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Updated: Aug 26, 2025

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    This summary is machine-generated.

    This study introduces a sinc series method for optical diffraction, offering superior accuracy and avoiding artificial periodicity issues found in Fourier transform-based methods like the angular spectrum method (ASM). The new approach provides reliable parameter selection for precise optical propagation simulations.

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    Area of Science:

    • Computational optics
    • Numerical methods in physics

    Background:

    • Traditional methods like the angular spectrum method (ASM) suffer from artificial periodicity due to their reliance on Fourier series and finite domains.
    • The sinc series approximation offers an alternative basis suited for infinite domains, potentially overcoming limitations of existing techniques.

    Purpose of the Study:

    • To present a numerical implementation of the sinc series method for computing optical diffraction integrals.
    • To provide rigorous error analysis and derive parameter selection criteria for the sinc method.
    • To demonstrate the method's accuracy and efficiency through simulations of optical propagation.

    Main Methods:

    • Numerical implementation of the sinc series approximation for diffraction integrals.
    • Rigorous error analysis to determine convergence properties and accuracy dependencies.
    • Parameter selection criteria derived from error analysis for user guidance.
    • Numerical simulations of Gaussian beam and optical phased array propagation.
    • Comparison with the angular spectrum method (ASM) and band-limited ASM.

    Main Results:

    • The sinc method exhibits super-algebraic convergence, indicating high accuracy.
    • Accuracy is independent of wavelength, propagation distance, and observation plane discretization, depending solely on source field approximation.
    • Numerical simulations confirm the high-order accuracy and computational efficiency of the sinc method.
    • Provided Matlab code facilitates reproduction of results for Fresnel diffraction.

    Conclusions:

    • The sinc series method is a powerful and accurate alternative for computing optical diffraction integrals.
    • The derived parameter selection criteria enable users to achieve desired error tolerances.
    • The method avoids artificial periodicity, offering advantages over FFT-based techniques like ASM for optical propagation problems.