Carrier-envelope Phase Research Articles

Carrier-envelope-phase-independent field sampling of single-cycle transients using homochromatic attosecond streaking

The recent development of homochromatic attosecond streaking (HAS) has enabled a novel, highly precise method for ultrafast metrology of attosecond electron pulses as well as for real-time sampling of the instantaneous field waveforms of light transients. Here, we evaluate the potential of HAS as a method for precisely sampling the field waveform of non-phase-stabilized single-cycle transients of light. We show that the extreme nonlinearity of field emission and the core properties of HAS as a field sampling technique allow one to track the waveform of a single carrier-envelope phase (CEP) setting whose field dynamics results in the most energetic electron cutoff. Our results establish HAS as a robust, compact, all-solid-state method for characterizing light fields with attosecond-level precision and as a powerful tool in light field synthesis.

Higher Harmonic Generation Arising from the Bessel Function Expansions of the Carrier-Envelope-Phase Driven by the Femtosecond Optical Kerr Effect

This paper expands upon previous reports based on the EM Kerr model-based HHG simulation from the carrier-envelope phase (CEP) of the electromagnetic laser light wave based on electronic self-phase modulation (ESPM) from the optical Kerr index. The underpinning mechanism described for generating HHG arises from the CEP of the nonlinear index of refraction, which yields a series of Bessel functions. The envelope of the electric field E(t) of the intense ultrashort light pulses drives the CEP, resulting in many Bessel functions, one of the salient features of HHG. The HHG from the large number of Bessel function modes can produce attosecond pulses and possibly can even produce zeptosecond pulses by Kerr mode-locking among the large number N of Bessel functions.

Modulation of electron correlation dynamics in atomic non-sequential double ionization by counter-rotating two-color circularly polarized laser fields.

We investigate the ultrafast electron correlation effects during non-sequential double ionization (NSDI) of argon subjected to a combined femtosecond field composed of counter-rotating two-color circularly polarized (TCCP) pulse laser using a 3D classical ensemble model (CEM). Our simulation results reveal that manipulation of the carrier-envelope phase (CEP) of the external driving field modulates the dynamical behavior of the two electrons, resulting in a notable sensitivity of their momentum distribution to the relative phase of two components of the counter-rotating TCCP field. Through inversion analysis, we uncover the capability to direct electrons toward a single direction, thereby facilitating focused ion-electron collisions on the attosecond timescale. Furthermore, we observe that adjusting the CEP exerts a substantial influence on the NSDI ionization process, modifying the relative contributions of the recollision-induced ionization (RII) mechanism and recollision excitation with subsequent ionization (RESI) mechanism.

Carrier-envelope-phase characterization of ultrafast mid-infrared laser pulses through harmonic generation and interference in argon

The propagation of an intense, femtosecond, mid-infrared laser pulse in a gaseous medium results in the efficient generation of spectrally overlapping low-order harmonics, whose optical carrier phases are linked to the carrier-envelope phase (CEP) of the mid-infrared driver pulse. Random peak-power fluctuations of the driver pulses, converted to the fluctuations of the nonlinear phases, acquired by the pulses on propagation, cause this phase correlation to smear out. We show that this seemingly irreversible loss of phase can be recovered, and that the complete information needed for the phase correction is contained in the harmonic spectra itself. The optical phases of the intense driver pulse and its harmonics, as fragile as they appear to be against even weak disturbances, evolve deterministically during highly nonlinear propagation through the extended ionization region.

Systematic analysis of an attosecond pulse generation by a subcycle laser field

We investigated the influence of subcycle driving fields on high-order harmonic generation (HHG), with a focus on driver's intrinsic chirp, carrier-envelope phase (CEP), and number of laser cycles. Our findings reveal that the center frequency of a laser pulse scales as τ−5/4 with pulse duration τ, and that attochirp exhibits a similar dependence on pulse duration. Additionally, we identified CEP-specific trends in harmonic yield: it increases as τ5/4 for ϕ0=0∘ and decreases as τ−4.1 for ϕ0=−90∘. Although subcycle pulses can generate intense isolated attosecond pulses (IAPs), they also tend to produce higher attochirp and reduced cutoff energies. However, effective compensation for attochirp can mitigate these drawbacks, thereby increasing the capability of subcycle pulses to generate short-duration, high-intensity IAPs. These results offer valuable insights into HHG using subcycle pulses and have important implications for the advancement of ultrafast light sources and the understanding of ultrafast phenomena at the attosecond timescale. Published by the American Physical Society 2025

Mode-resolved optical frequency comb fixed point localization via dual-comb interferometry.

