Composition law for polarizers

Abstract

The polarization process when polarizers act on an optical field is studied. We give examples for two kinds of polarizers. The first kind presents an anisotropic absorption - as in a polaroid film - and the second one is based on total reflection at the interface with a birefringent medium. Using the Stokes vector representation, we determine explicitly the trajectories of the wave light polarization during the polarization process. We find that such trajectories are not always geodesics of the Poincar\'e sphere as it is usually thought. Using the analogy between light polarization and special relativity, we find that the action of successive polarizers on the light wave polarization is equivalent to the action of a single resulting polarizer followed by a rotation achieved for example by a device with optical activity. We find a composition law for polarizers similar to the composition law for noncollinear velocities in special relativity. We define an angle equivalent to the relativistic Wigner angle which can be used to quantify the quality of two composed polarizers.Comment: 23 pages, 9 figures, accepted for publication in Physical Review

Vectorial pure operatorial Pauli algebraic approach in polarization optics: a theoretical survey and some applications

“…The generalized Malus' law is a classical subject in the theory of light polarization [5,7,[23][24][25][26], which is intimately connected with that of determining the gain given by a partial polarizer for partially polarized incident light.…”

On a quasi-relativistic formula in polarization theory

“…Vigoureux, who showed that the reflection coefficient of any stratified planar structure can be obtained using a complex generalization of Einstein's composition law for parallel relativistic velocities [8,10,11]. Recently, Lages et al [21] extended this quasi-relativistic result, showing that the composition law for polarizers is analogous with the composition law for noncolinear relativistic velocities. They also have determined the Wigner angle that corresponds to a sequence of two polarizers, as a natural consequence of the noncomutativity of this composition law.…”

“…(3) Finally, I must stress that this vectorial composition rule that governs the interaction between a partially polarized SOP and a dichroic device-unlike the "quasirelativistic composition rule for two successive polarizers" [21]-does not imply a Wigner rotation per se.…”

“…(21)], these quantities are vectorialthe Poincaré vectors of the incoming light, p i n i , and of the dichroic device, p d n d , and they, as well as the Poincaré vector of the outgoing light, p o n o , can vary from zero to a unit vector only.…”

“…It gives a straightforward suggestion for the fact that, from a geometric algebraic viewpoint, all these phenomena rely on hyperbolic geometry. This geometric approach is rigorously justified and largely adopted in polarization optics, as well as in multilayer or in paraxial geometrical optics [4,18,21,30].…”