Synchronized proton acceleration by ultraintense slow light in a low-density target Brantov et al (2016 Phys. Rev. Lett.116 085004) is studied for a circularly polarized laser pulse. This study demonstrates the advantage of circularly polarized light compared with linearly polarized light used for high-energy proton generation. At the same time, high-energy electron production for gamma-ray generation is not sensitive to the polarization of the laser pulse. Both the proton and the electron sources are considered in application to petawatt-class lasers.