Electromagnetic-wave propagation along curved surfaces

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 u1,u2,u3, can be fully separated in the spatial dimensions. It is shown that surface electromagnetic wave solutions decay exponentially away from the surface (along the u3 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.