23 December 1997 Polarization and phase sphere of tangential phasors and its applications
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Abstract
The Poincare sphere of polarization points concept has been extended to the polarization and (spatial) phase sphere (the Pp sphere) by inclusion ofphase information when introducing the tangentialpolarization phasors. Tangential phasors represent polarization helices ofplane, monochromatic, completely polarized EM waves. Such helices, considered as models of waves, can be shifted with the velocity of light in two opposite directions along a propagation zaxis. Spatial phase of the wave has been defined by the position of the moving helix, in time t 0, versus the z-axis coordinates, independently of direction of wave's propagation. The double value of that spatial phase has been represented by the angle of phasor's orientation. It means that phasors rotate in time with angular velocity of 2a in two opposite direcüons depending on direction ofwave's propagation In the paper, the PP sphere is considered as a kind of the two-folded Riemann surface. The concept of the ONP PP basis is introduced and the orientation of their phasors explained, together with the rules of phasors' multiplication and addition. Mvantages of the proposed engineering notation are shown on examples of various transformations. In the Appendix some useful formulae of spherical trigonometry of special value for polarimetry are attached. Keywords: polarization sphere, Riemann surface, tangential phasor, polarization helix, polarization and phase vector
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Zbigniew H. Czyz, Zbigniew H. Czyz, "Polarization and phase sphere of tangential phasors and its applications", Proc. SPIE 3120, Wideband Interferometric Sensing and Imaging Polarimetry, (23 December 1997); doi: 10.1117/12.300635; https://doi.org/10.1117/12.300635
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