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Abstract
By analogy with the representation of the polarization of light on the Poincaré sphere, we describe the propagation and the reflection/transmission of light in a multilayer on a hyperbolic surface. We show that the propagation of light corresponds to a classical rotation on this surface and that its reflection/transmission corresponds to a hyperbolic rotation.
Highlights
It is common to describe the evolution of the polarization of light interacting with birefringent and/or rotator systems on the Poincaresphere
We have shown that, in the case where there are neither absorption nor evanescent waves, the propagation of light through a multilayer can by illustrated by a path drawn on a hyperboloid
The case of light propagating in a multilayer where there are evanescent waves in one or more layers is more complicated
Summary
It is common to describe the evolution of the polarization of light interacting with birefringent and/or rotator systems on the Poincaresphere. This representation permits a simple and elegant geometrical interpretation of the geometric phase arising when the polarization state of light evolves by passing through birefringent (or rotator) devices. In this physical problem, the polarization state of light is classically described by a complex vector (two components), whereas its evolution is given by the wellknown 2ϫ2 Jones matrix of the system.[1,2,3]. It would be of interest to find a geometrical interpretation of the evolution of the electric field as well as of the geometric phase[5] that appears in a multilayer system
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