  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.
