Properties of the complex-plane representation of polarization are derived which include first the resolution of an arbitrary polarization into two orthogonal states, and secondly the definition of nearness functions that express the closeness of the polarization states represented by two points in the complex plane. Applications where these results are significant are discussed.
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R.M.A.Azzam, N.M.Bashara: Appl. Phys.1, 203 (1973)
H.Poincaré:Théorie mathématique de la lumière (Gauthier-Villars, Paris, 1892), Vol. 2, Chap. 12
G.A.Deschamps: Proc. IRE39, 540 (1951)
This proof is available for the interested reader. [We also have the solution of the reverse problem whereby (8) is obtained from the cosine-squared law as a starting point by the use of the stereographic projection that links the complex plane and the Poincaré sphere]
The discussion also applies to the construction of an optical polarizer that produces a specified state (linear, circular or elliptic) at its output
R.M.A.Azzam, N.M.Bashara: J. Opt. Soc. Am.62, 336 (1972)
R.M.A.Azzam, N.M.Bashara: J. Opt. Soc. Am.62, 222 (1972)
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Azzam, R.M.A., Bashara, N.M. New properties of the complex-plane representation of polarization. Appl. Phys. 2, 59–61 (1973). https://doi.org/10.1007/BF00934174
- Complex-plane representation