Recent advances in petahertz electric field sampling

The ability to resolve the complete electric field of laser pulses from terahertz to mid-infrared spectral ranges has enriched time-domain spectroscopy for decades. Field-resolved measurements in this range have been performed routinely in ambient air by various techniques like electro-optic sampling, photoconductive switching, field-induced second harmonic generation, and time stretch photonics. On the contrary, resolving the electric field of light at the near-infrared spectral range has been limited to attosecond streaking and other techniques that require operation in vacuum. Recent advances are circumventing these shortcomings and extending the direct, ambient air field detection of light to petahertz frequencies. In the first part of this letter, recent field-resolved techniques are reviewed. In the second part, different approaches for temporal scanning are discussed, as the temporal resolution of the time-domain methods is prone to temporal jitter. The review concludes by discussing technological obstacles and emerging applications of such advancements.


Introduction
Laser has been a fundamental tool to simultaneously excite and interrogate dynamics in matter. In combination with the advances in the generation of laser pulses with ever shorter temporal duration, this unique property has allowed for mon- * Author to whom any correspondence should be addressed. 3 Present address: Deutsches Elektronen-Synchrotron (DESY), Notkestrasse 85, D-22603 Hamburg, Germany. 4 Present address: Université de Bordeaux-CNRS-CEA, CELIA, F-33405 Talence, France.
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When the temporal duration of a short pulse reaches the few-cycle regime, the relative phase offset between the envelope of the pulse and the fast oscillating electric field at carrier frequency becomes evident and crucial. Evaluation of the carrier-envelope phase (CEP) offset via f-2f interferometry [8,9] has enabled the precise control of the oscillating electric field under the envelope of a short pulse [10] and the emergence of the entirely new research field of frequency comb metrology [11][12][13]. In 2001, the first isolated attosecond pulses were generated from the interaction of CEP-stable, nearly single-cycle pulses and a noble gas, paving the path towards a better understanding of the ultrafast motion of electrons [14].
Limited by the bandwidth of the available technology for compensating the spectral phase of super-octave high energy pulses [15][16][17][18][19][20], shorter pulses and even light transients were generated by coherent field synthesis [21][22][23][24][25][26][27]. Here, by constructive interference of several few-cycle pulses at different carrier frequencies, temporally confined waveforms with a temporal duration shorter than individual pulses are generated. Furthermore, the waveforms can be shaped arbitrarily by fine-tuning the relative phase and amplitude between the superimposed pulses.
The electric field of ultrashort pulses upon interaction with media contains a detailed description of the internal dynamics of the atoms, molecules, or solids that it encountered. Resolving the electric field of light with sub-cycle resolution after it interacts with the sample under scrutiny allows obtaining precise time-frequency analyses of the system's dynamics. In particular, light transients offer an unprecedented degree of control over atomic-scale electronic motions and can induce dramatically different responses in the electronic system of matter [28][29][30][31][32].
But how can one measure and characterize such short pulses in the time domain? 'Isn't it that to measure a short event in time, you must use a shorter one?' [33]. Over the last decades, dozens of different techniques have been developed to characterize few-cycle pulses, which can be divided into two major categories: (i) techniques, which rely on the determination of the spectral amplitude and phase of the electric field , which have been even used for CEP stabilization [35,61,62], (ii) techniques for the direct measurement of the electric field of ultrashort pulses in the time domain, offering high temporal resolution [63][64][65][66][67][68][69][70][71][72].
A fast temporal gate (ideally with a duration below the halfcycle duration of the field oscillation to be measured) is the primary requirement for extending the detection bandwidth of field-resolved measurements to petahertz (PHz) frequencies.
In 2001, the generation of isolated attosecond pulses via high harmonic generation (HHG) [86,87] provided such short gate pulses and allowed for the direct measurement of the electric field at near-infrared (NIR) frequency ranges by attosecond streaking [31,88,89].
In a streak camera, upon the interaction of the attosecond pulses with the atoms of a noble gas, the ionised gas atoms emit free photo electrons. Simultaneously applying the sample field to the atoms accelerates the free electrons and shift their final momentum in proportion to the vector potential of the sample field at the instant of ionization. Therefore, the electric field of the sample pulse can be mapped by changing the temporal delay between the two fields, and recording the electron's momentum at a time-of-flight spectrometer. Alternatively, subcycle electron trajectories during the HHG process can be used to measure a light wave [90][91][92]. While powerful, these techniques require significant pulse energies for the HHG process, a costly time-of-flight spectrometer, as well as an expensive and complex high-vacuum setup in order to avoid the absorption of extreme ultraviolet (UV) pulses in ambient air. These technical challenges have limited their application and slowed down their practicality.
