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Transformation matrices for the Mueller-Jones formalism
Authors:Rafael Espinosa-Luna  David Rodríguez-Carrera  Sinhué Hinojosa-Ruíz
Institution:a Applied Optics Complutense Group, Optics Department, Universidad Complutense de Madrid Facultad de Ciencias Físicas, Ciudad Universitaria s/n, 28040 Madrid, Spain
b Centro de Investigaciones en Optica, A.C., Loma del Bosque 115, Colonia Lomas del Campestre, 37150 León, Guanajuato, México
c Facultad de Física, Universidad Autónoma de Zacatecas, Avenida Preparatoria 301, Fraccionamiento Progreso, 28040 Zacatecas, Zac., México
Abstract:The Mueller-Jones (MJ) or pure Mueller matrix formulation has been reported by using two different matrix transformations in a condensed representation. The possibility to find other transformation matrices is explored. A complete set of unitary operators (R) is found to be closely related with the MJ matrices and with the evolution of pure states on the Poincaré sphere surface. We propose an alternative deduction for the condensed representation of the MJ matrices, obtained by using the Kronecker product operation and use of R unitary matrices as a tool to combine different Mueller matrices and changes of polarized states on the Poincarè sphere surface. Finally, it is shown explicitly that the columns of the transformation matrices are the eigenvectors of the MJ matrix associated to a non-depolarizing optical system and a corollary is established as a criterion to differentiate a Mueller matrix from an MJ matrix.
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