Tight focusing properties of double-ring-shaped azimuthally polarized beam through annular high numerical aperture

By using the Richards-Wolf vector diffraction theory, the focusing properties of a double-ring-shaped azimuthally polarized beam through an annular lens with high numerical aperture are studied. Expressions of intensity distribution on the focal field are derived. Numerical calculations are performed to compare the influence of the beam and lens parameters on the tight focusing properties. It is shown that sub-wavelength focal spots of wide applications can be obtained on the focal plane, and correlated parameters of the incident beam and the numerical-aperture of the lens do affect the focusing. Moreover, longer depth of focus (nearly 28 times the incident wavelength) can be generated with a lens of higher numerical aperture.