We investigate the electromagnetic energy flow in a relativistically self-guided laser pulse. Three dimensional particle-in-cell (PIC) simulations show the formation of spatiotemporal phase defects in the pulse, corresponding to vortical centers in the Poynting vector. Spatio-temporal vortex formation and propagation is a universal and dominant feature of relativistic self-focusing collapse and filamentation. As an example, these vortices control the dynamics of filament reformation if self-guiding is disrupted.
Relativistic self-focusing and self-guiding is a process fundamental to laser wakefield acceleration (LWFA). Advances in dense gas targets now make relativistic self-guiding and LWFA available even to modest laser systems . We present results from 3D PIC simulations investigating details of energy flow within a relativistically self-guiding laser pulse. We find, similar to our recent results for optical filamentation in air , that relativistic self-focusing and collapse arrest give rise to spatio-temporal optical vortices (STOVs) in the laser pulse’s electromagnetic energy flow.
Borrowing language from atmospheric optical filamentation, we identify a ‘core’ of laser energy contained within a nonlinear plasma wave, with a co-propagating ‘reservoir’ of laser energy surrounding it. The core and the reservoir exchange energy, approaching a state of dynamic equilibrium. We present a framework for a moving-window Poynting’s theorem by defining a moving-window Poynting vector. This Poynting vector exhibits vortices in energy flow corresponding to STOVs in the laser phase identified by Jhajj et al.
Characterization of the transverse energy distribution reveals a significant fraction of the total energy in the reservoir outside of the relativistic filament core. The injection of accelerated electrons is seen to disrupt the relativistic filament, causing the laser energy to diffract away to radii several times the plasma wavelength. STOV dynamics then cause this energy to coalesce and form a new filament some distance later, illustrating the “self-healing” of relativistic filaments.
Laser pulses with preformed STOVs are implemented using a superposition of LG modes and are shown to have significant effect on the formation of relativistic filaments. Pulses with pre-formed STOVs impose an initial perturbation to the Poynting vector field which hinders or assists filament formation, depending on vorticity.
 A.J. Goers et al. Phys. Rev. Lett. 115, 194802
 N. Jhajj et al. arXiv:1604.01751[physics.optics]
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