3.7 Summary
141
A variety of multimode and single-mode optical fibers are used in telecommunication, access, and enterprise networks. The ITU-T has created a series of recommendations for manufacturing and testing various classes of multimode and single-mode
optical fibers used in telecommunications.
Problems
3.1 Verify the expression given in Eq. (3.3) that relates α, which is in units of
dB/km, to α p , which is in units of km
−1 .
3.2 A certain optical fiber has an attenuation of 0.6 dB/km at 1310 nm and
0.3 dB/km at 1550 nm. Suppose the following two optical signals are launched
simultaneously into the fiber: an optical power of 150 μW at 1310 nm and
an optical power of 100 μW at 1550 nm. What are the power levels in μW
of these two signals at (a) 8 km and (b) 20 km?
3.3 An optical signal at a specific wavelength has lost 55% of its power after
traversing 7.0 km of fiber. What is the attenuation in dB/km of this fiber?
3.4 A continuous 40 km long optical fiber link has a loss of 0.4 dB/km. (a) What
is the minimum optical power level that must be launched into the fiber to
maintain an optical power level of 2.0 μW at the receiving end? (b) What is
the required input power if the fiber has a loss of 0.6 dB/km?
3.5 The optical power loss resulting from Rayleigh scattering in a fiber can be
calculated from either Eq. (3.7) or Eq. (3.8). Compare these two equations
for silica (n = 1.460 at 630 nm), given that the fictive temperature T f is
1400 K, the isothermal compressibility β T is 6.8 × 10
−12 cm
2 /dyn, and the
photoelastic coefficient is 0.286. How does this agree with measured values
ranging from 3.9 to 4.8 dB/km at 633 nm?
3.6 Consider a graded-index multimode fiber that has a core radius a = 25 μm,
a refractive index profile α = 2.0, a cladding index n 2 = 1.478, and an index
difference = 0.01. Using Eq. (3.11) compare the ratio M eff /M ∞ for a
1310 nm wavelength when the bending radius R = 2.5 cm and when R =
1.0 cm.
3.7 Consider a graded-index fiber having an index profile α = 2.0, cladding refractive index n 2 = 1.478, and an index difference = 0.01. Using Eq. (3.11)
compare the ratio M eff /M ∞ for a 1550 nm wavelength for R = 2.5 cm when
(a) a = 25 μm and (b) a = 50 μm.
3.8 Equation (3.13) gives an expression for the factor by which microbending
loss is reduced when a compressible jacket is extruded over a fiber. Consider
the case when a jacket material that has a Young’s modulus E j = 21 MPa is
extruded over a glass fiber that has a Young’s modulus E j = 64 GPa and a
cladding-to-core ratio b/a = 2.0.
(a) Show that when the refractive index difference = 0.01, the reduction
factor is
F(α M ) = 0.0038 = 0.38%.
(b) Show that when the refractive index difference = 0.001, the reduction
factor is F(α M ) = 0.75 = 75%.
141
A variety of multimode and single-mode optical fibers are used in telecommunication, access, and enterprise networks. The ITU-T has created a series of recommendations for manufacturing and testing various classes of multimode and single-mode
optical fibers used in telecommunications.
Problems
3.1 Verify the expression given in Eq. (3.3) that relates α, which is in units of
dB/km, to α p , which is in units of km
−1 .
3.2 A certain optical fiber has an attenuation of 0.6 dB/km at 1310 nm and
0.3 dB/km at 1550 nm. Suppose the following two optical signals are launched
simultaneously into the fiber: an optical power of 150 μW at 1310 nm and
an optical power of 100 μW at 1550 nm. What are the power levels in μW
of these two signals at (a) 8 km and (b) 20 km?
3.3 An optical signal at a specific wavelength has lost 55% of its power after
traversing 7.0 km of fiber. What is the attenuation in dB/km of this fiber?
3.4 A continuous 40 km long optical fiber link has a loss of 0.4 dB/km. (a) What
is the minimum optical power level that must be launched into the fiber to
maintain an optical power level of 2.0 μW at the receiving end? (b) What is
the required input power if the fiber has a loss of 0.6 dB/km?
3.5 The optical power loss resulting from Rayleigh scattering in a fiber can be
calculated from either Eq. (3.7) or Eq. (3.8). Compare these two equations
for silica (n = 1.460 at 630 nm), given that the fictive temperature T f is
1400 K, the isothermal compressibility β T is 6.8 × 10
−12 cm
2 /dyn, and the
photoelastic coefficient is 0.286. How does this agree with measured values
ranging from 3.9 to 4.8 dB/km at 633 nm?
3.6 Consider a graded-index multimode fiber that has a core radius a = 25 μm,
a refractive index profile α = 2.0, a cladding index n 2 = 1.478, and an index
difference = 0.01. Using Eq. (3.11) compare the ratio M eff /M ∞ for a
1310 nm wavelength when the bending radius R = 2.5 cm and when R =
1.0 cm.
3.7 Consider a graded-index fiber having an index profile α = 2.0, cladding refractive index n 2 = 1.478, and an index difference = 0.01. Using Eq. (3.11)
compare the ratio M eff /M ∞ for a 1550 nm wavelength for R = 2.5 cm when
(a) a = 25 μm and (b) a = 50 μm.
3.8 Equation (3.13) gives an expression for the factor by which microbending
loss is reduced when a compressible jacket is extruded over a fiber. Consider
the case when a jacket material that has a Young’s modulus E j = 21 MPa is
extruded over a glass fiber that has a Young’s modulus E j = 64 GPa and a
cladding-to-core ratio b/a = 2.0.
(a) Show that when the refractive index difference = 0.01, the reduction
factor is
F(α M ) = 0.0038 = 0.38%.
(b) Show that when the refractive index difference = 0.001, the reduction
factor is F(α M ) = 0.75 = 75%.