2.6 Reflection and Refraction by Zero-Index Metamaterials
41
Fig. 2.14 High reflection in
case of ENZ metamaterials
R =
z − 1
z + 1
2
(2.14)
and the transmission coefficient
T = 1 − R
(2.15)
Let us see how the reflection and the transmission get modified in various types of
zero-index media.
2.6.1.1 Case 1: Epsilon-near-zero (ENZ)
Let us first consider the case of an ENZ metamaterial, in which ≈ 0 but μ = 1, hence
the refractive index n =
√
μ = 0 and the impedance z =
√ μ/ → ∞. Therefore,
the reflection coefficient R is given by
R = lim
z→∞
z − 1
z + 1
2
(2.16)
= lim
z→∞
1 −
1
z
1 −
1
z
2
(2.17)
=
1 −
1
∞
1 −
1
∞
2
(2.18)
= 1
(2.19)
The reflection coefficient R being equal to unity indicates that the light falling
on an ENZ medium is 100% reflected. The deduction seems predictable since the
impedance of the EMZ medium is very large. It results in an astronomical impedance
41
Fig. 2.14 High reflection in
case of ENZ metamaterials
R =
z − 1
z + 1
2
(2.14)
and the transmission coefficient
T = 1 − R
(2.15)
Let us see how the reflection and the transmission get modified in various types of
zero-index media.
2.6.1.1 Case 1: Epsilon-near-zero (ENZ)
Let us first consider the case of an ENZ metamaterial, in which ≈ 0 but μ = 1, hence
the refractive index n =
√
μ = 0 and the impedance z =
√ μ/ → ∞. Therefore,
the reflection coefficient R is given by
R = lim
z→∞
z − 1
z + 1
2
(2.16)
= lim
z→∞
1 −
1
z
1 −
1
z
2
(2.17)
=
1 −
1
∞
1 −
1
∞
2
(2.18)
= 1
(2.19)
The reflection coefficient R being equal to unity indicates that the light falling
on an ENZ medium is 100% reflected. The deduction seems predictable since the
impedance of the EMZ medium is very large. It results in an astronomical impedance