Numerical Simulations of the Nonlinear Quantum Vacuum in the Heisenberg-Euler Weak-Field Expansion
The Heisenberg-Euler theory of the quantum vacuum supplements Maxwell's theory of electromagnetism with nonlinear light-light interactions. These originate in vacuum fluctuations, a key prediction of quantum theory, and can be triggered by high-intensity laser pulses, causing a variety of intriguing phenomena. A highly accurate numerical scheme for solving the nonlinear equations due to the leading orders of the Heisenberg-Euler weak-field expansion is presented. The algorithm possesses an almost linear vacuum dispersion relation even for comparably small wavelengths and incorporates a nonphysical modes filter. The implemented solver is tested in one spatial dimension against a set of known analytical results for vacuum birefringence and harmonic generation. More complex scenarios for harmonic generation are demonstrated in two and three spatial dimensions.