Generating single attosecond pulses via spatial filtering

Isolated attosecond pulse generation in a semi-infinite gas cell driven by time-gated phase matching

Isolated attosecond pulse (IAP) generation usually involves the use of short-medium gas cells operated at high pressures. In contrast, long-medium schemes at low pressures are commonly perceived as inherently unsuitable for IAP generation due to the nonlinear phenomena that challenge favourable phase-matching conditions. Here we provide clear experimental evidence on the generation of isolated extreme-ultraviolet attosecond pulses in a semi-infinite gas cell, demonstrating the use of extended-medium geometries for effective production of IAPs. To gain a deeper understanding we develop a simulation method for high-order harmonic generation (HHG), which combines nonlinear propagation with macroscopic HHG solving the 3D time-dependent Schrödinger equation at the single-atom level. Our simulations reveal that the nonlinear spatio-temporal reshaping of the driving field, observed in the experiment as a bright plasma channel, acts as a self-regulating mechanism boosting the phase-matching conditions for the generation of IAPs.

Compact realization of all-attosecond pump-probe spectroscopy

The ability to perform attosecond-pump attosecond-probe spectroscopy (APAPS) is a longstanding goal in ultrafast science. While first pioneering experiments demonstrated the feasibility of APAPS, the low repetition rates (10 to 120 Hz) and the large footprints of existing setups have so far hindered the widespread exploitation of APAPS. Here, we demonstrate two-color APAPS using a commercial laser system at 1 kHz, straightforward post-compression in a hollow-core fiber, and a compact high-harmonic generation (HHG) setup. The latter enables the generation of intense extreme-ultraviolet (XUV) pulses by using an out-of-focus HHG geometry and by exploiting a transient blueshift of the driving laser in the HHG medium. Near-isolated attosecond pulses are generated, as demonstrated by one-color and two-color XUV-pump XUV-probe experiments. Our concept allows selective pumping and probing on extremely short timescales in many laboratories and permits investigations of fundamental processes that are not accessible by other pump-probe techniques.

Optimal generation and isolation of attosecond pulses in an overdriven ionized medium

We identify optimal conditions for the generation and isolation of attosecond pulses in an overdriven ionized medium. In a high-pressure and highly ionized gas, the spatiotemporal wavefront rotation of a driving laser can be optimized, leading to complete spatial separation of successive attosecond bursts in the far field. The resulting isolated attosecond pulses (IAPs) are much more divergent such that they are spatially separated from the driving laser in the far field. We show that the time delay of near-field harmonic emission along the radial distance determines the divergence of the attosecond burst in the far field. The generated IAPs are phase matched upon propagation in the second half of the gas medium. Validity of the generation scheme is tested at different carrier-envelope phases for a few-cycle laser pulse and by synthesizing the fundamental and its second harmonic field for a long-duration pulse.

Analytical wave function of an atomic electron under the action of a powerful ultrashort electromagnetic field pulse

The interaction of atomic systems with high-power ultrashort electromagnetic field pulses (USPs) is currently the subject of many theoretical and experimental studies. However, a wave function has yet to be developed for the atomic electron located in such fields, including relativistic fields. In this Letter, an equation is obtained that is similar to the Schrödinger equation for the fields under consideration, but which takes into the account relativistic effects in powerful spatially inhomogeneous fields of USPs. Using the sudden disturbance approximation, an exact solution of the resulting equation is obtained in the form of an analytical wave function which is suitable for any type and form of ultrashort pulse, and which takes into account its magnetic component. It is shown that the obtained wave function satisfies the necessary completeness condition in quantum mechanics.

Optics-less focusing of XUV high-order harmonics

By experimentally studying high-order harmonic beams generated in gases, we show how the spatial characteristics of these ultrashort extreme-ultraviolet (XUV) beams can be finely controlled when a single fundamental beam generates harmonics in a thin gas medium. We demonstrate that these XUV beams can be emitted as converging beams and thereby get focused after generation. We study this optics-less focusing using a spatially chirped beam that acts as a probe located inside the harmonic generation medium. We analyze the XUV beam evolution with an analytical model and obtain very good agreement with experimental measurements. The XUV foci sizes and positions vary strongly with the harmonic order, and the XUV waist can be located at arbitrarily large distances from the generating medium. We discuss how intense XUV fields can be obtained with optics-less focusing and how the order-dependent XUV beam characteristics are compatible with broadband XUV irradiation and attosecond science.

Generation of an Adjustable Optical Cage through Focusing an Apertured Bessel-Gaussian Correlated Schell-Model Beam

An adjustable optical cage generated by focusing a partially coherent beam with nonconventional correlation function named the Bessel–Gaussian correlated Schell-model (BGCSM) beam is investigated in detail. With the help of the generalized Huygens–Fresnel integral and complex Gaussian function expansion, the analytical formula of the BGCSM beam passing through an apertured ABCD optical system was derived. Our numerical results show that the generated optical cage can be moderately adjusted by the aperture radius, the spatial coherence width, and the parameter β of the BGCSM beam. Furthermore, the effect of these parameters on the effective beam size and the spectral degree of coherence were also analyzed. The optical cage with adjustable size can be applied for particle trapping and material thermal processing.

