Analytical Framework for Structured Light Beam Transitions from Ring to Top-Hat Profiles
Physicists have developed exact closed-form analytical expressions describing how structured light beams can continuously transition from annular ring profiles to uniform top-hat intensity distributions under paraxial propagation. The work solves the Fresnel diffraction integral in cylindrical coordinates for an initial field combining a Gaussian-weighted power-law core and a singular inverse-quadratic modulation term with an azimuthal phase factor. Top-hat beams are widely sought in applications such as laser machining, optical trapping, and lithography, where uniform intensity profiles are critical.
A new preprint posted to arXiv presents an exact analytical framework for the paraxial propagation of structured light beams that evolve from ring-shaped annular intensity profiles into flat top-hat distributions. The initial field is constructed as a superposition of a Gaussian-weighted power-law core and a singular inverse-quadratic modulation term, both carrying an azimuthal phase factor encoding orbital angular momentum. By analytically solving the Fresnel diffraction integral in cylindrical coordinates, the authors obtain closed-form expressions valid at arbitrary propagation planes. The resulting field evolution is governed by a Cauchy-Riemann beam term together with an infinite series of modified Bessel functions of the second kind, weighted by the azimuthal phase. In the fundamental mode (l=0), the singular component fills the central intensity null characteristic of ring beams, producing a flat transverse plateau. The framework shows that continuously tuning the source parameters allows smooth control over the beam profile, offering a practical route to generating top-hat beams without purely numerical or approximate methods.
What's missing
The preprint has not yet undergone peer review. The study does not address experimental validation of the analytical predictions, nor does it quantify the sensitivity of the top-hat uniformity to realistic imperfections in the source field preparation. The convergence properties and practical truncation of the infinite Bessel function series are not explicitly characterized in the abstract.
What different sources said
- arXiv physicsCenter
From Rings to Top-Hat beams
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