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Multifunctional Materials 313

be easily used for design purposes. Pendry et al. provide the following analytical formula for
1
thin wire media :
v ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
u
c 0 u 1
f p ¼ u (12:2)
d t d 1
2p(ln (1 þ ln p))
r 2
where c 0 denotes the speed of light in vacuum, d is the lattice spacing, and r is the radius of the wires
(Pendry et al., 1996). Straight wire arrays, such as those shown in Figure 12.3, are designed such
that the radius of the wires is very small compared to the lattice spacing, so that the wavelength of
the electromagnetic excitation frequency is large compared to the lattice size. For the medium to
behave as a plasma at microwave frequencies, for instance, the wire radius must be on the order of
tens of micrometers and spaced on the order of centimeters. To integrate such electromagnetic

Figure 12.3 (Top) Schematic of two-dimensional thin wire array. One hundred micrometer wires are periodically
embedded between composite laminates with layup jig to yield a processed fiberglass/epoxy laminate with array
visible inside. (Bottom) Laminating hot presses for processing composite panels.