THOMPSON, I. and LINTON, C.M., 2010. Guided surface waves on one- and two-dimensional arrays of spheres. SIAM Journal of Applied Mathematics, 70(8), pp.2975-2995.
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.