Value Of Carrier-envelope Phase Research Articles

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.

Strong Laser Field-Driven Coupled Electron-Nuclear Dynamics: Quantum vs Classical Description.

We have performed a coupled electron-nuclear dynamics study of H2+ molecular ions under the influence of an intense few-cycle 4.5 fs laser pulse with an intensity of 4 × 1014 W/cm2 and a central wavelength of 750 nm. Both quantum and classical dynamical methods are employed in the exact similar initial conditions with the aim of head-to-head comparison of two methodologies. A competition between ionization and dissociation channel is explained under the framework of quantum and classical dynamics. The origin of the electron localization phenomena is elucidated by observing the molecular and electronic wave packet evolution pattern. By probing with different carrier envelope phase (CEP) values of the ultrashort pulse, the possibility of electron localization on either of the two nuclei is investigated. The effects of initial vibrational states on final dissociation and ionization probabilities for several CEP values are studied in detail. Finally, asymmetries in the dissociation probabilities are calculated and mutually compared for both quantum and classical dynamical methodologies, whereas Franck-Condon averaging over the initial vibrational states is carried out in order to mimic the existing experimental conditions.

Does Carrier Envelope Phase Affect the Ionization Site in a Neutral Diatomic Molecule?

A recent work shows how to extract the ionization site of a neutral diatomic molecule by comparing Quantum Trajectory Monte Carlo (QTMC) simulations with experimental measurements of the final electron momenta distribution. This method was applied to an experiment using a 40-femtosecond infrared pulse, finding that a downfield atom is roughly twice as likely to be ionized as an upfield atom in a neutral nitrogen molecule. However, an open question remains as to whether an assumption of the zero carrier envelope phase (CEP) used in the above work is still valid for short, few-cycle pulses where the CEP can play a large role. Given experimentalists’ limited control over the CEP and its dramatic effect on electron momenta after ionization, it is desirable to see what influence the CEP may have in determining the ionization site. In this paper, we employ QTMC techniques to simulate strong-field ionization and electron propagation from neutral N2 using an intense 6-cycle laser pulse with various CEP values. Comparing simulated electron momenta to experimental data indicates that the ratio of down-to-upfield ions remains roughly 2:1 regardless of the CEP. This confirms that the ionization site of a neutral molecule is determined predominantly by the laser frequency and intensity, as well as the ground-state molecular wavefunction, and is largely independent of the CEP.

Field-resolved THz-pump laser-probe measurements with CEP-unstable THz light sources

Radiation sources with a stable carrier-envelope phase (CEP) are highly demanded tools for field-resolved studies of light-matter interaction, providing access both to the amplitude and phase information of dynamical processes. At the same time, many coherent light sources, including those with outstanding power and spectral characteristics lack CEP stability, and so far could not be used for this type of research. In this work, we present a method enabling linear and non-linear phase-resolved terahertz (THz) -pump laser-probe experiments with CEP-unstable THz sources. THz CEP information for each pulse is extracted using a specially designed electro-optical detection scheme. The method correlates the extracted CEP value for each pulse with the THz-induced response in the parallel pump-probe experiment to obtain an absolute phase-resolved response after proper sorting and averaging. As a proof-of-concept, we demonstrate experimentally field-resolved THz time-domain spectroscopy with sub-cycle temporal resolution using the pulsed radiation of a CEP-unstable infrared free-electron laser (IR-FEL) operating at 13 MHz repetition rate. In spite of the long history of IR-FELs and their unique operational characteristics, no successful realization of CEP-stable operation has been demonstrated yet. Being CEP-unstable, IR-FEL radiation has so far only been used in non-coherent measurements without phase resolution. The technique demonstrated here is robust, operates easily at high-repetition rates and for short THz pulses, and enables common sequential field-resolved time-domain experiments. The implementation of such a technique at IR-FEL user end-stations will facilitate a new class of linear and non-linear experiments for studying coherent light-driven phenomena with increased signal-to-noise ratio.

Absolute carrier-envelope-phase dependences of single and double ionization of methanol in a near-IR few-cycle laser field.

