Control over the carrier-envelope offset frequency and its time-domain counterpart, the carrier-envelope phase (CEP), on the one hand, allowed for the link between optical and microwave domains with unprecedented precision, leading to important advances in metrology [1,2]; on the other hand, allowed for the stabilization of the electric field waveform of optical pulses, with major developments in strong-field physics [3]. Controlling the precise optical waveform enabled the generation and shaping of attosecond optical pulses via high harmonic generation and sparked a demand for ultrafast CEP-stable single-cycle sources in the near-infrared (NIR) [4]. A recent frontier in the development of novel single-cycle sources is the mid-infrared (MIR) spectral region, which opened the door to attosecond pulses spanning the soft x ray region or controlling states of solid matter [5,6]. Despite scientific motivation, the generation of milliwatt-level few- to single-cycle MIR pulses has proven difficult, and many different approaches have been explored [7]. One viable approach is to rely on parametric downconversion based on very mature and robust ytterbium pump laser technology. Krogen et al. implemented a first demonstration of single-cycle ultrabroadband MIR pulses through adiabatic difference frequency generation (ADFG) [8]. The benefit of adiabatic frequency conversion is that the MIR pulse inherits directly the amplitude and phase of the input NIR pulse [9]. This allows for tight control of the output MIR pulse properties by controlling the properties of the input NIR pulse. Remarkably, this allows one to precisely predict the MIR dispersion after the conversion process independent of seed intensity and spectral phase. Using this novel frequency conversion technique, Krogen et al. generated 11-fs pulses at a central wavelength of 2.8 µm with a pulse energy of 1.5 µJ and a repetition rate of 1 kHz, corresponding to 1.5 mW. To achieve such a short pulse duration, the system featured an acousto-optical programmable dispersive filter (AOPDF), including a grism compressor, allowing to shape the near-IR input. To compensate for the high losses introduced by the AOPDF setup, it was necessary to implement a two-stage NIR OPCPA scheme. This implementation allows compensating for higher-order dispersion of the ADFG process and for full pulse shaping of the MIR output around the optimum compression point. The carrier-envelope phase stability of pulses generated via adiabatic frequency conversion has not yet been characterized. This is extremely important for field-controlled experiments, which require tight control over the CEP while preserving a quasi-single-cycle waveform [4,10,11].

Here, we report a high repetition rate implementation of a passively CEP-stable adiabatic frequency downconverter, relying only on material dispersion to compensate for the large ADFG dispersion and compress the octave-spanning MIR pulses to 16 fs at a center wavelength of 2.7 µm. At a repetition rate of 50 kHz, we achieve a pulse energy of 84 nJ resulting in 4.2 mW of average power. A simple dispersion management scheme based on bulk materials offers robust operation of the laser system. At the core of the laser system is the adiabatic difference frequency generation process, which allows the conversion of a broadband NIR pulse into an octave-spanning MIR pulse mediated by a strong intermediate wavelength narrowband pump. Detailed background on ADFG is found in Refs. [8,9]. During an ADFG conversion process, the input pulse propagates through the adiabatically poled crystal, experiencing a slowly swept phase-matching condition that eventually crosses the $\Delta k=0$ phase-matching point for every wavelength within its spectrum (see Supplement 1) [9]. When the ideal phase matching is crossed, NIR waves at frequency $\omega _{NIR}$ undergo an almost instantaneous conversion into MIR waves at frequency $\omega _{MIR}=\omega _{NIR}-\omega _{Pump}$, called rapid adiabatic passage [9]. Therefore, the total ADFG dispersion $\tau _{ADFG}(\omega )$ as a function of frequency $\omega$ is considered to be the group delay of the NIR photon $\tau _{NIR}$ acquired until the phase matching point $z_c (\omega )$ plus the group delay $\tau _{MIR}$ acquired propagating as an MIR photon after the phase-matching point [8,9]. This can be summarized in the following analytic expression describing the resulting group delay in the mid-IR:

