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19 March 2015 Family of three-dimensional asymmetric nonparaxial Lommel modes
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Abstract
We study a non-paraxial family of nondiffracting laser beams whose complex amplitude is proportional to an n-th order Lommel function of two variables. These beams are referred to as Lommel modes. We also study finite-energy paraxial Lommel-Gaussian beams with their complex amplitude being proportional to the Lommel function and to the amplitude of the Gaussian beam. Explicit analytical relations for orbital angular momentum of the Lommel modes and Lommel-Gaussian beams have been derived. Asymmetry of the Lommel modes depends on a complex parameter с. Besides, with the modulus of the с parameter increasing from 0 to 1, the orbital angular momentum of the Lommel modes increases from a finite value proportional to the topological charge n to infinity. The orbital angular momentum of the Lommel modes undergoes continuous variations, in contrast to its discrete changes in the Bessel modes. Simulation by the beam propagation method showed that in initial plane the transverse intensity distribution of the Lommel-Gaussian beam contains a light ellipse with two bright spots. During propagation, these spots rotate by an angle, close to 90 degrees, at a much smaller distance than the Rayleigh range.
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Alexey A. Kovalev and Victor V. Kotlyar "Family of three-dimensional asymmetric nonparaxial Lommel modes", Proc. SPIE 9448, Saratov Fall Meeting 2014: Optical Technologies in Biophysics and Medicine XVI; Laser Physics and Photonics XVI; and Computational Biophysics, 944828 (19 March 2015); https://doi.org/10.1117/12.2179882
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