Wavenumber matching is crucial to proper designs of optical devices such as ring-bus waveguides or planar cavities. In particular, the range of in-plane wavenumbers needs to be adequately determined along the coupling direction. Oftentimes, numerically intensive search is necessary for its accurate determination for surface plasmon resonances in particular nanostructures. In this paper, a method based on contour integrals is employed in order to provide a rough idea on the coupling capability of participating optical components. An example is provided for a semi-infinite metal–dielectric periodic multilayer bounded by another semi-infinite medium.
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