Photonic Band Gaps for Fields in Continuous and Lattice Structures

Abstract

In the recent paper Poulton et al (2000) analysed eigenvalue problems for elastic solids containing doubly periodic arrays of circular voids, and the issue of particular interest was the study of the so-called photonic/phononic band gaps — intervals of frequencies for which all the propagating vibrations in the material are suppressed. It was noted that the effect of phononic band gaps occurs when the voids are sufficiently close to each other, so that the normalised thickness of a “bridge” between the voids is small. It is also natural in this case to compare the configuration mentioned with a lattice structure (thin bridges between voids can be replaced by linear springs, for example). The expectation that the same effect of band gap modes will exist for a “homogeneous” lattice fails, and we show that a multi-level lattice structure is required in order to observe trapped modes and band gaps on the dispersion diagram.