Long-term stabilization of the carrier-envelope phase of few-cycle laser pulses

The temporal variation of the electromagnetic field of a few-cycle laser pulse depends on whether the maximum of the pulse amplitude coincides with that of the wave cycle or not, i.e., it depends on the phase of the field with respect to the pulse envelope. Fixation of this carrier-envelope phase has only very recently become possible for amplified laser pulses. This paved the way for a completely new class of experiments and for coherent control down to the attosecond time scale because it is the field and not the pulse envelope which governs laser-matter interactions. However, this novel technique still affords much potential for optimization. In this paper we demonstrate a novel stabilization scheme for the carrier-envelope phase that not only guarantees a stable phase for arbitrarily long measurements, but also makes it possible to restore any given phase for an application after a pause of any kind. This is achieved by combining a stereo-ATI phase meter with a feedback loop to correct phase drifts inside and outside the laser system. PACS 07.05.Dz; 32.80.Rm; 42.50.Hz     

Improved carrier-envelope phase locking of intense few-cycle laser pulses using above-threshold ionization

A robust nonoptical carrier-envelope phase (CEP) locking feedback loop, which utilizes a measurement of the left-right asymmetry in the above-threshold ionization (ATI) of Xe, is implemented, resulting in a significant improvement over the standard slow-loop f-to-2f technique. This technique utilizes the floating average of a real-time, every-single-shot CEP measurement to stabilize the CEP of few-cycle laser pulses generated by a standard Ti:sapphire chirped-pulse amplified laser system using a hollow-core fiber and chirped mirror compression scheme. With this typical commercially available laser system and the stereographic ATI method, we are able to improve short-term (minutes) CEP stability after a hollow-core fiber from 450 to 290 mrad rms and long-term (hours) stability from 480 to 370 mrad rms.     

Measurement of the carrier-envelope phase of few-cycle laser pulses by use of asymmetric photoionization

Using numerical solutions of the time-dependent Schr?dinger equation for a hydrogen and a helium atom in a linearly polarized, few-cycle laser field, we calculate the photoelectron left-right asymmetry measured by two opposing detectors placed along the laser polarization vector, with the laser focus in the center. We find a simple dependence of this asymmetry on carrier-envelope (CE) phase phi for laser intensities slightly below the tunneling regime, which may allow us to measure (or to calibrate) and to stabilize the CE phase. In particular, we suggest that the condition of zero asymmetry for few-cycle pulses may be useful for both these goals.     

Role of the carrier-envelope offset phase of few-cycle pulses in nonperturbative resonant nonlinear optics

We study the influence of the carrier-envelope offset phase of few-cycle pulses on nonperturbative resonant extreme nonlinear optics in a semiconductor. If the Rabi frequency becomes comparable to the light frequency, the different Rabi sidebands interfere around twice the laser center frequency, giving rise to a signal which strongly depends on the carrier-envelope offset phase. This signature should be measurable in GaAs samples.     

Variation of the carrier-envelope phase of few-cycle laser pulses owing to the Gouy phase: a solid-state-based measurement

The carrier-envelope phase of a laser pulse has recently become an important quantity in extreme nonlinear optics. Because of the topological Gouy phase, it changes while the pulse propagates through the focus of a lens. This variation is measured by a simple solid-state-based approach. The experimental results are analyzed by comparison with simple analytical model calculations.     

Parametric amplification of few-cycle carrier-envelope phase-stable pulses at 2.1 microm

We demonstrate an optical parametric chirped-pulse amplifier producing infrared 20 fs (3-optical-cycle) pulses with a stable carrier-envelope phase. The amplifier is seeded with self-phase-stabilized pulses obtained by optical rectification of the output of an ultrabroadband Ti:sapphire oscillator. Energies of -80 microJ with a well-suppressed background of parametric superfluorescence and up to 400 microJ with a superfluorescence background are obtained from a two-stage parametric amplifier based on periodically poled LiNbO3 and LiTaO3 crystals. The parametric amplifier is pumped by an optically synchronized 1 kHz, 30 ps, 1053 nm Nd:YLF amplifier seeded by the same Ti:sapphire oscillator.     

