Electromagnetic guided waves on linear arrays of spheres

Guided electromagnetic waves propagating along one-dimensional arrays of dielectric spheres are studied. The quasi-periodic wave field is constructed as a superposition of vector spherical wavefunctions and then application of the boundary condition on the sphere surfaces leads to an infinite system of real linear algebraic equations. The vanishing of the determinant of the associated infinite matrix provides the condition for surface waves to exist and these are determined numerically after truncation of the infinite system. Dispersion curves are presented for a range of azimuthal modes and the effects of varying the sphere radius and electric permittivity are shown. We also demonstrate that a suitable truncation of the full system is precisely equivalent to the dipole approximation that has been used previously by other authors, in which the incident field on a sphere is approximated by its value at the centre of that sphere. © 2012 Elsevier B.V.