Generation of a focused hollow beam by an 2π-phase plate and its application in atom or molecule optics

We propose a new scheme to generate a focusing hollow beam (FHB) by use of an azimuthally distributed 2π-phase plate and a convergent thin lens. From the Fresnel diffraction theory, we calculate the intensity distributions of the FHB in free propagation space and study the relationship between the waist w₀ of the incident Gaussian beam (or the focal length f of the lens) and the dark spot size (or the beam radius) at the focal point and the relationship between the maximum radial intensity of the FHB and the dark spot size (or the beam radius) at the focal point, respectively. Our study shows that the FHB can be used to cool and trap neutral atoms by intensity-gradient-induced Sisyphus cooling due to an extremely high intensity gradient of the FHB itself near the focal point, or to guide and focus a cold molecular beam. We also calculate the optical potential of the blue-detuned FHB for ⁸⁵Rb atoms and find that in the focal plane, the smaller the dark spot size of the FHB is, the higher the optical potential is, and the greater the corresponding optimal detuning δ is; these qualities are beneficial to an atomic lens not only because it is profitable to obtain an atomic lens with a higher resolution, but also because it is helpful to reduce the spontaneous photon-scattering effect of atoms in the FHB.