16
1 Electromagnetics for Zero-Index Metamaterials
Fig. 1.11 a A square lattice of dielectric rods, b its square reciprocal lattice, and c Brillouin zone
and the irreducible Brillouin zone
1.7 Photonic Crystals
The purpose of discussing the concept of reciprocal lattice and the Brillouin zone in
the previous section was to ensure easy comprehension of photonic crystals. Photonic crystals (PhC) are artificial materials that have a periodic variation of refractive
index in one, two, or three dimensions. They influence the incoming photons in a
similar manner as the crystals do to the incoming electrons; however, the difference
is that the former has a periodic variation of potential while the latter has a periodic
distribution of the refractive index. Similar to the electronic band structure for crystals, photonic band structures can be calculated for photonic crystals too [37, 40].
Shown below are the three types of photonic crystals based on the dimensions of periodicity. Figure 1.12a shows a one-dimensional photonic crystal, also called Bragg
mirror [37], in which the refractive index varies periodically only in one dimension
and is invariant in the remaining two dimensions. Similarly, the variation of refractive index in two and three dimensions yields two-dimensional and three-dimensional
photonic crystals shown in Fig. 1.12b and c, respectively.
(a) One dimensional
(b) Two dimensional
(c) Three dimensional
Fig. 1.12 The three types of photonic crystals based on dimensions
1 Electromagnetics for Zero-Index Metamaterials
Fig. 1.11 a A square lattice of dielectric rods, b its square reciprocal lattice, and c Brillouin zone
and the irreducible Brillouin zone
1.7 Photonic Crystals
The purpose of discussing the concept of reciprocal lattice and the Brillouin zone in
the previous section was to ensure easy comprehension of photonic crystals. Photonic crystals (PhC) are artificial materials that have a periodic variation of refractive
index in one, two, or three dimensions. They influence the incoming photons in a
similar manner as the crystals do to the incoming electrons; however, the difference
is that the former has a periodic variation of potential while the latter has a periodic
distribution of the refractive index. Similar to the electronic band structure for crystals, photonic band structures can be calculated for photonic crystals too [37, 40].
Shown below are the three types of photonic crystals based on the dimensions of periodicity. Figure 1.12a shows a one-dimensional photonic crystal, also called Bragg
mirror [37], in which the refractive index varies periodically only in one dimension
and is invariant in the remaining two dimensions. Similarly, the variation of refractive index in two and three dimensions yields two-dimensional and three-dimensional
photonic crystals shown in Fig. 1.12b and c, respectively.
(a) One dimensional
(b) Two dimensional
(c) Three dimensional
Fig. 1.12 The three types of photonic crystals based on dimensions