1. INTRODUCTION

The prospects offered by strong-field physics and attosecond science [1,2] have been a key motivation for the development of long wavelength sources of intense ultrashort pulses [3,4]. Utilizing the wavelength scaling of strong-field electron recollision for high harmonic generation [5,6] has made possible the generation of coherent x-ray radiation in the water window [7,8]. Driving high harmonic generation with a carrier envelope phase (CEP)-stable sub-2-cycle pulse at 2 μm has recently resulted in the first source of isolated attosecond soft x-ray pulses in this spectral region [9], thereby combining attosecond temporal resolution with the element specificity of x rays [10,11]. An important demand on laser drivers for strong-field physics is hence the capacity to counteract the unfavorable long-wavelength scaling of the underlying processes that results in very low event rates in measurements. Examples are the photoionization with mid-IR radiation [3,4] or attosecond x-ray generation. Therefore, our near-decadelong development of ultrafast mid-IR sources [12,13] aimed at balancing the repetition rate against the achievable pulse energy. Our development of a 160 kHz mid-IR OPCPA that could reach focused intensities of ${10}^{14}\mathrm{W}/{\mathrm{cm}}^2$ was instrumental to developing laser-induced electron diffraction [14–17] to image bond breaking in a single polyatomic molecule with a 6 pm spatial and 0.6 fs temporal resolution [18].

The combination of ultrafast high peak power and average power represents an important frontier in laser science itself, quite apart from the importance of achieving a measured balance between high repetition rate and high pulse energy in strong-field experiments. Ultimately, these requirements present a tremendous challenge for, e.g., OPCPA development due to material imperfections, nonlinear effects, and thermal issues [19]. As a result, only a few sources exist that are capable of delivering ultrashort mid-IR pulses at micro-joule pulse energies [12,20–23] together with CEP stability [12,24]. In previous works, we have shown that filamentation of pulses in the mid-IR [25], i.e., at 3 μm and above, can lead to efficient self-compression by exploiting the interplay of linear and nonlinear propagation effects in the anomalous dispersion regime [26] to reach the few-cycle regime. Employing this method, self-compression was demonstrated in solids [26,27] as well as in gases through self-guiding [28] and in hollow-core waveguides [29]. Common to all these demonstrations is the fact that, despite the vastly varying parameters of the systems used, the average compressed output power always ended up in the milliwatt-level power regime.

Here, we report a mid-IR OPCPA and the compression of its output in a gas-filled hollow core antiresonant-reflection photonic crystal fiber (ARR-PCF), extending in this way the existing parameters by more than an order of magnitude to achieve peak powers of 3.9 GW at a 160 kHz repetition rate with intrinsically CEP-stable pulses near the single-cycle limit.

2. MID-IR OPCPA AT 21 W

Figure 1 shows the conceptual layout. The CEP-stable and broadband mid-IR seed was generated, identical to our previous system [30], from a two-color fiber laser (Toptica Photonics AG) by means of difference frequency generation (DFG) [31]. The Er-fiber system had two parallel outputs of sub-100 fs pulses with 220 mW power at a center wavelength of 1550 nm and with a 100 MHz repetition rate. One of these outputs was frequency downshifted in a photonic crystal fiber to 1050 nm, thereby yielding two phase-coherent pulses that originated from a common pulse, but with different center wavelengths. DFG between those two pulses, at 1550 nm and 1050 nm, in a 1-mm-thin periodically poled lithium niobate (PPLN) crystal resulted in a CEP-stable mid-IR pulse with 7 pJ energy; the spectrum is shown in Fig. 2. After propagation through 50 mm of sapphire, the seed pulse was negatively stretched to a duration of 3 ps. As pump, we used a neodymium-doped vanadate ($\mathrm{Nd}\text{:}{\mathrm{YVO}}_4$)-based master oscillator power amplifier (MOPA) from Coherent, Inc., providing 1.1 mJ 9 ps pulses at a 1064 nm wavelength and 160 kHz repetition rate. The temporal overlap between the pump and the seed was ensured via electronic synchronization between the two lasers to a level better than 300 fs.

 

Fig. 1. Setup of the high-power, mid-IR OPCPA system. (a) The seed is generated by a two-color fiber front-end in combination with a DFG stage. Afterward, the mid-IR pulses are stretched and consecutively amplified in a preamplifier and two booster amplifiers. Maximum conversion efficiencies are achieved by multiple use of the pump beam and by individually tailored seed-to-pump pulse durations. The mid-IR output is compressed in a bulk stretcher and (b) the final compression to a single optical cycle is performed using an Ar-filled ARR-PCF.

