Metamaterials: Negative refractive index in ... - Theory.nipne.ro

3.2. Def<strong>in</strong>ition of n: two possible solutions- Plane wave-type solution: E(t,r) = E 0 exp j(ωt –kr); analogously H(t,r)∇ 2 E + μσ ∂E/∂t + με ∂ 2 E/∂t 2 = 0; analogous for H∇ = – jk; ∂/∂t = jω; ∇ 2 = – k 2 ; ∂ 2 /∂t 2 = – ω 2HEkRHMk x E = + ωμH E, H, k is right-handed for ε > 0; μ > 0k x H = – ωεE E, H, k is left-handed for ε < 0; μ < 0- Solution (perfect, absorption-free dielectric): k 2 = ω 2 εμ = ω 2 /v p2 = ω 2 n 2 /c 2c 2 = 1/(ε 0 μ 0 ) n 2 = ε r μ r ; ε > 0; μ > 0 n > 0 usual caseε = – |ε| = e jπ |ε| < 0; μ = – |μ| = e jπ |μ| < 0; n = e jπ √|ε r μ r | = – |n| < 0- Poynt<strong>in</strong>g vector: S = E x H; For n > 0 k II S; For n < 0 k anti II SkSHELHMSn = ±√ε r μ r VeselagoASTiGMAT