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A flexible numerical calculation method of angular spectrum based on matrix product.

Wanli Zhao, Chenlu Wei, Caojin Yuan

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    A new matrix product angular spectrum method (ASM) overcomes limitations of Fast Fourier Transform (FFT) based methods. This approach enhances diffraction calculations by extending propagation distance and observation window range.

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    Area of Science:

    • Optics and Photonics
    • Computational Physics
    • Numerical Methods

    Background:

    • Fast Fourier Transform (FFT) is widely used for numerical calculations, including the Angular Spectrum Method (ASM) for diffraction.
    • FFT-based ASM is constrained by frequency and spatial sampling rules, limiting effective propagation distance and observation window size.

    Purpose of the Study:

    • To propose a novel matrix product-based method for angular spectrum diffraction calculations.
    • To overcome the limitations of FFT-based ASM regarding propagation distance and observation range.

    Main Methods:

    • Developed a matrix product approach for fast Discrete Fourier Transform (DFT) calculation.
    • Orthogonally decomposed the sampling matrix into two vectors.
    • Replaced FFT with matrix product calculation for ASM, termed Matrix Product ASM.

    Main Results:

    • Achieved maximum compression of the frequency domain sampling interval via mathematical transformation.
    • Significantly increased the effective propagation distance for angular spectrum calculations.
    • Enabled enlargement of the observation window size by modifying output plane spatial sampling.

    Conclusions:

    • The Matrix Product ASM offers a viable alternative to FFT-based methods for diffraction calculations.
    • This novel method enhances the effective propagation distance and observation range, improving the utility of ASM.