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A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half has...
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Gauss's Law: Planar Symmetry01:27

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Related Experiment Video

Updated: Apr 20, 2026

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
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Asymmetric Bessel-Gauss beams.

V V Kotlyar, A A Kovalev, R V Skidanov

    Journal of the Optical Society of America. A, Optics, Image Science, and Vision
    |November 18, 2014
    PubMed
    Summary

    We introduce asymmetric Bessel-Gauss (aBG) beams carrying orbital angular momentum (OAM). These beams exhibit controllable asymmetry and unique vortex dynamics during propagation, offering new possibilities for optical manipulation.

    Area of Science:

    • Physics
    • Optics
    • Laser Science

    Background:

    • Bessel-Gauss (BG) beams are known for their self-reconstruction properties and radial symmetry.
    • Orbital angular momentum (OAM) in optical beams enables advanced applications in communication and microscopy.
    • Controlling beam asymmetry and vortex behavior is crucial for tailored optical field generation.

    Purpose of the Study:

    • To propose and characterize a novel family of asymmetric Bessel-Gauss (aBG) beams.
    • To investigate the influence of asymmetry on the orbital angular momentum (OAM) properties.
    • To analyze the propagation dynamics and optical vortex behavior of aBG beams.

    Main Methods:

    • Theoretical formulation of a three-parameter family of asymmetric Bessel-Gauss (aBG) beams.

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  • Mathematical description using the product of a Gaussian function and a Bessel function of complex argument.
  • Analysis of intensity distribution, optical nulls, and vortex center dynamics during propagation.

    • Main Results:

    • The aBG beams exhibit tunable asymmetry, transitioning from radial symmetry to semicrescent and elongated shapes with a parameter c.
    • Optical nulls in the transverse intensity distribution generate optical vortices with controllable topological charge and sign.
    • Vortex centers undergo non-uniform rotation during propagation, with characteristic turns at specific distances.

    Conclusions:

    • The proposed aBG beams offer a versatile platform for generating and controlling optical vortices with tailored OAM.
    • The asymmetry parameter c provides a means to manipulate beam shape and vortex dynamics.
    • Experimental generation of a rotating semicrescent vortex laser beam validates the theoretical framework.