Abstract
Based on the vectorial Debye theory, the focusing properties of the Gaussian beam through an annular high numerical aperture are studied numerically, including the intensity, the phase and the orbital angular momentum properties. Then the influence of certain parameters on the focusing properties is also investigated. It is shown that sub-wavelength elliptical light spots can be obtained. And there exists a vortex in the longitudinal component of the focused field even though the incident beam is Gaussian beam, indicating that the spin angular momentum of the elliptically polarized Gaussian beam is converted into the orbital angular momentum by the focusing.
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