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    Array theory explains negative refraction in triangular prisms without a negative refractive index. This method accurately predicts beam transmission angles and identifies frequencies for negative refraction, utilizing the prism's staircase-shaped hypotenuse.

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    Area of Science:

    • Physics
    • Optics
    • Metamaterials

    Background:

    • Negative refraction is a phenomenon where light bends in the opposite direction than usual.
    • Traditional explanations often involve materials with a negative refractive index.
    • Understanding negative refraction in structured materials is crucial for advanced optical applications.

    Purpose of the Study:

    • To explain negative refraction in a triangular prism using array theory.
    • To demonstrate that a negative refractive index is not necessary for negative refraction.
    • To accurately predict beam transmission angles and the frequency range of negative refraction.

    Main Methods:

    • Application of array theory to model a triangular prism with a staircase-shaped hypotenuse.
    • Analysis of the phase delay imparted by cubic unit cells.
    • Full-wave simulations using the finite-difference time-domain (FDTD) method.

    Main Results:

    • Array theory accurately predicts the beam transmission angle through the prism.
    • The staircase shape of the hypotenuse and the phase delay from unit cells create conditions for negative refraction.
    • An estimate of the frequency interval for negative refraction was provided.

    Conclusions:

    • Negative refraction can be explained by array theory without invoking a negative refractive index.
    • The geometric structure (staircase hypotenuse) and unit cell properties are key to achieving negative refraction.
    • Array theory offers a valid and accurate method for analyzing such optical phenomena.