By using the sparse-matrix canonical-grid method, we performed large-scale multiple-scattering calculations to study the gap structures and wave functions of classical waves in two-dimensional quasiperiodic structures. We observed many interesting phenomena arising from the quasiperiodic long-range order. In particular, a self-similar wave function with resonant structures was observed at a band edge. Our findings indicate that two-dimensional quasiperiodic systems exhibit a universal behavior that applies to both electrons (or phonons) in discrete lattices and classical waves in continuous media.

• Received 8 May 2006

DOI:https://doi.org/10.1103/PhysRevB.74.054305