Electromagnetic-wave propagation along curved surfaces

Abstract

We show that Maxwell's equations for a nonmagnetic, isotropic, but electrically inhomogeneous medium in the absence of charges or current sources lead to a wave equation governing surface electromagnetic wave propagation along a general curved, smooth surface which, when recasted using an appropriate choice of curvilinear coordinates ${u}^{1},{u}^{2},{u}^{3}$, can be fully separated in the spatial dimensions. It is shown that surface electromagnetic wave solutions decay exponentially away from the surface (along the ${u}^{3}$ coordinate) with the same decay rate independent of the shape of the surface. Transmission and reflection coefficients governing scattering of electromagnetic waves on a varying surface shape are derived. Two test cases of a Gaussian-shaped and a sinusoidal-shaped surface are solved in details and discussed numerically in terms of transmission and reflection coefficients including dependencies on surface-shape parameters in the wavelength range 250--750 nm. The present method for determining surface electromagnetic wave propagation along complex-shaped metal-dielectric surfaces allows better insight into the importance of surface geometry as well as considerably faster computational speeds than those provided by standard numerical methods.