We investigate the carrier-envelope phase (CEP) dependences of the single and double ionization processes of methanol (CH3OH) in an intense near-IR few-cycle laser field (2.1 × 1014 W/cm2) by the asymmetry in the ejection direction of CH3 + for the non-hydrogen migration channels and CH2 + for the hydrogen migration channels created through the C-O bond breaking after the ionization. Based on the absolute CEP values at the laser-molecule interaction point, calibrated by the method using intense few-cycle circularly polarized laser pulses [Fukahori et al., Phys. Rev. A 95, 053410-1-053410-14 (2017)], we confirm that methanol cations are produced by tunnel ionization and methanol dications are produced by the recollisional double ionization. We obtain the phase offset for the double ionization accompanying no hydrogen migration to be 1.85π as the absolute CEP at which the extent of the asymmetry becomes maximum. We interpret the phase shift of 0.85π from the phase offset of 1.0π for the tunnel ionization, estimated by a tunnel ionization model incorporating the chemical bond asymmetry, as the corresponding time delay associated with the electron recollisional ionization. The positive phase shift of 0.13π for the single ionization in the non-hydrogen migration channel is interpreted as the additional time (165 as) with which a methanol cation can be excited electronically prior to the decomposition. The additional phase shift of 0.22π for the single ionization in the hydrogen migration channel is interpreted as the additional time (280 as) required for a methanol cation to be excited electronically leading to the hydrogen migration prior to the decomposition.

Spider Structure of Photoelectron Momentum Distributions of Ionized Electrons from Hydrogen Atoms for Extraction of Carrier Envelope Phase of Few-Cycle Pulses**Supported by the National Natural Science Foundation of China under Grant Nos. 11674243 and 11674242, and the Fundamental Research Funds for the Central Universities under Grant No. 3122016D014.

The spider structure in the photoelectron momentum distributions (PMDs) of ionized electrons from the hydrogen atom is simulated by solving the time-dependent Schrödinger equation (TDSE). We find that the spider structure exhibits sensitive dependence on carrier envelope phase (CEP) of the few-cycle pulses. To elucidate the striking CEP dependence of the spider structure, we select three physical parameters IL, IR, and IR/IL to quantitatively characterize the variations of the spider structure induced by altering the CEPs. IL is the sum of the left half panel of the transverse cut curves (i.e., the sum of all the negative momenta along the laser polarization direction), IR is the sum of the right half panel of the transverse cut curves (i.e., the sum of all the positive momenta along the laser polarization direction), and IR/IL is the ratio between the two sums. These parameters are shown to have monotonic relation with the CEP value, which is exploited to extract the CEPs. We anticipate that our method will be useful for obtaining CEPs encoded in the spider structure of PMDs.

Carrier-envelope-phase dependence of harmonics induced by a few-cycle vortex laser

When a few-cycle vortex laser interacted with an inversion-symmetric atomic-like system, beyond the usual odd-order harmonics, some additional components also occur. The detailed numerical investigation on their transverse field distributions discloses that they depend sensitively on the carrier-envelope-phase (CEP) and the rotation period of the transverse distribution is 2π. This could be used to directly determine the CEP value of an incident pulse, unique without falling back on specific polar molecules or static electric fields.

Carrier-envelope-phase dependence of harmonics induced by a few-cycle vortex laser

When a few-cycle vortex laser interacted with an inversion-symmetric atomic-like system, beyond the usual odd-order harmonics, some additional components also occur. The detailed numerical investigation on their transverse field distributions discloses that they depend sensitively on the carrier-envelope-phase (CEP) and the rotation period of the transverse distribution is 2π. This could be used to directly determine the CEP value of an incident pulse, unique without falling back on specific polar molecules or static electric fields.

