Symmetry between partially polarised light and partial polarisers in the vectorial Pauli algebraic formalism

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The problem of the gain of dichroic devices is analysed in a framework based on a vectorial pure operatorial (non-matrix) Pauli algebraic approach to polarisation optics. We show that the partially polarised light and the partial polarisers can be described in this framework by absolutely similar, symmetric quantities. In this sense, a physically essential device parameter, the degree of dichroism, is defined. This symmetry between the description of the polarised light and of the polarisation devices leads to an expressive form of the generalised Malus’ law, the consequences of which are analysed in detail. Most importantly, one can for the first time describe and graphically illustrate the generalised structure of the gain of a dichroic device.