Fundamentals of Metamaterials

Fundamentals of Metamaterials

DOI: 10.4018/978-1-5225-4180-6.ch003
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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.
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3.2 Fundamentals Of Metamaterials

To 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.

(3.4) where 978-1-5225-4180-6.ch003.m05 [V/m] and 978-1-5225-4180-6.ch003.m06 [H/m] are the electric and magnetic field intensity, respectively and 978-1-5225-4180-6.ch003.m07 [C/m2] and 978-1-5225-4180-6.ch003.m08 [W/m2] are the electric and magnetic flux density. Respectively, 978-1-5225-4180-6.ch003.m09 [A/m2] and 978-1-5225-4180-6.ch003.m10 [V/m2] are the electric and magnetic current density, respectively, and 978-1-5225-4180-6.ch003.m11 [C/m3] and 978-1-5225-4180-6.ch003.m12 [C/m3] are the electric and magnetic charge density, respectively. In linear and non-dispersive medium, the constitutive equations are given by
(3.6) where 978-1-5225-4180-6.ch003.m15 [F/m] is the permittivity and 978-1-5225-4180-6.ch003.m16 [H/m] is the permeability of free space, and 978-1-5225-4180-6.ch003.m17 and 978-1-5225-4180-6.ch003.m18 are the medium’s relative permittivity and permeability, respectively, and 978-1-5225-4180-6.ch003.m19 and 978-1-5225-4180-6.ch003.m20 are the losses in 978-1-5225-4180-6.ch003.m21 and 978-1-5225-4180-6.ch003.m22, respectively, due to dielectric and magnetic damping and finite conductivity. Note that 978-1-5225-4180-6.ch003.m23 and 978-1-5225-4180-6.ch003.m24 must be positive due to the conversation about energy.

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