3.7 Summary
143
this fiber is 20 ps/(nm km) at 1550 nm. What is the pulse spreading when a
laser diode with a 1 nm spectral width at 1550 nm is used?
3.14 Verify the plots for b, d(Vb)/dV, and Vd
2 (Vb)/dV
2 shown in Fig. 3.10. Use
the expression for b given by Eq. (3.43).
3.15 Derive Eq. (3.18) for modal delay by using a ray-tracing method.
3.16 Consider a step-index fiber with core and cladding diameters of 62.5 and
125 μm, respectively. Let the core index n 1 = 1.48 and let the index difference
= 1.5%. Compare the modal dispersion in units of ns/km at 1310 nm of
this fiber as given by Eq. (3.18) with the more exact expression
σ mod
L
=
n 1 − n 2
c
1 −
π
V
where L is the length of the fiber and n 2 is the cladding index.
3.17 Consider a standard G.652 non-dispersion-shifted single-mode optical fiber
that has a zero-dispersion wavelength at 1310 nm with a dispersion slope
of S 0 = 0.0970 ps/(nm
2 km). Plot the dispersion in the wavelength range
1270 nm ≤ 1 ≤ 1340 nm. Use Eq. (3.52).
3.18 Starting with Eq. (3.50), derive the dispersion expression given in Eq. (3.52).
Answers to Selected Problems
3.2 The input powers in dBm are P(100 μW) = −10.0 dBm; P(150 μW) = −
8.24 dBm
(a) P 1310 (8 km) = −13.0 dBm = 50 μW; P 1550 (8 km) =
−12.4 dBm = 57.5 μW
(b) P 1310 (20 km) = −20.2 dBm = 9.55 μW; P 1550 (20 km) =
−16.0 dBm = 25.1 μW
3.3 α = 0.5 dB/km
3.4 (a) P in = 79.6 μW = −11 dBm;
(b) P in = 502 μW = −3 dBm
3.5 From Eq. (3.7) α scat = 0.0462 km
−1
= 0.40 dB/km
From Eq. (3.8) α scat = 0.0608 km
−1
= 0.26 dB/km
3.6 0.758 and 0.423 for R = 2.5 cm and 1.0 cm, respectively
3.7 0.753 and 0.553 for a = 25 μm and 50 μm, respectively
3.9
Mode order
P clad /P
α νm = α 1 + (α 2 − α 1 )P clad /P
01
0.02
3.0 + 0.02 dB/km
11
0.05
3.0 + 0.05
21
0.10
3.0 + 0.10
02
0.16
3.0 + 0.16
143
this fiber is 20 ps/(nm km) at 1550 nm. What is the pulse spreading when a
laser diode with a 1 nm spectral width at 1550 nm is used?
3.14 Verify the plots for b, d(Vb)/dV, and Vd
2 (Vb)/dV
2 shown in Fig. 3.10. Use
the expression for b given by Eq. (3.43).
3.15 Derive Eq. (3.18) for modal delay by using a ray-tracing method.
3.16 Consider a step-index fiber with core and cladding diameters of 62.5 and
125 μm, respectively. Let the core index n 1 = 1.48 and let the index difference
= 1.5%. Compare the modal dispersion in units of ns/km at 1310 nm of
this fiber as given by Eq. (3.18) with the more exact expression
σ mod
L
=
n 1 − n 2
c
1 −
π
V
where L is the length of the fiber and n 2 is the cladding index.
3.17 Consider a standard G.652 non-dispersion-shifted single-mode optical fiber
that has a zero-dispersion wavelength at 1310 nm with a dispersion slope
of S 0 = 0.0970 ps/(nm
2 km). Plot the dispersion in the wavelength range
1270 nm ≤ 1 ≤ 1340 nm. Use Eq. (3.52).
3.18 Starting with Eq. (3.50), derive the dispersion expression given in Eq. (3.52).
Answers to Selected Problems
3.2 The input powers in dBm are P(100 μW) = −10.0 dBm; P(150 μW) = −
8.24 dBm
(a) P 1310 (8 km) = −13.0 dBm = 50 μW; P 1550 (8 km) =
−12.4 dBm = 57.5 μW
(b) P 1310 (20 km) = −20.2 dBm = 9.55 μW; P 1550 (20 km) =
−16.0 dBm = 25.1 μW
3.3 α = 0.5 dB/km
3.4 (a) P in = 79.6 μW = −11 dBm;
(b) P in = 502 μW = −3 dBm
3.5 From Eq. (3.7) α scat = 0.0462 km
−1
= 0.40 dB/km
From Eq. (3.8) α scat = 0.0608 km
−1
= 0.26 dB/km
3.6 0.758 and 0.423 for R = 2.5 cm and 1.0 cm, respectively
3.7 0.753 and 0.553 for a = 25 μm and 50 μm, respectively
3.9
Mode order
P clad /P
α νm = α 1 + (α 2 − α 1 )P clad /P
01
0.02
3.0 + 0.02 dB/km
11
0.05
3.0 + 0.05
21
0.10
3.0 + 0.10
02
0.16
3.0 + 0.16