Let () / 0 = 1 2 p / 2 be the dielectric function of the half-space z > 0. The half-space

Let ϵ(ω) ϵ / 0 = 1 − ω²_p/ω² be the dielectric function of the half-space z > 0. The half-space z

(a) Relate κ to q_ІІ in each medium.
(b) Use ∇ · D = 0 and the matching conditions for E to deduce that

(c) Derive the dispersion relation

and find the physically allowed solution ω(q) for the specific choice of (ω) given. Sketch ω(q) and investigate the limits q → 0 and q →∞.

E(x, z)= [Ein/out(x, z) + Ein/out(x, z)2] exp[i (qx - wt)] exp(-Kin/out |Z|).