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Eigenvalue analysis of plasmonic waveguides in layered geometries

An eigenvalue analysis of plasmonic waveguides built in a general layered medium is introduced by combining the Multiple Multipole Program (MMP) with modified layered media Green's functions (LMGF). The new method, first, provides the possible locations of the eigenvalues on a given complex plane (called search functions in the MMP analysis), which provides a very useful information when locating the eigenvalues not only by MMP but also by other numerical methods. Special eigenvalue search and tracing routines are then used to determine the exact locations of the eigenvalues around the possible locations provided by the search functions. The details of the MMP and the modification on LMGF is introduced, together with various numerical examples demonstrating the efficiency of the method.