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    Area of Science:

    • Optics and Photonics
    • Computational Physics

    Background:

    • Accurate calculation of three-dimensional (3D) complex wavefields is crucial for advanced optical simulations.
    • The angular spectrum method provides an efficient and accurate approach for calculating diffracted fields.

    Purpose of the Study:

    • To provide a tutorial on high-speed calculation of 3D complex wavefields.
    • To develop algorithms for generating focused wavefields using the angular spectrum method.
    • To lay the groundwork for nonlinear ray tracing methods.

    Main Methods:

    • Utilized the angular spectrum method for wavefield propagation.
    • Developed two algorithms: one based on the thin lens approximation and another using an ideal lens model (optical Fourier transform).
    • Analyzed computational and memory efficiency for focused laser beams (TEM00 and TEM01).

    Main Results:

    • Presented two distinct algorithms for generating 3D complex wavefields in the focal region.
    • Detailed the three-dimensional sampling requirements for focused fields.
    • Provided expressions for the computational and memory efficiency of the developed algorithms.

    Conclusions:

    • The developed algorithms efficiently compute 3D complex wavefields, serving as a precursor to flux tracing.
    • This work offers a practical tutorial for computing focused fields in three dimensions.
    • The methods are foundational for subsequent papers on nonlinear ray tracing and lens aberrations.