Refraction of light by light in vacuum

In very intense electromagnetic fields, the vacuum refractive index is expected to be modified due to non linear QED properties. Up to now, these predictions are tested by searching phase shifts in the propagation of polarized light through uniform magnetic fields. We propose a new approach which consists in producing a vacuum index gradient and send a light beam trough it in order to detect its angular deviation. The vacuum index gradient, similar to a "prismatic vacuum", is created by the interaction of two very intense and ultra short laser pulses, used as pump pulses. At the maximum of the index gradient, the deflection angle of the probe pulse is estimated to be $2 \ 10^{-13} \times (\frac{w_0}{10 \mu\mathrm{m}})^{-3} \times \frac{I}{1 \mathrm{J}}$ radians, where $I$ is the total energy of the two pump pulses and $w_0$ is the minimum waist (fwhm) at the interaction area of the two pump pulses. 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 $w=10 \mu\mathrm{m}$ (fwhm) (corresponding to an intensity of the order of $10^{21}$ W/cm$^2$), the expected deflection angle is about $5 \ 10^{-12}$ radians at the maximum of the index gradient. We propose to measure it with a Sagnac interferometer.