WAVES AND VIBRATIONS IN INHOMOGENEOUS STRUCTURES ...

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0. Sigmund and J. S. Jensen
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lower frequency higher frequency
Figure 1. Scalar wave propagation in two-dimensional domains with absorbing boundary condi-
tions and forced vibrations at the left edge. (a) Wave propagation through homogeneous struc-
ture; (b) wave propagation with higher frequency through a homogeneous structure; (c) wave
propagation through a structure with periodic inclusions; (d) (no) wave propagation with higher
frequency through a periodic structure; (e) wave propagation through a periodic structure with
a defect; and (f) waveguiding a higher frequency through a periodic structure with a defect.
Interest in the photonic band gap materials and structures over the last decade
has been large. Based on the theory developed (see, for example, Joannopoulos et al.
1995; Yablonovitch 2001), industrial applications such as improved waveguides (see
figure le, f) and lasers have emerged. The work on photonic band gaps has caused a
renewed interest in phononic band gap materials. The basic principles of wave prop-
agation in elastic media are well established (e.g. Brillouin 1953; Elachi 1976), but
more recent research in this field has focused on theoretical and experimental demon-
stration of band gaps in two-dimensional and three-dimensional periodic materials
(e.g. Sigalas & Economou 1992; Vasseur et al. 1998; Liu et al. 2000; Kushwaha 1996).
Phil. Trans. R. Soc. Lond. A (2003)