We describe improved methods for locating the fixed point of an optical frequency comb. Two continuous-wave lasers are locked to a reference frequency comb and track the optical phase of a second comb-under-test (CUT) at two points separated by approximately 1.6 THz. Carrier-envelope and optical phase tracking (OPT) yields a precise fixed point measurement across a range of pump modulation frequencies (400 Hz-250 kHz). Sub-nanometer shifts of the fixed point are observed. The fixed point is also determined with high precision using dual-comb interferometry (DCI), and the value closely matches the calculation from the dual-point tracking method.

MIR laser CEP estimation using machine learning concepts in bulk high harmonic generation

Monitoring the carrier-envelope phase (CEP) is of paramount importance for experiments involving few-cycle intense laser fields. Common measurement techniques include f-2f interferometry or stereo-ATI setups. Here we demonstrate a new concept, both by simulations and by experiments, for CEP estimation in the mid-infrared regime using machine learning (ML) techniques that rely on the observation of the spectrum of high harmonic generation (HHG) in bulk material. Once the ML model is trained, the method provides a way for cheap and compact in-situ CEP tagging. This technique can complement other CEP monitoring methods, can capture the complex correlation between the CEP and the observable HHG spectra, and is readily generalizable for any laser wavelengths.

Theoretical analysis of the phase characteristics in few-cycle laser coherent beam combining

To meet the increasing demand for high-energy (Joule-level) few-cycle pulses in strong-field physics research, coherent beam combining (CBC) presents an effective method to further enhance the power of few-cycle pulse sources. However, due to the broad spectrum and ultrashort pulse duration of few-cycle pulses, achieving efficient beam combining is particularly challenging. In this paper, we employ the angular spectrum (ASM) method to numerically simulate the propagation of few-cycle pulses in a focusing system. By constructing a three-dimensional (2D + 1D) model, we accurately quantify the effects of laser parameters such as carrier-envelope phase (CEP) difference, time delay (TD), dispersion between beams, and combining configurations on the combining efficiency and CEP shift. The study results provide design guidelines for high energy few-cycle laser systems based on coherent beam combining and reveal the possibility to significantly enhance the combining efficiency while maintaining high CEP stability, which will finally provide a reliable light source for advancing the frontier of strong-field physics.

On-chip petahertz electronics for single-shot phase detection

Attosecond science has demonstrated that electrons can be controlled on the sub-cycle time scale of an optical waveform, paving the way towards optical frequency electronics. However, these experiments historically relied on high-energy laser pulses and detection not suitable for microelectronic integration. For practical optical frequency electronics, a system suitable for integration and capable of generating detectable signals with low pulse energies is needed. While current from plasmonic nanoantenna emitters can be driven at optical frequencies, low charge yields have been a significant limitation. In this work we demonstrate that large-scale electrically connected plasmonic nanoantenna networks, when driven in concert, enable charge yields sufficient for single-shot carrier-envelope phase detection at repetition rates exceeding tens of kilohertz. We not only show that limitations in single-shot CEP detection techniques can be overcome, but also demonstrate a flexible approach to optical frequency electronics in general, enabling future applications such as high sensitivity petahertz-bandwidth electric field sampling or logic-circuits.

180 mW, 1 MHz, 15 fs carrier-envelope phase-stable pulse generation via polarization-optimized down-conversion from gas-filled hollow-core fiber

Gas-filled hollow core fibers allow the generation of single-cycle pulses at megahertz repetition rates. When coupled with difference frequency generation, they can be an ideal driver for generating carrier-envelope phase stable, octave-spanning pulses in the short-wavelength infrared. In this work, we investigate the dependence of the polarization state in gas-filled hollow-core fibers (HCF) on the subsequent difference frequency generation stage. We show that by adjusting the input polarization state of light in geometrically symmetric systems, such as hollow-core fibers, one can achieve precise control over the polarization state of the output pulses. This manipulation preserves the temporal characteristics of the generated ultrashort pulses, especially when operating at a near single-cycle regime. We leverage this property to boost the downconversion efficiency of the near single-cycle pulses in a type I difference frequency generation stage. Our technique overcomes the bandwidth and dispersion constraints of the previous methods that rely on broadband waveplates or adjustment of crystal axes relative to the laboratory frame. This advancement is crucial for experiments demanding pure polarization states in the eigenmodes of the laboratory frame.

Universal and waveform-resolving dual pulse reconstruction through interferometric strong-field ionization.

