Tight focusing with very small f-numbers is necessary to achieve the highest at-focus irradiances. However, tight focusing imposes strong demands on precise target positioning in-focus to achieve the highest on-target irradiance. We describe several near-infrared, visible, ultraviolet and soft and hard X-ray diagnostics employed in a ∼1022 W/cm2 laser–plasma experiment. We used nearly 10 J total energy femtosecond laser pulses focused into an approximately 1.3-μm focal spot on 5–20 μm thick stainless-steel targets. We discuss the applicability of these diagnostics to determine the best in-focus target position with approximately 5 μm accuracy (i.e., around half of the short Rayleigh length) and show that several diagnostics (in particular, 3$\omega$ reflection and on-axis hard X-rays) can ensure this accuracy. We demonstrated target positioning within several micrometers from the focus, ensuring over 80% of the ideal peak laser intensity on-target. Our approach is relatively fast (it requires 10–20 laser shots) and does not rely on the coincidence of low-power and high-power focal planes.

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.