Chapter 2
Zero-Index Metamaterials
2.1 Introduction
As explained in the previous chapter, the way light interacts with a particular material
depends on the number of electrons in it, and also on how strongly the bound electrons
are held by the nucleus. For a wavelength very large compared to the lattice constant,
e.g., the visible wavelength range 4000–7000 A
o compared to the lattice constant of
silicon ≈5 A
o , different materials exhibit different effective material parameters, viz.,
the refractive index (n), the impedance (z), the permittivity (), and the permeability
(μ) [19, 71, 72, 86–88]. Similarly, the artificial structures called metamaterials
exhibit effective material parameters for the wavelengths very large compared to
the resonator size and array periodicity. However, the advantage of metamaterial is
that their effective material parameters depend more on their design peculiarities
than their material. Hence, abnormal values of material parameters such as negative
refractive index, negative permeability, near-zero permeability, near-zero refractive
index, etc. are achievable, which is not possible with natural materials [17, 18,
27, 30, 79, 89–92]. Having near-zero material parameters is not an unprecedented
phenomenon. All metals exhibit zero permittivity at the plasma frequency and a few
polaritonic materials like silicon carbide (SiC) exhibit zero permeability [93, 94].
However, metamaterials have opened a way to achieve near-zero optical parameters
in a more controlled and versatile manner. Depending on whether permittivity or
permeability or both are zero, metamaterials can be classified into epsilon-near-zero
(ENZ), mu-near-zero (MNZ), and epsilon-and-mu-near-zero (EMNZ) categories. All
these metamaterials are zero-index metamaterials (ZIMs). However, the majority of
the literature presents the definition of ZIM as the one which has both = 0 and
μ = 0. The zero refractive index phenomenon has opened doors to numerous useful
applications, which will be discussed in the later chapters of this book.
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
N. Shankhwar and R. K. Sinha, Zero Index Metamaterials,
https://doi.org/10.1007/978-981-16-0189-7_2
27
Zero-Index Metamaterials
2.1 Introduction
As explained in the previous chapter, the way light interacts with a particular material
depends on the number of electrons in it, and also on how strongly the bound electrons
are held by the nucleus. For a wavelength very large compared to the lattice constant,
e.g., the visible wavelength range 4000–7000 A
o compared to the lattice constant of
silicon ≈5 A
o , different materials exhibit different effective material parameters, viz.,
the refractive index (n), the impedance (z), the permittivity (), and the permeability
(μ) [19, 71, 72, 86–88]. Similarly, the artificial structures called metamaterials
exhibit effective material parameters for the wavelengths very large compared to
the resonator size and array periodicity. However, the advantage of metamaterial is
that their effective material parameters depend more on their design peculiarities
than their material. Hence, abnormal values of material parameters such as negative
refractive index, negative permeability, near-zero permeability, near-zero refractive
index, etc. are achievable, which is not possible with natural materials [17, 18,
27, 30, 79, 89–92]. Having near-zero material parameters is not an unprecedented
phenomenon. All metals exhibit zero permittivity at the plasma frequency and a few
polaritonic materials like silicon carbide (SiC) exhibit zero permeability [93, 94].
However, metamaterials have opened a way to achieve near-zero optical parameters
in a more controlled and versatile manner. Depending on whether permittivity or
permeability or both are zero, metamaterials can be classified into epsilon-near-zero
(ENZ), mu-near-zero (MNZ), and epsilon-and-mu-near-zero (EMNZ) categories. All
these metamaterials are zero-index metamaterials (ZIMs). However, the majority of
the literature presents the definition of ZIM as the one which has both = 0 and
μ = 0. The zero refractive index phenomenon has opened doors to numerous useful
applications, which will be discussed in the later chapters of this book.
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
N. Shankhwar and R. K. Sinha, Zero Index Metamaterials,
https://doi.org/10.1007/978-981-16-0189-7_2
27