Diffraction-free lommel beams
A.A. Kovalev
, V.V. Kotlyar

Full text of article: Russian language.

Abstract:
We consider a new family of nonparaxial diffraction-free laser beams with their complex amplitude being proportional to the n-th order Lommel function of two variables. Therefore, these beams are called Lommel beams (L-beams). We obtained explicit analytical expressions for the angular spectrum of plane waves and for the orbital angular momentum of the L-beams. Transverse intensity of the L-beams has a reflective symmetry with respect to both Cartesian coordinate axes. Since transverse intensity distribution of L-beams does not change upon propagation, L-beams are modes of free space (L-modes). Functions of complex amplitudes of even (n = 2p) and odd (n = 2p + 1) L-modes are mutually orthogonal. For certain parameter, L-modes become traditional Bessel modes.

Key words:
diffraction-free laser beam, Bessel mode, Lommel mode of two variables, orbital angular momentum.

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