Investigation of axial and transverse focal spot sizes of Fresnel zone plates

An axial spot size formula is given for a standard binary Fresnel zone plate (FZP) illuminated with a linearly polarized beam. The axial spot size, characterized by the full width at half-maximum (FWHM), can be accurately expressed by the Jiang-Wilson formula, viz., dz = 0.97λ₀/[η-(η²-NA²)^1/2], when the number of transparent annuli is no less than 3. λ₀ is the illumination light wavelength, Ç is the refractive index, and NA is the equivalent numerical aperture of a FZP. The transverse spot sizes are near linear with the radial width of the outmost annulus when the corresponding numerical aperture is not very large. This study is carried out based on vectorial angular spectrum theory and has been rigorously confirmed by the three-dimensional finite-difference time-domain method. This finding provides the theoretical basis for applying FZPs in a variety of applications, such as nanolithography, nanoscopy, and high-density data storage.