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Abstract In this paper we will show that photon–photon collision experiments using extreme lasers can provide measurable effects giving fundamental information about the essence of QED, its Lagrangian. A possible scenario with two counterpropagating ultra-intense lasers for an experiment to detect scattering between optical photons is analyzed. We discuss the importance of the pulse widths and waists, the best scenario for overlapping the beams and signal detection, as well as ways to distinguish the signal from the noise. This would need a high-precision measurement, with control of temporal jitter and noise. We conclude that such experiment is barely feasible at 10²³ W cm⁻²and very promising at 10²⁴ W cm⁻². 

We present a technique to assess the focal volume of petawatt-class lasers at full power. Our approach exploits quantitative measurement of the angular distribution of electrons born in the focus via ionization of rarefied gas, which are accelerated forward and ejected ponderomotively by the field. We show that a bivariate (θ,φ) angular distribution, which was obtained with image plates, not only enables the peak intensity to be extracted, but also reflects nonideality of the focal-spot intensity distribution. In our prototype demonstration at intensities of a few ×1019 to a few ×1020 W/cm2, an f/10 optic produced a focal spot in the paraxial regime. This allows a planewave parametrization of the peak intensity given by tan θ_c = 2/a_0 (a_0 being the normalized vector potential and θc the minimum ejection angle) to be compared with our measurements. Qualitative agreement was found using an a0 inferred from the pulse energy, pulse duration, and focal spot distribution with a modified parametrization, tan θ_c = 2η/a_0 (η = 2.02+0.26−0.22). This highlights the need for (i) better understanding of intensity degradation due to focal-spot distortions and (ii) more robust modeling of the ejection dynamics. Using single-shot detection of electrons, we showed that while there is significant shot-to-shot variation in the number of electrons ejected at a given angular position, the average distribution scales with the pulse energy in a way that is consistent with that seen with the image plates. Finally, we note that the asymptotic behavior as θ → 0◦ limits the usability of angular measurement. For 800 nm, this limit is at an intensity ∼10^21 W/cm^2.