In this paper we extend the fast-all-modes method and the numerical modified steepest-descent-path method to the optical frequency range by finding all modes and solving the total electric field in three dimensions that is due to a point source above a lossy thin metal film with a negative permittivity situated between two dissimilar dielectric materials. We show that up to four proper surface wave modes may propagate on the film surface, including both backward and forward waves. We also solve for the electric field below the lossy thin metal film and verify the existence of superlensing of the electric field, comparing that case to the case of a dielectric film where no superlensing occurs. The CPU time using the fast-all-modes method and the numerical modified steepest-descent-path method is considerably less than that using the conventional method of integration along the Sommerfeld integration path.
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