102
3 Optical Signal Attenuation and Dispersion
α scat =
8π
3
3λ 4 n
8 p
2 k B T f β T
=
8π
3
3(1.3) 4 (1.45)
8
(0.286)
2
1.38 × 10
−23
(1400)
6.8 × 10
−12
= 6.08 × 10
−2 nepers/km = 0.26 dB/km
.
Example 3.5 For pure silica glass an approximate equation for the Rayleigh
scattering loss is given by
α(λ) = α 0
λ 0
λ
4
where α 0 = 1.64 dB/km at λ 0 = 850 nm. This formula predicts scattering losses of
0.291 dB/km at 1310 nm and 0.148 dB/km at 1550 nm.
Drill Problem 3.4 Using Eq. (3.8) and the parameter values from Example
3.4, show that the estimated scattering loss in a silica fiber at 850 nm where n
= 1.455 is 1.49 dB/km.
For multicomponent glasses the scattering at a wavelength λ (measured in μm)
is given by [4]
α =
8π
3
3λ 4
δn
2
2 δV
(3.9)
where the square of the mean-square refractive-index fluctuation (δn
2 )
2 over a volume
of δV is
δn
2
2 =
∂n
2
∂ρ
2
(δρ)
2
+
m
i=1
∂n
2
∂C i
2
(δC i )
2
(3.10)
Here, δρ is the density fluctuation and δC i is the concentration fluctuation of
the ith glass component. Their magnitudes must be determined from experimental
scattering data. The factors ∂n
2 /∂ρ and ∂n
2 /∂C i are the variations of the square of
the index with respect to the density and the ith glass component, respectively.
Structural inhomogeneities and defects created during fiber fabrication can also
cause scattering of light out of the fiber. These defects may be in the form of trapped
gas bubbles, unreacted starting materials, and crystallized regions in the glass. In
general, the preform manufacturing methods that have evolved have minimized these
extrinsic effects to the point where scattering that results from them is negligible
compared with the intrinsic Rayleigh scattering.
3 Optical Signal Attenuation and Dispersion
α scat =
8π
3
3λ 4 n
8 p
2 k B T f β T
=
8π
3
3(1.3) 4 (1.45)
8
(0.286)
2
1.38 × 10
−23
(1400)
6.8 × 10
−12
= 6.08 × 10
−2 nepers/km = 0.26 dB/km
.
Example 3.5 For pure silica glass an approximate equation for the Rayleigh
scattering loss is given by
α(λ) = α 0
λ 0
λ
4
where α 0 = 1.64 dB/km at λ 0 = 850 nm. This formula predicts scattering losses of
0.291 dB/km at 1310 nm and 0.148 dB/km at 1550 nm.
Drill Problem 3.4 Using Eq. (3.8) and the parameter values from Example
3.4, show that the estimated scattering loss in a silica fiber at 850 nm where n
= 1.455 is 1.49 dB/km.
For multicomponent glasses the scattering at a wavelength λ (measured in μm)
is given by [4]
α =
8π
3
3λ 4
δn
2
2 δV
(3.9)
where the square of the mean-square refractive-index fluctuation (δn
2 )
2 over a volume
of δV is
δn
2
2 =
∂n
2
∂ρ
2
(δρ)
2
+
m
i=1
∂n
2
∂C i
2
(δC i )
2
(3.10)
Here, δρ is the density fluctuation and δC i is the concentration fluctuation of
the ith glass component. Their magnitudes must be determined from experimental
scattering data. The factors ∂n
2 /∂ρ and ∂n
2 /∂C i are the variations of the square of
the index with respect to the density and the ith glass component, respectively.
Structural inhomogeneities and defects created during fiber fabrication can also
cause scattering of light out of the fiber. These defects may be in the form of trapped
gas bubbles, unreacted starting materials, and crystallized regions in the glass. In
general, the preform manufacturing methods that have evolved have minimized these
extrinsic effects to the point where scattering that results from them is negligible
compared with the intrinsic Rayleigh scattering.