We demonstrated the linear, radial, and annular ripple formation on the surface of GaAs. The formation of linear ripples was optimized by the number of shots and the fluence of 30 ps, 532 nm pulses. The radial and annular nanoripples were produced under the ablation using doughnut-like beams possessing azimuthal and radial polarizations, respectively. We compare the ripples and grooves formed by a linearly polarized Gaussian beam relative to an annular vector beam. The joint overlap of sub-wavelength grooves with ripples formed by azimuthally and radially polarized beams was reported. The conditions under which the shape of radial and ring-like nano- or micro-relief on the GaAs surface can be modified by modulating the polarization of laser pulse were determined. The resultant surface processing of GaAs using a laser beam with different polarization modes is useful for exploring valuable insights and benefits in different applications.