Page 29 - Electrical Properties of Materials

12 The electron as a particle

Medium 1 Medium 2
Vacuum Conductor
Incident wave
Transmitted wave
Reflected wave
Fig. 1.4
Incident electromagnetic wave partly
reflected and partly transmitted. ωτ < < 1, ω > ω p

Medium 1 Medium 2
Vacuum Conductor
Incident wave
No transmitted wave
Fig. 1.5 Reflected wave
Incident electromagnetic wave
reflected by the conductor. ωτ < < 1, ω > ω p

Let us take the case when ωτ 1; k is given by eqn (1.53), and our con-
ductor fills half the space, as shown in Fig. 1.4. What happens when an
electromagnetic wave is incident from the left?
1. ω> ω p . The electromagnetic wave propagates in the conductor.
There is also some reflection, depending on the amount of mismatch. Energy
conservation says

energy in the incident wave = energy in the transmitted wave
+ energy in the reflected wave.

Is there any absorption? No, because ωτ 1.
2. ω< ω p . In this case k is purely imaginary; the electromagnetic wave
decays exponentially. Is there any absorption? No. Can the electromagnetic
wave decay then? Yes, it can. Is this not in contradiction with something or
other? The correct answer may be obtained by writing out the energy balance.
Since the wave decays and the conductor is infinitely long, no energy goes out
at the right-hand side. So everything must go back. The electromagnetic wave
is reflected, as shown in Fig. 1.5. The energy balance is energy in the incident
wave = energy in the reflected wave.
3. Let us take now the case shown in Fig. 1.6 when our conductor is of fi-
nite dimension in the z-direction. What happens if ω< ω p ? The wave has a
chance to get out at the other side, so there is a flow of energy, forwards and
backwards, in the conductor. The wider the slab, the smaller is the amplitude
of the wave that appears at the other side because the amplitude decays expo-
nentially in the conductor. There is decay, but no absorption. The amplitudes
of the reflected and transmitted waves rearrange themselves in such a way as
If there is a smaller amplitude to conserve energy.
transmitted, there will be a larger If we choose a frequency such that ωτ 1, then, of course, dissipative
amplitude reflected. processes do occur and some of the energy of the electromagnetic wave is