Calculation of plane wave diffraction by divergent fractional axicon taking into account evanescent waves

We performed theoretical and numerical analysis of plane wave diffraction by fractional axicon whose degree is less than unity, in the near-field taking into account evanescent waves. For calculating the Rayleigh -Sommerfeld integral of first type was used. It is shown that application of the method of stationary phase to obtain analytical estimates in near diffraction zone is insufficiently accurate. For adjustment the obtained solution additional corrections are introduced to obtain qualitative agreement of theoretical and numerical results. It is shown that divergent fractional axicon with degree significantly less than unity can create a light spot having longitudinal and transverse size of one tenth of the wavelength in the zone of ??evanescent waves.