Generation of optical vortex array with transformation of standing-wave Laguerre-Gaussian mode

We develop a novel method of creating optical vortex array by the conversion of a standing-wave Laguerre-Gaussian (LG) mode. Theoretically, by employing the transformational relation, the standing-wave LG mode is verified to be transformed from a pair of crisscrossed Hermite-Gaussian (HG) modes, embedded with optical vortex array, consists of a TEM_n,m mode and a TEM_m,n mode. Due to close correspondence between the transformational relation and the mode conversion of astigmatic lenses, we successfully generate the optical vortex array by transforming a standing-wave LG mode into the crisscrossed HG modes via a π/2 cylindrical lens mode converter. The investigation may provide useful insight in the study of the vortex light beam and its further applications.