In dielectric and magnetic material, unusual situations arise when the electric permittivity and magnetic permeability are both real and negative. Consider a plane wave with electric field E = E0 exp[-i(k.r - ωt)] and magnetic field H = H0 exp[-i(k.r - ωt)].
(a) First consider a standard material with permittivity ε and magnetic permeability μ both real and positive. Find the Maxwell equations satisfied by E0 and H0 in such a medium, the velocity of light in such a medium, and what combination of E0, k and H0 form a right-handed set.
(b) From now on we consider a doubly-negative meta-material and write ε = - | ε | and μ = - |μ| Write the Maxwell equations satis_ed by E0 and H0 in the meta-material and show that the role of E0 and H0 are interchanged compared to the standard case explored in (1). (c) What can you state about the set (E0;H0; k)?