Using LC model to recast the problem Consider the current induced by the electric field along the wires related by the total inductance (self and mutual)per unit length (L), E:=-iwLI=iwLnr2nev. the dipole moment per unit volume in the homogenized medium is neffev Ea P =-neffer= iw o2a2L' We can calculate the inductance L by using =LI a/2 polarization P=(s-1)snE r<<a. 2Tc2 e(w)=1-w2amn(a/r)' If we add the effects of finite conductivity in the wires,then E;=-iwLI+I 0Tr2) where o is the conductivity,which modifies the expression for the dielectric permittivity to =1- 好 w+i- .E0a2w2
We can calculate the inductance L by using If we add the effects of finite conductivity in the wires, then Using LC model to recast the problem + - I
Discontinuous metallic wire segment behaves 1 Es =-iwLI+ca(ld) Kr2a Cs =E0EnA/d a permittivity function for this composite to be of the Lorentz form: e(w)=1+昭-w2-w where wo is the resonance frequency given by 1 2πc2d wo=IC(e+d)EhA(e+d)ln(a/r) T=_ 20 2 This gives a frequency bandwidth of where the dielectric per- mittivity of the composite is negative
Discontinuous metallic wire segment behaves
3D structure Figure 3.4 A three-dimensional lattice of thin conducting wires behaves as an isotropic low frequency plasma.(Reproduced with permission from Ra- makrishna (2005).C 2005,Institute of Physics Publishing,U.K.)
3D structure
30 Electric-field-couple resonator (ELC) 20 H⑧+E (D.R.Smith 2006) 10 0 (a) .2 1015202530 f[GHz] a (b) 30 20 k⑧→H FIG.1.(Color online)(a)The fabricated sample.(b)The geometric design: 2 a=3.333 mm,d=3 mm,/=1 mm,w=g=0.25 mm.The copper thickness was 0.017 mm and the FR4 substrate thickness was 0.203 mm.(c)A pro- posed multilayer design with lower resonant frequency.(d)An equivalent circuit. EELC=8d[1-Ff2/(f2-fo+iyf)] 0 16 1820 [GHz]
Electric-field-couple resonator (ELC) (D. R. Smith 2006)
Metamaterial with negative permeability (Pendry 1999) The axial magnetic field inside the cylinders is H=+j-1 2 H=Ho+j 个22 Ho a2
Metamaterial with negative permeability (Pendry 1999) The axial magnetic field inside the cylinders is H0 j j a