We obtain the surface mode solution for the Helmholtz equation using an analog formalism for diffracted free beams. By means of a linear superposition of the surface modes we obtain an expression similar to the angular spectrum model which allows us the generation of surface diffraction fields. For the understanding of the physical features implicit in this representation, we describe the interaction between two counter-propagating surface modes, generating a standing plasmonic wave, whose nodes then generate a stationary local charge distribution. The study is reinforced by associating extremal features to the surface modes and an eikonal equation for plasmonic fields is obtained, where a plasmonic refractive index appears naturally. This representation allows us to interpret the surface optical field as a geodesic flow which in principle enables us to associate coherence features to plasmon modes and to analyze the stability of the surface fields under small perturbations of the refractive index.
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