Over the past few years, various innovative solutions have been demonstrated, and remarkable progress has been made in developing alternative field-sensitive methods operating in ambient air. Like attosecond streaking, the majority of these field-sampling techniques rely on the use of a short auxiliary pulse providing a sub-cycle nonlinear gate, or on a strongfield response of matter, such as tunnel ionization, high-order harmonic generation or multi-photon excitation in solids. Figure 1 summarizes the common pulse characterisation techniques at optical frequencies and compares their performance in terms of sensitivity and frequency coverage. The offered detection sensitivity and bandwidth in field sampling techniques, in addition to their ambient air operation, pave the path not only for sub-cycle electron-dynamic interrogation of matter, but also for novel spectro-microscopic techniques with an unprecedented spatial and temporal resolution.
This review presents a summary of the growing field of field-resolved metrology at optical frequencies with an outlook on its emerging applications. In all the techniques described below, short laser pulses in combination with different nonlinear phenomena are used to probe the electric field of an arbitrary pulse. Throughout the paper we labeled the pulse/event which enables temporal gating the 'gate pulse/event' and the one that is being measured the 'sample pulse'.

Field sampling based on strong-field electron dynamics
In strong-field approximation for an atomic system [93], the strong-field interaction of light and matter can be described by the Keldysh parameter γ [94]: where ω is the carrier frequency of the strong field, F is the peak field strength, I 0 is the ionization potential of the gas medium, and e and m are the electron charge and effective electron mass, respectively. In solids, the strong-field approximation translates into the neglect of excitonic effects. The Keldysh parameter becomes: where E g is the transition bandgap. The presence of a strong electric field in a dielectric medium injects electrons from the valence band into the conduction band. The Keldysh parameter classifies adiabatic tunneling for γ 1, and frequencydependent multiphoton excitation for γ 1 [95][96][97][98][99][100][101][102][103]. Since for both, multi-photon absorption and tunneling ionization, high field strengths are required, the type of the transition is mainly dominated by the frequency of the incident wave.
Upon the interaction of an intense laser field with atoms, molecules, and solids at the tunneling regime, electron dynamics directly follow the electric field of the laser pulses, with exponential dependence. Therefore, they are temporally confined to subcycle timescales, making them suitable for serving as a fast gate for electric field sampling.

Photoconductive sampling in gas
In 2018, Park et al demonstrated how the tunneling ionization in a gas could generate an ultrashort gate event for resolving the electric field of an arbitrary sample pulse up to 1.5 PHz, limited by the absorption in the lightest gases of H and He [104]. The technique is based on tunneling ionization with a perturbation for the time-domain observation of an electric field (TIPTOE). Upon the interaction of an intense, sub-cycle laser pulse with a gas, the atomic potential is deformed. At each half-cycle of the laser pulses, part of the wave-function tunnels through the Coulomb barrier creating an electron wave packet, which is used as the fast temporal gate to probe the electric field of a sample pulse (E S ).
Due to the exponential dependence of the ionization rate at the peak of the pulse, the fast temporal gate can be temporally confined to 190 as [104]. When the weak arbitrary sample pulse is superimposed with the intense laser pulse at the same polarization direction, it gently perturbs the process of the tunneling ionization and consequently the total ionization yield by δN. For intense pulses as short as 1.5 optical cycles, the ionization event effectively occurs only at the peak of the electric field. Therefore, the modulation of the ionization yield becomes proportional to the field amplitude of the weak sample pulse: that can be measured directly as an electric current (see figure 2). Employing this technique, direct sampling of the electric field up to 0.6 PHz in ambient air [104] and over a wide spectral range spanning from UV to MIR [67] by collecting the ion current or the plasma fluorescence intensity [105] as a function of the time delay between the two pulses has been demonstrated.
As TIPTOE relies on field ionization, it is an utterly phasematching-free technique. Moreover, the method can resolve the electric field of multi-cycle laser pulses as long as the duration of the intense laser pulse is three times shorter than the transform-limited duration of the weak sample pulse [104]. However, TIPTOE requires intense nearly single-cycle pulses to generate a temporally confined gate. The two interacting pulses have to be CEP-stable, and the precision of the measurement is prone to their relative temporal jitter. Furthermore, the ionization yield can also be modulated by the power fluctuation of the laser pulses unless differential detection is employed.
