The carrier-envelope phase (CEP), $\varphi$, i.e., the phase shift between the absolute maximum of the carrier wave and the maximum of the envelope, plays a crucial role in attosecond physics [1–3] and strong-field light–matter interaction, such as control of high-harmonic generation (HHG) [4,5] and electron dynamics in atomic [6,7], molecular [8–11], and solid-state [12,13] systems. It can be measured by a number of techniques, such as $f\text{-}2f$ interferometers [14] or analysis of HHG spectra [15]. In the last few years, the carrier-envelope phasemeter (CEPM), which is based on the measurement of stereographic above-threshold ionization (ATI) spectra, specifically in the plateau region [16], has proven to be a robust, precise, real-time, and single-shot CEP measurement technique [17–20]. A specific feature of the stereo-ATI CEPM is the ability for simultaneous characterization of the pulse duration. The CEPM has proven to be particularly useful in the so-called phase-tagging scheme [20,21], where CEP-dependent effects are measured with laser pulses having randomly varying CEP by correlating the events with the output of a CEPM. However, the stereo-ATI CEPM has, so far, largely been confined to wavelengths close to 0.8 μm due to the dynamics underlying ATI [22].

Increasing the driving laser wavelengths in strong-field physics is interesting from multiple perspectives. For example, the ponderomotive energy $U_p$ grows with the wavelength, $U_p\propto I·{\lambda }^2$, where $I$ is the laser intensity and $\lambda$ is the center wavelength of the laser field. The increased $U_p$ thereby increases the cutoff of high-harmonic spectra at $I_p+3.17U_p$, where $I_p$ is the ionization potential [23,24]. As a consequence of increased photon energy and bandwidth in the extreme ultraviolet, shorter attosecond pulses can be obtained [25]. For the CEPM, however, longer wavelengths result in a dramatic reduction of the high-energy ATI-plateau electrons that are utilized for the CEP measurement. This is demonstrated in Fig. 1 where CEP-averaged ATI spectra of xenon at 1.8 μm and 0.8 μm, measured by a high-resolution time-of-flight (TOF) photoelectron spectrometer [20,21], are compared. The physical reasons are: (i) larger wavelengths lead to longer travel times between ionization and rescattering such that stronger electron wave packet spreading [26] decreases the return current density, and (ii) larger kinetic energies of the photoelectrons due to the increased $U_p$ cause a lower rescattering probability. In addition, technical aspects such as the reduction of the photoelectron flight times due to their larger kinetic energies make the CEP measurement more challenging.

 

Fig. 1. CEP-averaged ATI spectra of xenon at 1.8 μm and 0.8 μm [21]. The energy is plotted in units of the ponderomotive energy $U_p$. The peak intensity for both measurements is $\sim 0.8\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$.

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In this Letter, we report on the development and implementation of a CEPM based on stereo-ATI in xenon and operating at short-wave infrared (sw-IR) wavelengths around 1.8 μm. By evaluating the normalized differences of the spatial asymmetry in two energy intervals in the ATI spectra, a parametric asymmetry plot (PAP) can be obtained, as detailed below. The pulse length can be inferred from the mean radius of the PAP and referenced to a frequency-resolved optical gating (FROG) [27] measurement. The precision of the CEP measurement is determined by the standard deviation of the radial distributions in the PAP. The performance of the 1.8 μm CEPM is proven by phase-tagging experiments. To this end, an independent high-resolution TOF photoelectron spectrometer is used to measure the CEP-dependent ATI spectra of xenon at 1.8 μm.

