Guided surface waves on one- and two-dimensional arrays of spheres

Guided acoustic waves propagating along one- and two-dimensional arrays of rigid spheres are studied semianalytically. The quasi-periodic wavefield is constructed as a superposition of spherical wave functions, 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. In the case of a two-dimensional array, we consider arbitrary skew lattices and compute surface modes which are either symmetric or antisymmetric about the plane of the array. Our numerical calculations make extensive use of previous work by the authors on the accurate and efficient computation of lattice sums.