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Path-integral formulation of nonuniform optical coupled wave problems.

R R Syms

    Applied Optics
    |May 22, 2010
    PubMed
    Summary

    Path integration offers a novel solution for 1-D optical coupled wave problems with spatially varying parameters. This perturbation method yields an infinite series solution that accurately matches conventional approaches.

    Area of Science:

    • Optics
    • Wave Propagation
    • Mathematical Physics

    Background:

    • Solving one-dimensional (1-D) optical coupled wave problems with distance-varying parameters presents significant challenges.
    • Conventional methods may be computationally intensive or limited in applicability for complex systems.

    Purpose of the Study:

    • To introduce and validate path integration as an effective method for solving 1-D optical coupled wave problems.
    • To demonstrate the method's applicability to systems with spatially dependent optical parameters.

    Main Methods:

    • The path integration method is derived using thin section decomposition.
    • It is formulated as a perturbation solution to the general matrix eigenvalue problem.
    • The solution is expressed as an infinite series.

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    Main Results:

    • The path integration method successfully provides an infinite series solution for the 1-D optical coupled wave equation.
    • Evaluations across multiple examples show excellent agreement between the path integration results and those obtained by conventional methods.
    • The technique is robust for systems where optical parameters change with distance.

    Conclusions:

    • Path integration is a viable and accurate technique for analyzing 1-D optical coupled wave propagation.
    • The method offers a powerful alternative for problems with spatially varying system parameters.
    • Its agreement with established methods validates its utility in optical physics and engineering.