An implicit ODE-based numerical solver for the simulation of the Heisenberg-Euler equations in 3+1 dimensions

Abstract

With the advent of ultra-high power lasers the nonlinear nature of the vacuum of quantum electrodynamics (QED) can be probed. Due to the highly nonlinear structure of the underlying equations new numerical algorithms are required. A numerical scheme for simulating the nonlinear optical effects of the QED vacuum in up to 3 spatial dimensions plus time is derived. Its properties are discussed. The validity of the numerical approach is verified with the help of known analytic results. The algorithm is used to explore nonlinear all optical effects of the nonlinear vacuum for which analytic methods are inefficient or impossible.

References in corpus (2)

• Vacuum birefringence in strong inhomogeneous electromagnetic fields
• Vacuum high harmonic generation in the shock regime

Cited by in corpus (6)

• Advances in QED with intense background fields
• All-optical signatures of Strong-Field QED in the vacuum emission picture
• Photon-photon scattering at the high-intensity frontier
• All-optical signatures of quantum vacuum nonlinearities in generic laser fields
• The effect of interference on the trident process in a constant crossed field
• Numerical Simulations of the Nonlinear Quantum Vacuum in the Heisenberg-Euler Weak-Field Expansion