Starting from the vectorial Rayleigh-Sommerfeld formulas, the nonparaxial propagation of radially polarized light beams in free space is investigated analytically and numerically. The paraxial case can be treated as a special case of the general result. The exact expression of the radially polarized light beams, which is valid for the fields to be predicted for an arbitrary transverse beam size, has been derived in closed-form terms for any on-axis point. The validity of the analytical results is confirmed by the numerical results.
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Dongmei Deng (2006) studied this question.
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