Plasmons on adiabatically varying surfaces

TL;DR

This paper provides a theoretical analysis of surface plasmon polaritons on smoothly curved interfaces, deriving explicit asymptotic formulas and showing how curvature influences wave propagation and attenuation.

Contribution

It introduces a new asymptotic formula for EM waves on curved surfaces and reveals how curvature affects plasmon propagation and loss reduction.

Findings

Explicit asymptotic formula for wave traveling along geodesics

Curvature-dependent correction term in wave attenuation

Curvature can reduce SPP attenuation in lossy media

Abstract

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 a distinction between the planar and curved cases. A curvature-dependent correction term in the exponent demonstrates a strong dependence on transverse curvature and a weak dependence on 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.