Nonparaxial circular grating diffraction properties of radially polarized beams

The Rayleigh-Sommerfeld diffraction integral is employed to study the circular grating nonparaxial diffraction properties of the radially polarized beams, and the analytical expression for the diffraction electric field is derived. The analyses indicate that the properties of the nonparaxial diffraction field strongly depend on the grating parameters and beam waist. When the radially polarized beam is diffracted by the sub-wavelength grating, only the 0th diffraction ring is obtained, or the distinct higher order diffraction rings will emerge. Compared with the paraxial diffraction, the nonparaxial diffraction intensity field is weaker. But when the beam waist is larger than 3λ the paraxial approximation is valid; thus their distinction will be negligible. At last, it shows that in the radially polarized beams nonparaxial diffraction field, the longitudinal component not only leads to stronger diffraction intensity than the azimuthally polarized beams, but also makes the polarization degenerate.