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    Area of Science:

    • Physics
    • Electromagnetism
    • Mathematical Physics

    Background:

    • Electromagnetic time reversal is a key technique for field imaging and focusing.
    • The time-reversal cavity is the theoretical foundation for time reversal theory.

    Purpose of the Study:

    • To investigate electromagnetic field behavior in complex media using advanced mathematical physics.
    • To develop a direct expression for time-reversed fields in anisotropic, nonreciprocal media.
    • To predict the focusing quality of time-reversed fields in anisotropic media.

    Main Methods:

    • Utilizing Colombeau generalized functions for field analysis.
    • Applying modern mathematical physics methods to electromagnetic theory.
    • Analyzing fields in anisotropic, time-reversal-invariant, and nonreciprocal media.

    Main Results:

    • A direct expression for time-reversed electric and magnetic fields was derived.
    • The approach accommodates arbitrary localized sources beyond the dipole approximation.
    • A general formula predicts focusing quality based on permittivity and permeability tensors.

    Conclusions:

    • The study provides a robust framework for understanding time reversal in complex media.
    • The findings are applicable to metamaterials and contribute to super-resolution imaging.
    • This work enhances the theoretical understanding of electromagnetic field manipulation.