content_image/334996.jpg content_image/334997.jpg content_image/334998.jpg content_image/334999.jpg content_image/335000.jpg
interaction with the left or right handed structure is defined by the relation 

<img src='content_image/334996.jpg'>

The output state defines a Stokes vector X$_{L}$$_{,}$$_{R}$ such that | X$_{L}$$_{,}$$_{R}$ | ≤ 1. A typical value for this radius is given by F ( M L , $_{R}$). 

If the input state is linearly polarized the input Stokes vector is: 

<img src='content_image/334997.jpg'>

$^{and draw a circle (}$∑ in ) along the equator contained in the plane X$_{1}$, X$_{2}$ of the unit radius Poincar´ e sphere. Using equation (14) the output Stokes vector is now a function of θ : X$_{L}$$_{,}$$_{R}$ ( θ $^{) drawing a closed curve (}$∑ L , $_{R}$) (see Fig. 3) which is the image, through the Mueller $^{matrix transformation, of the equator circle (}$∑ in ) above mentioned. Importantly, since the Mueller matrix M given by equation (5) represents a linear relation connecting X in to X out , we conclude that the image of the incident polarization state contained in the equator plane X$_{1}$, X$_{2}$ through M must also be contained in a plane in the space X$_{1}$, X$_{2}$, X$_{3}$ . 

To analyze this point more in details we consider the normalized Vector product 

<img src='content_image/334998.jpg'>

and we write it 

<img src='content_image/334999.jpg'>

with | U$_{L}$$_{,}$$_{R}$ | 2 + | V$_{L}$$_{,}$$_{R}$ | 2 + | W$_{L}$$_{,}$$_{R}$ | 2 = 1. It represents a typical normal to the closed curve $^{(}$∑ L , $_{R}$). We have 

<img src='content_image/335000.jpg'>

