Optimal structures for classical wave localization: an alternative to the ioffe-regel criterion

Using the Korringa-Kohn-Rostoker method we compute the band structure for a classical scalar wave scattering from a periodic array of dielectric spheres in a uniform background. The optimal volume filling fraction $f$ of spheres for the creation of a total gap in the density of states, and hence localization, is found to be approximately 11%. This gap persists for refractive index ratios as small as 2.8.