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    Area of Science:

    • Computational electromagnetics
    • Nanophotonics modeling
    • Waveguide analysis

    Background:

    • Fourier modal methods (FMM) are established for periodic structures.
    • Previous FMM extensions handled rotationally symmetric open structures.
    • Modeling open, non-symmetric 3D nanophotonic devices remains computationally challenging.

    Purpose of the Study:

    • To generalize the open geometry Fourier modal method to 3D Cartesian coordinates.
    • To enable accurate and efficient modeling of non-symmetric, open nanophotonic structures.
    • To improve the description of radiation modes in open structures.

    Main Methods:

    • Extension of an open boundary condition and non-uniform k-space discretization to 3D Cartesian coordinates.
    • Utilizing a non-uniform circular "dartboard" sampling for Fourier integral discretization.
    • Comparison with conventional discretization methods and factorization rules.

    Main Results:

    • Demonstrated accurate modeling of rectangular geometries in open space.
    • Achieved a more precise description of leaking radiation modes.
    • Showed significantly improved convergence for optical waveguide structures.

    Conclusions:

    • The generalized 3D method provides a powerful tool for open nanophotonic structure analysis.
    • The non-uniform k-space sampling is key to improved accuracy and efficiency.
    • Enables more reliable simulations of complex 3D nanophotonic devices.