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We present an approach for both efficient generation and amplification of 4–12μm pulses by tailoring the phase matching of the nonlinear crystal Zinc Germanium Phosphide (ZGP) in a narrowband-pumped optical parametric chirped pulse amplifier (OPCPA) and a broadband-pumped dual-chirped optical parametric amplifier (DC-OPA), respectively. Preliminary experimental results are obtained for generating 1.8–4.2μm super broadband spectra, which can be used to seed both the signal of the OPCPA and the pump of the DC-OPA. The theoretical pump-to-idler conversion efficiency reaches 27% in the DC-OPA pumped by a chirped broadband Cr2+:ZnSe/ZnS laser, enabling the generation of Terawatt-level 4–12μm pulses with an available large-aperture ZGP. Furthermore, the 4–12μm idler pulses can be compressed to sub-cycle pulses by compensating the tailored positive chirp of the idler pulses using the bulk compressor NaCl, and by indirectly controlling the higher-order idler phase through tuning the signal (2.4–4.0μm) phase with a commercially available acousto-optic programmable dispersive filter (AOPDF). A similar approach is also described for generating high-energy 4–12μm sub-cycle pulses via OPCPA pumped by a 2μm Ho:YLF laser.
So far, isolated attosecond pulses as short as 67 as have been generated via high harmonic generation (HHG) driven by few-cycle near infrared pulses at ~800nm1. Because the single atom cutoff photon energy of HHG is proportional to wavelength squared, long-wavelength laser sources are needed to extend the cutoff2,3. Recently, two-cycle mJ-level driving lasers around 1.7μm has been used to generate high-flux soft X-ray pulses in the water-window region (280 to 530eV)4,5, supporting 10 as transform limited pulses. To significantly increase both center photon energy and bandwidth of high harmonics for generating shorter attosecond or even zeptosecond X-ray pulses, the development of high-energy few-cycle pulses further into the mid-infrared (mid-IR) region is in demand. Beyond attosecond science, the high-energy few-cycle long-wavelength pulses are ideal tools for studying incoherent hard X-ray generation6, acceleration of electrons in dielectric structures and plasma7,8,9, breakdown of dipole approximation10 and filamentation in air. In addition, the high-repetition-rate few-cycle long-wavelength pulses would benefit the study of rotational and vibrational dynamics of molecules11, time-resolved imaging of molecular structures12, and strong-field science in plasmonic systems13.
High-energy few-cycle infrared pulses are primarily enabled by optical parametric chirped pulse amplification (OPCPA) pumped by few-picosecond lasers, which allows a trade-off between the gain bandwidth and the damage threshold of nonlinear crystals14,15. Among a number of few-cycle IR OPCPA sources that have been reported16,17,18,19,20,21,22, only a few of them have yielded mJ-level, carrier-envelope-phase (CEP)-stable, and near-octave pulses (two cycles and below) at-1.2–2.2μm21,22 and 1.6–2.7μm18. We have previously experimentally demonstrated 3 mJ, CEP-stable two-cycle pulses from 1.2μm to 2.2μm with the highest 18% pump-to-signal conversion efficiency22 and numerically demonstrated for the first time a robust approach for generation of mJ-level, CEP-stable, two-cycle pulses from 2.4μm to 4.0μm23. Recently, rapid progress has been made on the generation of short-pulse mid-IR laser sources around 5μm or above24,25,26. However, the compression of such pulses down to the transform limit has remained a great challenge due to lack of higher-order phase control over broadband mid-IR.
In this paper, we present a design that enables not only generating, for the first time to the best of our knowledge, mJ-level, CEP-stable 4–12μm pulses through dual-chirped optical parametric amplification (DC-OPA)22,23,27,28,29,30, but also compressing such pulses to sub-cycle duration through indirect pulse shaping. We have experimentally generated aμJ-level super broadband spectrum, which covers 1.8–4.2μm generated by difference frequency generation (DFG) in a BIBO crystal. On one hand, the spectrum can be used to seed the signal for generating 4–12μm pulses in an OPCPA pumped by a 2μm narrowband laser source; on the other hand, the 1.8–4.2μm pulses can be used to seed a Cr2+:ZnSe/ZnS chirped pulse amplifier (CPA), which is used for pumping the amplification stage of the 4–12μm DC-OPA. The 4–12μm optical parametric bandwidth is achieved by tailoring the phase matching of ZGP. The second-order phase of high-energy 4–12μm pulses can be compensated by using NaCl, which has a very small n2 and a high damage threshold; the higher-order phase can be compensated indirectly by controlling the signal phase with a commercially available acousto-optic programmable dispersive filter (AOPDF).
