Birefringence - Vacuum Birefringence

Vacuum Birefringence

Due to quantum effects, the vacuum can behave like a birefringent medium. In the limit of weak fields and slowly varying fields, the Euler-Heisenberg Lagrangian becomes:

where is the fine structure constant and m the electron mass.

The effective electric permittivity tensor and magnetic permeability tensor are then given by :

$\begin{align} \epsilon_{ik}&= \left\delta_{ik} + \frac{28\alpha^{2}}{45 m^{4}}B_{i}B_{k}\\ \mu_{ik}&=\left\delta_{ik} + \frac{28\alpha^{2}}{45 m^{4}}E_{i}E_{k} \end{align}$

In the case of a plane wave propagating through a region of constant magnetic field, one finds that there are two eigenmodes. One has the electric component of the plane wave perpendicular to the plane spanned by the wavevector and the magnetic field, the other has the magnetic component perpendicular to this plane. The former has an index of refraction of where is the angle between the wave vector and the magnetic field, while the latter has an index of refraction of .

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Famous quotes containing the word vacuum:

“If it were possible to have a life absolutely free from every feeling of sin, what a terrifying vacuum it would be!”
—Cesare Pavese (1908–1950)