$^{Actually  if each curve (}$∑ L   $_{R}$) is contained in a (different) plane P$_{L}$$_{ }$$_{R}$ we must have for every θ . This was indeed checked numerically up to a precision of 10 − $^{11}$. It was also checked that | X$_{L}$$_{ }$$_{R}$ ( θ ) | $^{= 1 up to the same precision. This proves that each curve (}$∑ L   $_{R}$) must be a circle. The equations of the two planes P$_{L}$$_{ }$$_{R}$ are given by n$_{L}$$_{ }$$_{R}$ · ( X − X$_{L}$$_{ }$$_{R}$ (0)) = 0 where X is the Stokes vector associated with a running point belonging to each plane. We write with D$_{L}$ = − 0 . 0237 and D$_{R}$ = − 0 . 0266. | D$_{L}$$_{ R}$ | represents the distance separating the center $^{of the circle (}$∑ L   $_{R}$) to the origin of the poincar´ e sphere. This proves that the planes are not going through the center of the sphere. It was checked after lengthy calculations that if | B | = | C | in the Jones matrix (see equation (1)) then D = 0. This shows that the property | D$_{L}$$_{ R}$ | ̸ = 0 is a characteristic of planar chirality (i.e  the condition | B | ̸ = | C | ). The radius of $^{each circle (}$∑ L   $_{R}$) is given by r$_{L}$$_{ }$$_{R}$ = √ (1 − D 2 L $_{ R}$) and we have r$_{L}$ = 0 . 9997 and r$_{L}$ = 0 . 9996 which are slightly smaller than r = 1 in agreement with the fact that P$_{L}$$_{ }$$_{R}$ are not going through the center of the sphere. n$_{L}$$_{ }$$_{R}$ · ( X$_{L}$$_{ }$$_{R}$ ( θ ) − X$_{L}$$_{ }$$_{R}$ (0)) = 0 (19) U$_{L}$$_{ }$$_{R}$X$_{1}$ + V$_{L}$$_{ }$$_{R}$X$_{2}$ + W$_{L}$$_{ }$$_{R}$X$_{3}$ + D$_{L}$$_{ }$$_{R}$ = 0 (20) [1] D. -F. M. Arago “M´ emoire sur une modification remarquable qu’´ eprouvent les rayons lu- mineux dans leur passage ` a travers certains corps diaphanes  et sur quelques autres nouveaux ph´ enom` enes d’optique ” M´ em. Inst. France  Part I 12 (1811). [2] L. Pasteur  “M´ emoire sur la relation qui peut exister entre la forme cristalline et la composition chimique  et sur la cause de la polarization rotatoire ” C. R. Acad. Sci. Paris 26   535-539 (1848). [3] E. Hecht  Optics 2 nd ed. (Addison-Wesley  Massachusetts  1987). [4] L. D. Landau  E. M. Lifshitz  L. P. Pitaevskii  Electrodynamics of continuous media 2 nd ed. (Pergamon  New York  1984). [5] V. A. Fedotov  P. L. Mladyonov  S. L. Prosvirnin  A. V. Rogacheva  Y. Chen and N. I. Zhe- ludev  “Asymmetric propagation of electromagnetic waves through a planar chiral structure ” Phys. Rev. Lett. 97   167401 (2006). 15