A proof-of-principle schematic setup shown in Fig. 1, which will be analyzed in detail, is used to facilitate all discussions in this paper. In this section, we first present the experimental generation of aμJ-level super broadband spectrum, which covers 1.8–4.2μm generated by DFG in a BIBO crystal, followed by discussions on how to tailor the phase matching of ZGP in order to achieve 4–12μm parametric bandwidth and on indirect pulse shaping toward sub-cycle pulses. Numerical simulations on generation in an OPCPA and amplification in either a DC-OPA or an OPCPA of 4–12μm pulses are shown in the latter part of this section.
We first present the results for generating broadband seed pulses through intra-pulse DFG. DFG is commonly used to generate the seed source due to its broad optical parametric bandwidth and passive-stable CEP16,18,19,20,31. Here we used spectrally broadened Ti:Sapphire pulses as the driving source for DFG. Nanojoule-level Ti:Sapphire oscillator pulses (730–830nm) were stretched to 360ps in an Offner-type stretcher, boosted to 4mJ with a home-made 14-pass amplifier, and compressed to 30fs with 3.5mJ pulse energy. Part of the energy, 2.2mJ, was focused into a 0.5-mm-diameter hollow core fiber (HCF) filled with 30psi neon for white light generation (WLG). The WLG pulses from the HCF were compressed to below 7fs. Finally 0.75mJ, <7fs pulses were obtained for driving DFG.
Guided by numerical simulation, we experimentally demonstrated that BIBO could generate more than one octave spectrum. Figure 2 shows the 1.8–4.2μm DFG with 15μJ energy experimentally achieved in a 0.4μm BIBO crystal, which falls under the gain spectrum of Cr2+:ZnSe/ZnS crystals32 and could be amplified in a Cr2+:ZnSe/ZnS CPA laser system33 that serves as the pump for the amplification stage of the 4–12μm DC-OPA. Meanwhile, the 2.4–4.0μm portion of the spectrum can be used as the signal for seeding the generation stage of the 4–12μm OPCPA. This is the first time, to the best of our knowledge, that such broadband pulses have been generated in BIBO. Moreover, the 15μJ energy is sufficiently high enough for studying high-harmonic generation in solids34.
In an OPA, the phase of the third output wave is determined by the phases of the two input waves:
Hence, it is feasible to indirectly control the phase of the third wave by controlling the phase of either of the two input waves. In a DC-OPA, if both the pump and the signal are linearly chirped, ωp,s(t)=ωp0,s0+βp,st, in which ω0 is the central angular frequency and β is the chirp (the subscripts p and s refer to the pump and signal, respectively). By conservation of energy, the angular frequency of the idler is thus
Hence, the chirp of the generated idler pulse is equal to the difference between the chirps of the pump and signal pulses. Chirp management in a DC-OPA has been analyzed and experimentally utilized to generate both few-cycle IR laser pulses22,23,28,29,30 and tunable narrowband mid-IR laser pulses27. Here we use chirp management combined with phase-matching tailoring to not only generate the 4–12μm broadband laser pulses, but also compress such broadband pulses to sub-cycle pulse duration via indirect pulse shaping. ZnGeP2 (ZGP) crystal is chosen as the nonlinear crystal as it has a high second-order nonlinearity (~80pm/V), wide transparency, and broad parametric bandwidth. There are several considerations on phase-matching tailoring and indirect pulse shaping in order to generate and compress the 4–12μm idler pulses:
Due to the many advantages mentioned in the last section, ZGP has been used in both OPA and OPCPA pumped around 2μm to generate short MIR laser pulses. For example, an OPA in ZGP generated 53μJ, 700fs laser pulses at 5μm when pumped by another OPA at around 2μm24; an OPCPA in ZGP generated 100μJ, 69fs (calculated transform limit) laser pulses at 5.3μm when pumped by a Ho:YAG CPA at 2.09μm26; another OPCPA in ZGP generated 200μJ, 360fs laser pulses at 7μm when pumped by a Ho:YLF CPA at 2μm25. Here we simulate the OPCPA discussed in the last section to generate 4–12μm idler pulses. A one-dimensional three-wave mixing numerical model has been developed by modifying the previous one37. All three waves are assumed to be plane waves. This model can be applied more accurately to situations where a flat top beam profile and a flat top pulse shape are used.
