Page 161 - Semiconductor For Micro- and Nanotechnology An Introduction For Engineers

The Electromagnetic System
4.2 Basic Description of Light
Around the beginning of the 20th century, new experimental evidence
indicated that light, when interacting with a solid material, seems to
behave also as a “particle” – now called a photon. Up to that stage, the
wave nature model of light had sufficed, and could be cleverly used to
explain most phenomena observed. Each model of course has major tech-
nological significance. The difference between the models becomes clear
when we consider what happens to a light wave when it has to have a
finite energy.

4.2.1 The Harmonic Electromagnetic Plane Wave
We can consider the harmonic electromagnetic plane wave in a vacuum
that satisfies Equation (4.10) as a basic component with which to build
up more detailed descriptions. Thus, following Equation (4.11), we select

(
•
E = E exp [ i – ωt – kr)] (4.41)
0
We first insert (4.41) into (4.1c), noting that ρ = 0 , to give
(
∇• E = 0 = iE • exp [ i – ωt – kr)] or E • k = 0 (4.42)
•
k
0
0
We next use (4.1b), noting that, since σ = 0 that J = 0 , to obtain
1
(
•
H = ----------k × E exp [ i – ωt – kr)] or H = k × E 0 (4.43)
0
0
ωµ
0
k
We see that E , H and are cyclically perpendicular to each other.
0 0
B
E
Thus the mutually orthogonal vectors and always lie in a plane per-
pendicular to the direction of propagation . Without sacrificing general-
k
ity for the plane wave case, we can assume now that the wave propagates
along the -axis, the E -field lies parallel to the -axis and the B -field
y
x
lies parallel to the -axis, hence
z
E = E cos ( ωt – kx) B = B cos ( ωt – kx – α)
0
z
0
y
(4.44)
E = E = 0 B = B = 0
z
x
x
z
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