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Accurately determining beam deflection and slope under various loading conditions in structural engineering is crucial for ensuring safety and structural integrity. Singularity functions offer a streamlined approach to analyzing beams, especially when multiple loading functions complicate the bending moment equation.
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Double and Square Bessel-Gaussian Beams.

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Area of Science:

  • Optics and Photonics
  • Beam Propagation
  • Laguerre-Gaussian Beams

Background:

  • Bessel-Gaussian (BG) beams are fundamental in optics.
  • Existing BG beams have limitations in stability and control.
  • Need for novel beam structures for advanced applications.

Purpose of the Study:

  • To derive and characterize new types of Bessel-Gaussian beams.
  • To analyze the propagation properties of these novel beams in free space.
  • To explore potential applications of these beams.

Main Methods:

  • Derivation of a transform relating standard BG beams to half-integer order BG beams.
  • Analysis of square vortex BG beams and double-BG beams.
  • Development of propagation expressions as series of Bessel function products.

Main Results:

  • Obtained a transform for half-integer order BG beams with quadratic radial dependence.
  • Characterized square vortex BG beams and double-BG beams.
  • Derived expressions for free-space propagation of these beams.
  • Introduced a vortex-free power-function BG beam that propagates as a superposition of lower-order beams.

Conclusions:

  • The study expands the toolkit of finite-energy vortex beams with orbital angular momentum.
  • These novel beams show promise for stable light propagation in turbulent atmospheres.
  • Potential applications include wireless optical communications and particle manipulation in micro-machines.