© Kwok-Wai Ng, 1998.
1. Surface plasmons. Consider a semi-infinite plasma
on the positive side of the plane z = 0. The negative side (z<0)
is vacuum. Given solution of Laplace's equation 2=0 in the
plasma is i(x,z) = A cos kx e-kz and
that of vacuum is 0(x,z) = A cos kx ekz.
(a) Write down all boundary conditions of electric fields at
the boundary z=0. (b) Show that the frequency s of
a surface plasma oscillation is 
, where
p is the plasma frequency. (c) The electron concentration
in a copper sample is 81022 cm-3, mean free
path is ~400, and the Fermi velocity is 1.6108 cm s-1.
Mass of an electron is 9.1110-28 g. Estimate the plasma
frequency at the surface of this sample.
Solution:
