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    Optical beams shift position when following curved paths, sensitive to refractive index profiles. This behavior offers insights into curved-path geodesics and optical tunneling, analogous to quantum dynamics.

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    Area of Science:

    • Optics
    • Waveguide Optics
    • Quantum Dynamics Analogy

    Background:

    • Optical beams deviate from path curvature centers.
    • This deviation depends on refractive index spatial profiles.
    • Existing models lack a unified framework for curved-path beam dynamics.

    Purpose of the Study:

    • To analyze the positional shift of optical beams in curved paths.
    • To establish an analogy between optical beam behavior and quantum dynamics.
    • To provide a theoretical framework for understanding bending-induced optical phenomena.

    Main Methods:

    • Evolution-operator analysis applied to optical beam propagation.
    • Mathematical modeling of beam shift in bending waveguides.
    • Comparison with time-evolution-operator treatments in quantum mechanics.

    Main Results:

    • Optical beam position shift is sensitive to refractive index gradients.
    • The shift acts as a vectorial pointer for curved-path geodesics.
    • Bending-induced optical tunneling phenomena are elucidated.

    Conclusions:

    • The study provides a novel perspective on optical beam dynamics in curved geometries.
    • An analogy with quantum evolution operators deepens the understanding of optical path sensitivity.
    • The findings have implications for designing advanced optical waveguides and devices.