Phase control and stabilization in attosecond beamline with fast Fourier transform

With the unveiling of molecular and atomic dynamics, scientists crave finer and faster tools to communicate with the microworld. Attosecond pump-probe enjoys its reputation as the fastest camera, hinting ultrafast movements in the delay graph. To employ this camera, the stability and delay control should have very great accuracy comparable to the camera resolution. It is also of significant importance for stabilizing the carrier envelope phase (CEP) in few-cycle laser field. When dealing with a huge quantity of data, conventional Fourier transform algorism is challenging in high-speed control. Here we put forward the efficient calculation method, fast Fourier transform (FFT) algorism in Mach-Zehnder interferometer for arm length locking and <i>f</i>-2<i>f</i> for CEP locking. In the interferometer locking, 532 nm continuous wave laser is used in the Mach-Zehnder interferometer, and the phase of the FFT term corresponding to the delay between the two arms of the interferometer serves as a feedback signal on piezo transducer (PZT) in the delay line to reduce the change of the arm length. In the CEP control experiment, data to be analyzed are the <i>f</i>-2<i>f</i> spectrum interference fringes recorded by the spectrometer. The CEP values are obtained from the first order of FFT module output of the integrated spectrum interference fringes, and a labview program examines the relative phase drift and sends a feedback voltage signal to the PZT through the proportion integration differentiation module to compensate slow CEP drift after the chirped pulse amplification system by changing the insert length of a prism pair. The results show that the root mean square (RMS) of the arm length difference is 1.24 nm (4.1 attosecond for light to travel) per meter in the interferometer locking over 12 h, and the RMS of CEP is 227 mrad under 3 ms integration time in the CEP locking over 20 min. These results are able to meet the requirement of the accuracy for attosecond pulse generation and attosecond pump-probe experiments. We also use FFT to stabilize the CEP and relative time simultaneously in the waveform synthesis for 8 h (Huang P, Fang S, Gao Y, Zhao K, Hou X, Wei Z 2019 <i>Appl. Phys. Lett.</i> <b>115</b> 031102), the phase-locking system results in a CEP stability of 280 mrad and a relative time stability of 110 as at a repetition rate of 1 kHz. These results imply that the FFT is versatile and reliable in ultrafast control.

Sub-50-as isolated extreme ultraviolet continua generated by 1.6-cycle near-infrared pulse combined with double optical gating scheme

We demonstrate the generation of ultrabroad bandwidth attosecond continua extending to sub-50-as duration in the extreme ultraviolet (EUV) region based on a 1.6-cycle Ti:sapphire laser pulse. The combination of the amplitude gating scheme with a sub-two-cycle driver pulse and the double optical gating scheme achieves the continuum generation with a bandwidth of 70 eV at the full width at half maximum near the peak photon energy of 140 eV, which supports a Fourier-transform-limited pulse duration as short as 32 as. The carrier-envelope-phase (CEP) dependence of the attosecond continua shows a single-peak structure originating from the half-cycle cut-off at appropriate CEP values, which strongly indicates the generation of a single burst of an isolated attosecond pulse. Our approach suggests a possibility for isolated sub-50-as pulse generation in the EUV region by compensating for the intrinsic attosecond chirp with a Zr filter.

Characterizing carrier envelope phase of an isolated attosecond pulse with annular photoionization momentum spectra

The carrier envelope phase (CEP) has a direct impact on the physical properties of an isolated attosecond pulse (IAP) and many strong field processes, but it is difficult to measure in reality. Aiming at obtaining more accurate and complete characterization of CEP, we numerically investigate the annular photoelectron momentum spectra of the hydrogen atom ionized by overlapped fields of an IAP and an infrared (IR) pulse. By defining an overlapping parameter, the momentum patterns are classified and optimized for unambiguously measuring the rotation angle of a momentum pattern versus the CEP value. A series of simulations verify its robustness.

Polarization gating of high harmonic generation in the water window

We implement the polarization gating (PG) technique with a two-cycle, 1.7 μm driving field to generate an attosecond supercontinuum extending to the water window spectral region. The ellipticity dependence of the high harmonic yield over a photon energy range much broader than previous work is measured and compared with a semi-classical model. When PG is applied, the carrier-envelope phase (CEP) is swept to study its influence on the continuum generation. PG with one-cycle (5.7 fs) and two-cycle (11.3 fs) delay are tested, and both give continuous spectra spanning from 50 to 450 eV under certain CEP values, strongly indicating the generation of isolated attosecond pulses in the water window region.

