The measurement of vacuum polarisation effects, in particular vacuum birefringence, using combined optical and X-ray laser pulses are now actively pursued. Here we briefly examine the feasibility of two alternative set-ups. The first utilises an alternative target, namely a converging dipole pulse, and the second uses an alternative probe, namely the synchrotron-like emission from highly energetic particles, themselves interacting with a laser pulse. The latter set-up has been proposed for experiments at ELI-NP.

When one takes into account the presence of virtual charged states in the quantum vacuum, a nonlinear self-interaction can arise in the propagation of electromagnetic fields. This self-interaction is often referred to as ‘real photon–photon scattering’. When the centre-of-mass energy of colliding photons is much lower than the rest energy of an electron–positron pair, this quantum effect can be included in the classical field equations of motion as a vacuum current and charge density using the Heisenberg–Euler Lagrangian. Using analytical and numerical methods for subcritical fields, the intrinsic solution to Maxwell’s equations has been found for counterpropagating probe and pump plane waves in the presence of vacuum four- and six-wave mixing. In the corresponding all-order solution for the scattered probe, a route to vacuum high-harmonic generation is identified in which a long phase length can compensate for the weakness of interacting fields. The resulting shocks in the probe carrier wave and envelope are studied for different parameter regimes and polarisation set-ups. In this special issue, we study two additional set-ups: that of a slowly varying single-cycle background to highlight the effect of an oscillating background on the probe harmonic spectrum, and that of a few-cycle probe to highlight the smoothing of the harmonic peaks produced by a wider spectrum of probe photons. We also correct sign errors in an earlier publication.

We study in detail the strong-field QED process of nonlinear Compton scattering in short intense plane wave laser pulses of circular polarization. Our main focus is placed on how the spectrum of the backscattered laser light depends on the shape and duration of the initial short intense pulse. Although this pulse shape dependence is very complicated and highly nonlinear, and has never been addressed explicitly, our analysis reveals that all the dependence on the laser pulse shape is contained in a class of three-parameter master integrals. Here we present completely analytical expressions for the nonlinear Compton spectrum in terms of these master integrals. Moreover, we analyse the universal behaviour of the shape of the spectrum for very high harmonic lines.

Counter-propagating and suitably polarized light (laser) beams can provide conditions for pair production. Here, we consider in more detail the following two situations: (i) in the homogeneity regions of anti-nodes of linearly polarized ultra-high intensity laser beams, the Schwinger process is dynamically assisted by a second high-frequency field, e.g. by an XFEL beam; and (ii) a high-energy probe photon beam colliding with a superposition of co-propagating intense laser and XFEL beams gives rise to the laser-assisted Breit–Wheeler process. The prospects of such bi-frequent field constellations with respect to the feasibility of conversion of light into matter are discussed.

Based on the beating of two Laguerre–Gaussian laser beams in a rippled plasma medium, the effective factors such as plasma density, Gouy phase and orbital angular momentums of input lasers on the output twisted terahertz radiation are investigated. As a result, the amplitude of the generated vortex terahertz radiation is an increasing function of plasma density. The vortex terahertz intensity is strongly dependent on the orbital angular momentum of the input lasers. The terahertz output amplitude increases by decreasing the orbital angular momentum of the Laguerre–Gaussian input lasers. Here, by employing a suitably ripple wavenumber, the destroyer effect of the relative Gouy phase of the input lasers is removed, and perfect phase matching is satisfied.

In this article, self-focusing of an intense circularly polarized laser pulse in the presence of an external oblique magnetic field in hot magnetized plasma, using Maxwell’s equations and the relativistic fluid momentum equation, is studied. An envelope equation governing the spot size of the laser beam for both of left- and right-hand polarizations has been derived and the effects of the plasma temperature and oblique magnetic field on the electron density distribution of hot plasma with respect to variation of the normalized laser spot size has been investigated. Numerical results depict that in right-hand polarization, self-focusing of the laser pulse along the propagation direction in hot magnetized plasma becomes better and more compressed with increasing $\unicode[STIX]{x1D703}$. Inversely, in left-hand polarization, increase of $\unicode[STIX]{x1D703}$ in an oblique magnetic field leads to enhancement of the spot size and reduction self-focusing. Besides, in the plasma density profile, self-focusing of the laser pulse improves in comparison with no oblique magnetic field. Also it is shown that plasma temperature has a key role in the laser spot size, normalized laser output power and the variation of plasma density.