Surface plasmon polaritons (SSP), moving along a smooth curved interface between two isotropic media with slowly varying dielectric permittivities and magnetic permeabilities and supporting SSP, are studied theoretically. Solutions of Maxwell equations are investigated within a small wavelength limit in the boundary layer of the wavelength order near the surface. An explicit asymptotic formula for an EM wave traveling along geodesics on the surface is obtained. An exponential factor reflects the distinction between the planar and curved cases. The curvature-dependent correction term in the exponent demonstrates a strong dependence on the transverse curvature and a weak dependence on the longitudinal curvature. The closer the parameters to the resonance case, the more pronounced this tendency. It is found that the attenuation of the SPP in the case of lossy media may be reduced by changing the curvature. If the signs of the magnetic permeability of the medium on both sides of the interface are opposite, the surface magnetic plasmon polariton may propagate. Its short-wavelength asymptotics is found.
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