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Accurate signal sampling and reconstruction are crucial in various signal-processing applications. A time-domain signal's spectrum can be revealed using its Fourier transform. When this signal is sampled at a specific frequency, it results in multiple scaled replicas of the original spectrum in the frequency domain. The spacing of these replicas is determined by the sampling frequency.
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    We developed a new wave optical modeling framework, the geometry-aware, phase-compensated angular spectrum method (GAPC-ASM), for efficient design of complex optical systems. This method significantly reduces computational demands for thick refractive and diffractive elements.

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    Area of Science:

    • Optics and Photonics
    • Computational Electromagnetics
    • Optical Engineering

    Background:

    • Conventional angular spectrum method (ASM) has limitations in modeling thick optical systems due to dense grid requirements.
    • Scalability issues arise in ASM for wide-angle and large-aperture optical configurations.
    • Accurate modeling of thick refractive and diffractive elements is crucial for advanced optical design.

    Purpose of the Study:

    • To introduce an efficient wave optical modeling framework for thick refractive and diffractive systems.
    • To overcome the computational bottlenecks of conventional ASM.
    • To enable gradient-based inverse design for complex optical systems.

    Main Methods:

    • Developed a geometry-aware, phase-compensated angular spectrum method (GAPC-ASM).
    • Unified carrier frequency shifting and global phase compensation.
    • Introduced a local phase compensation mechanism for geometry-dependent path length variations.

    Main Results:

    • GAPC-ASM enables single-slice modeling of thickness-induced geometrical distortion.
    • Significantly reduced axial sampling requirements in multi-slice ASM.
    • Demonstrated efficiency, differentiability, and suitability for inverse design.

    Conclusions:

    • The proposed GAPC-ASM framework is a reliable and physically consistent tool for wave optical design.
    • Validated through inverse design of lenses and fabrication of a freeform phase mask.
    • The fabricated mask improved lensless imaging reconstruction quality, matching simulations.