General theory of carrier-envelope phase effects

We present a general framework for understanding carrier-envelope phase (CEP) effects in a quantum system interacting with an intense, short laser pulse. We establish a simple connection between the CEP and the wave function that can be exploited to obtain the full CEP dependence of an observable given the wave function at a single CEP. Within this framework, all CEP effects are interpreted as interference between different photon amplitudes which, in turn, can be used to put limits on the pulse lengths and intensities required to see significant CEP effects.     

Nonlinear phase noise generated in air-silica microstructure fiber and its effect on carrier-envelope phase

We present measurements of the nonlinear phase noise that is due to amplitude-to-phase conversion in air-silica microstructure fiber that is utilized to broaden the frequency comb from a mode-locked femtosecond laser to an optical octave. When the octave of the continuum is employed to phase stabilize the laser-pulse train, this phase noise causes a change in the carrier-envelope phase of 3784-rad/nJ change in pulse energy. As a result, the jitter on the carrier-envelope phase that is due to fiber noise, from 0.03 Hz-55 kHz, is ~0.5rad .     

Long-term carrier-envelope phase coherence

The carrier-envelope phase of the pulse train emitted by a 10-fs mode-locked laser has been stabilized such that carrier-envelope phase coherence is maintained for at least 150 s (measurement limited). The phase coherence time was measured independently of the feedback loop.     

Role of the carrier-envelope phase in laser filamentation

We numerically study the influence of the initial carrier-envelope phase (CEP) on the filamentation of ultrashort laser pulses in noble gas. Emphasis is put on the CEP-induced changes of pulses that reach their clamping intensity during near-cycle self-compression. In other propagation regimes, the CEP does not significantly alter the pulse evolution. Our results indicate that third-harmonic generation, compared to plasma generation, is dominant in driving these changes. Finally, the stability of the filament CEP against shot-to-shot fluctuations is examined.     

Determining the phase-energy coupling coefficient in carrier-envelope phase measurements

For f-to-2f interferometers based on white-light generation in sapphire plates, the accuracy of the carrier-envelope (CE) phase measurement and stabilization is affected by the laser energy fluctuation. The coupling coefficient between the CE phase and the laser energy has been determined by modulating the pulse energy in an in-loop f-to-2f interferometer while measuring the CE phase variation with an out-loop interferometer. When the total spectral phase measured by the in-loop interferometer was locked, a 1% change in laser energy caused a 160 mrad shift in the CE phase of the output pulses.     

Effects of the carrier-envelope phase in the multiphoton ionization regime

We theoretically investigate the effects of the carrier-envelope phase of few-cycle laser pulses in the multiphoton ionization regime. For atoms with low ionization potential, total ionization yield barely exhibits phase dependence, as expected. However, population of some bound states clearly shows phase dependence. This implies that the measurement of the carrier-envelope phase would be possible through the photoemission between bound states without energy-and-angle-resolved photoelectron detection. The considered scheme could be particularly useful to measure the carrier-envelope phase for a light source without an amplifier, such as a laser oscillator, which cannot provide sufficient pulse energy to induce tunneling ionization.     

Single-atom effects in high-order harmonic generation: role of carrier-envelope phase in the few-optical-cycle regime

Recently the role of the carrier-envelope phase of few-optical-cycle light pulses on high-order harmonic generation has been experimentally observed. By using a three-dimensional nonadiabatic propagation model, we show that the observed carrier-envelope phase dependence of the spectral characteristics of the harmonic radiation is essentially a single-atom effect. Nonadiabatic single-atom response has been calculated in the framework of the saddle-point approximation. PACS 42.65.Ky; 42.65.Re; 42.50.Hz     

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     

Carrier-wave Rabi flopping: role of the carrier-envelope phase

Recently, a dependence of Rabi flopping on the carrier-envelope phase of the exciting laser pulses was predicted theoretically [Phys. Rev. Lett. 89, 127401 (2002)] for excitation of a thin semiconductor film with intense few-cycle pulses. Here, we report corresponding experiments on 50-100-nm thin GaAs films excited with 5-fs pulses. We find a dependence on the carrier-envelope phase arising from the interference of sidebands from the fundamental or the third-harmonic Mollow triplet, respectively, with surface second-harmonic generation.     