Alternatively, photo-emitted electrons, which are generated via the interaction of a strong field and air, can be used to probe the electric field of an arbitrary sample pulse, similar to attosecond streaking [65,71]. Superposition of the strong field with a weak sample field induces an asymmetry in the angleresolved photo-emission of electrons. The induced current is measured by positioning two electrodes in the asymmetry plane.
Here the strong laser field has to be polarized along the direction of the electrodes to avoid any background signal. The weak waveform is polarized across the electrodes. It displaces the electrons toward one of the electrodes and separates them from positively charged ions. The separation leads to the formation of a dipole, which is screened by Weak sample pulses (E S ) are generated via second harmonic generation. The residual fundamental laser pulses (E F ) after second harmonic generation serve as the intense excitation pulse for field-sampling. A portion of the intense pulse is superposed with the sample pulse in air for direct electric field detection, where the ionization yield N 0 + δN is measured. The other portion is used as a reference arm for differential detection, where the ionization yield N 0 of the intense pulse is measured. BS: beam splitter; w: wedges; HWP: half wave plate; CP: compensation plate [104].
the metal electrodes and results in a measurable current (see figure 3). The electric field of the weak pulse is retrieved by recording the measured current at a different relative time delay of the two laser fields. Field sampling in air for frequencies up to 0.13 PHz was reported by employing this technique [71].
The induced asymmetry in angle-resolved photoemission can be caused by the combined action of the laser fields and the Coulomb potential of the ion on the electron. In the absence of the sample field, this asymmetry is parallel to the injection (gate) field (figure 3(b)), while the symmetry with respect to the field direction of the electrodes is broken by the driving field (figure 3(c)) [65]. The electrons undergo ponderomotive motion in the strong field direction, while they are being accelerated by the weak waveform, leading to a complicated Coulomb-laser-coupling. Similar to attosecond streaking, this coupling influences the relative timing of the signal [106][107][108]. The simulation results in [65] confirm that the measured signal as a function of time delay approximates the vector potential of the weak waveform, but with a significant delay. Similar to TIPTOE, this technique requires ultrashort, CEP-stable laser pulses with high field strength to probe the electric field of a weak pulse and is sensitive to the relative timing jitter of the two pulses.

Photoconductive sampling in solid
A strong laser field can induce rapid changes to the electronic properties of dielectric solids by transforming the dielectric into a state of highly increased polarizability [98]. The light-field-induced currents upon this interaction results in a macroscopic charge separation that is detectable in an external circuit. Due to the high nonlinearity of the carrier injection process in wide bandgap materials, mostly the optical cycles with high electric field strength contribute to this interaction. Therefore, the gate event is temporally well confined and effectively shorter than the driving pulse.
This temporary modification of dielectrics forms the basis of the field sampling method called nonlinear photoconductive sampling [63]. Here, a strong single-cycle gate pulse with 1 to 2 V Å −1 field strength interacts with crystalline quartz, which induces a transition from the filled valence to the empty conduction band. This transition probability is temporally confined to sub-fs duration and strongly localized to instants slightly after the peak of the electric field.
At the temporal overlap of the cross-polarized weak sample pulse and the intense laser field, the injected electron-holes are displaced in the band structure and form a macroscopic dipole. The induced dipole gives rise to a screening signal and thus a measurable current in the pair of electrodes. Scanning the relative delay between the two fields allows for the complete field characterization of the weak sample pulse from MIR to UV (figure 4). The rate of energy deposition in this scheme is approximately proportional to the eighth power of the electric field. Therefore, carrier injection is temporally confined to a sub-500 as time interval. The authors demonstrate up to 1 PHz sampling bandwidth at a detection dynamic range of 30 dB. Like gas-based techniques, CEP-stable, single-cycle pulses and temporal synchronization of the interacting pulses are prerequisites for resolving the electric field of arbitrary waveforms.
