We review common extensions of particle-in-cell (PIC) schemes which account for strong field phenomena in laser-plasma interactions. After describing the physical processes of interest and their numerical implementation, we provide solutions for several associated methodological and algorithmic problems. We propose a modified event generator that precisely models the entire spectrum of incoherent particle emission without any low-energy cutoff, and which imposes close to the weakest possible demands on the numerical time step. Based on this, we also develop an adaptive event generator that subdivides the time step for locally resolving QED events, allowing for efficient simulation of cascades. Further, we present a unified technical interface for including the processes of interest in different PIC implementations. Two PIC codes which support this interface, picador and elmis, are also briefly reviewed.

We demonstrate that charged particles in a sufficiently intense standing wave are compressed toward, and oscillate synchronously at, the antinodes of the electric field. We call this unusual behavior anomalous radiative trapping (ART). We show using dipole pulses, which offer a path to increased laser intensity, that ART opens up new possibilities for the generation of radiation and particle beams, both of which are high energy, directed, and collimated. ART also provides a mechanism for particle control in high-intensity quantum-electrodynamics experiments.

The generation of ultrastrong attosecond pulses through laser-plasma interactions offers the opportunity to surpass the intensity of any known laboratory radiation source, giving rise to new experimental possibilities, such as quantum electrodynamical tests and matter probing at extremely short scales. Here we demonstrate that a laser irradiated plasma surface can act as an efficient converter from the femto- to the attosecond range, giving a dramatic rise in pulse intensity. Although seemingly similar schemes have been described in the literature, the present setup differs significantly from the previous attempts. We present a model describing the nonlinear process of relativistic laser-plasma interaction. This model, which is applicable to a multitude of phenomena, is shown to be in excellent agreement with particle-in-cell simulations. The model makes it possible to determine a parameter region where the energy conversion from the femto- to the attosecond regime is maximal. Based on the study we propose a concept of laser pulse interaction with a target having a groove-shaped surface, which opens up the potential to exceed an intensity level of ${10}^{26}$ W/cm${}^2$ and observe effects due to nonlinear quantum electrodynamics with upcoming laser sources.

We study nonperturbative pair production in intense, focused laser fields called $e$-dipole pulses. We address the conditions required, such as the quality of the vacuum, for reaching high intensities without initiating beam-depleting cascades, the number of pairs which can be created, and experimental detection of the created pairs. We find that $e$-dipole pulses offer an optimal method of investigating nonperturbative QED.

Accelerated charges radiate, and therefore must lose energy. The impact of this energy loss on particle motion, called radiation reaction, becomes significant in intense-laser matter interactions, where it can reduce collision energies, hinder particle acceleration schemes, and is seemingly unavoidable. Here we show that this common belief breaks down in short laser pulses, and that energy losses and radiation reaction can be controlled and effectively switched off by appropriate tuning of the pulse length. This “quenching” of emission is impossible in classical physics, but becomes possible in QED due to the discrete nature of quantum emissions.