12.11 Summary
505
Answers to Selected Problems
12.1 First using Eq. (3.3) change 0.55 dB/km to 0.127 km
−1 and 0.28 dB/km to
0.0645 km
−1 . Then from Eq. (12.1) L eff (1310) = 7.9 km and L eff (1550) =
14.9 km.
12.2 Using Eq. (3.3) change 0.20 dB/km to 0.046 km
−1 and 0.40 dB/km to
0.092 km
−1 . Then using Eq. (12.1) it follows that L eff (1550) = 18.3 km
and L eff (1310) = 10.6 km. Then using Eq. (12.5), P th (1550) = 12.4 mW and
P th (1310) = 21.4 mW.
12.3 The following nine 3rd-order waves are generated due to FWM:
ν113 = 2(ν2 - ν) – (ν2 + ν) = ν2 - 3ν.
ν112 = 2(ν2 - ν) – ν2 = ν2 - 2ν.
ν123 = (ν2 - ν) + ν2 – (ν2 + ν) = ν2 - 2ν.
ν223 = 2ν2 – (ν2 + ν) = ν2 - ν = ν1.
ν132 = (ν2 - ν) + (ν2 + ν) – ν2 = ν2.
ν221 = 2ν2 – (ν2 - ν) = ν2 + ν = ν3.
ν231 = ν2 + (ν2 + ν) – (ν2 - ν) = ν2 + 2ν.
ν331 = 2(ν2 + ν) – (ν2 - ν) = ν2 + 3ν.
ν332 = 2(ν2 + ν) – ν2 = ν2 + 2ν.
12.4 P peak = 11.0 mW; L disp = 43 km, L period = 67.5 km; P peak = 3.1 mW.
12.6 (a) From the equation L coll = 80 km;
(b) From the given condition L amp = 0.5 L coll ≤ 40 km.
12.7 From the equation and conditions in Problem 12.6, λ max =
T s
DL amp
= 2 nm.
Therefore, the maximum number of channels = 2.0 nm/0.4 nm = 5.
References
1. A.D. Ellis, M.E. McCarthy, M.A.Z. Khateeb, I.M. Sorokina, N.J. Doran, Performance limits
in optical communications due to fiber nonlinearity: Tutorial. Adv. Optics Photonics 9(3),
429–502 (2017)
2. J. Toulouse, Optical nonlinearities in fibers: Review, recent examples, and systems applications.
J. Lightw. Technol. 23, 3625–3641 (2005)
3. R.H. Stolen, The early years of fiber nonlinear optics. J. Lightw. Technol. 26(9), 1021–1031
(2008)
505
Answers to Selected Problems
12.1 First using Eq. (3.3) change 0.55 dB/km to 0.127 km
−1 and 0.28 dB/km to
0.0645 km
−1 . Then from Eq. (12.1) L eff (1310) = 7.9 km and L eff (1550) =
14.9 km.
12.2 Using Eq. (3.3) change 0.20 dB/km to 0.046 km
−1 and 0.40 dB/km to
0.092 km
−1 . Then using Eq. (12.1) it follows that L eff (1550) = 18.3 km
and L eff (1310) = 10.6 km. Then using Eq. (12.5), P th (1550) = 12.4 mW and
P th (1310) = 21.4 mW.
12.3 The following nine 3rd-order waves are generated due to FWM:
ν113 = 2(ν2 - ν) – (ν2 + ν) = ν2 - 3ν.
ν112 = 2(ν2 - ν) – ν2 = ν2 - 2ν.
ν123 = (ν2 - ν) + ν2 – (ν2 + ν) = ν2 - 2ν.
ν223 = 2ν2 – (ν2 + ν) = ν2 - ν = ν1.
ν132 = (ν2 - ν) + (ν2 + ν) – ν2 = ν2.
ν221 = 2ν2 – (ν2 - ν) = ν2 + ν = ν3.
ν231 = ν2 + (ν2 + ν) – (ν2 - ν) = ν2 + 2ν.
ν331 = 2(ν2 + ν) – (ν2 - ν) = ν2 + 3ν.
ν332 = 2(ν2 + ν) – ν2 = ν2 + 2ν.
12.4 P peak = 11.0 mW; L disp = 43 km, L period = 67.5 km; P peak = 3.1 mW.
12.6 (a) From the equation L coll = 80 km;
(b) From the given condition L amp = 0.5 L coll ≤ 40 km.
12.7 From the equation and conditions in Problem 12.6, λ max =
T s
DL amp
= 2 nm.
Therefore, the maximum number of channels = 2.0 nm/0.4 nm = 5.
References
1. A.D. Ellis, M.E. McCarthy, M.A.Z. Khateeb, I.M. Sorokina, N.J. Doran, Performance limits
in optical communications due to fiber nonlinearity: Tutorial. Adv. Optics Photonics 9(3),
429–502 (2017)
2. J. Toulouse, Optical nonlinearities in fibers: Review, recent examples, and systems applications.
J. Lightw. Technol. 23, 3625–3641 (2005)
3. R.H. Stolen, The early years of fiber nonlinear optics. J. Lightw. Technol. 26(9), 1021–1031
(2008)