interaction with the left or right handed structure is defined by the relation 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: $^{and draw a circle (}$∑ 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 and we write it 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     S$_{L}$$_{,}$$_{R}$$_{;0}$ S$_{L}$$_{,}$$_{R}$$_{;1}$ S$_{L}$$_{,}$$_{R}$$_{;2}$ S$_{L}$$_{,}$$_{R}$$_{;3}$     = M L , R     S$_{0}$ S$_{1}$ S$_{2}$ S$_{3}$    $^{.}$ (14) X in ( θ ) =    cos (2 θ ) sin (2 θ ) 0   $^{,}$ (15) n$_{L}$$_{,}$$_{R}$ = ( X$_{L}$$_{,}$$_{R}$ (0) − X$_{L}$$_{,}$$_{R}$ (2 π/ 3)) × ( X$_{L}$$_{,}$$_{R}$ (0) − X$_{L}$$_{,}$$_{R}$ ( π/ 2)) | ( X$_{L}$$_{,}$$_{R}$ (0) X$_{L}$$_{,}$$_{R}$ (2 π/ 3)) ( X$_{L}$$_{,}$$_{R}$ (0) X$_{L}$$_{,}$$_{R}$ ( π/ 2)) | (16) n$_{L}$$_{,}$$_{R}$ =    U$_{L}$$_{,}$$_{R}$ V$_{L}$$_{,}$$_{R}$ W$_{L}$$_{,}$$_{R}$   $^{,}$ (17) n$_{L}$ =    0 . 2845 − 0 . 3065 − 0 . 9084   $^{,}$$^{n$_{R}$}$ =    0 . 2861 0 . 3139 0 . 95053   $^{.}$ (18) 14