Structure of the axial intensity minima in the Fresnel diffraction on a circular opening and superluminous effects

The “classical” problem of plane-wave diffraction by a circular opening is inspected with one particular interest to check the existence of axial zeroes of amplitude, which can produce a specific type of phase singularities. We investigate the problem using paraxial and nonparaxial solutions of scalar wave equation based on Hankel transform. The main result of investigation is the detection of the absence of any exact amplitude zeroes in the Fresnel diffraction field. Instead, sharp phase variations localized at the regions of axial amplitude minima with longitudinal and transversal dimensions of the order of one wavelength are revealed. These phase variations influence on the phase velocity, which drops up to c/2 in the point of axial amplitude minimum. Also, superluminous effects of wavefront propagation are discussed.