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Once the fields have been calculated using Maxwell's four equations, the Lorentz force equation gives the force that the fields exert on a charged particle moving with a certain velocity. The Lorentz force equation combines the force of the electric field and of the magnetic field on the moving charge. Maxwell's equations and the Lorentz force law together encompass all the laws of electricity and magnetism. The symmetry that Maxwell introduced into his mathematical framework may not be...
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In electrostatics, the electric field can be written as the negative gradient of the potential. In magnetostatics, the zero divergence of the magnetic field ensures that the magnetic field can be expressed as the curl of a vector potential. This potential is known as the magnetic vector potential.
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A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...
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Generation of perfect helical Mathieu vortex beams.

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    Researchers developed novel perfect helical Mathieu vortex (PHMV) beams, a new type of optical vortex beam. These beams offer controllable patterns and fractional orbital angular momentum, advancing optical vortex research.

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    Area of Science:

    • Optics and Photonics
    • Quantum Optics
    • Beam Physics

    Background:

    • Optical vortex beams are crucial in various applications due to their unique properties.
    • Perfect optical vortex (POV) beams offer enhanced stability and controllable parameters.
    • Existing methods for generating optical vortex beams have limitations in control and properties.

    Purpose of the Study:

    • To introduce and theoretically construct a novel type of perfect optical vortex beam: perfect helical Mathieu vortex (PHMV) beams.
    • To experimentally generate PHMV beams and validate the theoretical predictions.
    • To investigate the unique optical properties of PHMV beams, including topological charge independence and fractional orbital angular momentum (OAM).

    Main Methods:

    • Theoretical construction involving the stationary phase method for generating helical Mathieu (HM) beams, followed by Fourier transformation to obtain PHMV beams.
    • Experimental generation using an amplitude-type spatial light modulator (SLM) and a radial-helical phase mask for complex amplitude modulation.
    • Utilizing an achromatic Fourier transform lens to realize the transformation from HM beams to PHMV beams on the focal plane.

    Main Results:

    • Successful experimental generation of PHMV beams consistent with theoretical predictions.
    • PHMV beams maintain a ring radius independent of topological charge values, similar to classical POV beams.
    • The spatial distribution patterns of PHMV beams can be precisely controlled by topological charges and elliptical parameters.

    Conclusions:

    • PHMV beams represent a novel class of optical vortex beams with enhanced controllability.
    • PHMV beams carry a fractional order orbital angular momentum (OAM).
    • The complex amplitudes of PHMV beams with the same elliptical parameter but different order numbers exhibit orthogonality.