Field-induced birefringence, also known as cross-polarization wave generation, has played an important role in ultrafast nonlinear optics. In this paper we analyze birefringence induced by relativistic collective motion of electrons driven by a high-intensity laser field. An analytical expression for the phase difference between the parallel and perpendicular polarizations of a weak probe pulse with respect to the polarization of a strong pump pulse as a function of intensity, density, and wavelengths is derived. It is shown that under typical experimental conditions of high-field physics, the effect is well above detection threshold. The analysis is compared with particle-in-cell simulations, and the agreement provides good support for the theory.