Ionization of atoms by few-cycle EUV laser pulses: carrier-envelope phase dependence of the intra-pulse interference effects

We have investigated the ionization of the H atom by intense few-cycle laser pulses, in particular the intra-pulse interference effects, and their dependence on the carrier-envelope phase (CEP) of the laser pulse. In the final momentum distribution of the continuum electrons the imprint of two types of intra-pulse interference effects can be observed, namely the temporal and spatial interference. During the spatial interference electronic wave packets emitted at the same time, but following different paths interfere leading to an interference pattern measurable in the electron spectra. This can be also interpreted as the interference between a direct and a scattered wave, and the spatial interference pattern as the holographic mapping (HM) of the target. This HM pattern is strongly influenced by the carrier-envelope phase through the shape of the laser pulse. Here, we have studied how the shape of the HM pattern is modified by the CEP, and we have found an optimal CEP for the observation of HM.     

Generation of intense,carrier-envelope phase-locked few-cycle laser pulses through filamentation

Intense, well-controlled light pulses with only a few optical cycles start to play a crucial role in many fields of physics, such as attosecond science. We present an extremely simple and robust technique to generate such carrier-envelope offset (CEO) phase locked few-cycle pulses, relying on self-guiding of intense 43-fs, 0.84 mJ optical pulses during propagation in a transparent noble gas. We have demonstrated 5.7-fs, 0.38 mJ pulses with an excellent spatial beam profile and discuss the potential for much shorter pulses. Numerical simulations confirm that filamentation is the mechanism responsible for pulse shortening. The method is widely applicable and much less sensitive to experimental conditions such as beam alignment, input pulse duration or gas pressure as compared to gas-filled hollow fibers. PACS 45.65.Ky; 42.65.Re     

载波-包络相位对于基频光与其自身倍频光脉冲合成的影响

将基频光与其自身的倍频光合成，是一种得到超过一个倍频程的超宽光谱的简单方法，而载波_包络相位(CEP)对合成超宽光谱产生的超短脉冲有重要的影响. 本文从光频梳的角度，根据钛宝石激光器中产生的超短脉冲光谱，计算载波_包络相位对该脉冲与其自身的倍频脉冲合成产生的超短脉冲的影响，说明了调整载波_包络相位对于脉冲合成的重要性. 关键词： 超短脉冲 载波_包络相位 光频梳 脉冲合成     

Broadband difference frequency mixing between visible and near-infrared pulses for few-cycle pulse generation with stable carrier-envelope phase

Difference frequency generation between broadband visible noncollinear optical parametric amplifier (NOPA) pulses and the fundamental pump laser pulses allows the generation of ultrashort infrared pulses with passively stabilized carrier-envelope phase. A simple prism compressor for the visible NOPA pulses is sufficient to generate few-cycle pulses in the infrared and no additional compression is needed. We theoretically investigate the concept, explain the principles, and demonstrate it for high repetition rate, long pulse durations, and various wavelengths by applying it to a Ti:sapphire and an Yb:KYW-based laser systems. For the latter sub-15 fs phase stable pulses around 1.8 μm with an energy of 100 nJ are obtained at 100 kHz repetition rate.     

Measurement of the phase of few-cycle laser pulses

For the shortest pulses generated to date, the amplitude of the electromagnetic wave changes almost as rapidly as the field oscillates. The temporal variation of the field, which directly governs strong-field interactions, therefore depends on whether the maximum of the pulse amplitude coincides with that of the wave cycle or not, i.e., on the phase of the field with respect to the pulse envelope. It is demonstrated that the direction of electron emission from photoionized atoms can be controlled by varying the phase of the field, providing for the first time a tool for its accurate determination. Directing fast electron emission to the right or to the left with the light phase constitutes a new kind of coherent control.     

