We present a regime where an ultra-intense laser pulse interacting with a foil target results in high $gamma$-photon conversion efficiency, obtained via three-dimensional quantum-electrodynamics particle-in-cell simulations. A single-cycle laser pulse is used under the tight-focusing condition for obtaining the $mathrm{lambda}^3$ regime. The simulations employ a radially polarized laser as it results in higher $gamma$-photon conversion efficiency compared to both azimuthal and linear polarizations. A significant fraction of the laser energy is transferred to positrons, while a part of the electromagnetic wave escapes the target as attosecond single-cycle pulses.
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