Polarization of a probe laser beam due to nonlinear QED effects

Nonlinear QED interactions induce different polarization properties on a given probe beam. We consider the polarization effects caused by the photon-photon interaction in laser experiments, when a laser beam propagates through a constant magnetic field or collides with another laser beam. We solve the quantum Boltzmann equation within the framework of the Euler-Heisenberg Lagrangian for both time-dependent and constant background field to explore the time evolution of the Stokes parameters Q, U, and V describing polarization. Assuming an initially linearly polarized probe laser beam, we also calculate the induced ellipticity and rotation of the polarization plane.

Figure 1

Photon-photon interactions in the background of electromagnetic fields, where B represents the classical magnetic field and E represents the classical electric field.

Figure 2

In the left panel, the time evolution of dimensionless Stokes parameters U [upper half plane (green)] and Q [lower half plane (blue)]. In the right panel, the time evolution of dimensionless Stokes parameter V. They are plotted for a 10-keV linearly polarized probe laser beam interacting with a target laser beam in optical frequency $\omega =1\text{eV}$ and peak intensity $I=3\times {10}^{22}\text{W}/{\text{cm}}^2$. These figures show the impact of collision geometry for two laser beams on the evolution of Stokes parameters, for different polar angles $\theta =\pi$ (dashed lines), $\pi /2$ (dotted lines), $\pi /3$ (dot-dashed lines), and $\pi /5$ (solid lines) at a fixed azimuthal angle $\varphi =\pi /8$.

Figure 3

The polarization rotation angle $\mathrm{\Psi }$ (left) and the ellipticity parameter $\epsilon$ as a function of time (right) for the cases depicted in Fig. 2.

Figure 4

Comparison between dimensionless Stokes parameters U, Q, and V in both time-dependent and static background fields. In the time-dependent case we used the numerical solution of Sec. 4b to plot U [dashed (green) line] and Q [dot-dashed (red) line] in the left panel and for V [dotted (red) line] in the right panel. In the static magnetic field we have used the analytic solution of Sec. 4a to plot Q and U [solid (blue) line] in the left panel and V [solid (blue) line] in the right panel. These figures are plotted for a 10-keV linearly polarized probe laser beam interacting with a target laser beam in optical frequency $\omega =1\text{eV}$ and peak intensity $I=3\times {10}^{22}\text{W}/{\text{cm}}^2$.