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A charge distribution has cylindrical symmetry if the charge density depends only upon the distance from the axis of the cylinder and does not vary along the axis or with the direction about the axis. In other words, if a system varies if it is rotated around the axis or shifted along the axis, it does not have cylindrical symmetry. In real systems, we do not have infinite cylinders; however, if the cylindrical object is considerably longer than the radius from it that we are interested in,...
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The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
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Vortex Hermite-Gaussian laser beams.

V V Kotlyar, A A Kovalev, A P Porfirev

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    We investigated elliptical vortex Hermite-Gaussian beams, revealing how a parameter controls optical vortex positions and topological charges. This work enables intensity modification without altering orbital angular momentum.

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    Area of Science:

    • Optical physics
    • Quantum optics
    • Laser physics

    Background:

    • Hermite-Gaussian (HG) beams are fundamental solutions in paraxial optics.
    • Vortex beams carry orbital angular momentum (OAM), crucial for applications like optical manipulation and communication.
    • Controlling the properties of vortex beams is essential for advancing optical technologies.

    Purpose of the Study:

    • To analyze the characteristics of elliptical vortex Hermite-Gaussian (vHG) beams.
    • To investigate the influence of the parameter 'a' on the optical nulls and topological charge of vHG beams.
    • To derive and analyze the orbital angular momentum (OAM) of vHG beams and its dependence on beam parameters.

    Main Methods:

    • Theoretical derivation of the complex amplitude for vHG beams.
    • Analysis of optical nulls and their positions based on the parameter 'a'.
    • Mathematical formulation for calculating the OAM of vHG beams.

    Main Results:

    • Identified distinct locations for optical nulls (vortices) on the vertical axis for |a|<1 and horizontal axis for |a|>1.
    • Demonstrated that the topological charge of the vortices is +1 for a<0 and -1 for a>0.
    • Derived an equation for OAM showing dependence on parameter 'a' and Gaussian beam ellipticity.
    • Showcased the ability to alter transverse intensity profiles without changing OAM.

    Conclusions:

    • Elliptical vortex Hermite-Gaussian beams exhibit controllable vortex properties based on the parameter 'a'.
    • The derived OAM equation provides a method to decouple intensity profile from OAM.
    • The findings offer new possibilities for designing and controlling light beams with specific OAM values.