In an alternative study, a field-sampling technique based on the sub-cycle changes in the reflectivity of dielectrics, when subjected to a strong field was demonstrated [66]. A strong, few-cycle pulse with a field strength of 0.78 to 1.33 V Å −1 excites electron dynamics in a quartz crystal. In the reciprocal space and at the minimum bandgap (zone center), due to the coherent multiphoton excitation, the electrons can transit from the valence band to the conduction band at the peak of the electric field and are accelerated towards the Brillouin zone boundaries, following the vector potential of the driver field in the conduction band. As the sign of the electric field in the subsequent half-cycle changes, the electrons accelerate back to the other side of the Brillouin zone boundary crossing the zone center [109]. At the zone center, there is a possibility for population transfer from the conduction band back to the valence band, which results in a sub-cycle modulation of the refractive index. Hui et al demonstrate that probing the sub-cycle modulation of the reflectivity allows for the full reconstruction of the electric field of the strong pulse.
The probe pulse can be generated by using a mask to split the main pulse into two beams: intense sample pulses to induce the dynamic and weak pulses to probe the induced sub-cycle  Upon the interaction of a nearly single-cycle strong gate pulse and a quartz crystal, a transition from the valence to the conduction band in the material is induced. This transition is temporally restricted to field crests. In the presence of the orthogonally polarized weaker sample field, the light-field-induced currents result in a detectable macroscopic current between the gold electrodes [63]. reflectivity changes. The two beams are focused on a 100 μmthick quartz crystal. An optical spectrometer is used to measure the reflected spectrum of the probe beam from the sample at various delays (figure 5). The technique offers a broad detection bandwidth and is not restricted by phase mismatch. However, the detection sensitivity is restricted to the pulses with high-field strength.
In 2021, Liu et al reported on the first field-sampling technique based on electron tunneling in solids [69]. In a setup similar to TIPTOE, the solid-state TIPTOE technique employs tunneling or multiphoton excitation as a fast gate process. In the tunneling regime, an intense pulse with central frequency well below the bandgap excites the valence band electrons into the conduction band of a dielectric. The excitation fraction is perturbed by a weak sample pulse and its relative changes can be detected by monitoring the visible band fluorescence emission from the crystal surface on sub-nanosecond time scales (figure 6) [110,111]. The authors demonstrate full characterisation of an electric field with spectral components spanning from 2.9 μm to 4 μm and a few-cycle pulse centered at 1.1 μm.

Field sampling based on short optical gate pulses
Short optical probe pulses have been used to sample the electric field of waveforms from THz to MIR and recently to visible spectral range by EOS [24,59,73,[112][113][114][115][116][117][118][119]. The interaction of a laser field and a dielectric solid at critical field strengths results in its sub-cycle refractive index modulation due to multiphoton carrier excitation from the valance band to the conduction band, aswell as electron motion dynamics in the conduction band (shown in reciprocal space). (c) Experimental setup of the all-optical implementation. A spatial mask is used to split the main beam to two parts of different intensities: a strong pump to drive the strong field dynamics and a weaker probe to detect the resulting changes in refractive index. Subsequently the two beams are focused on a 100 μm thick SiO 2 crystal. A piezo-stage controls the relative delay between the two pulses. A spectrometer measures the reflectivity of the weak pulse at each delay point, while a polarizer and a one-hole mask enhance the signal-to-noise ratio of the reflectivity modulation measurements [66].
In EOS, gate pulses and sample pulses propagate collinearly in a nonlinear crystal. When the phasematching condition is fulfilled, new spectral components at the sum and difference frequencies of the two interacting pulses are generated, which have partial spectral overlap with the gate pulse [118,119]. The field-sensitive signal arises from the interference between the original gate photons and the newly generated photons, containing phase information similar to homodyne detection. Spectral short and long pass filters in this setup isolate the spectral region of the gate pulse that has overlap either with the sum or difference frequency signal [122].
In the absence of the sample pulse, an ellipsometer is designed in a way that the gate pulse is equally split on two photo diodes of a balanced detector, and the detected voltage is zero. A nonzero voltage is detected in the presence of the sample pulse, when the polarisation of the gate pulse is modified by interference with the newly generated components. This change in polarisation varies relative to the temporal delay between the gate pulse and the sample pulse ( figure 7(a)). This ellipsometric analysis of the interfering fields gives direct access to either the electric field of the sample field or its Hilbert transform [119]. The excess technical noise of the gate pulse is suppressed by a lock-in amplifier and the balanced detection, leaving the shot noise of the gate pulse the limiting factor on detection sensitivity.
