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We employ the $\lambda ^{3}$
regime where a near-single-cycle laser pulse is tightly focused, thus providing the highest possible intensity for the minimal energy at a certain laser power. The quantum electrodynamics processes in the course of the interaction of an ultra-intense laser with a solid target are studied via three-dimensional particle-in-cell simulations, revealing the generation of copious $\gamma$
-photons and electron–positron pairs. A parametric study of the laser polarisation, target thickness and electron number density shows that a radially polarised laser provides the optimal regime for $\gamma$
-photon generation. By varying the laser power in the range of 1 to 300 PW we find the scaling of the laser to $\gamma$
-photon energy conversion efficiency. The laser-generated $\gamma$
-photon interaction with a high-$Z$
target is further studied using Monte Carlo simulations revealing further electron–positron pair generation and radioactive nuclide creation.