Our system design is shown in Fig. 1. The pump laser is a commercial Yb:KYW regen producing 420-fs duration pulses at a wavelength of 1.03 µm and a repetition rate of 50 kHz. We use 70 µJ of the available 120 µJ of pulse energy for our generation scheme. To generate a broadband NIR seed for the ADFG process, we use a noncollinear OPA. This OPA is pumped by the second harmonic of the laser fundamental (515 nm, 22 µJ, generated in 2-mm-long $\beta$-barium borate crystal) and seeded via white light (WL) generation in a 4-mm-long yttrium aluminum garnet (YAG) crystal [13]. The WL pulse is short-pass filtered with a cutoff at 900 nm and stretched by 2 mm of dense flint glass (H-ZF12) to match its duration to the duration of the OPA pump in the crystal. The OPA crystal is $\beta$-barium borate cut at $\alpha =$24.1° and 1.5 mm long). The angle between the pump and the seed is $\sim$2.4° inside the crystal. The center wavelength of the broadband amplified signal can be tuned by controlling the pump-seed delay via the insertion of a fused silica wedge in the pump beam path. The resulting NIR spectrum is shown in Fig. 2. The NIR signal with a central wavelength of $\sim$750 nm (see Fig. 2) has an energy of 1.8 µJ. To precompensate for the dispersion of the ADFG stage and the bulk material placed afterward, the NIR seed is initially stretched by bulk 2-mm H-ZF12 and 3-mm BK7. Afterward, an antireflection coated wedge pair of H-ZF12 with a thickness of 5 mm and a tuning range of $\pm$2 mm allows continuous control of NIR dispersion. The pulse duration of the NIR seed at the input of the ADFG is <1 ps. To avoid temporal walk-off during the ADFG process, the pump laser is stretched in a transmission grating stretcher to $\sim$10 ps. The pump pulse with 20-$\mathrm{\mu}$J energy is then shallowly focused a few cm in front of the crystal to allow for a large and slightly divergent mode of $\sim$0.75-mm diameter (at 1/e$^2$) and a peak intensity of <1 GW cm⁻² within the crystal. The NIR seed is focused in the center of the ADFG crystal with a mode size diameter of 280 µm (at 1/e$^2$) and collinearly propagates with the pump beam. This mode configuration sufficiently approximates a spatially homogeneous pump intensity perceived by the seed. The resulting MIR spectrum is shown in Fig. 2. In addition, we emphasize the great flexibility of the adiabatic downconverter supporting spectra at different central wavelength making it continuously tunable from 2 µm to 3.5 µm, see Supplement 1.

 

Fig. 1. Schematic system overview. The whole system consists of a pump laser at $1.03$-$\mathrm{\mu}$m wavelength distributing 60 $\mathrm{\mu}$J of energy to a white light, an OPA, and an ADFG stage. Bottom right corner inset shows a mid-infrared far-field beam profile after 2 m of propagation. YAG, yttrium aluminum garnet; H-ZF12, dense flint glass; BBO, $\beta$-barium borate; BaF$_2$, barium fluoride glass; FS, fused silica.

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Fig. 2. Optical seed and output spectra. Spectral intensities of the white light seed, the near-infrared input measured on an Si-CCD spectrometer, and the corresponding MIR spectra measured with a PbSe-CCD based spectrometer (Spectral Products, SM301EX, $\Delta \lambda = \sim$25–30 nm).

