Extending Malus's law to the general case.

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An extension of Malus's law can indeed be applied to circular and elliptical polarization by decomposing an elliptically polarized wave into two orthogonal linearly polarized components. Each of these linear components can be analyzed using Malus's law to determine their individual transmission. By applying Malus's law to both components, the total transmitted wave can be calculated by summing the contributions from each linear polarization. This approach allows for a comprehensive understanding of the behavior of elliptical polarization in terms of linear polarization principles. Thus, the extension of Malus's law is applicable in this context.
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Is there an equation that is an extension of Malus's law that can handle circular and elliptical polarisation?

I have read that a linearly polarised wave can be decomposed into two opposite circularly polarised law. Is the converse true? Can an elliptically polarised wave be decomposed into two linearly polarised waves in such a way that we can apply Malus's law to each of the linear components and obtain a solution for the transmission of a elliptical wave?
 
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Yes, you can decompose an elliptically polarized wave into two orthogonal linearly components. Then apply Malus's law to each component, and add the two transmitted components to get the transmitted wave.
 

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