Analysis of four-wave mixing of high-power lasers for the detection of elastic photon-photon scattering

We derive expressions for the coupling coefficients for electromagnetic four-wave mixing in the nonlinear quantum vacuum. An experimental setup for detection of elastic photon-photon scattering is suggested, where three incoming laser pulses collide and generate a fourth wave with a new frequency and direction of propagation. An expression for the number of scattered photons is derived and, using beam parameters for the Astra Gemini system at the Rutherford Appleton Laboratory, it is found that the signal can reach detectable levels. Problems with shot-to-shot reproducibility are reviewed, and the magnitude of the noise arising from competing scattering processes is estimated. It is found that detection of elastic photon-photon scattering may be achieved.

Figure 1

(Color online) Configuration of the incoming laser beams and the direction of the scattered wave for the wave vectors defined in Eq. (15), which satisfies the matching conditions (10, 11).

Figure 2

(Color online) The upper panel shows the number of scattered photons $N_{3d}$ per shot, normalized by the number of photons $N_{\max }$ per shot for an optimal choice of polarization, as a function of polarization angle ${\beta }_3$ of the wave with direction ${\widehat{\mathbf{k}}}_3$. The lower panel shows $N_{\max }$ predicted by Eq. (17) when increasing the laser power while keeping the beam width constant at $b=1.6\mu \mathrm{m}$, for a system where two source beams are used and one of the beams is split into two (solid line) and when three source beams are used, hence no beam splitting is required (dashed line).

Figure 3

(Color online) An alternative experimental configuration for detection of photon-photon scattering through four-wave coupling.

Figure 4

(Color online) The maximum intensity felt by the electron relative to the peak intensity of the laser pulse, for different laser intensities. No initial radial displacement of the electron from the propagation axis of the laser pulse. Laser wavelengths are 800 and $400\mathrm{nm}$.

Figure 5

(Color online) The maximum intensity felt by the electron relative to the peak intensity of the laser pulse, for different initial radial displacements from the axis of propagation of the laser pulse. The intensity is $5\times {10}^{21}\mathrm{W}{\mathrm{cm}}^{-2}$, and the wavelengths are 800 and $400\mathrm{nm}$.

Figure 6

(Color online) The average cross section, ${\sigma }_{\Delta }$, for inverse Compton scattering of incident light with wavelengths 800 and $400\mathrm{nm}$ into the wavelength interval $216–316\mathrm{nm}$, as a function of increasing intensity of the incident pulse.