Page 175 - Fiber Optic Communications Fund

156 Fiber Optic Communications

D.c. Extinction Ratio
So far we have assumed equal power splitting between two arms of the interferometers. In practice, the power
splitting may not be exactly 50 ∶ 50 due to temperature or stress fluctuations. In general, the optical field
distribution entering the arm j is
A exp (−i2f t), j = 1, 2, (4.63)
0 j c
2
2
with + = 1. Now, Eq. (4.47) is modified as
1 2
A exp (−i2f t)
c
0
out = [ exp (i )+ exp (i )] (4.64)
1
2
1
2
+ 2
1
and the output optical power is
P 0
2
2
P out = [ + + 2 cos ( − )]. (4.65)
1 2
1
2
2
1
( + ) 2
1 2
When − = 0, the interference is constructive and the output is maximum:
2
1
P max = P . (4.66)
out 0
When − = , the interference is destructive and the output is minimum:
2
1
P ( − ) 2
0
2
1
min
P = . (4.67)
out 2
( + )
1
2
The d.c. extinction ratio is defined as the ratio of maximum to minimum power:
P max ( + 2 ) 2
out
1
= = . (4.68)
P min − 2
1
out
In dB units, it may be expressed as
(dB)= 10 log . (4.69)
10
√
In the ideal case, = = 1∕ 2 and is infinite. For ASK, it is desirable to have zero power for bit ‘0’. How-
1 2
ever, because of the power-splitting imperfections, the minimum power is not zero and, as a result, the distance
between constellation points becomes smaller, which leads to performance degradations (see Chapter 8).
Eq. (4.68) can be written in a different form [5], [6],
√
− 1
, (4.70)
r = √
+ 1
where r = ∕ . Eq. (4.54) provides the biasing condition to obtain zero chirp. However, Eq. (4.54) is
1
2
obtained for the ideal case of infinite d.c. extinction ratio. For the case of finite extinction ratio, there will
be residual chirp even when the zero-chirp biasing condition given by Eq. (4.54) is used, which degrades the
performance [5].