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In the early 17th century, German astronomer and mathematician Johannes Kepler postulated three laws for the motion of planets in the solar system. His first law states that all planets orbit the Sun in an elliptical orbit, with the Sun at one of the ellipse's foci. Therefore, the distance of a planet from the Sun varies throughout its revolution around the Sun.
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Kepler's law for optical beams.

A Jaimes-Nájera, J E Gómez-Correa, M D Iturbe-Castillo

    Optics Express
    |October 29, 2020
    PubMed
    Summary

    Researchers found that Kepler's second law applies to optical beams with orbital angular momentum under specific conditions. This optical law is satisfied only for cylindrical symmetric beams, unlike in classical mechanics.

    Area of Science:

    • Optics
    • Classical Mechanics
    • Angular Momentum

    Background:

    • Classical mechanics describes particles in central potentials, leading to Kepler's laws.
    • Kepler's second law relates to the conservation of orbital angular momentum.

    Purpose of the Study:

    • To investigate the conditions for Kepler's second law in optical beams with orbital angular momentum.
    • To analyze the energy flow streamlines of optical beams.

    Main Methods:

    • Analyzing energy flow streamlines of optical beams.
    • Observing the propagation of the Arago's spot as a light-tracer.

    Main Results:

    • Kepler's second law for optical beams is satisfied exclusively for cylindrical symmetric beams.

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  • Classical mechanics accommodates parabolic, elliptical, and hyperbolic geometries.

    • Conclusions:

    • The study establishes an optical analogue of Kepler's second law.
    • Experimental observations of Arago's spot confirm the theoretical predictions for optical beams.