Consider a plane electromagnetic wave incident normally on an infinite plane plasma slab occupying the space 0 ≤ x ≤ L, with vacuum for x < 0 and x > L, as indicated in Fig. 30. Use the following representation for the wave electric field vector:

(a) Calculate the corresponding expressions for the associated magnetic fields.

(b) Calculate the amplitudes E_r, E_f, E_b, and E_t by applying the condition of continuity of E_y and H_z at the boundaries x = 0 and x = L .

(c) Show that the ratio of the average power transmitted out of the plasma slab to the incident average power is given by

where

(d) For ω < ω_pe, where k₁ = iα, with α real, show that

This result shows that some power is transmitted through the plasma slab, even with β = R{k₁} = 0. This effect is known as the tunneling effect.

Figure 30.

Transcribed Image Text:

Ey exp (ikox - iwt) = EryEr exp (-ikox - iwt) = Ef=yEf exp (ik₁x - iwt) EỹE, exp (-ik₁x - iwt) = Et=yEt exp [iko (x - L) - iwt)] (incident wave) (reflected wave) (forward wave) (backward wave) (transmitted wave)