In the first simulation, the phase matching tailored in Fig. 3(a) is used to demonstrate the generation of the 4–12μm idler. The 2.4–4.0 μm signal pulse, which can be generated in BIBO using DFG, is negatively stretched to 6.0ps, while the 2.0μm pump pulse has a pulse duration (FWHM) of 7.8ps, as shown in Fig. 4(c). The input signal energy is assumed to be 1μJ, which is realistic according to the BIBO DFG experiment. The input pump energy is 100μJ. The input signal and pump intensities are 0.44GW/cm2 and 20GW/cm2, respectively, which are realistic since ZGP has a high damage threshold and can withstand 20GW/cm2 intensity at 2μm and 10ps pulse duration25. The pump-to-signal pulse duration ratio is chosen to optimize the parametric gain bandwidth without losing significant conversion efficiency. The ZGP crystal has a Type I phase-matching angle of 54°. The optimized crystal length is 0.4mm, which can give a decent conversion efficiency without reduction of the 4–12μm parametric gain bandwidth. The simulation results are shown in Fig. 4. As shown in Fig. 4(a), the amplified idler spectrum spans from 4μm to 12μm, supporting a 19.4fs (FWHM) transform-limited sub-cycle pulse, as can be seen from Fig. 4(d). The pump-to-idler conversion efficiency reaches 11.8% with a signal gain of 23.4, which can give an output idler energy more than 10μJ.
It is worth mentioning the synchronization between the pump and the signal. While the 2μm pump source can be generated with a Ho:YLF amplifier seeded with the BIBO DFG, the narrowband 2μm would have very low energy, which needs to be amplified with a regenerative Ho:YLF amplifier. However, the long optical path (several hundred meters) of the regenerative amplifier would make it rather difficult to synchronize the pump and the signal. Here, a DC-OPA is proposed instead to generate the narrowband 2μm pump, as shown in Fig. 5(a). Broadband spectrum around 2μm has been demonstrated using OPA in BBO38. In order to generate the narrowband 2μm spectrum, the DC-OPA is designed using the phase matching shown in Fig. 5(b). The key principle, illustrated in Fig. 5(c), is that when the pump and signal have an equal amount of chip, the generated idler would have a zero chirp and thus have narrow bandwidth. The idler bandwidth and center wavelength can be easily tuned by changing the chirps of the pump and signal and the delay between them, respectively. One example for the generated spectrum is shown in Fig. 5(d). In the simulation, the pump pulse is positively chirped using a 13.5-mm thick SF57, while the signal pulse is positively chirped using a 6.2-mm thick ZnSe. The center wavelengths of the pump (790nm) and the signal (1298nm) have an equal group delay dispersion of 3016fs2. The pump and signal intensities are 10.5GW/cm2 and 1kW/cm2, respectively. The BBO thickness is set to be 10mm with a Type I phase-matching angle of 20°. The pump-to-idler efficiency reaches 22.7% with a signal gain of 4×106, which can give more than 200μJ energy around 2.0μm with a 1mJ Ti:Sapphire pump.
Recently, the rapid development of Cr2+:ZnSe/ZnS CPA has opened up the opportunity to pump ZGP at a longer wavelength32,33. Ideally, ZGP should be pumped at around 2.5μm in order to achieve the broadest parametric bandwidth. Unlike the pump wavelength required for generating 4–12μm idler pulses in ZGP, which is predetermined by the available signal wavelength, the pump wavelength required for amplifying 4–12μm idler pulses is quite flexible, which can be tailored to meet a convenient gain bandwidth of Cr2+:ZnSe/ZnS CPA. The required pump center wavelength can be tailored by changing the phase-matching angle. One example of such phase-matching tailoring is shown by the shaded line in Fig. 6, which shows that the chirp signs of the pump and the idler have to be opposite. Since the chirp of the idler, which has been predetermined inside the OPCPA for generating the idler, is positive, the chirp of the pump has to be negative.
The results from simulating the amplification of 4–12μm idler pulses in DC-OPA are shown in Fig. 7. The high-energy 2.3–2.5μm pump pulse can be generated directly in a multi-pass Cr2+:ZnSe/ZnS CPA by using a high energy (15μJ) seed pulse generated in BIBO DFG. Thus, a regenerative amplifier can be avoided, which would make the synchronization between the pump pulse and the signal pulse rather difficult. The pump pulse is negatively stretched to 10ps, while the 4–12μm idler pulse is positively stretched to 6.3ps, as shown in Fig. 7(c). The input pump-to-idler energy ratio is assumed to be 104. The input idler and pump intensities are 4.1MW/cm2 and 20GW/cm2, respectively. The ZGP thickness is set to be 0.76mm with a Type I phase-matching angle of 48.5°. As shown in Fig. 7(a), the amplified idler spectrum spans from 4μm to 12μm, supporting 18.0fs transform-limited sub-cycle pulses, as can be seen from Fig. 7(d). The pump-to-idler conversion efficiency reaches 27.1% (gain: 2706). The broad phase matching can be tailored for the amplification of the 4–12μm idler in ZGP to accommodate both a flexible pump bandwidth and a flexible center wavelength from any specific Cr2+:ZnSe/ZnS CPA laser.
