Chapter 4
Nonlinear Optics with Zero-Index
Metamaterials
4.1 What Is Nonlinear Optics?
When any material is subject to an external electric field, electrons of each atom
get displaced by a certain amount depending on the strength of the electric field.
Displacement of the electron cloud results in the separation of positive and negative
charge centers, thus inducing a polarization.
Polarization ˜
P is written as a function of the applied electric field as
1
˜
P(t) = 0 (χ
(1) ˜
E(t) + χ
(2) ˜
E
2
(t) + χ
(3) ˜
E
3
(t) + · · · )
(4.1)
in which the first term represents the linear dependence of polarization on the electric
field and the second term onward represents the nonlinear behavior. In general, χ
(n)
is the nth-order nonlinear susceptibility. Hence, Eq. 4.1 can be written as
˜
P(t) = ˜
P
(1)
+ ˜
P
N L
(4.2)
1 Tilde sign on P, E, and D indicates time dependence.
© 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_4
83