New Method in the Theory of Surface Polaritons

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Abstract
A new method for the treatment of surface polaritons is presented. It is based on a variant of the Ewald-Oseen extinction theorem, which holds for any point inside the medium. Surface polaritons correspond to those solutions of Maxwell equations which are subject to the Ewald-Oseen extinction theorem with no incident field. The method is quite general being applicable to any kind of medium, and it leads immediately to surface-polariton dispersion relations as well as to the structure of the fields associated with them. The power of the present method is demonstrated by applying it to (i) an isotropic nonmagnetic medium having different shapes; (ii) an anisotrpic nonmagnetic medium; (iii) and isotropic but magnetic medium; and (iv) an isotropic nonmagnetic, but spatially dispersive, medium. Surface-polariton response functions are also calculated using the extinction theorem in the above form. A specialized form of extinction theorem is used to discuss surface polaritons without retardation. Finally, a variation of the present approach is used to discuss Brewster modes.