High-flux soft x-ray harmonic generation from ionization-shaped few-cycle laser pulses

Laser-driven high-harmonic generation provides the only demonstrated route to generating stable, tabletop attosecond x-ray pulses but has low flux compared to other x-ray technologies. We show that high-harmonic generation can produce higher photon energies and flux by using higher laser intensities than are typical, strongly ionizing the medium and creating plasma that reshapes the driving laser field. We obtain high harmonics capable of supporting attosecond pulses up to photon energies of 600 eV and a photon flux inside the water window (284 to 540 eV) 10 times higher than previous attosecond sources. We demonstrate that operating in this regime is key for attosecond pulse generation in the x-ray range and will become increasingly important as harmonic generation moves to fields that drive even longer wavelengths.

Spatial characterization of Bessel-like beams for strong-field physics

We present a compact, simple design for the generation and tuning of both the spot size and effective focal length of Bessel-like beams. In particular, this setup provides an important tool for the use of Bessel-like beams with high-power, femtosecond laser systems. Using a shallow angle axicon in conjunction with a spherical lens, we show that it is possible to focus Bessel-like modes to comparable focal spot sizes to sharp axicons while maintaining a long effective focal length. The resulting focal profiles are characterized in detail using an accurate high dynamic range imaging technique. Quantitatively, we introduce a metric (R_0.8) which defines the spot-size containing 80% of the total energy. Our setup overcomes the typical compromise between long working distances and small spot sizes. This is particularly relevant for strong-field physics where most experiments must operate in vacuum.

Optimal generation of spatially coherent soft X-ray isolated attosecond pulses in a gas-filled waveguide using two-color synthesized laser pulses

We numerically demonstrate the generation of intense, low-divergence soft X-ray isolated attosecond pulses in a gas-filled hollow waveguide using synthesized few-cycle two-color laser waveforms. The waveform is a superposition of a fundamental and its second harmonic optimized such that highest harmonic yields are emitted from each atom. We then optimize the gas pressure and the length and radius of the waveguide such that bright coherent high-order harmonics with angular divergence smaller than 1 mrad are generated, for photon energy from the extreme ultraviolet to soft X-rays. By selecting a proper spectral range enhanced isolated attosecond pulses are generated. We study how dynamic phase matching caused by the interplay among waveguide mode, neutral atomic dispersion, and plasma effect is achieved at the optimal macroscopic conditions, by performing time-frequency analysis and by analyzing the evolution of the driving laser's electric field during the propagation. Our results, when combined with the on-going push of high-repetition-rate lasers (sub- to few MHz's) may eventually lead to the generation of high-flux, low-divergence soft X-ray tabletop isolated attosecond pulses for applications.

Efficient generation of high beam-quality attosecond pulse with polarization-gating Bessel-Gauss beam from highly-ionized media

Single attosecond pulse generation with polarization gating Bessel-Gauss beam in relatively strongly-ionized media is investigated. The results show that Bessel-Gauss beam has the ability to suppress the spatial plasma dispersion effects caused by high density of free electrons, thus the laser field can maintain its spatial profile through highly-ionized medium. This indicates the use of Bessel-Gauss beam has advantages over Gaussian beam in high harmonic generation under high ionization conditions. In our scheme, significant improvement of spatiotemporal properties of harmonics is achieved and an isolated attosecond pulse with high beam quality is filtered out using polarization gating.

Dramatic cutoff extension and broadband supercontinuum generation in multi-cycle two color pulses

We propose a method to markedly increase the electron-recollision kinetic energy, using the combination of a 0.8 μm/13 fs driving pulse with a much weaker multi-cycle mid-infrared pulse at 10.4 μm. The results show that the synthesized field effectively lengthens the accelerated distance of electron wave packet and the harmonic cutoff is significantly extended to IP+26UP, which is covered with the water-window spectral region. In addition, only one single quantum path contributes to harmonics, and those higher than IP+15UP become continuous. This supercontinuum can support the generation of an isolated sub-100 as pulse with tunable central wavelength and also the pulse with the duration below one atomic unit of time (24 as). Moreover, our scheme can further extend to more longer driving pulses, which provides a dramatic approach for cutoff extension and broadband supercontinuum generation with multi-cycle pump pulses.

