Page 497 - Fiber Optic Communications Fund

478 Fiber Optic Communications

−1
−1
= 1.1W −1 km , loss coefficient = 0.0461 km , spontaneous emission factor n = 1.5. Find the
sp
variance of (a) linear phase noise, (b) nonlinear phase noise at the receiver.
Solution:
The PSD of ASE is
= hf(G − 1)n ,
sp
G = exp (L )= exp (0.0461 × 80)= 39.96,
a
c 3 × 10 8
f = = Hz = 193.54 THz,
1550 × 10 −9
= 6.626 × 10 −34 × 193.54(39.96 − 1)× 1.5J = 7.495 × 10 −18 J.

The pulse energy is
E = PT = 2 × 10 −3 × 25 × 10 −12 J = 5 × 10 −14 J.
b
The variance of linear phase noise is
N −18
2 a 20 × 7.495 × 10 2 −3 2
= = rad = 1.499 × 10 rad .
lin 2E 2 × 5 × 10 −14
The effective length is
1 − exp (−L ) 1 − exp (−0.0461 × 80)
a
L = = km = 21.14 km.
eff
0.0461
The variance of the nonlinear phase noise is
2 2
(N − 1)N (2N − 1)E L
a
a
a
2
= eff
nl 2
3T
b
3 2
19 × 20 × 39 × 7.495 × 10 −18 × 5 × 10 −14 ×(1.1 × 10 −3 × 21.14 × 10 ) 2
= rad
3 ×(25 × 10 −12 2
)
2
= 1.603 × 10 −3 rad .
The total variance is
2
tot = 2 lin + 2 nl
= 1.499 × 10 −3 + 1.603 × 10 −3 rad 2
2
= 3.102 × 10 −3 rad .

10.11 Stimulated Raman Scattering

When a light wave propagates in a medium, a small fraction of light emerges in directions other than that
of the incident wave. Most of the scattered light has the same frequency as the incident light, a small part
has frequencies different from the incident light. This phenomenon was first observed by Raman [77] (and