Full text of article: Russian language.
Abstract:
We obtained exact solution of the scalar Helmholtz equation. This solution describes light beam propagating in the positive direction of the optical axis. Complex amplitude of such beam is proportional to multiplication of two linearly independent solutions of the Kummer’s differential equation. Expressions for partial cases – Hankel-Bessel beams have been obtained. Focusing of Hankel-Bessel beams has been studied.
Key words:
Helmholtz equation, nonparaxial diffraction, parabolic coordinates, Kummer’s equation, confluent hypergeometric function (Kummer’s function), optical vortex, Bessel function, Hankel function.
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