The description of EOS is simplified, when the spectrum of the sample pulse lays within the far-infrared or THz spectral range. Here, the oscillation cycle of the sample pulse is significantly longer than the temporal duration of the gate pulse at NIR. The electric field of the sample pulse can be assumed to be a quasi-static electric field in relation to the gate pulse. This quasi-static field induces a birefringence in the crystal due to the electro optic effect (hence the name 'electro optic sampling'), resulting in a measurable change in polarisation of the gate pulse. This picture can be motivated by the nature of the electro optic effect, or Pockels-effect, as it is described by second order nonlinear mixing of two fields, where one of them is a static electric field. [73,123].
One way to enhance the detection sensitivity in EOS beyond the limitations imposed by the shot noise of the gate pulses is to use the overlapped region of the difference and sum frequency signals for phase information retrieval. As the complete interference between the sum and difference frequencies is only possible at the center of the gate spectrum, the suppression of the background relies on polarization filtering of the gate pulses ( figure 7(b)). Employing this technique allows for the complete retrieval of the sample pulse with high detection sensitivity, but with sign ambiguity [121].  The region with spectral overlap between the newly generated frequencies and the gate pulse are spectrally isolated. An ellipsometer detects the changes in the polarisation state of the gate pulse resulting from the interference with the newly generated frequencies. The sample pulse is periodically blocked to allow lock-in detection BC: beam combiner; QWP: quarter-wave plate; WP: Wollaston prism; BPD: balanced photodetector [120]. (b) The sample pulse E Sam , the gate pulse E g and the newly generated field E (2) . In this alternative detection scheme, the newly generated components are isolated using a band-pass filter (BP) and a polarizer (Pol.). This scheme does not require balanced detection. EOX: electro-optic crystal [121].
EOS offers an appealing detection sensitivity and dynamic range. Nonetheless, its direct extension towards multi-PHz frequencies would require a gate pulse with twice the frequency of the field to be sampled [116]. Generation, handling, and dispersion-free propagation of such pulses is a major challenge. GHOST, generalized heterodyne optical-sampling technique, addresses these deficiencies (see figure 8). In GHOST, the sum or difference frequency generation between the gate and the sample pulses provides a heterodyne signal, while the higher harmonics of the gate pulse act as a local oscillator. The phase information of the sample pulse is extracted upon the four-wave mixing interaction of the higher harmonics of the gate pulse and the heterodyne signal. The concept shares some similarities with air-biased-coherent-detection at THz range [124,125]. The detection bandwidth can be scaled to higher frequencies by choosing the higher harmonics of the Two pulses overlap in a nonlinear crystal: a sample field and a gate pulse. As a result, two waves are generated: a local oscillator (LO) resulting from nonlinear propagation of the gate pulse in the crystal, and a signal, which is the result of nonlinear mixing of both input pulses. These waves pass through a polarizer and a spectral filter and are detected using a photo diode [59]. gate pulse. However, the CEP of the retrieved waveform does not follow the CEP changes of the sample waveform. It has been demonstrated that field detection via GHOST supports up to 1.25 PHz detection bandwidth with a signal-to-noise ratio of approximately 30 dB [59].

Time scanning methods
All techniques which are described in this paper share a similar concept: the electric field of a sample pulse is resolved by monitoring the variations of a correlation signal, which is generated through a fast event at different temporal delays. Therefore, the measurement's precision depends on the temporal stability and the jitter between the two interacting pulses. The intrinsic synchronization between the two pulses are assured as they originate from the same source. However, additional temporal jitter is introduced by air turbulence, mechanical vibrations of optical components, temperature drifts and the finite stability of the frontend. In what follows, different available techniques for enhancing the temporal stability in field-resolved measurements are reviewed.

Interferometric delay tracking
Two conventional methods to temporally delay two pulses relative to each other are step-scan or rapid-scan techniques, where the temporal delay between two pulses is varied by moving a retro-reflector mounted on a mechanical delay stage. The position of the stage can be determined either by the linear encoder of the delay stage or by a Michelson-type sensor head for precise tracking of the stage movements [126,127]. However, in these techniques the recorded position does not represent the actual relative delay between the two pulses at the moment of interaction.
