Generation of no-diffraction hollow vertex beams with adjustable angular momentum by wave plate phase plates

In this article, a new scheme is proposed to generate approximately no-diffraction hollow vertex beams by wave plates. By selecting the appropriate thickness values of wave plates based on the properties of the double refraction, four-step-phase plates for o-light or e-light are formed. With linearly polarized light irradiated at the phase plate, the diffractions of o-light and e-light would overlap according to their intensities. By focusing effect of quasi-Galileo telescope system, a no-diffraction hollow vertex beam can be generated. In this scheme, the optical path is simple and convenient to adjust. Under the adaxial condition, the distributions of diffraction intensity and angular momentum of two wave plates at the numbers of cycles, s=1 and s=4, are numerically simulated according to Fresnel diffraction theory and classical electromagnetic field angular momentum theory. Simulation results indicate that the approximately no-diffraction hollow vertex beams can be generated by each of two phase plates within a long distance. The distributions of intensity and the angular momentum are essentially the same as those generated by spiral phase plates at the same number of cycles. The distributions of intensity and the angular momentum are different at different numbers of cycles s. If s increases, the diffraction bright ring radius increases, the intensity decreases and the average orbital angular momentum increases. At s=4, the length of no-diffraction region is significantly greater than at s=1 and the average orbital angular momentum is four times that at s=1. Within the no-diffraction region, the distribution of orbital angular momentum intensity varies with distance but the total angular momentum is constant. A phase compensator is inserted in the diffraction path to adjust the phase difference between o-light and e-light. Whereas the spin angular momentum of the diffraction light can be adjusted by them, and thus the total angular momentum intensity and average photon angular momentum can be adjusted. This scheme can be utilized to guide the cold atoms or molecules to obtain the adjustable torque throughout the interacting process of atoms and photons.