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Op#cal
?Communica#ons:
?
Principles
?and
?Technologies
?
2015/05/06
Nonlinear
?Effects
?in
?Op#cal
?Fibers
Review
! The basis of the mathematical description
of linear optical effects are the Maxwell
equations.
! An external field leads to an internal
charge displacement in the molecules of a
dielectric. This effect is called polarization.
Review
! The polarizability of a material can be
described by the susceptibility χ. The
susceptibility is defined as the relative
permittivity minus 1.
Review
! In a dielectric the propagating wave can
be seen as a superposition between the
original injected wave and a secondary
wave.
! This secondary wave has its origin in the
polarization of the material and leads to a
phase shift in comparison to the original
wave.
Review
! The real part of the relative permittivity
leads to the refractive index, responsible
for a phase shift of the wave.
! On the other hand, the imaginary part
results in the attenuation constant of the
material, responsible for a decrease of the
intensity during propagation.
Review
! The propagation of electromagnetic waves
in an dielectric can be described by the
harmonic oscillator model.
! Both the refractive index and the
attenuation constant are wavelength
dependent.
Review
! The attenuation is especially large near
resonances of the oscillator.
! The losses in the fiber due to attenuation
can be compensated by optical amplifiers.
Each optical amplifier adds noise to the
signal.
Review
! The refractive index outside the range of
resonances can be approximated by the
Sellmeier equation.
! The velocity with which each point of
constant phase will move is the phase
velocity of the wave.
Review
! The wavelength dependence of the group
velocity is called dispersion, far away from
resonances it will always increase with
wavelength. This is called normal
dispersion.
Review
! Every pulse consists of a group of
f
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