Alternatively interferometric delay tracking can be used to precisely track the relative delay. Here a phase modulated continuous-wave laser is coupled to the optical path of the sample pulse and the gate event from the moment of separation until their recombination. The exact optical path difference of the two arms is extracted from the interference signal via quadrature detection. The layout of a typical interferometric delay tracking setup is shown in figure 9. Employing this technique allowed for delay tracking with 10 as precision [120,128].  TWINS uses birefringence to generate a tunable time delay between two collinear pulses. First a flat block A introduces a constant negative delay between the two orthogonal polarisation components of the input pulse. Wedge pair B introduces a tunable time delay between the pulses. Wedge pair C corrects the wavefront tilt, the angular dispersion and allows dispersion tuning. This results in two cross polarised output pulses with a time delay t, that are projected on a common axis by a polarizer P [138].

Acousto-optic modulator delay line
The acousto-optic programmable dispersive filter (AOPDF), also known as Dazzler, consists of a birefringent crystal in which an ordinarily polarized laser pulse propagates collinearly with a polychromatic acoustic shear wave. Upon acousto-optic interaction, the pulse diffracts into the extraordinary axis depending on the applied acoustic signal. Since its first proposal by P Tournois [18], the AOPDF has been used not only for pulse shaping and dispersion control, but also as a rapid scanning delay line [129][130][131][132][133].
The working principle of an acousto-optical delay line is depicted in figure 10. Various temporal delays can be introduced by confining the acoustic wave to a wave packet smaller than the length of the crystal (blue area in figure 10). Since the speed of light inside the bulk medium is six orders of magnitude higher than the velocity of the acoustic wave packet, the position of the acoustic wave packet appears to be stationary for an incoming laser pulse. Between two consecutive laser pulses, the position of the acousto-optic interaction changes as the acoustic wave packet travels a certain distance inside the crystal. Due to the difference in the refractive index of the ordinary (n o ) and extraordinary (n e ) axis, the diffracted pulse propagates with a velocity different from the non-diffracted pulse. Therefore, the time difference between one pulse entering the crystal and the diffracted pulse leaving the crystal depends on the diffraction position. Since the speed of the shear acoustic wave v sound inside the crystal is known, the acoustic wave packet travels a distance Δx = v sound ν rep between two consecutive optical pulses with repetition rate ν rep . Consequently, the introduced time delay Δt increases with each laser pulse by One significant benefit of the acousto-optical delay line is its high stability and repeatability at scan frequencies ranging up to 36 kHz [131]. Since the delay line contains no moving parts, it is not prone to beam-pointing fluctuations. Furthermore, the difference in the time delay between two consecutive pulses (equation (4)) depends solely on material properties and the repetition rate of the laser.
The high stability of the delay line allows for interleaved scanning, where multiple cycles of the acousto-optical delay line are used to create one scan with a shorter step size between the sampled time delays. Here, the launch of the acoustic wave packet is delayed for each cycle by 1 k·ν rep with respect to the previous one, resulting in a factor of k more sample points and a smaller time delay step size. Schubert et al reported on a scan with k = 128 interleaved cycles at a repetition rate of 40 MHz and a single cycle scan rate of 34 kHz in a TeO 2 crystal. The authors achieved a temporal resolution of 39 as [129].
Since the acousto-optical delay line is in its nature an AOPDF, the acoustic pulse can still act as a dispersive filter for dispersion control or pulse shaping, while scanning the group delay. This has been used to compensate for dispersion [131,132] as well as for spectral focusing [133]. However, simultaneous phase compensation of few-cycle pulses in the delay line is not practical. Moreover, the bandwidth of the  acousto-optical delay line is limited to one octave with a diffraction efficiency inversely proportional to the spectral bandwidth, making their application for few-cycle pulses limited [131].

Scanning mechanical resonator
A rapid scanning delay line can be created by employing a reflecting surface such as a glued mirror or a coated gold layer onto the end surface of a mechanical resonator [134][135][136] (figure 11) [134,136]. For an incident train of pulses, the sonotrode delay line scans the optical path length from zero to the peak-to-peak amplitude, which is in the order of 100-200 μm, corresponding to a time delay of several hundreds of femtoseconds. Therefore, multiple reflections on the moving surface are required in order to increase the scanning range.
The step size and the duty time of the scan depends on the specific scanning frequency of the delay line and the repetition rate of the laser. Here, the scanning frequency is two times the frequency of the mechanical oscillation, since a scan can be performed in both directions. Typical values for resonant frequencies of such mechanical oscillators lay in the range of sev-eral tens of kilohertz. Due to its rapid mechanical movement, the sonotrode based delay line is prone to beam pointing fluctuations, where multiple reflections on the oscillating surface increase the influence of slight imperfections of the sonotrode, resulting in even higher fluctuations [136].

