110
3 Optical Signal Attenuation and Dispersion
in the cladding travels faster than the light confined to the core. In addition, note
that the index of refraction depends on the wavelength (see Sect. 3.2.5) so that
different spectral components within a single mode have different propagation
speeds. Dispersion thus arises because the difference in core-cladding spatial
power distributions, together with the speed variations of the various wavelengths, causes a change in propagation velocity for each spectral component.
The degree of waveguide dispersion depends on the fiber design (see Sect. 3.3.1).
Waveguide dispersion usually can be ignored in multimode fibers, but its effect
is significant in single-mode fibers.
Polarization-mode dispersion results from the fact that light-signal energy at a given
wavelength in a single-mode fiber actually occupies two orthogonal polarization
states or modes (see Sect. 2.5). At the start of the fiber the two polarization states
are aligned. However, because fiber material is not perfectly uniform throughout its
length, each polarization mode will encounter a slightly different refractive index.
Consequently each mode will travel at a slightly different velocity. The resulting
difference in propagation times between the two orthogonal polarization modes will
cause pulse spreading. Section 3.2.8 gives more details on this effect.
3.2.2 Modal Delay Effects
Intermodal dispersion or modal delay appears only in multimode fibers. This signaldistorting mechanism is a result of each mode having a different value of the group
velocity at a single frequency. To see why the delay arises, consider the meridional ray
picture given in Fig. 2.17 for a multimode step-index fiber. The steeper the angle of
propagation of the ray congruence, the higher is the mode number and, consequently,
the slower the axial group velocity. This variation in the group velocities of the
different modes results in a group delay spread, which is the intermodal dispersion.
This dispersion mechanism is eliminated by single-mode operation but is important
in multimode fibers. The maximum pulse broadening arising from the modal delay is
the difference between the travel time T max of the longest ray congruence paths (the
highest-order mode) and the travel time T min of the shortest ray congruence paths
(the fundamental mode). This broadening is simply obtained from ray tracing and
for a fiber of length L is given by
T = T max − T min =
n 1
c
L
sinθ c
− L
=
Ln
2
1
cn 2
≈
Ln 1
c
(3.18)
where from Eq. (2.21) sin θ c = n 2 /n 1 and is the index difference.
Example 3.7 Consider a 1 km long multimode step-index fiber in which n 1 = 1.480
and = 0.01, so that n 2 = 1.465. What is the modal delay per length in this fiber?
Solution Equation (3.18) yields
3 Optical Signal Attenuation and Dispersion
in the cladding travels faster than the light confined to the core. In addition, note
that the index of refraction depends on the wavelength (see Sect. 3.2.5) so that
different spectral components within a single mode have different propagation
speeds. Dispersion thus arises because the difference in core-cladding spatial
power distributions, together with the speed variations of the various wavelengths, causes a change in propagation velocity for each spectral component.
The degree of waveguide dispersion depends on the fiber design (see Sect. 3.3.1).
Waveguide dispersion usually can be ignored in multimode fibers, but its effect
is significant in single-mode fibers.
Polarization-mode dispersion results from the fact that light-signal energy at a given
wavelength in a single-mode fiber actually occupies two orthogonal polarization
states or modes (see Sect. 2.5). At the start of the fiber the two polarization states
are aligned. However, because fiber material is not perfectly uniform throughout its
length, each polarization mode will encounter a slightly different refractive index.
Consequently each mode will travel at a slightly different velocity. The resulting
difference in propagation times between the two orthogonal polarization modes will
cause pulse spreading. Section 3.2.8 gives more details on this effect.
3.2.2 Modal Delay Effects
Intermodal dispersion or modal delay appears only in multimode fibers. This signaldistorting mechanism is a result of each mode having a different value of the group
velocity at a single frequency. To see why the delay arises, consider the meridional ray
picture given in Fig. 2.17 for a multimode step-index fiber. The steeper the angle of
propagation of the ray congruence, the higher is the mode number and, consequently,
the slower the axial group velocity. This variation in the group velocities of the
different modes results in a group delay spread, which is the intermodal dispersion.
This dispersion mechanism is eliminated by single-mode operation but is important
in multimode fibers. The maximum pulse broadening arising from the modal delay is
the difference between the travel time T max of the longest ray congruence paths (the
highest-order mode) and the travel time T min of the shortest ray congruence paths
(the fundamental mode). This broadening is simply obtained from ray tracing and
for a fiber of length L is given by
T = T max − T min =
n 1
c
L
sinθ c
− L
=
Ln
2
1
cn 2
≈
Ln 1
c
(3.18)
where from Eq. (2.21) sin θ c = n 2 /n 1 and is the index difference.
Example 3.7 Consider a 1 km long multimode step-index fiber in which n 1 = 1.480
and = 0.01, so that n 2 = 1.465. What is the modal delay per length in this fiber?
Solution Equation (3.18) yields