Page 154 - Principles and Applications of NanoMEMS Physics

142 Chapter 3

permittivity, ε < 0 , and an array of interspersed split-ring resonators
eff
which created a frequency region with negative permeability, µ < 0 .
eff
These materials have become known as metamaterials and, when
implemented so that both the permittivity and the permeability are
simultaneously negative, they exhibit a negative refractive index
ω
n () =ω ε ()µω () , which is real and gives rise to the existence of
eff eff
propagating modes with the remarkable property that they follow a “left-
G G G
hand” (LH) rule. In this case the vectors E , H , k form a left-handed
system, i.e., the direction of propagation is reversed with respect to the
direction of energy flow [169]. Left-handed materials have been the subject
of much attention because they exhibit unusual propagation properties. For
instance, they exactly reverse the propagation paths of rays within them,
which may be exploited to implement low reflectance surfaces by exactly
canceling the scattering properties of other materials. Another application,
exploits their potential to produce perfect lenses.

3.2.2.3.1 Negative Refraction and Perfect Lenses

The concept of a perfect lens was introduced by Pendry [170], upon
further examining the earlier analysis of Veselago [169] on the consequences
of negative refractive index materials. Veselago [169], in particular, had
indicated that reflection and refraction between vacuum and a negative
refraction material, would follow the situation depicted in Fig. 3-29.

1 1 2 2
φ φ φ φ
Vacuum
Va c u u m
R
ef
ract
I
i
ve
Refractive Index n n
ex
d
n
ψ
ψ
ψ ψ
3 3 4 4
Figure 3-29. Consequences of negative refractive index on refraction properties. 1—Incident
beam. 2—Reflected beam. 3—Refracted beam for n<0. 4—Refracted beam for n>0. (After
[169].)
Fig. 3-29 shows, that contrary to the usual case of a positive index, when the
refraction index is negative the angle of refraction is also negative with
respect to the surface normal. As a result, when such a medium is used as a