Roux, FS2014-01-152014-01-152013-11Roux, F.S. 2013. Coordinate invariance in stochastic singular optics. Journal of Optics, vol. 15(12), pp 1-82040-8978http://iopscience.iop.org/2040-8986/15/12/125722/pdf/2040-8986_15_12_125722.pdfhttp://hdl.handle.net/10204/7144Copyright: 2013 IOP Publishing. This is an OA journal. The journal authorizes the publication of the information herewith contained. Published in Journal of Optics, vol. 15(12), pp 1-8The study of optical vortices in stochastic optical fields involves various quantities, including the vortex density and topological charge density, that are defined in terms of local expectation values of the distributions of optical vortices. The complexity of these quantities often poses a formidable challenge. Here we address this challenge with the aid of the invariance that these quantities have with respect to rotations of the coordinate axes. This property allows one to express the quantities in terms of singlets of the SO(2) group that represents the coordinate rotations, resulting in expressions that are significantly simpler. We also show that the singlets can help to identify relationships among the different quantities.enStochastic singular opticsOptical vortex densityTopological charge densityCoordinate invarianceSO(2) singletArticleRoux, F. (2013). Coordinate invariance in stochastic singular optics. http://hdl.handle.net/10204/7144Roux, FS "Coordinate invariance in stochastic singular optics." (2013) http://hdl.handle.net/10204/7144Roux F. Coordinate invariance in stochastic singular optics. 2013; http://hdl.handle.net/10204/7144.TY - Article AU - Roux, FS AB - The study of optical vortices in stochastic optical fields involves various quantities, including the vortex density and topological charge density, that are defined in terms of local expectation values of the distributions of optical vortices. The complexity of these quantities often poses a formidable challenge. Here we address this challenge with the aid of the invariance that these quantities have with respect to rotations of the coordinate axes. This property allows one to express the quantities in terms of singlets of the SO(2) group that represents the coordinate rotations, resulting in expressions that are significantly simpler. We also show that the singlets can help to identify relationships among the different quantities. DA - 2013-11 DB - ResearchSpace DP - CSIR KW - Stochastic singular optics KW - Optical vortex density KW - Topological charge density KW - Coordinate invariance KW - SO(2) singlet LK - https://researchspace.csir.co.za PY - 2013 SM - 2040-8978 T1 - Coordinate invariance in stochastic singular optics TI - Coordinate invariance in stochastic singular optics UR - http://hdl.handle.net/10204/7144 ER -