Diode-pumped Nd:YVO4 lasers with cylindrical vector vortex output in continuous-wave and Q-switched operation

•Direct generation of a cylindrical vector vortex laser beam in a Nd:YVO4 laser incorporating a S-waveplate and an etalon.•Q-switched operation of Nd:YVO4 lasers with cylindrical vector vortex output.•Theoretical Jones matrix calculation in a resonator with a S-waveplate, allowing a radial or azimuthal polarized output.•Independent and simple selection of the polarization state and helicity by a S-waveplate and an etalon.