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    Area of Science:

    • Photonics and Optical Engineering
    • Applied Physics
    • Optical Signal Processing

    Background:

    • Phase-shifted Bragg gratings (PSBG) are versatile photonic structures.
    • Optical spatial differentiation is crucial for advanced optical data processing.
    • Existing methods for optical differentiation face limitations in flexibility and order of derivative calculation.

    Purpose of the Study:

    • To theoretically investigate a novel application of PSBG as an optical spatial differentiator in reflection.
    • To demonstrate the capability of PSBG to perform first-order spatial differentiation at oblique incidence.
    • To show PSBG's ability to perform second-order spatial differentiation at normal incidence.

    Main Methods:

    • Theoretical analysis of PSBG response under oblique and normal incidence.
    • Numerical simulations to validate the differentiation capabilities.
    • Demonstration of converting a 2D Gaussian beam to a 2D Hermite-Gaussian mode using the PSBG differentiator.

    Main Results:

    • The PSBG effectively functions as an optical spatial differentiator in reflection mode.
    • Successful calculation of the first-order spatial derivative at oblique incidence.
    • Successful calculation of the second-order spatial derivative at normal incidence.
    • Numerical verification of the conversion of a 2D Gaussian beam into a 2D Hermite-Gaussian mode.

    Conclusions:

    • The proposed PSBG-based optical spatial differentiator offers a new method for calculating spatial derivatives.
    • The demonstrated ability to perform both first and second-order differentiation enhances its utility.
    • This application holds significant potential for advancing all-optical data processing technologies.