Page 105 - Fiber Optic Communications Fund

86 Fiber Optic Communications

The net accumulated dispersion is
L
|D L + D DCF DCF | ≤ 1100 ps/nm. (2.259)
TF TF
Therefore, the accumulated dispersion of the DCF should be

L
D DCF DCF < −3380 ps/nm. (2.260)

Example 2.18
Let the input field envelope be
[ ]
2
t (1 + iC)
s (t)= A exp − , (2.261)
i
2T 2
0
where C is the chirp parameter. Show that the field envelope at the fiber output is
[ ]
AT 0 (1 + iC) t 2
s (t)= exp − ,
o 2
T
1 2T
1
where
[( 2 ) ] 1∕2
T = T + LC − i L .
2
2
1
0
Plot the power and frequency deviation at different fiber lengths for C > 0 and C < 0. Ignore fiber
2
2
loss and .
1
Solution:
Using Eqs. (2.150) and (2.152), we find
A 2
̃ s (f)= exp [−(f∕a) ], (2.262)
i
a
where
2
a = 1 + iC . (2.263)
2T 2
0
2
2
2
The output field envelope is given by Eq. (2.155), with b = a ∕(1 − i2 La ) as,
2
[ ]
AT 0 (1 + iC) t 2
s (t)= exp − , (2.264)
o
T 1 2T 2
1
where
2 1∕2
T =[(T + LC)− i L] . (2.265)
1 0 2 2
As in Example 2.6, the output pulse width can be calculated as
1∕2
( ) 2 ( ) 2
⎡ C L L ⎤
T out = T in ⎢ 1 + 2 + 2 ⎥ . (2.266)
FWHM FWHM 2 2
⎢ T T ⎥
⎣ 0 0 ⎦