
60 Optical Fiber Communication Systems with MATLAB
®
and Simulink
®
Models
3.3 Signal Distortion in Optical Fibers
3.3.1 Basics on Group Velocity
Consider
a m
onochromatic
eld
g
iven
b
y
E
x
= A cos(ωt − βz) (3.8)
where
A
i
s
t
he
w
ave
a
mplitude
ω
i
s
t
he
r
adial
f
requency
β is the propagation constant along the z-direction
If
w
e
s
et
ωt − β
z
t
o
b
e
a c
onstant
t
hen
t
he
w
ave
p
hase
v
elocity
i
s
g
iven
b
y
v
dz
dt
p
= =
ω
β
(3.9)
Now
we
consider
a
propagating
wave
consisting
of
two
monochromatic
elds
of
frequen-
cies
ω
+
∂ω a
nd
ω
−
∂ω
E
x
A t z
1
= + ∂ − + ∂cos[( ) ( ) )],ω ω β β
(3.10)
E A t z
x2
= − ∂ − − ∂cos[( ) ( ) )].ω ω β β (3.11)
The
t
otal
eld
i
s
t
hen
g
iven
b
y