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Explanation of errors inherent in the effective-index method for analyzing rectangular-core waveguides.

A Kumar, D F Clark, B Culshaw

    Optics Letters
    |September 12, 2009
    PubMed
    Summary
    This summary is machine-generated.

    The effective-index method for rectangular waveguides overestimates propagation constants by treating them as pseudorectangular. This explains discrepancies compared to other methods and variations based on initial dimension choice.

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    Area of Science:

    • Optics and Photonics
    • Waveguide Theory
    • Computational Electromagnetics

    Background:

    • Rectangular-core waveguides are fundamental in integrated optics.
    • The effective-index method is a common approximation for analyzing waveguide structures.
    • Previous analyses have noted discrepancies in results from the effective-index method.

    Purpose of the Study:

    • To elucidate the physical basis for the effective-index method's overestimation of propagation constants in rectangular waveguides.
    • To explain the origin of differing results based on the construction dimension of the effective-index waveguide.
    • To provide a clearer understanding of the effective-index method's limitations.

    Main Methods:

    • Analysis of the effective-index method applied to rectangular-core waveguides.
    • Comparison with pseudorectangular-core waveguide models.
    • Investigation of mode propagation constants.

    Main Results:

    • The effective-index method is equivalent to analyzing a pseudorectangular waveguide with an artificially increased dielectric constant in specific cladding regions.
    • This artificial increase in dielectric constant leads to higher calculated propagation constants for guided modes.
    • The method yields different results depending on whether the longer or shorter dimension is used to define the effective-index waveguide.

    Conclusions:

    • The effective-index method's approximations inherently introduce an overestimation of propagation constants for rectangular waveguides.
    • Understanding the pseudorectangular model clarifies the method's behavior and its dependence on initial geometric choices.
    • This work highlights the importance of considering the underlying assumptions when employing approximate analytical methods in waveguide design.