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Aperiodic differential method associated with FFF: an efficient electromagnetic computational tool for integrated

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    This study presents a new differential theory for modeling guided optical structures. The advanced method enhances convergence and accuracy for complex photonic devices.

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    Area of Science:

    • Optics and Photonics
    • Computational Electromagnetics

    Background:

    • Traditional differential theory for periodic structures has limitations for open or guided systems.
    • Modeling semi-infinite open problems requires specific outgoing wave conditions.
    • Excitation techniques need adaptation for guided optical structures.

    Purpose of the Study:

    • To reformulate the differential theory for fast Fourier factorization.
    • To adapt the theory for aperiodic and guided optical structures.
    • To enhance modeling capabilities for complex photonic devices.

    Main Methods:

    • Incorporation of a complex coordinate transformation in propagation equations.
    • Artificial periodization of space to model semi-infinite open problems.
    • Adjustment of excitation techniques for guided structures.

    Main Results:

    • The reformulated differential theory becomes an aperiodic tool.
    • Numerical results show enhanced convergence and accuracy compared to the aperiodic Fourier modal method.
    • The method is particularly effective for complex-shaped photonic guided devices.

    Conclusions:

    • The new differential theory provides an accurate and efficient method for analyzing guided optical structures.
    • This advancement facilitates the design and simulation of sophisticated photonic devices.
    • The approach overcomes limitations of previous methods for open and guided wave problems.