On the basis of the vectorial Rayleigh diffraction integrals and stationary-phase method, the analytic expression describing the vectorial field distribution of radially polarized Gaussian beams diffracted by an axicon is derived. The theoretical analysis and simulation calculation show that the radial component of the diffraction field is the propagation-invariant first-order Bessel beam when the radially polarized Gaussian beam illuminates the axicon. However, the longitudinal component possesses no such behavior because of its intrinsic r dependence, and its central intensity is the maximum. The longitudinal component is related to the open angle and index of the axicon, which has to be considered when the open angle and index are large. For a small open angle and index, the longitudinal component can be neglected, and the scalar approximation is valid.
The near-field focusing properties of actual hybrid amplitude–phase binary subwavelength Fresnel zone plates (HBSFZPs) are studied theoretically. The analysis based on the exact vector angular spectrum method is done for a radially polarized beam incident on the HBSFZPs. The results show that the near-field subwavelength focusing with a long depth of focus can be obtained using an HBSFZP, which is very useful for near-field subwavelength photolithography and high-resolution microscopy. The position of the actual focus in the near-field focusing HBSFZPs depends on the evanescent wave rather than the propagating wave. The etch depth has an important influence on focusing properties of HBSFZPs.
The fractional Fourier transform (FRT) is applied to a partially coherent off-axis Gaussian Schell-model (GSM) beam, and an analytical formula is derived for the FRT of a partially coherent off-axis GSM beam. The corresponding tensor ABCD law for performing the FRT of a partially coherent off-axis GSM beam is also obtained. As an application example, the FRT of a partially coherent linear laser array that is expanded as a sum of off-axis GSM beams is studied. The derived formulas are used to provide numerical examples. The formulas provide a convenient way to analyze and calculate the FRT of a partially coherent off-axis GSM beam.
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