Page 162 - Semiconductor For Micro- and Nanotechnology An Introduction For Engineers

Basic Description of Light
The argument of the cosine functions is called the phase of the wave
components, and is a maximum if the argument is an integer multiple of
2π . Assuming that we fix a point in space, say x = x , then the wave
0
varies in time as it passes our location with a period of
⁄
T = 2πω (4.45)
In exactly the same way we can fix a point in time, say t = t , to find
0
that the wave varies in space as it passes our time point with a spatial
period or wavelength of

⁄
λ = 2π k (4.46)
The speed of propagation of the peak of the wave is found from the
cosine argument again. We can write that, between two wave peaks m
cycles apart,

ωt – kx = 2πm (4.47)
Looking at one wave peak, so that m = 0 , and on dividing equation
(4.47) by kt , we obtain

ω x
---- = -- = c (4.48)
k t

Phase which is the phase velocity of the wave in a vacuum. Everywhere but in a
Velocity vacuum will the phase velocity become dependent on the frequency of
the wave. The factor α in equation (4.44) causes a relative phase shift
between the electric and magnetic field components. If α = 0 , then the
light is linearly polarized as shown in Figure 4.1 (a). If, however, α ≠ , 0
then the light is circularly polarized as illustrated in Figure 4.1 (b). The
α
sign of determines whether the wave is polarized left/right (or clock-
wise/anti-clockwise).

An electromagnetic wave has an energy density of

v x t,( ) = ε EE (4.49)
•
E 0

Semiconductors for Micro and Nanosystem Technology 159