Vacuum Birefringence in a Rotating Magnetic Field

Abstract

We calculate the vacuum polarization-induced ellipticity acquired by a linearly polarized laser beam of angular frequency $\bar{\omega }$ on traversing a region containing a transverse magnetic field rotating with a small angular velocity $\Omega$ around the beam axis. The transmitted beam contains the fundamental frequency $\bar{\omega }$ and weak sidebands of frequency $\bar{\omega }\pm 2\Omega$, but no other sidebands. To first order in small quantities, the ellipticity acquired by the transmitted beam is independent of $\Omega$, and is the same as would be calculated in the approximation of regarding the magnetic field as fixed at its instantaneous angular orientation, using the standard vacuum birefringence formulas for a static magnetic field. Also to first order, there is no rotation of the polarization plane of the transmitted beam. Analogous statements hold when the magnetic field strength is slowly varying in time.

20 pages; v2 has simplification of results of Eqs. (9a,b), and new Sec. 5 giving a perturbation theory derivation of results; v3 has minor revisions suggested by referee--this is final published version; v4, typos corrected

References in corpus (2)

• Experimental observation of optical rotation generated in vacuum by a magnetic field
• Higher Harmonics in Non-Linear Vacuum from QED Effects Without Low Mass Intermediate Particles

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