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Fig. 2. Spectrum of the mid-IR seed from the DFG (dashed black curve) together with the spectra from each OPA stage (solid curves) and the final output (filled and solid red curve).

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The OPCPA was comprised of a chain of oscillator power amplifier (OPA) stages including a preamplification section with three consecutive OPA stages and a booster section with four OPA stages. The three OPA stages in the preamplification section consisted of one 1.4-mm-long PPLN and two 5-mm-long PPLN crystals (HC Photonics), resulting in pulse energies of 50 nJ, 500 nJ, and 2.6 μJ. The first OPA used a fixed-period crystal to most efficiently implement the high-gain stage ($3.6\times {10}^3$), while the consecutive two preamplifier stages used AAPLN to maintain a broad seed spectrum. The entire preamplifier section achieved a cumulative gain of $3\times {10}^5$. The spectral evolution throughout the system is depicted in Fig. 2.

Before further amplification, we reversed the chirp of the mid-IR seed from negative to positive with a grating-based, Martinez-type chirp inverter. The chirp inverter served the purpose of giving control over the chirp and pulse duration within the OPCPA chain after the high-gain section and it permitted using bulk sapphire for compression, thus resulting in the highest possible compression efficiency.

For the booster section, we increased the seed pulse duration to 7 ps, which maximized the temporal overlap with the pump pulses. Each booster stage consisted of two identical crystals in which the residual pump from the first OPA crystal was recycled for the second OPA crystal, thus increasing the overall efficiency. 2-mm-long PPLN crystals were used for the first two OPAs (OPA4 and OPA5) which were pumped by 250 μJ (40 W) pulses, resulting in amplification of the mid-IR pulses, first to 10 μJ and then to 18 μJ, respectively. Here, and in the following two stages, we counteracted the spectral energy loss in the blue part of the spectrum in addition to slight spectral broadening in the red part by using a slightly detuned second stage. Based on our previous investigation of high-power effects in mid-IR amplification of different nonlinear media [19], we elected to use $5\mathrm{mm}\times 5\mathrm{mm}$ potassium niobate (${\mathrm{KNbO}}_3$) crystals for the last two OPAs (OPA6 and OPA7). Both stages employed antireflection (AR)-coated 2-mm-thick $5\mathrm{mm}\times 5\mathrm{mm}$ ${\mathrm{KNbO}}_3$ crystals that were cut at 40.5° for a noncollinear interaction, with an internal angle of 5.2°, using a combined pump energy of 625 μJ (100 W). We achieved amplification to 77 μJ and 131 μJ, respectively, corresponding to an average power of 21 W. Finally, compression was achieved by double passing through a 10-cm-long AR-coated sapphire rod. We measured a pulse duration of 97 fs (sub-9 optical cycles) with a pulse-to-pulse stability of 0.33% rms over 30 min (see Fig. 3).

 

Fig. 3. Output characteristics of the mid-IR OPCPA system. SHG-FROG retrieval of the mid-IR output pulses, showing (a) the spectral amplitude and phase, and (b) the temporal amplitude and instantaneous frequency. (c) The pulse-to-pulse power stability measured over 30 min. The inset shows the output beam profile.

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3. SINGLE-CYCLE COMPRESSION IN THE MID-IR

The conventional scheme of spectral broadening via self-phase modulation (SPM) in a gas-filled capillary followed by dispersion compensation cannot be applied to compress further the output of this system. The capillary loss scales as ${\lambda }^2/a^3$, where $\lambda$ is the wavelength and $a$ is the radius, while the characteristic length for SPM scales as $L_{\text{SPM}}=\lambda /(2\pi n_2{I}_0)$, where $n_2$ is the Kerr coefficient and $I_0$ is the laser peak intensity in the waveguide. Moreover, a specific challenge for employing gas-filled hollow-core waveguides for the mid-IR is material absorption. This translates into a very high propagation loss of mid-IR pulses in Bragg waveguides and fiber capillaries [32]. To overcome these limitations, we employed a new type of ARR-PCF [33–36] that consisted of a single ring of antiresonant capillaries with $\sim 1.2\mathrm{\mu m}$ wall thickness, surrounding a 88 μm central hollow core (see Fig. 4).

