Description
Electron-positron pairs are produced by ultra-intense (multi-petawatt) laser pulses through the multiphoton Breit-Wheeler process [1]. The required peak intensity can be reduced by forming a tightly confined hot spot using several counter-propagating pulses [2]. Our aim is to further optimise this approach and move it closer to experimentally achievable conditions.
Numerical simulations of this scheme are typically performed with particle-in-cell codes with additional radiation-reaction and QED modules, such as Smilei [3]. These codes usually employ a Cartesian grid. While we work with the precise design of the hot spot at the centre of the domain, the corresponding boundary conditions to describe the incident pulses are necessary. In our case, this requires propagating a general electromagnetic field between two arbitrarily tilted planes. An arbitrary rotation is more subtle than composing elementary rotations with respect to the simulation-box axes [4] because rotations form a non-commutative algebra. We therefore use a general formulation based on a full rotation matrix [5], analogous to a complete Euler-angle description.
This contribution presents the development and implementation of this technique and places it in the broader context of the scheme, which requires us to optimise the geometry of the incident beams and to consider feasible conditions for its realisation.
[1] G. Breit and J. A. Wheeler, Collision of Two Light Quanta, https://doi.org/10.1103/PhysRev.46.1087
[2] M. Jirka and S. Bulanov, Effects of colliding laser pulses polarization on $e^−e^+$ cascade development in extreme focusing, https://doi.org/10.1103/PhysRevLett.133.125001
[3] J. Derouillat et al., Smilei : A collaborative, open-source, multi-purpose particle-in-cell code for plasma simulation https://doi.org/10.1016/j.cpc.2017.09.024
[4] F. Pérez and M. Grech, Oblique-incidence, arbitrary-profile wave injection for electromagnetic simulations, https://doi.org/10.1103/PhysRevE.99.033307
[5] K. Matsushima et. al, Fast calculation method for optical diffraction on tilted planes by use of the angular spectrum of plane waves, https://doi.org/10.1364/JOSAA.20.001755