Page 205 - Principles and Applications of NanoMEMS Physics

194 Chapter 5

proposed by Barrelet, Greytak, and Lieber [216], employs semiconducting
nanowires and will be touched upon briefly.
In this chapter, we deal with the fundamental principles of
nanophotonics, the processing of light by nanometer-scale devices. In
particular, we address the topics of generation, propagation, and detection of
surface plasmons, and emerging devices based on them.

5.2 Surface Plasmons

The concept of plasmons emerges from considering the motion of a
G
concentration ( ) t,rn of free electrons, in a positive background n , as a
0
G
result of an applied electric field E . In particular, assuming the electrons to
G
behave as a fluid of velocity ( ) t,rv , their motion is prescribed by the
consistent solution of Newton’s and the continuity equations [132],
G
d v G G G
m + m (v ∇⋅ )v = − e E , (1)
dt

and
n ∂ + ∇ ⋅ G =
t ∂ ( ) 0vn . (2)
As a first step towards the solution, after neglecting the second term in (1)
G
due to its quadratic nature in v , one postulates that the effect of the electric
field is to cause the local electron density to deviate from the constant
background density by n =δ n − n . In this context, the extent of this
0
deviation is related to the electric field by Poisson’s equation,
G
∇ ⋅ E = − 4π e (n − n ) −= 4π eδ n , (3)
0
and, because of electron inertia and the restoring force supplied by Coulomb
attraction to regain equilibrium, i.e., n =δ 0 , oscillations ensue. These
collective bulk electron oscillations are denoted as volume plasmons, and
their frequency of oscillation is obtained by substitution of nδ into (2),
resulting in,
n δ ∂ + n ∇ ⋅ G
v =
t ∂ 0 0 , (4)

which, upon differentiating with respect to time, becomes,