1. Introduction

Recent progress in the development of intense long-wavelength light sources has opened the doorway to the generation of keV high harmonics from gas [1] as well as above-bandgap high harmonic generation in solids [2–6]. Especially, an intense long-wavelength electric field is advantageous for strong-field experiments in solids, because its photon energy is much lower than their band gap energy so that a high electric field can be applied without causing optical damage. Femtosecond optical pulses in the mid-infrared (MIR) spectral region are more favorable than sub-picosecond THz pulses that can produce a field strength of more than 1 MV/cm nowadays [7], because better focusability and shorter pulse duration of the MIR optical pulses allow to achieve much stronger electric fields. In addition, a shorter temporal period of MIR electric fields than THz fields offers an opportunity to access a coherent phenomenon before dephasing of strongly driven carriers and holes that occurs in less than ten femtoseconds Therefore, various intense MIR light sources have been developed recently [8–16]. So far, the generation of spectrally broad carrier-envelope phase (CEP)-stabilized seed pulses in the MIR region has been demonstrated using an IR optical parametric chirped-pulse amplifier, although their configuration is rather complicated [17].

In this development, CEP-stabilized MIR seed pulses are produced in intra-pulse difference frequency generation (DFG) of spectrally broadened pulses around 1.03 μm, which are obtained in a multiplate pulse compression (MPC) scheme [18–20] using a commercial Yb:KGW chirped-pulse amplifier. The output pulses of the Yb:KGW amplifier are compressed in a two-stage MPC approach [21, 22]. An initial pulse duration of 160 fs is shortened down to 40 fs in the first stage, then further compressed down to 6.5 fs in the second stage, allowing the generation of seed pulses up to 2.2 μm in wavelength based on intra-pulse DFG. The MPC provides an extremely broad spectrum in a relatively compact setup using 100-μJ-level femtosecond pulses. Therefore, it is advantageous for this intermediate pulse energy over other methods such as single-plate white light generation and gas-based spectral broadening. The single-plate filamentation can produce a white light with an input pulse of less than 10 μJ, which leads to too low spectral intensity to apply a DFG process afterwards. Gas-based hollow-core fiber or filamentation requires a sub-millijoule pulse energy, limiting its application to a low-repetition-rate laser system. Therefore, the MPC is a promising candidate to produce ultrashort femtosecond pulses as well as passively CEP-stabilized long-wavelength optical pulses with an intermediate repetition rate e.g. from 5 to 100 kHz. Megahertz-class, high-repetition-rate optical parametric amplifiers (OPA) have been realized by single-plate white light generation using a femtosecond oscillator as a pump source [23]. The CEP-stabilized MIR seed pulses generated by the intra-pulse DFG are then amplified in a wavelength-tunable KTiOAsO${ }_4$ (KTA)-based OPA from 2.7 to 3.8 μm. The energy and temporal duration of the KTA-based OPA output pulses range from 31 to 56 μJ and from 102 to 203 fs, respectively. The root mean square (RMS) value of their CEP errors is characterized to be 101 mrad for 2000 seconds in a single-shot f-to-2f interferometer.

2. Two-stage MPC for MIR seed generation

The output pulses (1 mJ, 160 fs, 1030 nm, 6 kHz) of a Yb:KGW chirped-pulse amplifier (PH1-SP-1mJ, Light Conversion) are used to generate passively CEP-stabilized seed pulses based on two-stage MPC and to pump a two-stage KTA-based OPA. We split off 200-μJ pulses for the MPC shown in Fig. 1. The split pulses are focused by a lens (f=300 mm) after reducing the pulse energy to 120 μJ to avoid sporadic optical damage on a first plate. A fused silica (FS) plate with a thickness of 0.5, 0.7, 1.0, or 2.0 mm is easily available with reasonable optical quality. In the first MPC stage, 1-mm-thick plates are found to be thinnest for sufficient self-focusing without optical damage, probably due to a long pulse duration (160 fs) from the Yb:KGW amplifier. In general, even number of plates is preferable to avoid aberration or chromatic dispersion with the Brewster geometry. In our case, four 1-mm-thick plates are found to be most effective rather than two or six plates. Two plates results in insufficient spectral broadening and six plates do not enhance the spectral width so much compared with the four-plate case. In the first MPC stage, a transmitted energy of more than 60 μJ is measured after selecting out a spatially homogeneous central part of the beam.

