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    We developed a new Supporting Quadric Method (SQM) that includes diffraction effects for designing diffractive optical elements (DOEs). This method accurately calculates the DOE phase function for specific intensity distributions.

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    Area of Science:

    • Optics and Photonics
    • Computational Electromagnetics

    Background:

    • Diffractive optical elements (DOEs) are crucial for shaping light intensity distributions.
    • Traditional methods like geometrical optics may not fully account for diffraction effects.

    Purpose of the Study:

    • To formulate an enhanced Supporting Quadric Method (SQM) that incorporates diffraction effects.
    • To enable the calculation of diffractive optical element (DOE) phase functions for precise intensity control.

    Main Methods:

    • Representing the DOE phase as a piecewise smooth function using quadric lenses.
    • Employing a gradient descent method to minimize the error between generated and target intensity distributions.
    • Deriving the error function's gradient analytically within the scalar diffraction theory (SDT) framework.

    Main Results:

    • Successfully calculated DOE phase functions considering diffraction.
    • Demonstrated the effectiveness of the SQM formulation in generating prescribed intensity distributions.
    • Validated the analytical gradient calculation within the scalar diffraction theory.

    Conclusions:

    • The proposed SQM formulation effectively accounts for diffraction in DOE design.
    • A hybrid approach, using geometrical-optics SQM as initialization, shows promising performance.
    • This method offers a robust way to design DOEs for complex intensity shaping applications.