Method and device to calculate and display the transformation of optical polarization states

Abstract

We have invented a set of calculation and display methods for polarized light using a representation that we call the Hybrid Polarization Sphere (HPS). The HPS incorporates the Poincaré Sphere and its dual, the Observable Polarization Sphere (OPS). The HPS uses a four-pole spherical polar coordinate system to map the transformation of the state(s) of polarization (SOP) of a beam of light as the beam propagates through one or more polarizing elements (polarizer, waveplate, or rotator). A simple computing aid based on the HPS leads to methods for solving optical polarization problems directly by visual measurement and interpolation. These avoid both the linear algebra and trigonometry of the underlying mathematics and the external apparatus needed to use the Poincaré Sphere for computing phase shifts. Furthermore, simulating and animating these methods on an electronic graphical display produces helpful visual explanations of numerical solutions to polarization problems.

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