Authors: Luke Kenneth Casson Leighton
Castillo demonstrates an important case of successful superposition of elliptically-polarised light by moving to spinor representations of electromagnetic plane waves: when the angle between the two unit spinors as represented on a Poincare sphere are (as a complex number) either 1, -1, i or -i. This paper demonstrates that there are additional conditions under which superposition is successful: phase-shifting of one of the waves by 90 degrees prior to superposition. Two and three superpositions are shown, and the candidate configurations for each are listed. The result is significant for Particle Physics at least, in that Castillo and Rubalcava-Garcia's prior work show a correspondance between Jones Calculus and SU(2), and gives a direct mapping between Jones and Pauli Matrices.
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