1.8 Transition from a Photonic Crystal to a Dielectric Metamaterial
25
X
M
X
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Frequency
a/2 c
Band 2
Band 4
(a)
X
M
X
0
0.2
0.4
0.6
0.8
1
Frequency
a/2 c
Band 2
Band 4
(b)
750
800
850
900
950
1000 1050 1100 1150 1200
Frequency
(10 12 rad/s)
-1.5
-1
-0.5
0
0.5
1
Refractive index
Band 2
Band 4
(c)
850
900
950
1000 1050 1100 1150 1200 1250 1300
Frequency
(10 12 rad/s)
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
Refractive index
Band 2
Band 4
(d)
(e)
(f)
Fig. 1.19 A photonic crystal as a negative-index metamaterial (a), (c), and (e) and zero-index
metamaterial (b), (d), and (f)
the bands 2 and 4 can be seen intersecting at a common point popularly known as the
Dirac point (details in Chap. 2) [27, 60, 85]. The refractive index curve for this case
has been shown in Fig. 1.19d, in which one can notice that the refractive index tends
to zero at ω = 1025 × 10
12 rad/s. The zero-index nature gets further confirmed by
zero refraction of light of frequency ω = 1025 × 10
12 rad/s, as shown in Fig. 1.19f,
as it travels from the photonic crystal to air. It will be later explained in Chap. 2
that a wave emerging from a zero-index medium always emerges normally, irrespective of the angle of incidence. This book is dedicated to zero-index metamaterials
and zero refraction property. The profound details of this category of metamaterials