Factorizations for 3-rotations and polarization of the light in Mueller-Stokes an Jones formalisms

V. M. Red'kov; N. G. Tokarevskaya

paper

Factorizations for 3-rotations and polarization of the light in Mueller-Stokes an Jones formalisms

arXiv:0808.0852

Abstract

Formulas describing all 2-element and 3-element factorizations of arbitrary element of the groups SU(2) and SO(3,R) are derived. Six 2-element factorizations, $(U_{2} U_{3} U_{2}^{'}), (U_{3} U_{2} U_{3}^{'}), (U_{3} U_{1} U_{3}^{'}), (U_{1} U_{3} U_{1}^{'}), (U_{1} U_{2} U_{1}^{'}), (U_{2} U_{1} U_{2}^{'})$ , provide all possible way to define Euler type angles; and six 3-element ones, $(U_{1} U_{2} U_{3}), (U_{1} U_{3} U_{2}^{'}), (U_{2} U_{3} U_{1}), (U_{2} U_{1} U_{3}), (U_{3} U_{1} U_{2}), (U_{3} U_{2} U_{1})$ provide all possible ways to parameterize the unitary and orthogonal groups by three elementary angles. In thecontext the light polarization formalism of Stokes-Mueller vectors and Jones spinors, relations produced give a base to resolve arbitrary pure polarization rotators into all possible sets of elementary rotators of two or three constituents.

24 pages, Proc. of XV Annual Seminar NPCS - 2008, May 22-25, 2008, Minsk, Belarus

Factorizations for 3-rotations and polarization of the light in Mueller-Stokes an Jones formalisms

Abstract

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