For the sake of comparison, we also simulate the amplification of 4–12μm idler pulses by an OPCPA in ZGP pumped by a 2μm picosecond Ho:YLF laser. Recently, tremendous progress has been made on 2μm Ho:YLF/YAG CPA lasers26,39,40,41, among which 55mJ, 4.3ps, 1kHz Ho:YLF laser system has been achieved. Subsequently, an OPA in ZGP pumped by a Ho:YAG CPA laser has generated 100μJ, 69fs (calculated transform limit) laser pulses at 5.3μm26, and an OPCPA in ZGP pumped by a Ho:YLF CPA laser has generated 200μJ, 360fs laser pulses at 7μm25. The MIR pulses in both cases have not been compressed to the near transform limit due to lack of higher-order phase compensation. The approach we proposed in Fig. 8(a) can not only generate and amplify a broader bandwidth (4–12μm) but also compress such broadband pulses to the near transform limit. The high-energy 2μm from the DC-OPA can seed directly a multipass Ho:YLF CPA, avoiding a regenerative amplifier that would complicate the synchronization between the pump and the idler in the 4–12μm OPCPA. The simulation results are shown in Fig. 8(b,c). The input pump centered at 2μm has a pulse duration (FWHM, transform-limited) of 10ps and a peak intensity of 20GW/cm2. The input idler pulses are stretched to 6.3ps from 4μm to 12μm with a peak intensity of 4.4MW/cm2. The input pump-to-idler energy ratio is 104. The type I phase matching angle of ZGP is 53°. It can be seen from Fig. 8 that the amplified idler spectrum spans from 4μm to 12μm. The conversion efficiency from the pump to the idler is 13.2% (gain: 1317), which is much lower compared with that from the 4–12μm DC-OPA due to poorer phase matching and unfavorable pump-to-idler photon ratio. The compression of 4–12μm can also be achieved by indirect pulse shaping in the idler pulse generation process. The phase of the generated positively chirped 4–12μm pulse can be coarsely controlled by a NaCl crystal and finely controlled indirectly by controlling the phase of the 2.4–4.0μm signal pulse using a commercial AOPDF.
In an OPA, the parametric gain is defined as ref. 42:
which grows exponentially with the crystal length Lc and nonlinear coefficient Γ, given as
where deff is the effective nonlinearity, Ip is the pump intensity, ni,s,p are the refractive indices of the idler, signal, and pump wavelengths respectively, λi,s are the wavelengths of the idler and signal, respectively, ε0 is the vacuum permittivity, and c is the speed of light in vacuum. The parametric gain, and thus the conversion efficiency, both grow exponentially with the crystal length and the square root of intensities. The maximum intensity allowed is limited by the crystal damage threshold, while the maximum length of crystal is limited by the preferred parametric gain bandwidth.
It would be meaningful to show quantitatively the conversion efficiencies with different pump intensities and crystal lengths, from which the energy scaling of specifically designed DC-OPA systems can be determined. For the OPCPA generating 4–12μm idler pulses discussed earlier, it is critical to maintain the 4–12μm broad gain bandwidth by using a ZGP crystal length shorter than 0.6mm. Thus, we do not discuss the energy scaling of the first-stage OPCPA that is used to produce seed idler pulses since the energy scaling is determined by later stages of DC-OPAs. Here we focus on the energy scaling of the DC-OPA for amplifying 4–12μm idler pulses. Table 1 shows 15 instances: 5 pump-to-idler input energy ratios and 3 different input pump intensities for each different ratio. For each combination of pump-to-idler ratio and input pump intensity, we show the corresponding crystal lengths that were optimized to achieve optimum conversion efficiencies, and the corresponding transform limited pulse durations of the output idler pulses. It can be seen that, at a fixed input pump intensity, the conversion efficiency decreases only slightly and the pulse duration of idler pulses does not increase much when the pump-to-idler input ratio increases by four orders of magnitude. Meanwhile, at a fixed input energy ratio, the changes of conversion efficiency and the pulse duration of idler pulses are not obvious when the pump intensity changes from 20GW/cm2 to 1.25GW/cm2. Thus, both the conversion efficiency and the idler pulse duration (or parametric gain bandwidth) depend weakly on the crystal length varying from 0.45mm to 4.4mm, which is due to the excellent phase matching in the DC-OPA. Energy scaling can be obtained by using Table 1. For example, at 10ps pump pulse duration and 20GW/cm2 intensity, a commercially available 20-mm-diameter ZGP crystal can withstand a pulse energy of 600mJ. If the input idler energy is assumed to be around 1μJ, the output idler energy would be 157mJ with a conversion efficiency of 26.2%, which gives sub 10TW peak power with a sub-cycle pulse duration of 18.5fs.