 

Fig. 1 Two-stage MPC of the 160-fs, 120-μJ pulses around 1030 nm down to 6.5 fs. FS1, 1-mm-thick fused silica plates; FS2, 0.5-mm-thick fused silica plates; FS3, 0.7-mm-thick fused silica plates; GTI, Gires-Tournois-interferometer mirror; AU, gold mirror; DFG, difference frequency generation crystal; CM1, 2, chirp-mirror pair; FROG, second-harmonic generation-based frequency-resolved optical gating apparatus.

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Intermediate pulse compression is achieved by two reflections on a Gires-Tournois interferometer mirror (89446, Edmund Optics). This compression introduces a negative group delay dispersion of -1200 fs${ }^2$ from 1020 to 1060 nm (-600 fs${ }^2$ per reflection). Using second-harmonic generation-based frequency-resolved optical gating (SHG-FROG) apparatus, the dispersion compensated pulses are characterized to be compressed down to ∼ 40 fs, close to the Fourier-transform-limited pulse duration within 10%.

The compressed pulses are focused again in the second MPC stage, which consists of four 0.5-mm-thick and four 0.7-mm-thick FS plates. It is noted that spectral broadening in the second half of the second MPC stage is significantly enhanced by employing the 0.7-mm-thick FS plates compared to 0.5-mm-thick FS plates. This fact indicates that a thicker plate placed after a thinner plate is advantageous to lengthen a self-confined interaction range and enhance spectral broadening further by compensating the decrease of the laser power due to the loss and the chirp of the optical pulses. The position of the FS plates with respect to the focal point is summarized in Table 1. More than 30-μJ pulses are obtained after the eight FS plates and a diaphragm to select out a spatially homogeneous center part of the beam. The output pulses from the second MPC stage are characterized by SHG-FROG to be positively chirped with a residual group delay dispersion of 200 fs${ }^2$ at 750 nm and 0 fs${ }^2$ at 1300 nm. This chirp is compensated using a pair of chirp mirrors (CM1 and CM2 in Fig. 1, Tokai Optical Co. Ltd.). After totally four reflections on the chirp mirror pair (two reflections on each of CM1 and CM2), 6.5-fs, 30-μJ pulses are obtained with reasonably weak pedestals as shown in Fig. 2. The FROG result shows that the retrieved spectrum spans from 800 to 1250 nm, allowing the generation of MIR optical pulses at a wavelength longer than 2200 nm in intra-pulse DFG. Using a Yb-based laser, this result demonstrates the generation of sub-two-cycle pulses with much less pedestals around the main peak and a much higher throughput without using a programmable pulse shaper than the previous demonstration of 3.1-fs pulse generation [22].

Table 1. Distance between a fused silica plate and the focus position. The first MPC stage (FS1) consists of four 1-mm-thick fused silica plates. The second MPC stage consists of four 0.5-mm-thick (FS2) and four 0.7-mm-thick (FS3) fused silica plates.

View Table

 

Fig. 2 Characterization of the compressed pulses with the two-stage MPC. The SHG FROG error is 1.1 %. (a) Retrieved spectral intensity (black solid curve) and phase (black dashed curve) and the spectrum measured by spectrometers (USB2000, NIRQuest512-2.5, Ocean Optics) (blue curve). Note that the FROG measurement and the spectral measurement by the spectrometers are not performed in the identical condition, but, in a similar condition.

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3. KTA-based OPA seeded by CEP-stabilized MIR pulses

Spectrally broadened pulses in the two-stage MPC are sent to a half-wave plate to rotate the polarization of spectral components around 0.88 μm and, then, focused into a 2-mm-thick KTA crystal (type II, $\theta \sim$ 40 degrees, e.g. 0.88 μm (o) → 1.2 μm (e) + 3.3 μm (o)) to generate passively CEP stabilized MIR pulses. The seed pulses are sent to a KTA-based two-stage OPA as illustrated in Fig. 3. Note that the positively chirped pulses from the MPC are not compressed because the DFG process compensates the differential group delay between the 0.88 μm (o) and 1.2 μm (e) spectral components. The seed pulses are amplified to approximately 4 μJ in the first OPA stage that consists of a 4-mm-thick KTA crystal pumped by 80-μJ pulses at 1030 nm with a peak pump intensity of 89 GW/cm${ }^2$. The phase matching condition is fulfilled in type II ($\theta \sim$ 41 degrees, 1.03 μm (o) → 1.5 μm (e) + 3.3 μm (o)), which is used in the second stage as well. After the second OPA stage that consists of a 4-mm-thick KTA crystal pumped by 720-μJ pulses at 1030 nm with a peak pump intensity of 86 GW/cm${ }^2$, the MIR pulses are further amplified to more than 30 μJ in a wavelength rage from 2.7 to 3.8 μm.

