This chapter describes the fundamentals of left-handed metamaterials. From Maxwell's equations, constant phase term is originated, and it is revealed that its negative value is chosen in a negative permittivity and negative permeability (DNG) medium whereas its positive value is designated in a DPS medium. The negative phase constant results in a negative phase velocity and negative index of refraction in the medium. Complementary split ring resonator (CSRR) as a valuable metamaterial component is illustrated. The resonant frequencies of the CSRR are associated with the features of their arrangements. CSRR is agitated with the E field of the electric and magnetic wave together with the axis of the CSRR. Consequently, the CSRR presents negative permittivity in a particular frequency band.
TopTo realize the fundamentals of left-handed metamaterials exist between the phase and group velocities, and negative refractive index in left-handed materials, Maxwell’s equations are repeated in the frequency realm.
(3.1)(3.2)(3.3)(3.4) where
[V/m] and
[H/m] are the electric and magnetic field intensity, respectively and
[C/m
2] and
[W/m
2] are the electric and magnetic flux density. Respectively,
[A/m
2] and
[V/m
2] are the electric and magnetic current density, respectively, and
[C/m
3] and
[C/m
3] are the electric and magnetic charge density, respectively. In linear and non-dispersive medium, the constitutive equations are given by
(3.5)(3.6) where
[F/m] is the permittivity and
[H/m] is the permeability of free space, and
and
are the medium’s relative permittivity and permeability, respectively, and
and
are the losses in
and
, respectively, due to dielectric and magnetic damping and finite conductivity. Note that
and
must be positive due to the conversation about energy.