128
3 Optical Signal Attenuation and Dispersion
where σ λ is the half-power spectral width of the optical source. To measure the
dispersion, one examines the pulse delay over a desired wavelength range.
As illustrated in Fig. 3.14, the dispersion behavior varies with wavelength and
also with fiber type. Thus, various standards have recommended different formulas
to calculate the chromatic dispersion for specific fiber types operating in a given
wavelength region. To calculate the dispersion for a non-dispersion-shifted fiber
in the region ranging from 1270 to 1340 nm, the standards recommend fitting the
measured group delay per unit wavelength to a three-term Sellmeier equation of the
form [20]
τ = A + Bλ
2
+ Cλ
−2
(3.50)
Here, A, B, and C are the curve-fitting parameters. An equivalent expression is
τ = τ 0 +
S 0
8
λ −
λ
2
0
λ
2
(3.51)
where τ 0 is the relative delay minimum at the zero-dispersion wavelength λ 0 , and S 0
is the value of the dispersion slope S(λ) = dD/dλ at λ 0 , which is given in ps/(nm
2
km). Using Eq. (3.48), the dispersion for a non-dispersion-shifted fiber is
D(λ) =
λS 0
4
1 −
λ 0
λ
4
(3.52)
To calculate the dispersion for a dispersion- shifted fiber in the 1500–1600 nm
region, the standards recommend using the quadratic expression
τ = τ 0 +
S 0
2
(λ − λ 0 )
2
(3.53)
which results in the dispersion expression
D(λ) = (λ − λ 0 )S 0
(3.54)
Finally, recall from Eq. (3.26) that the third- order dispersion β 3 can be given as
β 3 =
λ
2
(2π c) 2
λ
2 S 0 + 2λD
(3.55)
When measuring a set of fibers, one will get values of λ 0 ranging from λ 0,min
to λ 0,max . Figure 3.16 shows the range of the expected dispersion values for a set
of non-dispersion-shifted fibers in the 1270–1340 nm region. Typical values of S 0
are 0.092 ps/(nm
2 km) for standard non-dispersion-shifted fibers, and are between
0.06 and 0.08 ps/(nm
2 km) for dispersion-shifted fibers. Alternatively, the ITU-T
3 Optical Signal Attenuation and Dispersion
where σ λ is the half-power spectral width of the optical source. To measure the
dispersion, one examines the pulse delay over a desired wavelength range.
As illustrated in Fig. 3.14, the dispersion behavior varies with wavelength and
also with fiber type. Thus, various standards have recommended different formulas
to calculate the chromatic dispersion for specific fiber types operating in a given
wavelength region. To calculate the dispersion for a non-dispersion-shifted fiber
in the region ranging from 1270 to 1340 nm, the standards recommend fitting the
measured group delay per unit wavelength to a three-term Sellmeier equation of the
form [20]
τ = A + Bλ
2
+ Cλ
−2
(3.50)
Here, A, B, and C are the curve-fitting parameters. An equivalent expression is
τ = τ 0 +
S 0
8
λ −
λ
2
0
λ
2
(3.51)
where τ 0 is the relative delay minimum at the zero-dispersion wavelength λ 0 , and S 0
is the value of the dispersion slope S(λ) = dD/dλ at λ 0 , which is given in ps/(nm
2
km). Using Eq. (3.48), the dispersion for a non-dispersion-shifted fiber is
D(λ) =
λS 0
4
1 −
λ 0
λ
4
(3.52)
To calculate the dispersion for a dispersion- shifted fiber in the 1500–1600 nm
region, the standards recommend using the quadratic expression
τ = τ 0 +
S 0
2
(λ − λ 0 )
2
(3.53)
which results in the dispersion expression
D(λ) = (λ − λ 0 )S 0
(3.54)
Finally, recall from Eq. (3.26) that the third- order dispersion β 3 can be given as
β 3 =
λ
2
(2π c) 2
λ
2 S 0 + 2λD
(3.55)
When measuring a set of fibers, one will get values of λ 0 ranging from λ 0,min
to λ 0,max . Figure 3.16 shows the range of the expected dispersion values for a set
of non-dispersion-shifted fibers in the 1270–1340 nm region. Typical values of S 0
are 0.092 ps/(nm
2 km) for standard non-dispersion-shifted fibers, and are between
0.06 and 0.08 ps/(nm
2 km) for dispersion-shifted fibers. Alternatively, the ITU-T