Gap structures and wave functions of classical waves in large-sized two-dimensional quasiperiodic structures

Y. Lai,¹ Z. Q. Zhang,¹ C. H. Chan,² and L. Tsang²

¹Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong

²Department of Electronic Engineering, City University of Hong Kong, Kowloon, Hong Kong

(Received 8 May 2006; published 30 August 2006)

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.

©2006 The American Physical Society

URL: http://link.aps.org/abstract/PRB/v74/e054305

doi:10.1103/PhysRevB.74.054305

PACS: 71.23.Ft, 43.40.+s, 42.70.Qs, 61.44.Br