The experimental setup for CEP measurement in the short-wave infrared is shown in Fig. 2(a). It includes the generation of few-cycle pulses, the CEP-tagging experiment, and a FROG device as a reference for the measurement of the pulse duration. A commercial optical parametric amplifier (OPA) (HE-TOPAS) is pumped by 9.5 mJ, 35 fs laser pulses from a Ti:sapphire, chirped-pulse amplification system at a repetition rate of 1 kHz to produce 1.5 mJ, 60 fs idler pulses with a center wavelength around 1.8 μm. Compression to the few-cycle regime is achieved by nonlinear spectral broadening in an argon-filled differentially pumped hollow-core fiber [28]. The spectral phase is corrected by transmission through a pair of adjustable fused silica wedges [29]. By changing the gas pressure and adjusting the thickness of the glass in the beam path accordingly, nearly Fourier transform-limited pulses of different pulse lengths are generated. A flip mirror (M1) is used to switch the beam path between the CEPM and a homebuilt FROG that is used for conventional characterization of the pulse duration. For the phase-tagging measurement, the flip mirror is replaced by a 50/50 beam splitter, sending half of the beam to the CEPM for measuring the CEP and the other half to the high-resolution TOF spectrometer. Three independent pairs of fused silica wedges (W1, W2, and W3) are used to compensate the dispersion to obtain shortest pulses in each beam path. Focusing into the CEPM is facilitated by an $f=200\mathrm{mm}$ focusing mirror. The pulse energy is controlled by an adjustable aperture.

 

Fig. 2. (a) Experimental setup for CEP measurement and CEP tagging at sw-IR wavelengths. (b) An example for a pair of single-shot ATI spectra detected by the CEPM and (c) a parametric asymmetry plot for 20,000 consecutive laser shots obtained from the respective ATI spectra. 13 fs pulses at 1.8 μm and a peak intensity of $\sim 0.8\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$ were used.

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In the CEPM, the gas target is ionized by the laser and the photoelectrons emitted to the left and right within a cone angle of $\sim 5°$ (defined by the detector geometry) around the polarization axis of the laser are detected. The corresponding time-dependent currents are detected using micro-channel plates (MCPs) for every single laser shot. A photodiode is used to generate the trigger signal. Using the knowledge of the phasemeter’s geometry, the time-dependent photoelectron currents on the left and the right side are converted to photoelectron spectra, $S_l(E)$ and $S_r(E)$ ($E$ denotes the photoelectron energy). An example for a pair of measured single-shot ATI spectra is given in Fig. 2(b). A static repelling voltage in front of the MCPs is applied to discriminate the photoelectrons with energies below 65 eV such that only high-energy plateau electrons with strong CEP dependence are detected.

In order to extract the CEP from single-shot ATI spectra, two energy regions, i.e., one at low and one at high energy, are selected, see Fig. 2(b). Integration of $S_l(E)$ and $S_r(E)$ in each of the regions yields four quantities, $Y_{\mathrm{low}\_l}={\int }_{ll}^{lh}{S}_l(E)\mathrm{d}E,Y_{\mathrm{high}\_l}={\int }_{hl}^{hh}{S}_l(E),Y_{\mathrm{low}\_r}={\int }_{ll}^{lh}{S}_r(E)\mathrm{d}E$, and $Y_{\mathrm{high}\_r}={\int }_{hl}^{hh}{S}_r(E)\mathrm{d}E$ with $ll,lh,hl$, and $hh$ denoting the energy boundaries of the selected regions. By taking the normalized difference between left and right for each of the energy regions, two asymmetry parameters, $A_{\mathrm{low}}=(Y_{\mathrm{low}\_l}-Y_{\mathrm{low}\_r})/(Y_{\mathrm{low}\_l}+Y_{\mathrm{low}\_r})$ and $A_{\text{high}}=(Y_{\mathrm{high}\_l}-Y_{\mathrm{high}\_r})/(Y_{\mathrm{high}\_l}+Y_{\mathrm{high}\_r})$ are obtained. The asymmetries $A_{\mathrm{low}}$ and $A_{\mathrm{high}}$ have approximately sinusoidal CEP dependence. The energy intervals are selected such that two asymmetries have a phase difference of $\pi /2$, i.e., $A_{\mathrm{low}}\approx A_0\sin (\varphi +{\varphi }_0)$ and $A_{\mathrm{high}}\approx A_0\sin (\varphi +{\varphi }_0+\pi /2)$. Here, $A_0$ is the amplitude of the asymmetry, $\varphi$ is the CEP, and ${\varphi }_0$ is an arbitrary, but constant, offset phase. The so-called PAP is obtained by plotting ($A_{\mathrm{low}}$, $A_{\mathrm{high}}$) for every single laser shot as $x$- and $y$-coordinates, where the polar angle, $\theta$, corresponds to the CEP, $\varphi$. As a decreasing pulse length increases the asymmetry, the radius of the PAP, $r=A_0$, can be utilized to characterize the pulse length. An example of a PAP for 13 fs (2.1 cycles) pulses at 1.8 μm with 20 thousand consecutive laser shots is shown in Fig. 2(c). The boundaries of the low- and high-energy regions are optimized to (i) maximize the radius of the PAP, $r$, and (ii) minimize the standard deviation of the distribution in the PAP, $\mathrm{\Delta }r$. This is because the precision of the CEP measurement, $\mathrm{\Delta }\varphi$, which is dominated by the statistical error of the measurement, i.e., the electron yield in the region of interest, which in turn is limited by the gas density in the phasemeter. A good estimate is $\mathrm{\Delta }\varphi \approx \mathrm{\Delta }r/r$ [18].

