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Calculating corner singularities by boundary integral equations.

Hualiang Shi, Ya Yan Lu, Qiang Du

    Journal of the Optical Society of America. A, Optics, Image Science, and Vision
    |October 17, 2017
    PubMed
    Summary
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    Accurate numerical methods precisely calculate electromagnetic fields near sharp edges, crucial for nanophotonics. This study validates a boundary integral equation method, confirming its accuracy for these complex field calculations.

    Area of Science:

    • Physics
    • Computational Electromagnetics
    • Nanophotonics

    Background:

    • Accurate computation of electromagnetic fields near sharp corners and edges is vital for nanophotonics.
    • Strong near fields enhance light-matter interactions in nanophotonic devices.
    • Analytical solutions for field singularities exist for cylindrical structures, but general cases require numerical methods.

    Purpose of the Study:

    • To develop and validate a numerical method for computing electromagnetic fields near sharp edges.
    • To construct leading terms in asymptotic expansions using numerical solutions.
    • To ensure the accuracy of numerical solutions by comparing with known analytical results.

    Main Methods:

    • Utilized a boundary integral equation method to compute electromagnetic fields.

    Related Experiment Videos

  • Formulated integral equations with rescaled unknown functions to manage unbounded field components.
  • Employed a graded mesh and specialized quadrature schemes for numerical discretization.
  • Constructed leading terms in asymptotic expansions based on the computed numerical solutions.

    • Main Results:

    • The numerical method accurately computes electromagnetic fields near sharp edges.
    • Numerically determined singularity exponents closely match exact analytical values.
    • The developed approach demonstrates high accuracy across various test cases.

    Conclusions:

    • The boundary integral equation method provides accurate numerical solutions for electromagnetic fields near sharp edges.
    • This method is effective for nanophotonics applications requiring precise near-field calculations.
    • The validated numerical approach enhances the reliability of electromagnetic field simulations in complex geometries.