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We consider the Pleba{\'n}ski class of nonlinear theories of vacuumelectrodynamics, i.e., Lagrangian theories that are Lorentz invariant and gaugeinvariant. Our main goal is to derive the transport law of the polarizationplane in such a theory, on an unspecified general-relativistic spacetime andwith an unspecified electromagnetic background field. To that end we start outfrom an approximate-plane-harmonic-wave ansatz that takes the generation ofhigher harmonics into account. By this ansatz, the electromagnetic field iswritten as an asymptotic series with respect to a parameter $\alpha$, where thelimit $\alpha \to 0$ corresponds to sending the frequency to infinity. Wedemonstrate that by solving the generalized Maxwell equations to zeroth andfirst order with respect to $\alpha$ one gets a unique transport law for thepolarization plane along each light ray. We exemplify the general results withthe Born-Infeld theory.

Effects of non-linear vacuum electrodynamics on the polarization plane of light