2011/03/14 by Carlos L. Janer, Janer, Carlos L.
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Optics (physics.optics) #math-ph #math.MP #physics.optics
paper · pdf · doi:10.48550/arxiv.1103.2614
3 pages, 1 figure
arxiv created 2011/03/14 · arxiv updated 2011/03/15
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.