Chapter 1
Electromagnetics for Zero-Index
Metamaterials
1.1 History of Electrodynamics
The nineteenth century witnessed tremendous progress in electromagnetism, prior to
which electricity and magnetism were not perceived as the two sides of the same coin,
as they are today. It all started in 1820, when Hans Christian Øersted demonstrated
for the first time that an electric current flowing in a wire generated a circulating magnetic field around it (Fig. 1.1a) [1]. In the following year, André-Marie Ampère took
things further by showing that two parallel current-carrying wires exerted attractive
or repulsive force on each other depending upon the direction of current in one w.r.t.
the other (Fig. 1.1b) [1–3]. Besides, he also presented a theoretical explanation of the
phenomenon and established a mathematical relation between the magnitude of the
current flowing and the intensity of the magnetic field generated. As the news about
Øested’s experiment reached Michael Faraday in the Royal Society, he immediately
conceived the idea of a device that could harness the magnetic energy and furnish
some mechanical work. This led to the invention of the primordial electric motor
by him in the year 1821 (Fig. 1.1c). Moreover, Faraday envisioned the possibility of
realizing the reverse phenomenon. He ardently believed that symmetry was nature’s
innate property, and hence if electricity could produce magnetism, the vice versa
must be true as well. A series of painstaking experiments during the next 10 years
led to the discovery of electromagnetic induction in 1931 [4, 5]. By this time, the
coalition between electricity and magnetism had been established. Another significant milestone in this arena was set by James Clerk Maxwell, who established light as
a manifestation of the principles of electrodynamics. He argued that a varying electric field generated a varying magnetic field, which in turn generated another varying
electric field and the phenomenon perpetuated [6]. He brilliantly condensed entire
electromagnetic theory into four simple equations, now referred to as Maxwell’s
equation. These equations are the most generalized mathematical representations of
Gauss’s law for electricity and magnetism, Faraday’s law, and Ampere’s circuital
© 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_1
1
Electromagnetics for Zero-Index
Metamaterials
1.1 History of Electrodynamics
The nineteenth century witnessed tremendous progress in electromagnetism, prior to
which electricity and magnetism were not perceived as the two sides of the same coin,
as they are today. It all started in 1820, when Hans Christian Øersted demonstrated
for the first time that an electric current flowing in a wire generated a circulating magnetic field around it (Fig. 1.1a) [1]. In the following year, André-Marie Ampère took
things further by showing that two parallel current-carrying wires exerted attractive
or repulsive force on each other depending upon the direction of current in one w.r.t.
the other (Fig. 1.1b) [1–3]. Besides, he also presented a theoretical explanation of the
phenomenon and established a mathematical relation between the magnitude of the
current flowing and the intensity of the magnetic field generated. As the news about
Øested’s experiment reached Michael Faraday in the Royal Society, he immediately
conceived the idea of a device that could harness the magnetic energy and furnish
some mechanical work. This led to the invention of the primordial electric motor
by him in the year 1821 (Fig. 1.1c). Moreover, Faraday envisioned the possibility of
realizing the reverse phenomenon. He ardently believed that symmetry was nature’s
innate property, and hence if electricity could produce magnetism, the vice versa
must be true as well. A series of painstaking experiments during the next 10 years
led to the discovery of electromagnetic induction in 1931 [4, 5]. By this time, the
coalition between electricity and magnetism had been established. Another significant milestone in this arena was set by James Clerk Maxwell, who established light as
a manifestation of the principles of electrodynamics. He argued that a varying electric field generated a varying magnetic field, which in turn generated another varying
electric field and the phenomenon perpetuated [6]. He brilliantly condensed entire
electromagnetic theory into four simple equations, now referred to as Maxwell’s
equation. These equations are the most generalized mathematical representations of
Gauss’s law for electricity and magnetism, Faraday’s law, and Ampere’s circuital
© 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_1
1