Carrier envelope phase shifter for broadband terahertz pulses.

We demonstrated controlled shifting of the internal phase of broadband terahertz (THz) pulses. The internal phase of an ultrashort pulse is called the carrier envelope phase (CEP), which is an important parameter in the interaction of few-cycle light pulses and matter. Our CEP shifter utilizes the ultra-broadband feature of prism wave plates. We analytically derived the amount of CEP shift achievable by the CEP shifter using Jones matrixes. THz time-domain measurements clearly showed the shift of the CEP, and the results agreed well with the calculated values. The CEP shift was as high as 2π, indicating that any CEP values can be chosen using our CEP shifter.

Carrier Envelope Phase Effect of a Long Duration Pulse in the Low Frequency Region

Using the characteristic of small energy difference between two high Rydberg states, we theoretically investigate the carrier envelope phase (CEP) effect in a bound-bound transition of an atom in a low-frequency long laser pulse with tens of optical cycles. Particularly, we first prepare a Rydberg state of a hydrogen-like atom by a laser field with the resonant frequency between this state and the ground state. Then by using a low-frequency long laser pulse interacting with this Rydberg atom, we calculate the population of another Rydberg state nearby this Rydberg state at the end of the laser pulse and find that the population changes dramatically with the CEP of the low-frequency pulse. This CEP effect is attributed to the interference between the positive-frequency and negative-frequency components in one-photon transition. These results may provide a method to measure the CEP value of a long laser pulse with low frequency.

Laser-induced electron localization in a triatomic molecular ion

We demonstrate theoretically that by employing an intense few-cycle, circularly polarized laser pulse, two-dimensional localization of the electronic wave function in laser-driven H${}_{3}$${}^{2+}$ can be controlled by varying the carrier-envelope phase (CEP). In the reaction ${{\mathrm{H}}_{3}}^{2+}\ensuremath{\rightarrow}\mathrm{H}+{\mathrm{H}}^{+}+{\mathrm{H}}^{+}$, it is possible to select which one of the protons the electron finally binds to by tuning the value of the CEP. A complex asymmetry measure is introduced to quantify the degree of asymmetry induced by the laser field. In contrast to previous investigations of electron localization where only diatomic molecules were considered, our results extend CEP control of intramolecular electron motion to triatomic systems. This provides a step toward strong-field spatial and temporal control of electron dynamics in polyatomic molecules.

Carrier-envelope-phase control of plasmonic-field enhanced high-order harmonic generation

Plasmonic field-enhanced high-order harmonic generation (HHG) is investigated theoretically using the solutions of the three-dimensional time-dependent Schrödinger equation and a (semi)classical three-step model. Plasmonic field is modeled by a spatially inhomogeneous field with a time-dependent cosine squared pulse envelope. The dependence of the HHG yield on the carrier-envelope phase (CEP) is investigated. It is shown that the position of the cutoff of the HHG spectra is very sensitive to the value of CEP and that for the inhomogeneous field the dependence on the CEP is modulo. This enables both the CEP control of the plasmonic field-enhanced HHG and the determination of the CEP modulo by the measurement of the HHG cutoff position. Contrary to the homogeneous field case, for inhomogeneous field the difference between the maximum and minimum HHG cutoff (for the CEP in the interval from 0 to) remains substantial even for pulses longer than 10 optical cycles.

Carrier-envelope-phase effect in a long laser pulse with tens of optical cycles

The carrier-envelope phase (CEP) is a crucial parameter of a laser pulse, which can influence all dynamic processes in matter-laser interaction. In this work, we find a clear CEP effect in laser-driven atomic bound-bound transition for a long laser pulse. Especially, the CEP effect is attributed to the interference between the sum-frequency and the difference-frequency components within a two-photon transition, where the degree of this interference depends only on the atomic energy-level structure and is independent of the laser pulse duration. Therefore, the CEP effect can stay robust for a long laser pulse containing tens of laser cycles. This result provides a method to measure the CEP value of a long laser pulse and may thus shed light on the study of characteristics of high-frequency XUV and x-ray laser pulses.

