We study the field that is produced by a paraxial refractive axicon lens. The results from geometrical optics, scalar wave optics, and electromagnetic diffraction theory are compared. In particular, the axial intensity, the on-axis effective wavelength, the transverse intensity, and the far-zone field are examined. A rigorous electromagnetic diffraction analysis shows that the state of polarization of the incident beam strongly affects the transverse intensity distribution, but not the intensity distribution in the far zone.

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