title: Focusing of doughnut laser beams by a high numerical-aperture objective in free space.
abstract: We report on, in this letter, a phenomenon that the central zerointensity point of a doughnut beam, caused by phase singularity, disappears in the focus, when such a beam is focused by a high numerical-aperture objective in free space. In addition, the focal shape of the doughnut beam of a given topological charge exhibits the increased ring intensity in the direction orthogonal to the incident polarization state and an elongation in the polarization direction. These phenomena are caused by the effect of depolarization, associated with a high numerical-aperture objective, and become pronounced by the use of a central obstruction in the objective aperture.
authors.forename: Djenan
authors.initials: D
authors.lastname: Ganic
authors.forename: Xiaosong
authors.initials: X
authors.lastname: Gan
authors.forename: Min
authors.initials: M
authors.lastname: Gu