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It is shown that it is possible to realize strong coupling between a surface plasmon and a guided mode in a layered structure. The dispersion relation of such a structure is obtained through the S-matrix algorithm combined with the Cauchy integral technique that allows for rigorous computations of complex poles. The strong coupling is demonstrated by the presence of an anticrossing in the dispersion diagram and simultaneously by the presence of a crossing in the loss diagram. The temporal characteristics of the different modes and the decay of the losses in the propagation of the hybridized surface plasmons are studied.
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