Abstract

In this work, a comprehensive analytic study of the diffraction of vortex beams from structured apertures is presented. We formulate the near- and far-field diffraction of a vortex beam from an aperture having an arbitrary functionality in the Cartesian coordinates by two general and different approaches. We show that each of the resulting diffraction patterns can be determined by a number of successive derivatives of the 2D Fourier transform of the corresponding hypothetical aperture function or equally can be obtained by a summation of 2D Fourier transforms of the corresponding modified aperture function. We implement both introduced analytic approaches in predicting the diffraction of a vortex beam from an elliptic Gaussian aperture, an elliptic Gaussian phase mask, and a hyperbolic Gaussian phase mask in the near- and far-field regimes. It is shown that the predicted diffraction patterns by both these approaches are exactly the same. It is shown that the diffraction of a vortex beam from an elliptic Gaussian aperture at the far-field regime forms a light beam that belongs to a family of light beams we call elegant elliptical vortex Hermite–Gaussian beams. In addition, the diffractions of a vortex beam from a Fresnel zone plate in general form for the on- and off-axis situations are formulated, and sinusoidal and binary zone plates are investigated in detail. Our general analytic formula can be used for a large variety of apertures including off-center situations and asymmetrical cases.

© 2019 Optical Society of America

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References

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Supplementary Material (5)

NameDescription
» Visualization 1       Calculated diffraction patterns of two vortex beams with w=0.2mm and l=+/-3 from an elliptic Gaussian aperture with a=b=2w_eff at different propagation distances in a range from z=0 to z=2m.
» Visualization 2       Calculated diffraction patterns of two vortex beams with w=0.5mm and l=+/-3 from an elliptic Gaussian phase mask with a=b=2w_eff at different propagation distances in a range from z=0 to z=4m.
» Visualization 3       Calculated diffraction patterns of two vortex beams with w=0.5mm and l=+/-3 from a hyperbolic Gaussian phase mask with a=b=2w_eff at different propagation distances in a range from z=0 to z=4m.
» Visualization 4       On-axis diffraction of a vortex beam with w=0.5mm and l=+3 from a sinusoidal ZP with f=50mm under propagation from z=0 to z=2f.
» Visualization 5       Off-axis diffraction of a vortex beam with w=0.3mm and l=+3 from a sinusoidal ZP with f=40cm and offset x_0=3 mm, under propagation from z=0 to z=f. First row shows the intensity and the second row shows the corresponding phase profiles.

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Figures (16)

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Equations (81)

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