WAVES AND VIBRATIONS IN INHOMOGENEOUS STRUCTURES ...

1006
(a) - - - - - - _
- - - -
I
I
I
I
I
I
I (b)
I
I
I
I
I
(b)
(c)
r------------
I
I
(d)
l^^ ^ ^ ^
I- - -- -- -- - -- - - -
-
I
I
I
I
I
I
I
I
I
I
I
I
O. Sigmund and J. S. Jensen
I
U..
U I
.
U
80
I 60
g 40
x
a
cr
20
I I
I I
I I
I
II
I
I
I
I I
I
I
I
I I
o0 '" X M F r
80
60
a 40
5
20
100
U . * 80
_ 1111111 11
3 60 I
20
F X M
Figure 3. Left, single cell; middle, 3 x 3 arrays of cells; right, band diagram for coupled plane
waves in (a) pure phase 1, (b) pure phase 2 and (c) square phase 2 cylinders in matrix of phase 1
(high-contrast case). Hatched areas denote band gaps. The horizontal axes denote values of the
wave vector k on the boundary of the irreducible Brillouin zone. The band diagrams are based
on the solution of 30 eigenvalue problems with varying k solved for the six lowest eigenvalues.
(d) Band diagram for the scalar (out-of-plane) problem with the full band gap shown as a
hatched region and two partial band gaps indicated by cross-hatched regions. The size of the
base cells is 2 cm x 2 cm and the discretization is 10 x 10 elements.
Phil. Trans. R. Soc. Lond. A (2003)
r