We present a regime where an ultraintense laser pulse interacting with a foil target results in high γ-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 λ^{3} regime. The simulations employ a radially polarized laser as it results in higher γ-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.