Translating-wedge-based identical pulses encoding system
Since conventional delay lines split a beam into two separate paths with different optical lengths, mechanical vibrations in one arm (e.g. due to a moving delay stage) may not affect the other beam path. Accordingly, such asymmetric mechanical vibrations between the two beam paths can result in fluctuations of the optical length difference. This can lead to additional jitter in the introduced time delay between the pulses. A common path delay line, like the translating-wedge-based identical pulses encoding system (TWINS), can circumvent this problem [137,138]. TWINS has been used in a number of different applications such as 2D-spectroscopy [138], hyper-spectral imaging [139] or stimulated Raman scattering [140]. The working principle of TWINS is depicted in figure 12.
The system consists of one flat block and two wedge pairs consisting of an uniaxial crystal. The optical axis of the first block A is chosen to be oriented in x-direction. Therefore, an incoming pulse, polarized linearly at 45 • , is split evenly to an extraordinary and an ordinary components. Since the two normal modes see different group indices n g e and n g o , they travel at different group velocities and are temporally separated after the crystal.
The delay between the two pulses after the first block is a constant initial delay. The variability of the optical delay between the pulses is introduced in the second pair of wedges B placed on a translation stage. Here, the optical axis is orientated in z-direction for the first wedge and in y-direction for the second wedge. Therefore, both pulses experience the same ordinary group index for the first wedge. In the second wedge, the optical axis of the crystal is rotated by 90 • with respect to block A. Hence, the orientation of the ordinary axis of block A corresponds to the extraordinary axis of the second wedge in wedge pair B. This arrangement allows to counteract the initial introduced time delay between the two pulses since the previous fast (slow) axis becomes the slow (fast) axis. The pulses experience different time delays at different wedge position [138].
Employing TWINS offers attosecond temporal resolution with the temporal jitter limited to ∼5 as over 30 min operation [137,138,141,142]. However, since TWINS acknowledgerely on a mechanical moving delay stage, the scan rate of the delay line is limited by the speed of the stage from the sub-Hz to Hz-regime. Furthermore, the tunable temporal delay is limited by the design of the wedges and limited to 1 ps [138,140,143].

On chip electric field sampling
Until now, we discussed several novel techniques as feasible paths for the direct optical-field acknowledged sampling of an arbitrary waveform at PHz frequencies and in ambient air. While these techniques are used routinely for laboratoryscale measurements, they are seldom accessible for industrialgrade and real-world applications. All these methods require intense, near-single cycle, CEP-stable laser pulses to drive the fast gate, which requires bulky and expensive amplifiers that are primarily operating at kilohertz repetition rates.
For multi-shot measurements, excellent pulse-to-pulse stability is essential for enhancing the detection sensitivity, which is cumbersome at kilohertz repetition rates. Scaling the repetition rates to megahertz should allow higher laser stability down to the shot-noise limit due to the inverse scaling of the laser noise with its repetition rate. Despite the amazing progress of laser technology in recent years [25,[144][145][146][147][148][149], generation of CEP-stable pulses at sufficiently high peak-power and average-power remains cumbersome.
Two recent advancements tackle these shortcomings. Liu et al [68] report on the first single-shot field sampling at kilohertz repetition rates, while Bionta et al [64] demonstrate a sensitive field sampling device suitable for low peak-power, high repetition rate lasers. The two techniques are discussed in the following.
Liu et al achieve the single-shot field-sampling of a weak sample pulse in an approach similar to TIPTOE. Here, the temporal delay between the weak sample pulse and an intense pulse are mapped onto a transverse spatial coordinate of a silicon-based image sensor chip [68]. The intense pulses at 3.4 μm create charge packets in the image sensor via multiphoton excitation. At the same time, the co-propagating weak waveform perturbs the probability of the excitation, leading to modulation in the excitation probability and, therefore, the magnitude of the detected photocurrent. In a geometry similar to [150] the time delay is mapped onto a transverse spatial coordinate by crossing the two beams with cylindrical focusing, enabling a single-shot field sampling of the weak pulse ( figure 13). The detection bandwidth of such a scheme can be extended to higher frequencies by using different detector technologies, like ZnO [69] or AlGaN [151] sensors.
