption losses are unavoidable, applying a suitable dielectric coating to the YAG plate or operating at Brewster’s angle could increase throughput to 80%, a figure largely exceeding that of typical nonlinear compressor used at near-infrared wavelengths. Finally, the temporal pulse-to-pulse stability of the self-compressed pulses was measured recorded with a fast photodiode to 0.8% rms over 10 minutes. Long term drifts were not observed and the experiment could be repeated over days.
We demonstrate for the first time self-compression to few-cycle-duration by nonlinear propagation in the anomalous dispersion regime in dielectric media and find that the method is feasible as well as reliable. We demonstrate the generation of sub-3 cycle pulses in the mid-infrared spectral region with sufficient energy to reach peak intensities in the 1014 W/cm2 range and outstanding pulse-to-pulse stability (0.8% rms over 10 min) at 160 kHz repetition rate. The conditions for successful self-compression have been experimentally investigated and theoretically corroborated and we show applicability to the maximum output energy from our laser system. Our investigation suggest that further energy scaling is possible provided the highest intensity within the YAG plate remains in the range of a few TW/cm2 and when the position of the YAG plate is adjusted accordingly. These results now enable a wealth of investigations in the mid-IR spectral region whenever few-cycle or CEP dependent effects are warranted such as for strong field interactions or quantum interference effects in e.g. the solid state. Future work will investigate such effects and also further energy scaling whenever higher OPCPA energies become available.
We acknowledge support from MINISTERIO DE ECONOMÍA Y COMPETITIVIDAD through its Consolider Program Science (SAUUL CSD 2007-00013), through Plan Nacional (FIS2011-30465-C02-01), the Catalan Agencia de Gestio d’Ajuts Universitaris i de Recerca (AGAUR) with SGR 2009-2013, Fundacio Cellex Barcelona, and funding from LASERLAB-EUROPE, grant agreement 228334.
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