The shortest light pulses produced to date are of the order of a few tens of attoseconds, with central frequencies in the extreme UV range and bandwidths exceeding tens of electronvolts. They are often produced as a train of pulses separated by half the driving laser period, leading in the frequency domain to a spectrum of high, odd-order harmonics. As light pulses become shorter and more spectrally wide, the widely used approximation consisting of writing the optical waveform as a product of temporal and spatial amplitudes does not apply anymore. Here, we investigate the interplay of temporal and spatial properties of attosecond pulses. We show that the divergence and focus position of the generated harmonics often strongly depend on their frequency, leading to strong chromatic aberrations of the broadband attosecond pulses. Our argument uses a simple analytical model based on Gaussian optics, numerical propagation calculations, and experimental harmonic divergence measurements. This effect needs to be considered for future applications requiring high-quality focusing while retaining the broadband/ultrashort characteristics of the radiation.

No abstract

The ion-channel laser (ICL) is an ultra-compact version of the free-electron laser (FEL), with the undulator replaced by an ion channel. Previous studies of the ICL assumed transverse momentum amplitudes which were unrealistically small for experiments. Here we show that this restriction can be removed by correctly taking into account the dependence of the resonance between oscillations and emitted field on the betatron amplitude, which must be treated as variable. The ICL model with this essential addition is described using the well-known formalism for the FEL. Analysis of the resulting scaled equations shows a realistic prospect of building a compact ICL source for fundamental wavelengths down to UV, and harmonics potentially extending to x-rays. The gain parameter ρ can attain values as high as 0.03, which permits driving an ICL with electron bunches with realistic emittance.

Many applications of the extreme ultraviolet (XUV) radiation obtained by high-order harmonic generation (HHG) in gases require a small focus area in order to enable attosecond pulses to reach a high intensity. Here, high-order harmonics generated in Ar with a multiterawatt laser system in a loose focusing geometry are focused to a few micrometers using two toroidal mirrors in a Wolter configuration with a high demagnification factor. Using a knife-edge measurement technique, we determine the position and size of the XUV foci as a function of harmonic order. We show that the focus properties vary with harmonic order and the generation conditions. Simulations, based on a classical description of the harmonic dipole phase and assuming that the individual harmonics can be described as Gaussian beams, reproduce the experimental behavior. We discuss how the generation geometry affects the intensity and duration of the focused attosecond pulses.

The ponderomotive force is derived for a relativistic charged particle entering an electromagnetic standing wave with a general three-dimensional field distribution and a nonrelativistic intensity, using a perturbation expansion method. It is shown that the well-known ponderomotive gradient force expression does not hold for this situation. The modified expression is still of simple gradient form, but contains additional polarization-dependent terms. These terms arise because the relativistic translational velocity induces a quiver motion in the direction of the magnetic force, which is the direction of large field gradients. Oscillation of the Lorentz factor effectively doubles this magnetic contribution. The derived ponderomotive force generalizes the polarization-dependent electron motion in a standing wave obtained earlier [A.E. Kaplan and A.L. Pokrovsky, Phys. Rev. Lett. 95, 053601 (2005)]. Comparison with simulations in the case of a realistic, non-idealized, three-dimensional field configuration confirms the general validity of the analytical results.