We calculate the optical properties of a vacuum when a static magnetic field B₀ and electric field E₀ are applied perpendicular to the direction of light propagation. Apart from the known Cotton-Mouton and Kerr effects, with crossed fields we find magnetoelectric linear birefringence with optical axes parallel to the external fields. With parallel fields we find magnetoelectric Jones birefringence with optical axes under 45^∘{} with the external fields. Both birefringences are linear in E₀B₀, and have the same magnitude.
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Rikken et al. (2000) studied this question.
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