Isolated attosecond pulse generation from pre-excited medium with a chirped and chirped-free two-color field

We theoretically investigate the isolated attosecond pulse generation from pre-excited medium with a chirped and chirped-free two-color field. It is found that the large initial population of the excited state can lead to the high density of the free electrons in the medium and the large distortion of the driving laser field after propagation, though it benefits large enhancement of harmonic intensity in single atom response. These effects can weaken the phase-match of the macroscopic supercontinuum. On the contrary, the small initial population of 4% can generate well phase-match intense supercontinuum. We also investigate an isolated attosecond pulse generation by using a filter centered on axis to select the harmonics in the far field. Our results reveal that the radius of the spatial filter should be chosen to be small enough to reduce the duration of the isolated attosecond pulse due to the curvature effect of spatiotemporal profiles of the generated attosecond pulses in the far field.

Nonadiabatic propagation effect for generating isolated sub-100 as pulses in the high-order harmonic plateau

A robust scheme is proposed to generate an isolated sub-100 as pulse by using a 5fs/800nm driving pulse in combination with a macroscopic propagation effect. We demonstrate that one of the generated attosecond bursts in the high-order harmonic plateau can be efficiently dominant only when both the gas pressure and the gas cell length are properly chosen. We also show that this method can relax the dependence on the stabilization of the carrier-envelope phase (CEP) of the driving pulse. A single sub-100as pulse with only 10as duration variation can be produced even for about 50% fluctuation of the CEP. Under optimized conditions, an isolated 60as pulse can be directly generated without any additional phase compensation.

The robustness of attosecond streaking measurements

We investigate attosecond streaking measurements, where a spectrogram is described by an ensemble of electron wave packets. Such a description may be required for processes more complex than direct photoemission from an isolated atom; an ensemble of wave packets may also be needed to describe the role of shot-to-shot fluctuations or a non-uniform spatio-temporal profile of attosecond light pulses. Under these conditions, we examine the performance of conventional (FROG) analysis of attosecond streaking measurements.

Generating single attosecond pulse using multi-cycle lasers in a polarization gate

We analyze the macroscopic effects which are responsible for producing clean isolated pulses lasting few hundreds of attoseconds when starting from multi-cycle fundamental pulses. In particular, we consider a polarization gating scheme and show that, at high fundamental peak intensities, in the range 0.7-1 PWcm(-2), it usually produces three-four main attosecond pulses of radiation at single dipole level, just located in the leading edge of the laser pulse. We describe the physical mechanisms contributing to the formation of a single attosecond pulse by using a three dimensional non-adiabatic model and a quantum trajectory phase calculation. An analysis of the scheme optimization and stability against various parameters is performed in view of an experimental scheme implementation.

Measurement and optimization of isolated attosecond pulse contrast

An experimental method is presented to experimentally measure and control the carrier-envelope-phase (CEP)-dependent pulse-energy contrast of isolated attosecond pulses. By scanning the CEP and measuring the photoelectron spectrum produced by the combined action of the attosecond pulses and the high-harmonic driving laser pulses at zero relative time delay, one can extract the pulse-energy ratio between the main attosecond pulse and its neighboring satellite pulses arriving in preceding or subsequent half-cycles of the driver pulse. Moreover, this method allows fast and efficient in situ retrieval of the optimal CEP for high-contrast isolated attosecond pulse generation.

Characterizing isolated attosecond pulses from hollow-core waveguides using multi-cycle driving pulses

The generation of attosecond-duration light pulses using the high-order harmonic generation process is a rapidly evolving area of research. In this work, we combine experimental measurements with careful numerical analysis, to demonstrate that even relatively long-duration, 15 fs, carrier-envelope-phase (CEP) unstabilized near-infrared (NIR) pulses can generate isolated attosecond extreme-ultraviolet (EUV) pulses by the dynamically-changing phase matching conditions in a hollow-core waveguide geometry. The measurements are made using the laser-assisted photoelectric effect to cross-correlate the EUV pulse with the NIR pulse. A FROG CRAB analysis of the resulting traces (photoelectron signal versus photoelectron energy and EUV-NIR delay) is performed using a generalized projections (GP) algorithm, adapted for a wide-angle photoelectron detection geometry and non-CEP stabilized driving laser pulses. In addition, we performed direct FROG CRAB simulations under the same conditions. Such direct simulations allow more freedom to explore the effect of specific pulse parameters on FROG CRAB traces than is possible using the automated GP retrieval algorithm. Our analysis shows that an isolated pulse with duration of approximately 200 attoseconds can result from CEP unstabilized, high intensity approximately 15 fs multi-cycle driving pulses coupled into a hollow-core waveguide filled with low-pressure Argon gas. These are significantly longer driving pulses than used in other experimental implementations of isolated attosecond pulses.

Spectral signature of short attosecond pulse trains

We report experimental measurements of high-order harmonic spectra generated in Ar using a carrier-envelope-offset (CEO) stabilized 12 fs, 800 nm laser field and a fraction (less than 10%) of its second harmonic. Additional spectral peaks are observed between the harmonic peaks, which are due to interferences between multiple pulses in the train. The position of these peaks varies with the CEO and their number is directly related to the number of pulses in the train. An analytical model, as well as numerical simulations, support our interpretation.