Continuously Adjustable Cylindrical Vector and Vortex Beams by Programming Vortex Half-Wave Plates and Detection Based on Coaxial or Small-Angle Interference

Abstract

A convenient and versatile scheme to generate continuously adjustable cylindrical vector (CV) and vortex beams by multiplexing and cascading passive vortex half-wave plates (VHPs) is proposed. (\ensuremath{-}24)--24 order CV or vortex beams are generated only based on VHPs with m = 1, 3, and 8. The coaxial and small-angle interference are introduced to detect orders. For coaxial interference of ${l}_{1}$-order and ${l}_{2}$-order vortex beams, the intensity distribution is spirally fan shaped. The partition number is N = |${l}_{2}$\ensuremath{-} ${l}_{1}$|, and the spiral direction can distinguish the sign of topological charge with higher value. Fork-shaped fringes appear in the center for small-angle interference between vortex beams with incident angle ${\ensuremath{\beta}}_{1}$ and ${\ensuremath{\beta}}_{2}$. The forking number between two fringes meets N = |${l}_{2}$\ensuremath{-} ${l}_{1}$|, and the forks face upward when (${l}_{2}$\ensuremath{-} ${l}_{1}$)(${\ensuremath{\beta}}_{2}$\ensuremath{-} ${\ensuremath{\beta}}_{1}$) 0, and face downward when (${l}_{2}$\ensuremath{-} ${l}_{1}$)(${\ensuremath{\beta}}_{2}$\ensuremath{-} ${\ensuremath{\beta}}_{1}$) > 0. Particularly, when one of the beams is a Gaussian beam, such as ${l}_{1}$ = 0, the value and sign of the topological charge ${l}_{2}$ can be directly detected. And for the interference between CV and Gaussian plane beams, the partition number N is positively correlated with the polarization order P, with N = |P| or N = 2|P| for coaxial or small-angle interference, respectively, and corresponding sign can be identified by the polarization azimuth distributions measured by Stokes parameters. It is experimentally demonstrated that the proposed scheme can effectively generate continuously adjustable CV and vortex beams by programming limited VHPs, greatly expanding order numbers with low cost, low energy consumption, and high utilization, and the coaxial and small-angle interference method can conveniently detect the corresponding orders without borrowing redundant devices.