 

Fig. 3 MIR-OPA. MPC, two-stage multi-plate pulse compressor; DFG, difference frequency generation crystal; OPA1, first optical parametric amplifier stage; OPA2, second optical parametric amplifier stage.

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Fig. 4 Wavelength tunability of the MIR OPA. We characterize the wavelength-dependent output energy plotted by the black curve in the upper panel. SHG-FROG measurement is performed to obtain the pulse duration (pink curve in the upper panel) and the spectrum (lower panel) at each center wavelength.

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We examine wavelength tunability of the OPA output as shown in Fig. 4. The spectral width of the OPA output pulses is mostly determined by the phase-matching condition in the KTA-based OPA. The central wavelength of the amplified output is tuned by rotating the two KTA crystals in the OPA without rotating the KTA crystal for the intra-pulse DFG. After the phase-matching angle tuning, the delay between the pump and seed pulses is finely adjusted to confirm the temporal overlaps between the seed and pump pulses. In a wavelength range from 2.8 to 3.4 μm, the pulse energies are measured to be more than 45 μJ. The maximum and minimum output energies are 56 μJ at 3.0 μm and 31 μJ at 3.8 μm, respectively. The wavelength dependences of the pulse width (pink curve in the upper panel of Fig. 4) and the normalized spectrum (lower panel of Fig. 4) are obtained by SHG FROG measurements. The shortest and longest pulse durations are measured to be 102 fs at 3.72 μm and 203 fs at 2.81 μm, respectively.

 

Fig. 5 CEP stability characterization by a single-shot f-to-2f interferometer. A CaF${ }_2$ wedge pair is used to shift the interference fringe, verifying that the fringe pattern originates in the f-to-2f signal. This verification is performed in acquisition times of less than 50 seconds. The RMS value of the CEP errors is 101 mrad for 2000 seconds.

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4. CEP stability characterization

CEP stability of the KTA-based OPA output pulses around 3.1 μm is characterized in a single-shot f-to-2f interferometer. The MIR pulses are focused into a 5-mm-thick yttrium aluminum garnet plate to obtain an octave spanning spectrum, the red components of which are frequency-double in a 100-μm-thick β-barium borate [24] to be combined with the blue components of the spectrum by a polarizer. Figure 5 shows the f-to-2f spectra with the clear interference fringe for more than 2000 seconds. All spectra are acquired with intervals of 1 second. In front of the f-to-2f interferometer, we inserted a CaF${ }_2$ wedge pair to confirm the origin of this interference. The wedge pair is moved at the beginning of data acquisition (<50 sec) as can be seen in Fig. 5. The RMS value of the CEP errors is calculated to be 101 mrad for 2000 seconds.

5. Conclusion

We developed a KTA-based OPA in the MIR spectral region using a commercial Yb:KGW chirped-pulse amplifier. The output pulses from the Yb:KGW amplifier are sent to a two-stage MPC, resulting in spectral broadening spanning from 0.8 to 1.25 μm at ∼10 % intensity with respect to the peak of the spectrum. The spectrally broadened pulses are compressed down to a sub-two-cycle duration of 6.5 fs using a customary designed chirp-mirror pair. CEP-stable seed pulses are produced in intra-pulse DFG of the spectrally broadened pulses. The seed pulses are amplified in the KTA-based OPA with a wavelength-tunability between 2.7 and 3.8 μm. Their output energy and temporal duration range from 31 to 56 μJ and from 102 to 203 fs, respectively. The RMS value of their CEP errors is characterized to be 101 mrad for 2000 seconds. These results provide a versatile platform for a waveform-controlled MIR light source operating at a wavelength of longer than 2.2 μm. Waveform-controlled MIR light sources are a promising candidate for strong field experiments and sub-cycle spectroscopy in solids [25]. Furthermore, this platform can be directly applicable to potential applications such as (i) a broadband parametric amplifier in the MIR region [17], (ii) a front end of a millijoule-class MIR light source for high harmonic and attosecond pulse generation in a keV photon energy, and (iii) MIR generation for a spectral range from 5 to 12 μm using with LiGaS${ }_2$ or LiGaSe${ }_2$ crystals [12, 26–31] as well as beyond 12 μm with GaSe crystals.