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The measured spectrum shows complete downconversion of the broadband NIR signal spectrum into an octave-spanning MIR spectrum, covering 2 µm to 4.5 µm. The MIR output reaches an average power of 4.2 mW corresponding to 84 nJ, which includes reflection losses during the compression process. To separate the MIR from the residual signal and pump light, a custom long-pass filter with a cutoff at 1.25 µm and 2 mm of Si at Brewster’s angle are used. The resulting MIR beam profile measured on a pyroelectric camera is shown in the inset of Fig. 1. For the final compression, 39 mm of barium fluoride (BaF$_2$) are inserted. To benchmark the pulse-to-pulse intensity fluctuations, we measured the MIR output over 1 s at a bandwidth of 80 kHz on a mercury cadmium telluride detector and recorded a relative intensity noise of 1.3 % root mean square (rms). See Supplement 1 for the data. The fluctuations can be explained as follows: the intensity noise of the pump laser fundamental is $\sim$0.5% rms. The SHG output pulse has therefore $\sim$1% fluctuation that is imprinted on the NIR OPA output (plus additional fluctuations from the white light). In the ADFG, the pump fluctuation should be irrelevant, while the NIR fluctuation will be directly imprinted on the MIR output. For the spectral phase characterization, we adapted two-dimensional spectral shearing interferometry (2DSI). In 2DSI, the MIR pulses are upconverted with two narrowband ancillaries with a shear frequency of 1.35 THz derived from the pump laser [14,15]. This allows the upconverted spectrum to be in the easy-to-detect NIR spectral region between 650 nm and 850 nm. The resulting 2DSI measurement is shown in Fig. 3. The derived group delay shows a reasonably flat behavior between 2 µm and 4 µm. Furthermore, we note that there are strong group delay oscillations at $\sim$2.7 µm, which originate from several known water absorption lines in this spectral band [16]. The temporal envelope of the compressed MIR pulse is retrieved by combining the calibrated spectral amplitude measurement with the retrieved group delay, as presented in Fig. 4 [17]. The MIR pulse duration is 16 fs that, at a center wavelength of 2.7 µm, corresponds to 1.7 cycles at FWHM, see Fig. 4 and Fig. 5. We attribute the precursor pulse appearing at a time delay of $t=$−60 fs, to residual third-order dispersion, effectively interfering the low- and high-frequency wings of the pulse in the time domain. The achieved pulse duration is only 1.14 times longer than the transform limited duration of 14 fs.

 

Fig. 3. Two-dimensional spectral shearing interferometry. Recorded interferogram of the compressed broadband MIR pulse and two narrowband ancillaries at 1.03 µm separated by 1.35 THz. The 2D color map is shown with logarithmic color scaling. The secondary $y$ axis shows the group delay (red line) retrieved from the shown interferogram.

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Fig. 4. Temporal shape. Pulse shape (blue) and phase (black) retrieved from the measured MIR spectrum and the measured group delay from Fig. 3.

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Fig. 5. Electric field transient. Electric field transient calculated from the measured MIR spectrum and the group delay from Fig. 3 at an arbitrarily chosen CEP.

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To characterize the carrier-envelope phase of the system, we set up an $f$–2$f$ interferometer that frequency doubles the long wavelength side of the octave spanning MIR spectrum in a silver thiogallate crystal (AGS) and creates spectral interference on the short wavelength side [18]. The spectra are recorded with a bandwidth of 3 Hz and an integration time of 2 ms, corresponding to an average over 100 individual pulses. The filtered interference pattern from the measurement is shown in Fig. 6(a) with the retrieved phase in Fig. 6(b). To verify the control of the CEP, we linearly sweep the relative phase between pump and seed in the ADFG stage by simply shifting the delay of the pump over 5150 nm (five times the pump wavelengths). This causes a highly linear shift of the interference pattern, which is also reflected in the retrieved phase. After 50 s, the phase sweep is stopped and the CEP is running freely for the rest of the measurement. As can be seen, already the passive stability of the CEP is high with less than 190-mrad rms over 15 min (see Supplement 1 for the full data range).

 

Fig. 6. CEP-control and open-loop stability. (a) $f$–2$f$ interferogram of the octave spanning MIR pulse. The first 50 s show a linear ramp of the CEP and 50 s to 5 min show a open loop CEP. (b) Relative CEP obtained from panel (a), showing the linear phase ramp and the open loop phase stability.

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In conclusion, we have demonstrated the first passively CEP stable implementation of an ADFG based MIR source that provides 1.7-cycle pulses at a central wavelength of 2.7 µm with an excellent passive CEP stability of 190 mrad. Remarkably, close to transform limited compression is achieved by using only propagation in bulk materials, which improves the inherent stability of the system. This demonstration further emphasizes that the inherent one-to-one pulse transfer in adiabatic frequency conversion techniques allows for simple compressor designs, due to the precisely predictable system dispersion. With that information, one can also design custom chirped mirrors that compensate for the specific dispersion of a given adiabatic frequency converter, enabling the compression of even broader spectra than those demonstrated in this work and full elimination of higher-order dispersion components. The presented setup is an excellent addition to many existing OPA sources that can convert broadband non-CEP stable NIR pulses to octave-spanning CEP stable few- to single-cycle pulses in the MIR. This source provides pulses with ideal characteristics for many nonlinear field-sensitive experiments in solids, such as petahertz electronics and field sampling [10,19].