Full text of article: Russian language.

Abstract:
Diffraction of the truncated hyper-geometrical modes and generalized hyper-geometrical beams with use of Rayleigh-Sommerfeld integral of the first type in a near zone (an order of few wavelengths) is investigated. Possibility of overcoming the diffraction limit for phase-only logarithmic axicon (as special case of hyper-geometrical beams) is shown by numerical simulation in the context of scalar nonparaxial diffraction theory. The analysis of the received results is carried out on the basis of representation of logarithmic axicon phase function as a set of ring zones with linear axicons.

Key words: hyper-geometrical modes, generalized hyper-geometrical beams, nonparaxial inte­gral transform, diffractive logarithmic axicon, linear axicon, overcoming the diffraction limit.

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