As in Fig. 1, the yield of the high-energy ATI plateau at 1.8 μm is 1–2 orders of magnitude lower than that at 0.8 μm. In order to achieve single-shot, high-precision CEP measurement at 1.8 μm, a sufficiently high number of high-energy, backscattered photoelectrons must be generated per laser shot. The general rescattering probability roughly scales with $\sim {\lambda }^{-4}$ [22]. In order to obtain the same number of plateau electrons at long wavelengths, a larger ionization volume and/or higher target gas density are required to compensate for this factor. In our measurements, the pulse energy in the CEPM was $\sim 300\mathrm{\mu J}$, which is roughly 10 times larger than at 0.8 μm [20]. This energy increase cannot fully compensate the factor of ${\lambda }^{-4}$. Therefore, the openings, which allow ionized electrons to leave the gas target cell and enable differential pumping, have been reduced in size to roughly double the target density. However, the smaller openings make alignment more demanding.

The PAP distributions at different argon pressures inside the hollow-core fiber, and thus different pulse lengths, are shown in Fig. 3(a). For each gas pressure, 20,000 consecutive laser shots are recorded. Figure 3(b) shows the full width at half-maximum in intensity pulse length of few-cycle laser pulses at 1.8 μm measured by the FROG at different pressures together with the corresponding mean radius of the PAP obtained from the CEP measurement. For the FROG measurement, the wedges, W2 [Fig. 2(a)], are adjusted such that the shortest pulse length in the FROG setup is achieved, while the wedges, W1, are tuned to maximize the radius of the PAP. The Fourier transform-limited pulse duration is computed from the measured spectra. At low pressures ($<0.4\mathrm{bar}$), the pulse cannot be compressed to the Fourier transform-limit (FTL) as the pulses have negative group delay dispersion (GDD) after the OPA and thus cannot be compensated by fused silica, which also has negative GDD around 1.8 μm. Accordingly, the CEP measurement is not possible in this pressure range due to the long pulse durations. Starting from 0.4 bar, the pulse can be compressed close to the FTL due to the increase of the positive GDD provided by the nonlinear interaction inside the argon-filled fiber. For higher pressures, the GDD can still approximately be compensated with the wedges. However, the introduction of additional higher-order dispersions leads to a larger deviation from the FTL. At pressures larger than 1.2 bar, filamentation near the entrance of the fiber increases the fluctuations and introduces high-order nonlinear distortions of the spectral phase that cannot be compensated by transmission through the wedges only. This impedes the generation of usable PAPs.

 

Fig. 3. (a) Different PAP distributions at different argon pressures inside the hollow-core fiber. (b) The pulse length, $\tau$ measurement based on FROG, the PAP radius, $r$ at different pressures, and the Fourier transform limit (FTL) of the pulse duration. In (a), the corresponding pulse durations are 16 fs, 13 fs, and 11 fs for the pressures of 0.65 bar, 0.91 bar, and 1.20 bar, respectively. (c) The mean radius of the PAP, $r$ for pulses with a FTL of 10 fs at different thicknesses of the wedges in the beam path. (d) The mean radius of the PAP, $r$ and the corresponding precisions of the CEP measurement, $\mathrm{\Delta }\varphi$ at different pulse lengths. The pulse energy inside the CEPM is $\sim 300\mathrm{\mu J}$. The fitted lines are supposed to guide the eye but do not have an underlying physical model. The fitted relationship between the radius of the PAP, $r$, and the pulse duration, $\tau$, at 1.8 μm is $\tau =25.74r^2-39.12r+25$. For 1.8 μm wavelength, one optical cycle is $\sim 6\mathrm{fs}$. Thus, the pulse length ranges from 1.7 to 3 cycles.

