Photon polarization tensor in pulsed Hermite- and Laguerre-Gaussian beams

Abstract

In this article, we provide analytical expressions for the photon polarization tensor in pulsed Hermite-and Laguerre-Gaussian laser beams. Our results are based on a locally constant field approximation of the one-loop Heisenberg-Euler effective Lagrangian for quantum electrodynamics.Hence, by construction they are limited to slowly varying electromagnetic fields, varying on spatial and temporal scales significantly larger than the Compton wavelength/time of the electron. The latter criterion is fulfilled by all laser beams currently available in the laboratory. Our findings will, e.g., be relevant for the study of vacuum birefringence experienced by probe photons brought into collision with a high-intensity laser pulse which can be represented as a superposition of either Hermite-or Laguerre-Gaussian modes. * Electronic address: felix.karbstein@uni-jena.de † Electronic address: mosmanea@tpu.ru

Probing Vacuum Polarization Effects with High-Intensity Lasers

“…where we neglected subleading terms of O( 1 τ l ω l ); see Ref. [79] for a detailed discussion. Obviously, the dimensionless quantity 1 τ l ω l corresponds to a small parameter if the pulse consists of many cycles, as is typically the case for currently available high-intensity laser pulses, justifying this approximation.…”

X-ray photon scattering at a focused high-intensity laser pulse

“…To describe high-intensity laser pulses of finite energy, we have moreover supplemented the paraxial beam solution by a Gaussian temporal pulse profile of duration τ , ensuring that it reaches its maximum in the beam focus at t = z = 0. This ad hoc modification gives rise to violations of Maxwell's equations in vacuum of O( 1 τ Ω ), and hence should yield reliable results for τ Ω ≫ 1 [28,38]. The latter criterion is typically met for state-of-the-art high-intensity laser pulses.…”

“…[23,26]. To keep this article self-contained, we reproduce the result [28] for the photon polarization tensor in a linearly polarized pulsed LG beam here. Taking into account the quasi-elastic contribution only, it can be represented as…”

“…, in the limit of an infinitely long pulse duration τ we recover a strictly elastic contribution. Furthermore, note that the electric peak field strength of a given mode can be straightforwardly related to the energy put into that mode as [28]…”

“…The high-intensity laser field enters the calculation via the photon polarization tensor, which has been evaluated in the background of a pulsed LG beam in Ref. [28] based on a locally constant field approximation of the Heisenberg-Euler effective Lagrangian.…”