Geometrical interpretation of second-order PMD

A geometrical interpretation of second-order polarization mode dispersion (SOPMD) as the curved three-dimensional (3-D) area swept by the PMD vector as it increases with propagation in a birefringent system is introduced. The depolarization and polarization-dependent chromatic dispersion parts of the SOPMD can be viewed as projections of this area in orthogonal directions. This interpretation enables us to translate the problem of maximizing the SOPMD in, e.g., PMD emulators and programmable PMD sources to an isoperimetric problem, i.e., a problem of maximizing the area enclosed by a given perimeter, which has well-known solutions. Both the discrete problems corresponding to a set of birefringent wave plates are discussed, and the continuous problem in which an arbitrary birefringent medium is considered. Analytic formulas are derived for the first time for the maximum SOPMD, depolarization, and polarization-dependent chromatic dispersion that can be realized in PMD emulators.