A dual pulse retrieval algorithm is introduced that builds upon time-domain interferometric strong-field ionization to simultaneously reconstruct both involved laser pulses in a waveform-resolved manner. The pulse characterization scheme removes many restrictions posed by former methods, leaving the avoidance of resonant ionization as a single boundary. It is widely and easily applicable at low cost and effort for common attosecond beamlines and allows for the robust and accurate in-situ retrieval of two unknown laser fields. For spectrally similar pulses, our method can also extract the carrier-envelope phase of both waveforms. Furthermore, it enables the accurate envelope measurement of ultraviolet laser pulses without any dispersive media, using much longer, commonly available pulses in the infrared. The new technique is therefore ideally suited for the characterization of resonant dispersive waves.

Solid and hollow plasmonic nanoresonators for carrier envelope phase read-out

The geometry of gold plasmonic nanoantennae was numerically optimized to maximize their sensitivity to the carrier envelope phase (CEP) of the exciting ultra-short laser pulses. Three structure types, triangular, teardrop-shaped and plasmonic lens, were optimized in solid and hollow compositions as well. Hollow / solid singlets results in the largest/intermediate CEP dependent (Q1) – to – CEP independent (Q0) integrated current components’ ratio, while their Q1 was the smallest / intermediate. The largest / intermediate Q12/Q0 CEP sensitivity was achieved via solid / hollow plasmonic lenses due to their large near-field enhancement and Q1, while the Q1/Q0 ratio was smaller than for counterpart singlets.

Carrier-envelope phase effects on the reflectance of diamond films irradiated by ultrashort single-cycle light pulses: A comparison study in attosecond and femtosecond regimes

Diamond films irradiated with few-cycle laser pulses are emerging as a all-optical information processing device with high-speed and low-power-consumption. The possibility to steer, control or switch such few-cycle laser pulses with diamond films is expected to pave the way towards ultrafast all-optical switching. Here, we show theoretically the effect of the carrier-envelope phase (CEP) of the ultrashort single-cycle light pulses on the reflectance of diamond films within the framework of multi-scale theory. We observe clear variations in the reflectance behavior of femtosecond pulses and attosecond pulses. Our most important finding is that the reflectivity difference of attosecond pulses with different waveforms and the same spectrum on diamond films exhibits a perfect quadratic relationship with the CEP. This observation suggests that the nonlinearity of attosecond pulses is different from that of femtosecond pulses. Analysis of these results allows us to gain new insights in the interaction between attosecond light pulses and matter. This opens fascinating avenues for all-optical information processing over ultrashort lengths and timescales.

Modulation and real-time monitoring of the carrier-envelope phase of terahertz pulses based on shaping of near-infrared femtosecond pulses.

We propose a novel, to our knowledge, method for modulating and real-time monitoring of the carrier-envelope phase (CEP) of terahertz (THz) pulses. CEP is an essential parameter in the interaction of THz waves with matter due to the difference in temporal symmetry when the carrier is extended for several cycles. CEP can be continuously modulated at full range with high speed by oscillating the optical path length of the Michelson interferometer under 1 µm, as confirmed by electro-optic (EO) sampling. The proposed method can be combined with a data acquisition method that links the experimental parameters and measurements of individual high-repetition THz pulses to realize robust CEP modulation measurements. As the proposed CEP modulation and monitoring system does not require EO sampling but only extracts CEP dependence, the trend toward ultrafast physical property control and observation using THz pulses will spread to other fields.

Carrier-envelope phase-stabilized ultrashort pulses from a gas-filled multi-pass cell

Few-cycle laser pulses at a high repetition rate with a stable carrier-envelope phase are required for next-generation attosecond time-resolved spectroscopies. One way to generate these pulses is the nonlinear compression of laser pulses via gas-filled hollow-core fibers. Recently, an alternative approach based on multi-pass cells (MPCs) has been shown to be very efficient for post-compression of turn-key, industrial-grade, high average power Yb-doped solid-state laser amplifiers. However, to expand the system for exploring strong-field laser applications, its carrier-envelope phase stability needs to be demonstrated in the compressed pulses. In this Letter, we present the generation of carrier-envelope phase-stabilized 40 fs pulses with 380 μJ energy at 50 kHz by compressing the output of a Yb:KGW amplifier in a gas-filled MPC. Comparable short-term carrier-envelope phase errors of 412 and 435 mrad root mean square were observed from the amplifier and MPC, respectively, indicating that the phase stability of the amplified pulses is well-maintained during pulse compression in the MPC.

Ultra-Nonlinear Subcycle Photoemission of Few-Electron States from Sharp Gold Nanotapers.

