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Analysis of multimode interferometers.

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    A new analytical formula precisely describes multimode interference (MMI) coupler performance. This formula maps input to output, detailing self-image characteristics for advanced photonic device design.

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    Area of Science:

    • Photonics and Wave Optics
    • Integrated Optics
    • Optical Couplers

    Background:

    • Multimode interference (MMI) couplers are fundamental components in photonic integrated circuits.
    • Accurate modeling of MMI couplers is crucial for device design and performance prediction.
    • Existing models may lack generality or ease of application for arbitrary MMI geometries.

    Purpose of the Study:

    • To derive a general analytical formula for the transfer function of rectangular multimode interference (MMI) couplers.
    • To provide a method for determining the positions, amplitudes, and phases of self-images generated by MMI couplers.
    • To establish the transfer function as a propagation matrix for analyzing NxM MMI devices.

    Main Methods:

    • Utilized the elliptic theta function ϑ(x', z') to formulate the general analytical transfer function.
    • Applied the derived transfer function to analyze self-image formation for arbitrary input sources.
    • Developed simplified solutions for specific MMI configurations, including NxN, symmetric, and paired couplers.

    Main Results:

    • A general analytical formula for the MMI coupler transfer function was successfully derived.
    • The formula accurately predicts the characteristics (position, amplitude, phase) of all self-images.
    • The transfer function was demonstrated to function as a propagation matrix for NxM MMIs.
    • Simplified analytical solutions were obtained for NxN, symmetric, and paired MMI designs.

    Conclusions:

    • The derived general analytical formula offers a powerful tool for understanding and designing MMI couplers.
    • This approach simplifies the analysis of self-imaging phenomena within MMI devices.
    • The transfer function as a propagation matrix provides a versatile framework for analyzing complex MMI structures.