Publication: Transformation matrices for the Mueller–Jones formalism
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2008
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Gustav Fischer Verlag
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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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© 2007 Elsevier GmbH.
One of the authors, R.E.L., expresses his gratitude to CONACYT (Project 46969-F), to CONCYTEG (05-04-K117-066-A02) and to Grupo Santander (Program Visitantes Distinguidos at the Universidad Complutense de Madrid) for the support provided for the realization of this work.
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