Optical Bit Error Rate

Chapter 2.11 - Material Dispersion

2.11   MATERIAL DISPERSION

The refractive index of matter is related to the dielectric coefficient and to the characteristic
resonance frequency of its dipoles. These dipoles interact with optical frequencies
that are in the neighborhood of the resonant frequency. The closer they
are, the stronger they interact and the more optical energy they absorb. Consequently,
the refractive index becomes a function of the optical frequency ω, n(ω). However,
the propagation constant is also related to the refractive index and, as a result,
different optical frequencies propagate at different velocities. This velocity variabil-
ity causes dispersion, termed material dispersion, and over the length of fiber it is
measured in ps/nm. Dispersion is more easily explained if one considers an optical
signal that consists of a narrow band of frequencies. Then, dispersion represents a
time delay difference per nanometer of frequency, spectrally distributed in an optical
signal. That is, a 100 nsecond delay over a 10-frequency spectrum is different
than a 20 nsec delay over the same spectrum.

Silica, a key ingredient of optical fiber and cable, has a refractive index that
varies with optical frequency. Thus, dispersion plays a significant role in fiber-optic
communications.

The polarization of an electromagnetic wave, P, induced in the electric dipoles
of a medium by an electric field, E, is proportional to susceptibility, χ:

 

where ε0 is the permitivity of free space.

For an isotropic medium, the first-order term expresses the linear behavior of matter.
The second-order term is orthogonal and thus it vanishes. For anisotropic media,
the second order still holds. Higher-order terms are negligible (in optical communications,
this may not be true for long fiber lengths and for ultrahigh bit rates).

For an isotropic medium, the nonlinear terms vanish and the above series relation
is simplified to P = ε0 χ · E. However, nature is not as simple, and most materials
are either anisotropic, or become anisotropic under certain conditions. In such
cases, higher-order terms should also be considered. In particular, the third-order
term becomes significant and it results in nonlinear effects that may affect and limit
optical transmission.

The most influential nonlinear effects in optical transmission, particularly when
many wavelengths at high optical power are transmitted over the same medium
(e.g., DWDM), are four-wave mixing (FWM), stimulated Raman scattering (SRC),
and Brillouin scattering (BS).

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