Abstract
For focusing of radially polarized vector beams using an arbitrary opening paraboloid mirror, a quasi-rigorous integral representation of light field is derived based on a rigorous vectorial diffraction theory of electromagnetic waves. Under far-field approximation conditions, the derived integrals reduce to the results from vectorial Debye-Wolf diffraction integral. Numerical calculations show that a marked deviation, as represented by evident focal shift, appears for low-aperture paraboloid mirrors, e.g. the maximum focusing semi-angle α below π/9 with the focal length f being 103λ, or below π/6 when f reduces to 102λ. The radial light spot sharpens to be 0.39λ (FWHM) and purely longitudinally polarized when α is close to 115°, while the axial light spot continuously sharpens to be about half wavelength with α approaching π. For an annular paraboloid mirror, it is possible to further compress the radial light spot down to 0.36λ (FWHM).
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