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Complex modes in an open lossless periodic waveguide.

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    Complex modes in open periodic waveguides, even when lossless, exhibit unique band structures. These complex Bloch modes are crucial for understanding wave propagation in defective periodic structures.

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    Area of Science:

    • Photonics and Wave Phenomena
    • Electromagnetism and Optics
    • Materials Science

    Background:

    • Open periodic waveguides support guided Bloch modes with no transverse radiation loss.
    • Lossless periodic waveguides can host guided modes with complex propagation constants, known as complex modes.
    • Complex modes are physically relevant, particularly in the presence of waveguide discontinuities or defects.

    Purpose of the Study:

    • To investigate the band structure and classification of complex modes in open dielectric periodic waveguides.
    • To understand the physical origins and implications of complex modes in periodic structures.
    • To provide theoretical guidance for the practical application of periodic waveguides.

    Main Methods:

    • Analysis of complex Bloch wavenumbers in lossless open dielectric periodic waveguides.
    • Characterization of complex mode band structures.
    • Classification of band endpoints based on physical phenomena.

    Main Results:

    • Complex modes in open dielectric periodic waveguides form distinct bands.
    • Band endpoints correspond to specific physical scenarios: extrema of regular modes, bound states in the continuum, degenerate complex modes, and blazing diffraction solutions.
    • Demonstration of the physical relevance and excitation of complex modes in defective waveguides.

    Conclusions:

    • Complex modes are an integral part of the mode spectrum in open periodic waveguides.
    • The classification of complex mode band endpoints offers new insights into wave behavior in periodic structures.
    • This study enhances the theoretical understanding and practical design of periodic waveguides for various applications.