Frequency-resolved optical gating with electro-optic sampling

We have demonstrated a new pulse characterization technique, cross-correlation frequency-resolved optical gating with electro-optic sampling. Sub-single-cycle mid-infrared pulses were characterized with the absolute carrier-envelope phase values by using the method. Frequency-resolved optical gating (FROG) (1) is an important general technique to determine the intensity and phase evolution of an arbitrary ultrashort pulse. However, determination of its carrier- envelope phase (CEP) (2) was not possible with the method. On the other hand, electro-optic sampling (EOS) (3) is a method to obtain full information of the electric field including the absolute value of the CEP. Since the upper limit of the detectable frequency of the technique is the inverse of the pulse duration of the reference pulse, EOS has been used for characterization of the ultrashort pulses in rather low frequency region, specifically, from terahertz to mid-infrared region (4-6). In this contribution, we propose a new pulse characterization scheme which is a combination of FROG and EOS. The method enables us to characterize an ultrashort pulse with the information of the absolute CEP value by using a reference pulse whose pulse duration is much longer than the period of the carrier-wave of the target pulse. The time-averaged intensity of the delayed superposition of the fields of the reference pulse (Eref(t )) and the di erence frequency between the reference and test pulses (Etest(t)) is written as follows, Eref(t ) + Eref(t )E test(t) 2 = D jEref(t )j 2 E + Eref(t )E test (t) 2 + D 2< n Eref(t )E ref (t )Etest(t) oE ; (1) wherehi denotes time average and is a complex constant proportional to the nonlinear susceptibility of the di erence frequency generation assumed as an instantaneous process. The first term is indepen- dent of the delay time. The second term is the intensity cross-correlation signal between the test pulse and the reference pulse. The spectrally resolved second term corresponds to a cross-correlation FROG signal (XFROG) (7). The third term is the interference term, i.e., the EOS signal. If it is possible to assume Eref(t )E ref (t ) Iref(t ) as a delta function, the term becomes Etest( ), which provides the complete information of the electric field of the test pulse. Otherwise, the term is spectrally filtered with the Fourier transform of Iref(t). If we simultaneously measure the XFROG and EOS signals, i.e., the second and the third terms in eq. (1), the absolute value of the CEP obtained with EOS can be used for determining the CEP of the characterized pulse with XFROG. Thus, this technique permits us to completely retrieve an electric field which has too high frequency components to detect with EOS. In other words, the technique dramatically relaxes the requirement of the reference pulse for the full characterization of the target electric field.

Wavelength scaling of high-order-harmonic-generation efficiency by few-cycle laser pulses: Influence of carrier-envelope phase

We investigate the wavelength scaling of high-order-harmonic-generation (HHG) efficiency by few-cycle laser pulses where the influence of the carrier-envelope phase (CEP) becomes prominent. Based on the numerical solution of time-dependent Schr\"odinger equation, in the infrared region of $\ensuremath{\lambda}$ (0.8--1.8 $\ensuremath{\mu}$m), we observe that the power law of the form ${\ensuremath{\lambda}}^{\ensuremath{-}x}$ ($x\ensuremath{\approx}5$--6) is still present; but for constant intensity and a fixed energy interval, it differs markedly in the CEP. We find that for a specific value of CEP the wavelength dependence follows a ${\ensuremath{\lambda}}^{\ensuremath{-}4.6}$ scaling in high-harmonic yield. We also perform classical trajectory calculations to gain some understanding of the CEP dependence of the wavelength scaling.

Generation of carrier-envelope phase stabilized intense 15 cycle pulses at 175 μm

A three-stage high conversion efficiency optical parametric amplifier (OPA) with passively stabilized carrier-envelope phase (CEP) is presented. After passing through an argon-filled hollow fiber and the dispersion compensator for pulse compression, CEP stabilized 0.7 mJ, 1.5 cycle laser pulses at 1.75 μm center wavelength are obtained. Terahertz (THz) emission spectroscopy is adopted to determine the value of CEP, indicating an excellent long-term CEP stability.