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Sampling approach for singular system computation of a radiation operator.

Raffaele Solimene, Maria Antonia Maisto, Rocco Pierri

    Journal of the Optical Society of America. A, Optics, Image Science, and Vision
    |March 16, 2019
    PubMed
    Summary

    This study introduces a novel sampling method for computing the singular system of radiation operators with strip currents. The new approach overcomes limitations of traditional methods by using non-uniform sampling points for accurate results.

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    Area of Science:

    • Electromagnetics and Computational Physics
    • Numerical Analysis and Applied Mathematics

    Background:

    • The computation of singular systems for radiation operators with strip currents is challenging due to space-variant operators with non-band-limited kernels.
    • Existing sampling approaches are unsuitable for these non-band-limited systems.

    Purpose of the Study:

    • To develop a new computational method for the singular system of radiation operators with strip currents.
    • To adapt sampling theory for non-band-limited kernel functions in eigenvalue problems.

    Main Methods:

    • Recasting the non-band-limited kernel function as a varying band-limited function.
    • Applying pseudo-sampling series theory to derive a sampling approximation of the kernel.
    • Formulating a discrete eigenvalue problem using non-uniformly distributed sampling points.

    Main Results:

    • A novel sampling approximation for the kernel function is derived.
    • The discrete eigenvalue problem is successfully set up using this approximation.
    • Numerical examples validate the accuracy of the computed singular system.

    Conclusions:

    • The proposed pseudo-sampling method effectively computes the singular system for radiation operators with strip currents.
    • Accurate computation is achieved using a number of samples slightly exceeding the Shannon number.
    • This method offers a viable alternative to traditional approaches for specific electromagnetic problems.