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Vector spherical wave function truncation in the invariant imbedding T-matrix method.

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    Determining the optimal truncation number (N) is crucial for accurate invariant-imbedding T-matrix calculations. A new convergence criterion based on the scattering phase function improves accuracy and efficiency in optical property computations.

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    Area of Science:

    • Computational electromagnetics
    • Optical physics
    • Materials science

    Background:

    • The invariant-imbedding T-matrix method is essential for calculating single-scattering optical properties.
    • Computational cost and accuracy depend heavily on the truncation number (N).
    • Selecting an appropriate convergence criterion for N is vital for efficient and accurate simulations.

    Purpose of the Study:

    • To introduce a novel convergence criterion for the truncation number (N) in T-matrix calculations.
    • To investigate the relationship between the optimal truncation number and particle properties (size, refractive index, shape).
    • To develop a generalized formula for predicting the optimal truncation number.

    Main Methods:

    • Developed a new convergence criterion based on the scattering phase function.
    • Analyzed homogeneous particles used in prior single-scattering studies.
    • Investigated the influence of size parameter, refractive index, and particle shape on the optimal truncation number (N).
    • Explored a generalized functional form to relate optimal N to particle characteristics.

    Main Results:

    • The new criterion, based on the scattering phase function, offers an alternative to using the scattering cross section.
    • The optimal truncation number (N) is sensitive to the particle's refractive index and shape.
    • A generalized formula shows promise in summarizing computational results for optimal N.
    • Separating the influence of refractive index from particle shape on optimal N presents a challenge.

    Conclusions:

    • The proposed convergence criterion provides a more refined approach to determining the optimal truncation number (N).
    • Accurate T-matrix calculations necessitate careful consideration of the interplay between refractive index and particle shape.
    • The generalized formula offers a potential tool for optimizing T-matrix computations across various particle types.