Page 424 - Electrical Properties of Materials

406 Artificial materials or metamaterials

Natural materials Artificial materials
Crystal Photonic band gap
λ~d λ~d
Bragg Bragg
diffraction diffraction
X-rays, band gaps Visible, IR … band gaps
electrons
d d

Crystal Metamaterials
λ>>d Effective λ>>d Effective
Fig. 15.2 medium, medium,
Electromagnetic properties of natural ε, μ Microwaves ε, μ
Visible light (negative)
and artificial materials. radio waves

by some kind of averaging. An example is the Clausius–Mossotti equation, dis-
cussed in Section 10.10. This provides a method that leads to the derivation of
macroscopic quantities, such as permittivity and permeability.
Now let’s think of artificial materials in which atoms and molecules are re-
placed by macroscopic, man-made elements. Let’s not worry for the moment
how the elements remain in their allotted space. That may not be always obvi-
ous, but we can safely assume that we have complete freedom in choosing both
the elements and the distance between them. Now all dimensions are much lar-
ger than in natural materials, but the division into the above two categories
is still valid. When the separation between the elements is comparable with
the wavelength [Fig. 15.2(c)], we have again the Bragg effect. These materials
are known as photonic bandgap materials and will be briefly discussed in the
next section. They are quite similar to some of the man-made devices we have
already met, such as volume holograms and distributed Bragg reflection lasers.
When the separation between the elements is much smaller than the wavelength
[Fig. 15.2(d)], we again need some averaging technique to find the properties
∗
∗ Note that photonic bandgap materi- of the material, and we refer to these materials as metamaterials. Can we have
als are often regarded as a subset of a better definition of metamaterials? Not easily. The subject is still in its in-
metamaterials, but there is no need to fancy. There is broad agreement on what it is about, but not about the details.
worry about that. It is purely a question
of definition. It would need a fairly long description accompanied by a number of examples
to be more precise. We shall give here two definitions in current use.

1. Metamaterials are engineered composites that exhibit superior properties
not found in nature and not observed in the constituent materials.
2. A metamaterial is an artificial material in which the electromagnetic proper-
ties, as represented by the permittivity and permeability, can be controlled.
It is made up of a periodic array of metallic resonant elements. Both the
size of the element and the unit cell are small relative to the wavelength.

Definition 1 is too general, whereas definition 2 is not general enough. We
shall make no attempt here to give a comprehensive definition. Perhaps defin-
ition 2 could be made a little more general by adding that control, among
other things, means that it is possible to achieve, simultaneously, negative