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3. NANOMEMS PHYSICS: Quantum Wave Phenomena 141

n=1.2 n=1.8
1 1
Transmission coefficient 0 1 0.2 0.3 n=2.6 0.5 0.6 0 1 0.2 0.3 0.4 n=2.98 0.6

0.4
0.5

0 0
0.2 0.3 0.4 0.5 0.6 0.2 0.3 0.4 0.5 0.6
N o rm alized F requenc y (c/a)

Figure 3-28. Eleven-layer 2-D PBC transmission coefficient with index of refraction as a
parameter. The band gap attenuation increases from a few dB for n=1.2 to close to 80dB at
n=2.8.

3.2.2.3 Advanced PBC Structures

The initial investigations in the field of PBCs focused on dielectric
materials-based PBCs, whose structure consisted of either periodic arrays of
suitably shaped holes in a dielectric slab, thus forming a continuous
dielectric host matrix, or a periodic array of suitably shaped and isolated
dielectric objects. The former PBC is exemplified by a slab patterned with an
array of cylindrical air holes, whereas the latter PBC is exemplified by an
array of isolated cylinders embedded in air. These PBCs permitted the
creation of band gaps at finite frequencies, but did not produce them at DC.
Further investigations on metal-based PBCs, such as a wire mesh, soon
followed, which demonstrated the existence of band gaps down to DC [167],
[168].
While enabling the manipulation of electromagnetic waves, in particular,
achieving diffractionless guidance of light around sharp bends [162], the
overall propagation behavior in dielectrics and metallic meshes followed the
usual “right-hand” (RH) rule, in which the directions of the electric and
G G G
magnetic fields, E and H , and the propagation vector k form a right-
G
handed system with coincidence of the direction of energy flow and k .
Further work, aimed at manipulating the properties of the PBC medium, led
Pendry to propose two schemes, namely, a composite medium made up of an
array of metal posts which created a frequency region with negative