Analytical Framework for Structured Light Beam Transitions from Ring to Top-Hat Profiles
Researchers have developed exact analytical solutions for the propagation of structured light beams that transition from ring-shaped annular profiles to uniform top-hat intensity distributions. The work uses Fresnel diffraction theory in cylindrical coordinates to derive closed-form expressions involving Bessel functions and azimuthal phase factors. This theoretical framework could enable precise control of light beam shapes for applications in optical manipulation, imaging, and materials processing.
A new analytical study presents exact closed-form solutions for the paraxial propagation of structured light beams that smoothly transition between ring annular profiles and top-hat intensity distributions. The researchers model the initial field as a superposition of a Gaussian-weighted power-law core and a singular inverse-quadratic modulation term, both carrying azimuthal phase factors. By solving the Fresnel diffraction integral in cylindrical coordinates, they obtain expressions for the propagated field at arbitrary propagation distances, showing that the evolution is governed by Cauchy-Riemann beam terms and infinite series of modified Bessel functions. The analysis demonstrates that tuning source parameters enables continuous control over the beam shape transition, with the fundamental mode producing a flat transverse intensity plateau. This analytical framework provides theoretical tools for designing and controlling structured light beams with tailored intensity profiles.
What's missing
The study does not discuss potential experimental validation of the theoretical predictions, practical applications beyond general mention, or comparison with alternative beam-shaping methods. The limitations of the paraxial approximation and conditions under which the analytical solutions remain valid are not explicitly stated in the abstract.
What different sources said
- arXiv physicsCenter
From Rings to Top-Hat beams
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