3.2 Optical Signal Dispersion Effects
119
multimode fibers the waveguide dispersion is generally very small compared with
material dispersion and can therefore be neglected.
3.2.7 Dispersion Behavior in Single-Mode Fibers
Waveguide dispersion is of importance for single-mode fibers and can be of the same
order of magnitude as material dispersion. This can be seen by comparing the two
dispersion factors. The pulse spread σ wg occurring over a distribution of wavelengths
σ λ is obtained from the derivative of the group delay with respect to wavelength:
σ wg =
dτ wg
dλ
σ λ = L
D wg (λ)
σ λ =
V
λ
dτ wg
dV
σ λ =
n 2 L λ
cλ
V
d
2
(V b)
dV 2
(3.42)
where D wg (λ) is the waveguide dispersion. From an analysis of Maxwell’s equations,
for the HE 11 mode b can be expressed as [17]
b(V ) = 1 −
1 +
√
2
2
1 +
4 + V 4
1/4
2
(3.43)
Figure 3.10 shows plots of this expression for b and its derivatives d(Vb)/dV and
Vd
2 (Vb)/dV
2 as functions of V.
Example 3.12 From Eq. (3.42) the waveguide dispersion is
Fig. 3.10 The waveguide parameter b and its derivatives d(Vb)/dV and Vd 2 (Vb)/dV 2 plotted as a
function of the V number for the HE 11 mode (or the LP 01 mode)