My PhD thesis - Condensed Matter Theory - Imperial College London

CHAPTER 8. APPLYING THE PLASMON NORMAL MODE THEORY TO
SLAB SYSTEMS
1
Electrostatic surface plasmon dispersion relation for a thin slab
0.8
0.6
ω/ω p
0.4
0.2
0
0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05
k/k p
Figure 8.5: The dispersion relation for surface plasmons in the electrostatic theory. The slab
width is 20 au. For metallic densities, the Fermi wave vector is of order 1, whereas k p ∼ 0.01. The
plasmon frequency very rapidly reaches the large-k limit of ω p / √ 2; this is the result obtained for
a semi-infinite system, and indicates that the coupling between surface plasmon modes on the two
sides of the slab is weaker than that obtained when using the full dynamical theory.
and D is also determined, giving
⎧⎪
e kz when z < 0
⎨
φ k (r) = A k e −ikx e kz ∓e −k(z−s)
when 0 < z < s
⎪ ⎩
1∓e ks
∓e −k(z−s)
otherwise.
(8.83)
As with the bulk plasmons earlier, this result can be generalised to allow propagation
in any direction parallel to the slab by a rotation of the axes. The form of
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