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As mentioned above, the pulse length can be characterized by the radius of the PAP distributions, $r$, and the precision of the CEP measurement, $\mathrm{\Delta }\mathrm{\varphi }$, was found to be approximately determined by the relation $\mathrm{\Delta }\mathrm{\varphi }\approx \mathrm{\Delta }\theta \approx \mathrm{\Delta }r/r$ [18]. By analyzing these parameters during fine tuning the thickness of the wedges in the beam path, one can distinguish whether the pulse length is minimized at different experimental conditions. Figure 3(c) shows the mean radius of the PAP and the corresponding precisions of the CEP measurement at 1.2 bar argon in the fiber with different thicknesses of the wedges in the beam path. Here, the thickness of the wedges is defined as 0 for the shortest pulse, i.e., the largest radius of the PAP. Negative thickness of wedges means less glass in the beam path leading to positively chirped pulses and vice versa. For each measurement in Figs. 3(a), 3(b), and 3(d), the pulse length is minimized as outlined above. Figure 3(d) shows the mean radius of the PAP and the corresponding precisions at different pulse lengths. The quadratic fits, i.e., the dashed lines, are used to guide the eye and give an approximate expression for the relation between the radius and the pulse duration. Taking the 11 fs pulse as an example, the standard deviation $\mathrm{\Delta }r$ is $\sim 0.07$ and the mean radius $r$ is $\sim 0.55$. Thus, the precision of the CEP is $\sim 120\mathrm{mrad}$ ($\sim 8\mathrm{deg}$).

In order to demonstrate and validate the CEPM for CEP-tagging measurements with randomly varying few-cycle 1.8 μm pulses, an independent TOF photoelectron spectrometer is used to measure the CEP dependence of ATI spectra of xenon. This spectrometer has a five-times-longer flight tube and a four-times-higher temporal resolution. In addition, the target gas pressure is 3 orders of magnitude smaller as compared to the situation in the CEPM. Therefore, this spectrometer is well-suited for high-resolution photoelectron spectroscopy, but not single-shot phase measurement. The experimental setup is shown in Fig. 2(a). Figure 4(a) shows the CEP- and energy-dependent photoelectron yield measured by the TOF spectrometer. Figures 4(b) and 4(c) show the ATI spectra of xenon with different CEPs. The $10U_p$ cutoff of the ATI spectra is around 225 eV, corresponding to a peak intensity around $0.75\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$ at 1.8 μm. A strong CEP dependence of the spectra is observed at 50 eV, which is above the $2U_p$ cutoff for direct electrons [22]. The CEP- and energy-dependent asymmetry is calculated from the measured yield, shown in Fig. 4(d). To our knowledge, these are the first phase-resolved ATI spectra of xenon at 1.8 μm wavelength.

 

Fig. 4. (a) CEP- and energy-dependent ATI yield in xenon at 1.8 μm measured by a high-resolution TOF photoelectron spectrometer. (b), (c) The ATI spectra with different CEPs. (d) The CEP- and energy-dependent asymmetry for the CEP tagging. The pulse duration in this measurement is $\sim 14\mathrm{fs}$ and the peak intensity is $\sim 0.75\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$.

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We reported on the development and implementation of carrier-envelope phase measurement of few-cycle pulses based on stereo-ATI in xenon at 1.8 μm laser wavelength. The pulse duration of few-cycle laser pulses is characterized by the mean radius of the PAP and calibrated with a FROG measurement. The precision for the CEP measurement is 120–150 mrad for pulses with 10–15 fs (1.7–2.5 cycles) duration and the pulse energy consumption is $\sim 300\mathrm{\mu J}$. The CEPM has been operated at a repetition rate of 1 kHz, which is limited by the laser system. New electronics for the CEPM will allow repetition rates up to 100 kHz. In addition, CEP tagging has been demonstrated by the measurement of the CEP-dependent ATI spectra of xenon using an independent high-resolution TOF photoelectron spectrometer. The demonstrated achievements open new opportunities to investigate and control CEP-dependent effects with few-cycle fields in the sw-IR spectral range.