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Deformations in a Transverse Cross Section01:21

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When a material is subjected to uniaxial stress, it elongates or contracts in the direction of the applied force, and also undergoes changes in the perpendicular directions. This behavior is crucial for understanding how materials behave under stress and is governed by mechanical properties such as Poisson's ratio v, which measures the ratio of transverse strain to axial strain.
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Coordinate transformation method for modeling three-dimensional photonic structures with curved boundaries.

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    The coordinate transformation (C) method now models 3D photonic structures with complex curved boundaries. This extension enhances computational efficiency for nanophotonics and plasmonics research.

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    Area of Science:

    • Computational electromagnetics
    • Nanophotonics and plasmonics

    Background:

    • The coordinate transformation (C) method is efficient for 2D photonic structures.
    • Current limitations restrict the C method to 2D models, hindering analysis of complex 3D structures.

    Purpose of the Study:

    • To extend the C method for modeling three-dimensional (3D) photonic structures with curved boundaries.
    • To enhance the applicability of the C method in nanophotonics and plasmonics.

    Main Methods:

    • A hybrid coordinate transformation incorporating z-direction transformation and x-y matched coordinates from Fourier modal method (FMM).
    • Inclusion of perfectly matched layers (PMLs) for aperiodic structures and adaptive spatial resolution (ASR) for convergence.
    • A modified, numerically stable scattering-matrix algorithm to solve boundary conditions between layers using transformed covariant field-components.

    Main Results:

    • Successfully extended the C method to handle general 3D structures with varying curved boundary profiles between layers.
    • Demonstrated the method's validity through several numerical examples, confirming its capability for complex photonic and plasmonic structures.

    Conclusions:

    • The extended 3D-C method significantly broadens the scope of C method applications.
    • This advancement enables precise modeling of intricate 3D nanophotonic and plasmonic devices.