The on-chip, hyper-sensitive, field sampling technique demonstrated by Bionta et al addresses the lack of compact and integratable field-samplers at PHz frequencies [64]. Similar to solids, the photoemission from plasmonic nanoantennas shows a dependence on the CEP of the laser pulses, resulting in a sub-cycle optical-field emission [152][153][154][155][156]. The concept for miniaturizing the optical field-sampling technology is described in figure 14.
The device consists of an array of plasmonic gold nanoantennas, gold nanowires, and an external current detector. The nanoantenna functions as an electron source. Upon the interaction of strong few-cycle laser pulses and the nanoantenna/wire junction, optical-field-controlled electron bursts with the duration of several hundreds of attoseconds are emitted [157][158][159]. Owing to field enhancement at the tip, 50 pJ pulse energy is adequate to drive the attosecond electron bursts. In the presence of a weak sample pulse, the detected current can be described as: where I(τ ) describes the measured current, Γ nonlinear emission rate [160], E L D the local electric field at the nanoantenna tip, E L s weak local signal field, T rep the repetition rate of the laser, and τ the relative delay between the two interacting pulses. The second term in equation (5) is a cross-correlation term and its Fourier transform describes the full sampling response to the weak sample pulse. Therefore, scanning the delay between the two pulses and recording the modulated current allows direct electric-field sampling.
The authors demonstrate six orders of magnitude higher detection sensitivity than the current state of the art in this spectral range. Therefore, a compact and affordable laser oscillator combined with the electric field enhancement from an integratable nanoantenna could solve the complexity of the frontend of the current field samplers. Moreover, the numerical investigation predicts up to 1 PHz detection bandwidth, limited by the work function of the gold device and linear photoemission due to single-photon absorption. Furthermore, the nanoantennas are electrically wired together, and 10-15 of them are irradiated simultaneously and have a contribution to the detected current, making the device amenable to large-scale electronic integration [161,162].
However, in this scheme, special attention needs to be paid on the intensity of the strong pulse, and the relative intensity of the strong and weak pulses. At high intensities, the nanostructures experience deformation and changes in the resonance of the antenna [163], which eventually results in degradation of the photocurrent and increasing the measurement's noise away from shot-noise [161]. This also adds a limitation on irradiation time and average power scalability of the device.

Summary and future perspectives
In this paper we have reviewed the recent techniques for direct electric-field sampling at optical frequencies and in ambient air, overcoming the bandwidth limitations of the traditional field detection schemes. All techniques have a commutual requirement: a short auxiliary event to probe the electric field of light in the time domain. Such short events are generated either (i) from the strong-field interaction of a near-singlecycle laser pulse with matter, or (ii) by temporal compression of an optical gate pulse with a central frequency higher than the central frequency of the pulse to be measured.
In contrast to techniques that characterize solely the complex pulse envelope based on perturbative nonlinear optics, the field measurement techniques do not require reconstruction algorithms and allow for complete characterization of the electric field with a bandwidth approaching 1.5 PHz. Nonetheless, the temporal resolution of field-detectors is prone to the temporal jitter, and they require intense, CEP-stable laser pulse. Onchip field-resolved techniques significantly lower the required intensity of strong-field methods and is keeping promise for integratable field-samplers at PHz frequencies.
These recent advances offer new prospects in studying subcycle light-matter interactions such as attosecond electron dynamics and optical-field-driven nonlinear phenomena and is opening up new horizons in spectro-microscopy at extreme limits. PHz field-sampling, based on EOS has been already employed for sensitive field-resolved detection of the response of water molecules when excited at 1.9 μm in ambient air ( figure 15) [24,164].
Besides the high detection dynamic range and sensitivity, the technique offers a great potential for high-resolution, labelfree spectro-microscopy. Vibrational microscopy has been a method of choice for the non-perturbative, label-free identification of complex molecular composition and offers intrinsic chemical selectivity due to the specific vibrational frequency of different molecules [140,[165][166][167][168][169][170]. However, the spatial resolution of the current generation label-free microscopes is limited to Abbe's diffraction limit and unable to access molecular composition in live biological systems at a high spatial resolution. When vibrational microscopy is combined with nonlinear EOS, label-free images with a spatial resolution below the diffraction limit of the excitation pulses could be captured, as here the spatial resolution of the captured image is defined by the diffraction limit of the gate pulses [171]. Recent trends in PHz field-sampling are opening new routes for advancing precision spectroscopy down to sub-cycle regime and opening new eras in field-resolve spectro-microscopy.

Data availability statement
No new data were created or analysed in this study.