Standard Hermite-Gaussian and standard Laguerre-Gaussian diagonal beams can be expressed by similar summation of non-diagonal standard Hermite-Gaussian beams with expansion coefficients that are equal in magnitude in both cases. We show theoretically and numerically that the same relations hold also for elegant Hermite-Gaussian beams and elegant Laguerre-Gaussian beams. On the other hand, our theoretical estimations and numerical simulations show substantial differences between standard and elegant beams in their phase transverse distribution and evolution of this distribution during beam propagation.
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Fraunhofer diffraction patterns from a spiral phase element with an annular aperture are investigated, on normal incidence of a plane monochromatic wave, depending on a spiral distribution of the phase of a wave at the output from the element. Results of extensive numerical calculations are presented and analytical formulas are derived for a very thin aperture. Basic behaviour of diffraction patterns depending on the spiral’s slope is predictable from the analytical approximation.
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