 

Fig. 4. Measured transmission loss (red shaded) together with the dispersion obtained via the Marcatili [37] model (gray) and fitting FEM calculations (blue) for a 88 μm core evacuated fiber with 1.2 μm core wall thickness. The inset shows a scanning electron microscope image of the ARR-PCF fiber.

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It has been shown that the ARR-PCF achieves broadband transmission with a very low propagation loss in the mid-IR despite being manufactured from fused silica [35]. Thus, the ARR-PCF presents the enticing possibility for the mid-IR to exploit soliton dynamics for pulse self-compression in the mid-IR by balancing nonlinear propagation with waveguide dispersion [38]. Soliton self-compression is possible for propagation at soliton orders $N=\sqrt{L_d/L_{\text{SPM}}}>1$, where $L_d=T_0^2/{\beta }_2$ is the dispersion length, $T_0$ is the input pulse duration, ${\beta }_2$ is the group velocity dispersion (GVD) [39–41], and $L_{\text{SPM}}$ is the characteristic length for SPM. Under such conditions, the cumulated linear dispersion is balanced by nonlinear dispersion, and negative GVD causes new frequency components (generated through SPM) at the leading and trailing parts of the pulse to move toward the pulse center. Thus, the pulse self-compresses by a factor that is inversely proportional to $N$ upon propagating a distance $\sim L_d/N$ [38,40,42,43]. This distance becomes longer as higher-order dispersion terms become more important and for chirped input pulses. As the soliton order increases, the nonlinear chirp introduced by SPM is no longer balanced by negative GVD so that the amount of energy contained in the compressed pulse peak, rather than in its pedestal, decreases. As a result, small values of $N$ are required to achieve clean compression ($\mathrm{N}\precsim 5$) [39,43] with good pulse fidelity.

The spectral broadening and concomitant compression depend on the exact dispersion profile and propagation loss of the fiber. The measured transmission loss (Fig. 4) reveals a loss band at 2.4 μm, caused by an anti-crossing between the core mode and the first-order resonance in the capillary walls [44], which alters the dispersion landscape. Together with the absence of accurately tabulated gas properties from 2.4 μm [45] into the mid-IR, this meant that we had to resort to changing the gas species, pressure, and fiber length to optimize the performance. The ARR-PCF was set up inside a small gas cell with 3-mm-thick ${\mathrm{CaF}}_2$ input and exit windows and the fiber entrance was placed at the image plane of a diamond pinhole. This setup reduced the available pulse energy to 75 μJ (12 W), but it prevented possible damage of the ARR-PCF at high power through coupling mismatch. The light was coupled into the fiber using an achromatic lens with a 75 mm focal length and the emerging light was recollimated with a 100 mm focal length parabolic mirror. We recorded the spectra with a Fourier-transform infrared spectrometer (FTIR) and retrieved the temporal waveforms from second harmonic frequency-resolved optical gating (SH-FROG) with the time axis ambiguity removed. The SH-FROG employed all-reflective optics and a 30-μm-thin GaSe crystal for sum frequency mixing.

Figure 5 shows a summary of measured pulse durations (measured with SH-FROG) for various noble gases, fiber lengths, and pressures.

 

Fig. 5. Measured self-compressed FWHM pulse duration of mid-IR pulses in the ARR-PCF for different noble gas atmospheres and pressures.

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The parameter scan (Fig. 5) shows that gases with a high ionization potential and lower nonlinearity, such as helium (24.6 eV) and neon (21.6 eV), were found not to produce significant self-compression, even at pressures up to 70 bar. We attribute this to the change in dispersion caused by the anti-crossing at 2.4 μm. Decreasing the ionization potential and increasing the gas nonlinearity by choosing Ar (15.8 eV) resulted in significant compression to the few-cycle regime. Figure 6 shows the spectral evolution in a 14.9-cm-long fiber for a vacuum and for up to 15 bar of argon. Clearly visible is the onset of spectral broadening at pressures above 5 bar, and expanding from 2.5 μm to 4 μm for pressures higher than 10 bar. We found, in good agreement with the measurement shown in Fig. 4, that spectral broadening could be extended to 2.4 μm, but not further, due to resonant absorption within the ARR-PCF. Under these conditions, and taking the fiber dispersion calculated via the finite element method (FEM) into account, we estimated that $N$ equals 4.8.

