Linear and Circular Polarization Basis Sets

It is convenient to describe the polarization vector in terms of an orthogonal basis set of unit vectors, (a1 a2), such that aj a2 = 0. Two choices are commonly used, one for 

The subscripts l and r refer to left- and right-circularly polarized light, respectively. Any electric field, A, can be expressed in terms of either of these two sets. The Jones vectors for the two representations are related by the transformation  

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