Table 2 shows quantitatively the crystal lengths, idler pulse durations and conversion efficiencies for 5 pump-to-idler input energy ratios and 3 different input pump intensities for each different ratio in the OPCPA pumped by the Ho:YLF CPA laser. It can be seen that, at a fixed input pump intensity, the conversion efficiency decreases considerably and the pulse duration of idler pulses increases significantly when the pump-to-idler input idler ratio increases by four orders of magnitude. Meanwhile, at a fixed input energy ratio, the conversion efficiency also decreases substantially and the pulse duration of idler pulses increases considerably when the pump intensity decreases from 20GW/cm2 to 1.25GW/cm2. The decrease in conversion efficiency and increase in pulse duration is due to the use of a longer crystal, which inevitably results in poorer phase matching: 65.5fs, 4.0% in a 4mm ZGP crystal versus 20.1fs, 14.1% in a 0.37mm one. Thus, it is much more favorable to use a short ZGP crystal in the 4–12μm OPCPA pumped by a 2μm pump source, which can be achieved by using a short pump pulse at a few picosecond and a high-energy input idler around or aboveμJ level. Suppose the input idler energy is around 1μJ, the output idler energy would be 71mJ with a 600mJ pump, and the pump-to-idler conversion efficiency would be 11.9%, giving 2.9TW peak power with a 24.4fs (FWHM) pulse duration.
Several critical issues should be discussed here. First, it should be noticed that a single crystal was used in the simulation for amplification of idler pulses. In the actual experimental setup, two stages might be needed for achieving tens of mJ idler energy, where the first stage provides high gain with a relatively low efficiency and a second stage is used to amplify the idler efficiently. Second, the B-integral of a 157mJ 4–12μm pulse in a 1-mm thick ZPG with 10GW/cm2 intensity is estimated to be around 0.3 (n2=400×10−16cm2/W43), which is acceptable. Third, the superfluorescence buildup would be small because of high seed energy (several μJ). In addition, in order to preserve the passive CEP stability of the idler pulses in the generation stage, it is critical to maintain the time delay between the pump pulses and the signal pulses, which can be achieved by interferometric locking of the optical path length difference between the pump and the idler beams (20 as RMS)44.
By tailoring the phase matching of the nonlinear crystal ZGP, we propose to generate 4–12μm idler pulses in OPCPA pumped by a narrowband 2μm laser and then amplify the idler pulses in DC-OPA pumped by a Cr2+:ZnSe/ZnS CPA centered around 2.4μm. The 4–12μm pulses can be compressed to sub-cycle pulses by controlling the signal (2.4–4.0μm) phase using a commercially available AOPDF combined with a bulk material NaCl. The parametric gain bandwidth and conversion efficiency from the 4–12μm DC-OPA are barely limited by the ZGP crystal length, which can support up to 10TW peak power, provided that the ZGP crystal can withstand 20GW/cm2 peak intensity of the Cr2+:ZnSe/ZnS pump laser. Similarly, we propose to amplify high-energy 4–12μm sub-cycle pulses via an OPCPA pumped by a narrowband 2μm Ho:YLF laser. Unlike the 4–12μm DC-OPA, the OPCPA is significantly limited by the ZGP crystal length-both the parametric gain bandwidth and conversion efficiency. However, such an OPCPA can still support up to 3TW peak power.
How to cite this article: Yin, Y. et al. Towards Terawatt Sub-Cycle Long-Wave Infrared Pulses via Chirped Optical Parametric Amplification and Indirect Pulse Shaping. Sci. Rep. 7, 45794; doi: 10.1038/srep45794 (2017).
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This work has been supported Air Force Office of Scientific Research (FA9550-16-1-0013, FA9550-15-1-0037); Army Research Office (W911NF-14-1-0383, W911NF-15-1-0336); the DARPA PULSE program by a grant from AMRDEC (W31P4Q1310017). This material is also based upon work supported by the National Science Foundation under Grant Number (NSF Grant Number 1506345). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.
The authors declare no competing financial interests.
Author Contributions Y.Y. and Z.C. conceived the simulations and experiments. Y.Y. performed the simulations. Y.Y., A.C., X.R., J.Li., Y.W. and Y.W. developed the setup and carried out the experiments. Y.Y. wrote the manuscript. All authors reviewed and contributed to the final manuscript.