 

Fig. 6. (a) Spectra measured at the output of a 14.9 cm long length of fiber and (b) the corresponding temporal profile. Both are shown as functions of the Ar pressure inside the fiber. The temporal information was obtained by retrieving the traces measured with the SH-FROG.

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Based on this information, we modelled the optimal condition for pulse compression in the ARR-PCF with a unidirectional full-field equation code [46], with photoionization rates calculated according to the Ammosov, Delone, Krainov (ADK) model [47]. As there are no reported measurements for the nonlinear refractive index $n_2$ at 3.3 μm, we used the value measured at 1.05 μm [48]. To include the contribution of the loss band to the dispersion, we used the effective refractive index obtained through a fit of the results of FEM calculations. We found that, in the absence of the loss band at $\sim 2.4\mathrm{\mu m}$, pulses with a single-cycle duration should be achieved upon propagation in a 12-cm-long fiber filled with $\sim 30\mathrm{bar}$ He. Because of the steep change in ${\beta }_2$ associated with the loss band, however, the self-compression dynamics are delayed and a medium with larger nonlinearity is needed to balance the linear dispersion of the fiber. The plot in Fig. 5 supports this as it shows that filling the fiber with Ar rather than He or Ne yields much shorter pulses, which approach the single cycle. Searching for conditions for best compression, the simulation predicted the generation of 14.3 fs pulses after 16.9 cm of propagation at 12 bar Ar (see Fig. 7).

 

Fig. 7. (a) Simulated spectral and (b) temporal evolution of the experimental input pulse along a 25-cm-long ARR-PCF filled with 12 bar Ar. The dashed lines show the experimental fiber length of 16.9 cm. (c) The spectral and (d) the temporal profiles for the fiber length of 16.9-cm-long ARR-PCF at the fiber output.

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Our experimental findings are in striking agreement with the simulations. The combination of 16.9-cm-long fiber and 12 bar of argon yielded a pulse duration of 14.5 fs, which corresponds to 1.35 optical cycles at 3.3 μm center wavelength. Figure 8 shows the results.

 

Fig. 8. (a) Measured spectral density (shaded profile), spectral profile (red), and spectral phase (green) retrieved from the SH-FROG trace. (b) The retrieved temporal profile (blue) and retrieved instantaneous frequency (red) showing that about 60% of the energy is contained in the main peak. (c) The measured and (d) retrieved SH-FROG traces.

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We note that the pulse exited the gas cell through a 3-mm-thick ${\mathrm{CaF}}_2$ window and propagated through about 1 m of dry air. We added a 0.5-mm-thick silicon plate to counter-balance most of the accumulated dispersion acquired from propagation through the ${\mathrm{CaF}}_2$ window and through dry air to the GaSe crystal of the SH-FROG. Numerical backpropagation to the fiber exit resulted in an only slightly increased pulse duration of 17 fs. This clearly proves that soliton self-compression was the mechanism responsible for the reduction to a single cycle of the input duration of 97 fs, and not self-phase modulation with post-compression. This compression scheme was remarkably efficient, introducing only 20% loss, thereby yielding 60 μJ output energy, which corresponds to a single-cycle mid-IR pulse with 9.6 W average power and 3.9 GW peak power.

4. SUMMARY

In conclusion, we have demonstrated a CEP-stable mid-IR OPCPA with chirp inversion that delivers pulses with 131 μJ energy at a 160 kHz repetition rate and 21 W average power. We measured a pulse duration of 97 fs (sub-9 optical cycles) and an excellent pulse-to-pulse stability of 0.33% rms over 30 min, which corresponds to 288 million consecutive pulses. The laser output was compressed down to 1.35 cycles via soliton self-compression in a gas-filled ARR-PCF, yielding 14.5 fs pulses at 3.3 μm with 9.6 W average power. This unique system combines the highest demonstrated average power together with a single-cycle duration in the mid-IR and high peak power (3.9 GW) required for experiments in the strong-field regime. Furthermore, the fiber compressor offers the possibility of delivering mid-IR single-cycle pulses directly to a gas jet for high harmonic generation and possibly to control the harmonic spectrum via the soliton dynamics [49]. This system presents a significant step forward for the generation of coherent hard x rays and the subsequent access to the zeptosecond regime of light–matter interaction.