On the correct mathematical proof of the polarization mode dispersion equation

Details On the correct mathematical proof of the polarization mode dispersion equation On the correct mathematical proof of the polarization mode dispersion equation

2011-03-14

arxiv.org/abs/1103.2614v1

Physics

Optics

3 pages, 1 figure

Scientific paper

The fundamental equation that describes polarization mode dispersion does not have a mathematically correct and convincing proof. This problem stems from the fact that Poincare's sphere, where Stokes vectors are represented, is just a manifold (a representation space) devoid of metric. In this "space" orthogonal vectors are antiparallel and, therefore, it is hard to justify the use of a Euclidean metric. However, if one realizes that in Poincare's sphere only three-dimensional rotations are represented, a Euclidean pseudo-scalar product can be defined and a mathematically correct proof for the polarization mode dispersion can be given.

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