Refraction of light by light in vacuum

Abstract

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 × ( w 0 10µm ) −3 × I 1J picoradians, where I is the total energy of the two pump pulses and w0 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 = 10µm (fwhm) (corresponding to an intensity of the order of 10 21

An addendum to the Heisenberg-Euler effective action beyond one loop

“…Recently, indications have been reported for the relevance of QED vacuum birefringence for optical polarimetry of a neutron star [36]. Other theoretical proposals for optical signatures of quantum vacuum nonlinearity have focused on photon-photon scattering in the form of laser-pulse collisions [37][38][39][40], interference effects [41][42][43][44], quantum reflection [45,46], photon merging [47][48][49][50][51], photon splitting [19,[52][53][54][55][56][57][58][59][60], and higher-harmonic generation from laser driven vacuum [61][62][63][64]. Finally, and perhaps most strikingly, strong electric fields can facilitate the spontaneous formation of real electron-position pairs from the QED vacuum via the Schwinger effect [2,14,15].…”

Optical Kerr effect in vacuum

“…(24), and then to obtain the modification to Eq. (25). Indeed, it is straightforward to show that the matrix on the left-hand side of Eq.…”

“…Even before accounting for the constitutive equations (16) relating e and b to d and h, the probe must satisfy the independent set of equations (3). For a plane wave, these become 4 In this respect, the original DeLLight proposal [25] is over-complicated as it suggests using two counter-propagating pump beams to engender a nontrivial refractive index profile as seen by a probe; one of the key points of this paper (to be investigated further in Sec. IV) is that a single pump is sufficient for this purpose.…”

“…An alternative, complementary approach is to directly exploit the refractive index variation by looking for a deflection in the trajectory of a probe wave when traversing a region where strong background fields are present. This was attempted by Jones in 1960 [23,24] using a static magnetic field, while the recently proposed DeLLight experiment [25] aims to observe such a deflection using the much greater intensities within a tightly focused laser pulse.…”

“…Inspired by proposals to measure the change in the refractive index of vacuum (particularly that of DeLLight [25]), in this paper we take seriously the identification of the "dressed" vacuum as an effective linear medium (as far as its interaction with a weak probe is concerned). Following [16,17], we adopt an effective field theory approach, valid in the long-wavelength regime where individual photons have relatively low energy and where a classical treatment of the field is justified.…”