Velocity-selective optical pumping (VSOP) which is a Doppler-free spectroscopic method combining saturated absorption and optical pumping, has been applied to investigate the hyperfine structures of Doppler-broadened Na $D_1$ and $D_2$ lines. A polarization-modulated pump beam from the frequency-stabilized single mode cw dye (R6G) laser creates velocity-selective atomic orientation or alignment in a ground state of Na. A counterpropagating probe beam from the same laser provides Doppler-free signals corresponding to the velocity distribution of anisotropy related to these atomic observables by tuning the last frequency. The observables of atoms are evolved exactly within the rate theory of optical pumping in a four-level system and the relative signal intensities and line shapes of the VSOP spectra for the hyperfine resonances and their additional crossover resonances are calculated. The observed signals are compared with the theory and the effects of the strong pump beam intensity are discussed.