Controlling the phase evolution of few-cycle light pulses

Using a coherent nonlinear optical technique, slipping of the carrier through the envelope of 6-fs light wave packets emitted from a mode-locked-oscillator/pulse-compressor system has been measured, permitting the generation of intense, few-cycle light with precisely reproducible electric and magnetic fields. These pulses open the way to controlling the evolution of strong-field interactions on the time scale of the light oscillation cycle and are indispensable to reproducible attosecond x-ray pulse generation.     

Gouy phase shift for few-cycle laser pulses

We measured for the first time the influence of the Gouy effect on focused few-cycle laser pulses. The carrier-envelope phase is shown to undergo a smooth variation over a few Rayleigh distances. This result is of critical importance for any application of ultrashort laser pulses, including high-harmonic and attosecond pulse generation, as well as phase-dependent effects.     

Electron acceleration by tightly focused radially polarized few-cycle laser pulses

Within the framework of plane-wave angular spectrum analysis of the electromagnetic field structure, a solution valid for tightly focused radially polarized few-cycle laser pulses propagating in vacuum is presented. The resulting field distribution is significantly different from that based on the paraxial approximation for pulses with either small or large beam diameters. We compare the electron accelerations obtained with the two solutions and find that the energy gain obtained with our new solution is usually much larger than that with the paraxial approximation solution.     

Long-term passive stabilization of the carrier-envelope phase of an intense infrared few-cycle pulse source

We present long-term stability of the carrier-envelope phase of intense infrared few-cycle pulses at 1.6 μm, generated by optical parametric chirped-pulse amplification. The employed system is based on a passive stabilization scheme that obviates the need for active feedback loops, and requires only control of environmental parameters. The stabilization is demonstrated to last for up to 45 h, during which the carrier-envelope phase drift is measured to be less than \(250\,\text{mrad}\) . This marks, to the best of our knowledge, the longest demonstrated phase-stable operation of a passively stabilized, amplified few-cycle source to date.     

Accurate determination of the absolute phase and temporal-pulse phase of few-cycle laser pulses

A Fourier analysis method is used to accurately determine not only the absolute phase but also the temporal-pulse phase of an isolated few-cycle (chirped) laser pulse. This method is independent of the pulse shape and can fully characterize the light wave even though only a few samples per optical cycle are available. It paves the way for investigating the absolute phase-dependent extreme nonlinear optics, and the evolutions of the absolute phase and the temporal-pulse phase of few-cycle laser pulses.     

Wavelet-transform analysis for carrier-envelope phase extraction of amplified ultrashort optical pulses

We introduced a wavelet-transform technique into the carrier-envelope phase extraction from the spectral interferogram of amplified ultrashort optical pulses. With this technique, carrier-envelope phases were directly extracted from the ridges of the wavelet transforms. This technique did not need filters; therefore, the uncertainty introduced from filter was avoided naturally. The Wavelet transforms technique produced a two-dimensional topography on which the time-frequency information of the spectral interferogram was shown apparently.     

Symmetry of carrier-envelope phase difference effects in strong-field, few-cycle ionization of atoms and molecules

In few-cycle pulses, the exact value of the carrier-envelope phase difference (CEPD) has a pronounced influence on the ionization dynamics of atoms and molecules. We show that, for atoms in circularly polarized light, a change in the CEPD is mapped uniquely to an overall rotation of the system, and results for arbitrary CEPD are obtained by rotation of the results from a single calculation with fixed CEPD. For molecules, this is true only for linear molecules aligned parallel with the propagation direction of the field. The effects of CEPD are classified as geometric or nongeometric. The observations are exemplified by strong-field calculations on hydrogen.     

Carrier-envelope phase effects of over-saturated few-cycle laser pulses on high-order harmonic generation

We investigate theoretically the high-order harmonic generation driven by few-cycle laser pulses with intensities above the saturated intensity using the Lewenstein model. It is found that the carrier-envelope phase of the laser pulse has great influences on the coherence of the high-order harmonic spectrum in the plateau region when driven by a relatively weaker driver field in the oversaturated regime. While for a much higher intensity the coherence of the high-order harmonic spectrum is almost independent on the carrier-envelope phase.