Refraction of light by light in vacuum

In very intense electromagnetic fields, the vacuum refractive index is expected to be modified due to nonlinear quantum electrodynamics (QED) properties. Several experimental tests using high intensity lasers have been proposed to observe electromagnetic nonlinearities in vacuum, such as the diffraction or the reflection of intense laser pulses. We propose a new approach which consists in observing the refraction, i.e. the rotation of the waveplanes of a probe laser pulse crossing a transverse vacuum index gradient. The latter is produced by the interaction of two very intense and ultra short laser pulses, used as pump pulses. At the maximum of the index gradient, the refraction angle of the probe pulse is estimated to be $0.2 \times (\frac{w_0}{10 \mathrm{\mu m}})^{-3} \times \frac{I}{1 \mathrm{J}}$~picoradians, where $I$ is the total energy of the two pump pulses and $w_0$ is the minimum waist (fwhm) at the interaction area. Assuming the most intense laser pulses attainable by the LASERIX facility ($I = 25$~J, 30~fs fwhm duration, 800~nm central wavelength) and assuming a minimum waist of $w=10 \mathrm{\mu m}$ (fwhm) (corresponding to an intensity of the order of $10^{21}$~W/cm$^2$), the expected maximum refraction angle is about 5~picoradians. An experimental setup, using a Sagnac interferometer, is proposed to perform this measurement.