The generation of ultrashort electron wavepackets is crucial for the development of ultrafast electron microscopes. Recent studies on Coulomb-correlated few-electron number states, photoemitted from sharp metallic tapers, have shown emission nonlinearities in the multiphoton photoemission regime which scale with the electron number. Here, we study few-electron photoemission from gold nanotapers triggered by few-cycle near-infrared pulses, demonstrating extreme 20th-order nonlinearities for electron triplets. We report interferometric autocorrelation traces of the electron yield that are quenched to a single emission peak with subfemtosecond duration due to these high nonlinearities. The modulation of the emission yield by the carrier-envelope phase suggests that electron emission predominantly occurs during a single half cycle of the driving laser field. When applying a bias voltage to the tip, recollisions in the electron trajectories are suppressed and coherent subcycle electron beams are generated with promising prospects for ultrafast electron microscopy with subcycle time resolution.

Absence of quantum optical coherence in high harmonic generation

The optical phase of the driving field in the process of high harmonic generation and the coherence properties of the harmonics are fundamental concepts in attosecond physics. Here, we consider driving the process by incoherent classical and nonclassical light fields exhibiting an undetermined optical phase. With this, we introduce the notion of quantum optical coherence into high harmonic generation and show that high harmonics can be generated from incoherent radiation despite having a vanishing electric field. We explicitly derive the quantum state of the harmonics when driven by carrier-envelope phase unstable fields and show that the generated harmonics are incoherent and exhibit zero electric field amplitudes. We find that the quantum state of each harmonic is diagonal in its photon number basis, but nevertheless has the exact same photon statistics as the widely considered coherent harmonics. From this, we conclude that assuming coherent harmonic radiation can originate from a preferred ensemble fallacy. These findings have profound implications for attosecond experiments and how to infer the harmonic radiation properties. Published by the American Physical Society 2024

Phase-Sensitive Plasma Nonlinearity Controlled by Ultrashort Pulses

The generation of spectral components sensitive to the carrier-envelope phase of a laser pulse in a thin zinc selenide film has been experimentally demonstrated and confirmed by a numerical simulation. A pump–probe scheme has been implemented so that a pump pulse with a duration of about 1.5 field cycles, a central wavelength of 1.7 μm, and a stabilized carrier-envelope phase induces photoionization in a thin zinc selenide film. The probe pulse is scattered by the plasma, generating new phase-sensitive spectral components at the edges of its spectrum. The theoretical analysis has confirmed plasma nonlinearity as a mechanism for generating these components. The observed effect can be used to characterize the carrier-envelope phase of ultrashort pulses during the generation of high-order harmonics and sequences of attosecond pulses.

Attosecond two-color x-ray free-electron lasers with dual chirp-taper configuration and bunching inheritance

Attosecond x-ray pulses play a crucial role in the study of ultrafast phenomena occurring within inner and valence electrons. To achieve attosecond time-resolution studies and gain control over electronic wave functions, it is crucial to develop techniques capable of generating and synchronizing two-color x-ray pulses at the attosecond scale. In this paper, we present a novel approach for generating attosecond pulse pairs using a dual chirp-taper free-electron laser with bunching inheritance. An electron beam with a sinusoidal energy chirp, introduced by the external laser, passes through the main undulator and afterburner, both with tapers. Two-color x-ray pulses are generated from the main undulator and the afterburner, respectively, with temporal separations of several femtoseconds and energy separations of tens of electron volts. Notably, the afterburner is much shorter than the main undulator due to the bunching inheritance, which reduces the distance between two source points and alleviates the beamline focusing requirements of the two-color pulses. A comprehensive stability analysis is conducted in this paper, considering the individual effects of shot noise from self-amplified spontaneous emission and carrier-envelope phase jitter of the few-cycle laser. The results show that the radiation from the afterburner exhibits excellent stability in the proposed scheme, which is beneficial for x-ray pump-probe experiments. The proposed scheme opens up new possibilities for attosecond science enabled by x-ray attosecond pump-probe techniques and coherent control of ultrafast electronic wave packets in quantum systems. Published by the American Physical Society 2024

Control over the secondary collision of electron in high-order harmonic generation

We investigated the high-order harmonic generation by interacting linearly polarized laser pulses with the atomic target. The temporal evolution of harmonic emission and the underlying mechanisms of rescattering electrons are thoroughly investigated through a combination of quantum analysis and classical trajectory simulations. The manipulation of the carrier-envelope phase (CEP) provides a promising avenue for controlling electron recollisions, revealing a systematic linear relationship between ionization and recombination times across varying CEP values. Moreover, examining phase properties in emitted harmonics during secondary collisions presents intriguing modulations, offering a potential experimental approach to verify the presence of secondary recollisions.