Question 2 Surface Plasmons 851 N Medium 1 Vaccum Surface Wave Medium 2 0 Fig 3 Surface Waves Plasmons At 1 (28.01 KiB) Viewed 24 times
Question 2 Surface Plasmons 851 N Medium 1 Vaccum Surface Wave Medium 2 0 Fig 3 Surface Waves Plasmons At 2 (31.67 KiB) Viewed 24 times
Question 2: (Surface plasmons): 851 [ N Medium 1: vaccum Surface wave Medium 2: (0) Fig. 3. Surface waves (plasmons) at vacuum interface of dielectric material At the interface z = 0 between two dielectric materials we can observe the occurrence of transverse surface waves called surface plasmons. Let us assume that medium 1 for z > Ois vacuum, and that medium 2 for z <0 is a bulk material with dielectric constant (w). Let us also assume that the surface wave is travelling in the x – 2 plane (TM mode) with a phase factor exp(i(ki - wt)).
(c) A propagating surface wave occurs when ky is real and k (1) and k (2) are purely imaginary. Give [7] a criteria for E(W), which corresponds to this scenario, and state the corresponding wave function(s). [36] (d) Let medium 2 be a model solid containing a plasma of free electrons with € (w) = 1 - (1) Show that the dispersion relation of the corresponding surface plasmons is: w? (kx) = 1/2 [0% + 2c?k} + Jaws+ 4c*k} (8) (24) (11) Discuss the asymptotic behaviour of w+(kx) for kx + 0 and kx + (Hint: Use V1+xz1+ Ex-x2 + ...). Sketch w+(kx). 2 (iii) Why is w* (kx) not a surface wave as discussed above? (4)
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