Modern Optical Networks - Optical Signal Processing by Silicon Photonics - page 27

Waveguide dispersion is that type of dispersion which results when the speed
of a wave in a waveguide (such as an optical fiber) is totally dependent on its
frequency for geometric reasons, it however does not rely on any frequency
dependence of the materials from which it is build. More generally, “waveguide”
dispersion can arise for waves that are propagating through any structure, inho-
mogeneous in nature (e.g., a photonic crystal), whether or not the waves are lim-
ited to some section. Generally, both types of dispersion may be present, although
they are not firmly additive. Their combination leads to degradation of the signal
in optical fibers in telecommunications, because the unstable delay in the time of
arrival between different components of a signal “smears out” the in time signal.

3.6 Material Dispersion in Optics

The material dispersion can be a striking or undesirable effect in optical appli-
cations. The dispersion of light by glass prisms is utilized in the construction of
spectrometers and spectro-radiometers.

3.7 Group and Phase Velocity

Group and phase velocity is the result of dispersion marking itself as a temporal
effect. The formula given, v = c / n calculates the phase velocity of a wave; this is
the velocity at which the phase of any one frequency component of the wave will
propagate. This is not similar to the group velocity of the wave, which is the rate at
which the changes in amplitude (known as the envelope of the wave) will propa-
gate. The group velocity ' vg ' is associated to phase velocity for a homogeneous
medium as:

C ( N − λ D N / D Y ) − 1 ν G =

The group velocity v g is often taken into account as the velocity at which energy
or information is transmitted along the wave. In the majority cases this is based
on fact, and the group velocity can be considered as the signal velocity of the
waveform.

3.8 Optical Frequency Multiplier

An optical frequency multiplier is generally a nonlinear optical device, in this pho-
tons are in interaction with a nonlinear material and are effectively “combined”
forming new photons which are greater in energy, and thus have higher frequency.