Observation of carrier-envelope phase phenomena in the multi-optical-cycle regime

So far the role of the carrier-envelope phase of a light pulse has been clearly experimentally evidenced only in the sub-6-fs temporal regime. Here we show, both experimentally and theoretically, the influence of the carrier-envelope phase of a multi-optical-cycle light pulse on high-order harmonic generation. For the first time, we demonstrate that the short and long electron quantum paths contributing to harmonic generation are influenced in a different way by the pulse carrier-envelope phase.     

Control and precise measurement of carrier-envelope phase dynamics

The evolution of the carrier-envelope offset phase _CEO of a 10-fs Ti:Sapphire laser has been traced on time scales from microseconds to seconds using various techniques. Precise locking of this phase has been achieved down to an rms deviation of 1/40 of an optical cycle. Stability measurements have been performed independently of the feedback loop, focusing on the phase jitter introduced by the feedback loop itself, the pump laser, and a prism compressor. It is shown that a multi-mode pump laser introduces more phase noise on _CEO than a single-mode pump laser. PACS 42.65.Re; 42.60.Mi; 42.62.Eh     

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.     

Experimental implementation of optical clockwork without carrier-envelope phase control

We demonstrate optical clockwork without the need for carrier-envelope phase control by use of sum-frequency generation between a continuous-wave optical parametric oscillator at 3.39 microm and a femtosecond mode-locked Ti:sapphire laser with two strong spectral peaks at 834 and 670 nm, a spectral difference matched by the 3.39-microm radiation.     

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.     

A linear optical method for measuring the carrier-envelope phase drift

The carrier-envelope offset frequency of a laser oscillator is determined from the visibility of spectrally resolved fringes in a combined two-path multiple-path interferometer. At maximum visibility the pulses have zero carrier-envelope phase drift, while the visibility becomes zero for uncorrelated pulses. The method is widely independent of bandwidth and pulse energy. The effects of carrier-envelope offset phase noise, finite detection time, and dispersion are also discussed. M. G?rbe and C. Grebing have equally contributed to this paper.     

Bandwidth-independent linear method for detection of the carrier-envelope offset phase

We propose and demonstrate a novel linear procedure for measurement of the carrier-envelope offset (CEO) phase of femtosecond oscillators. The technique is based on a Mach-Zehnder interferometer, a ring resonator, and a spectrograph. In this scheme, interference between subsequent pulses from a pulse train may frustrate the interference between identical pulses in the Mach-Zehnder, resulting in a modification of interference contrast depending on the CEO phase. We suggest spectrally and spatially resolved interferometry for robust detection of the fringe visibility. It is shown by numerical simulations and experimentally demonstrated that the visibility of such fringes uniquely depends on the CEO phase of the pulse train. Since the method relies only on linear interactions and does not require any nonlinear conversion, it allows characterizing the CEO frequency of mode-locked oscillators with virtually arbitrarily low bandwidth and power levels.     

Influence of the carrier-envelope phase of few-cycle pulses on ponderomotive surface-plasmon electron acceleration

Control over basic processes through the electric field of a light wave can lead to new knowledge of fundamental light-matter interaction phenomena. We demonstrate, for the first time, that surface-plasmon (SP) electron acceleration can be coherently controlled through the carrier-envelope phase (CEP) of an excitation optical pulse. Analysis indicates that the physical origin of the CEP sensitivity arises from the electron's ponderomotive interaction with the oscillating electromagnetic field of the SP wave. The ponderomotive electron acceleration mechanism provides sensitive (nJ energies), high-contrast, single-shot CEP measurement capability of few-cycle laser pulses.     

Agile linear interferometric method for carrier-envelope phase drift measurement

A bandwidth-independent and linear interferometric method for the measurement of the carrier-envelope phase drift of ultrashort pulse trains is demonstrated. The pulses are temporally overlapped in a resonant multiple-beam interferometer. From the position of the spectral interference pattern, the relative carrier-envelope phase between two subsequent oscillator pulses is obtained at data acquisition rates up to 200 Hz. Cross calibration has been performed by f-to-2f interferometry in two independent experiments. The optical length of the interferometer has been actively stabilized, leading to a phase jitter of 117 mrad (rms). These results indicate a reduced noise and quicker data acquisition in comparison with previous linear methods for measuring the carrier-envelope phase drift.     

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