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    Area of Science:

    • Photonics
    • Optical Engineering
    • Computational Electromagnetics

    Background:

    • Wavelength selective photonic devices are crucial for optical communication and signal processing.
    • Current function-expansion-based topology optimization methods, often using Fourier series, can result in complex refractive index distributions.
    • Simpler device structures are desirable for fabrication and performance.

    Purpose of the Study:

    • To investigate the influence of different expansion functions on topology optimization for photonic devices.
    • To develop a method for achieving simpler refractive index distributions in optimized photonic devices.
    • To design and analyze a triplexer using alternative expansion functions.

    Main Methods:

    • Employed function-expansion-based topology optimization.
    • Investigated Fourier series, sampling function, and pyramid function as expansion functions.
    • Designed a triplexer device using the developed method.
    • Compared the optimized structures resulting from each expansion function.

    Main Results:

    • The sampling and pyramid functions yielded simpler optimized structures compared to the Fourier series.
    • The choice of expansion function significantly influences the complexity of the refractive index distribution.
    • The triplexer designed using the new method demonstrated the effectiveness of the approach.

    Conclusions:

    • Alternative expansion functions like sampling and pyramid functions can simplify the design of wavelength selective photonic devices.
    • Topology optimization with carefully chosen functions offers a pathway to more practical and potentially manufacturable photonic devices.
    • The study highlights the importance of expansion function selection in achieving desired structural properties in photonic device optimization.