Vacuum high-harmonic generation and electromagnetic shock

Abstract

When one takes into account the presence of virtual charged states in the quantum vacuum, a nonlinear self-interaction can arise in the propagation of electromagnetic fields. This self-interaction is often referred to as 'real photon-photon scattering'. When the centre-of-mass energy of colliding photons is much lower than the rest energy of an electron-positron pair, this quantum effect can be included in the classical field equations of motion as a vacuum current and charge density using the Heisenberg-Euler Lagrangian. Using analytical and numerical methods for subcritical fields, the intrinsic solution to Maxwell's equations has been found for counterpropagating probe and pump plane waves in the presence of vacuum fourand six-wave mixing. In the corresponding all-order solution for the scattered probe, a route to vacuum high-harmonic generation is identified in which a long phase length can compensate for the weakness of interacting fields. The resulting shocks in the probe carrier wave and envelope are studied for different parameter regimes and polarisation set-ups. In this special issue, we study two additional set-ups: that of a slowly varying single-cycle background to highlight the effect of an oscillating background on the probe harmonic spectrum, and that of a few-cycle probe to highlight the smoothing of the harmonic peaks produced by a wider spectrum of probe photons. We also correct sign errors in an earlier publication.

Numerical Simulations of the Nonlinear Quantum Vacuum in the Heisenberg-Euler Weak-Field Expansion

“…Analytical methods in [15,17] contain a derivation of iterative solutions to the nonlinear equations of motion for zero-frequency backgrounds. With the probe (p) and background (b) pulses as time-dependent 1D Gaussians with the parameters of table 4 the Gaussians are obtained to be, compared to (64),…”

“…Approximate analytical results for this scenario have been derived in [15,17]. The effective vertices for 4-and 6-photon scattering in figure 17 (a) can produce higher-frequency outgoing photons by photon merging.…”

“…There are numerous non-intuitive effects beside the commonly known Casimir effect and Lamb shift that are due to the quantum nature of the vacuum. Among those are vacuum birefringence [3][4][5], polarization rotation [6], vacuum diffraction [7][8][9][10], dispersion [11], scattering [12], reflection [13], generation of higher harmonics [14,15], or photon merging [14,16,17] and photon splitting [11,18,19].…”

“…The present paper introduces a numerical algorithm for the solution of the weak-field approximation of the Heisenberg-Euler equations [36,37] [15]. In [36,37] the numerical scheme outlined in 1D in [15] is extended to full 3D simulations while at the same time the computational load is reduced.…”

“…The present paper introduces a numerical algorithm for the solution of the weak-field approximation of the Heisenberg-Euler equations [36,37] [15]. In [36,37] the numerical scheme outlined in 1D in [15] is extended to full 3D simulations while at the same time the computational load is reduced. The accuracy of the numerical algorithm in [36,37] relies on the assumptions that the fields vary on scales larger than the Compton scale of the electron and the field strengths involved are below the critical field for pair creation in the vacuum.…”