The Jones vector as a spinor and its representation on the Poincaré sphere
G.F. Torres del Castillo* y I. Rubalcava García**
*Departamento de Física Matemática, Instituto de Ciencias, Universidad Autónoma de Puebla, 72570 Puebla, Pue., México.
**Facultad de Ciencias Físico Matemáticas, Universidad Autónoma de Puebla, Apartado postal 1152, Puebla, Pue., 72001 México.
]]> Recibido el 18 de febrero de 2011;
Abstract
It is shown that the two complex Cartesian components of the electric field of a monochromatic electromagnetic plane wave, with a temporal and spatial dependence of the form ei(kz-wt), form a SU(2) spinor that corresponds to a tangent vector to the Poincaré sphere representing the state of polarization and phase of the wave. The geometrical representation on the Poincaré sphere of the effect of some optical filters is reviewed. It is also shown that in the case of a partially polarized beam, the coherency matrix defines two diametrically opposite points of the Poincaré sphere.
Keywords: Jones vector; Poincaré sphere; polarization; spinors.
Resumen
Se muestra que las dos componentes Cartesianas complejas del campo eléctrico de una onda plana electromágnetica monocromática, con dependencia temporal y espacial de la forma ei(kz-wt), forma un espinor SU(2) que corresponde al vector tangente a la esfera de Poincaré que representa el estado de polarización y fase de la onda. Se revisa la representación geométrica en la esfera de Poincaré del efecto de algunos filtros ópticos. Se muestra también que en el caso de un haz parcialmente polarizado, la matriz de coherencia define dos puntos diametralmente opuestos de la esfera de Poincaré.
Descriptores: Vector de Jones; esfera de Poincaré; polarización; espinores.
]]>PACS: 02.20.Qs; 03.50.De; 42.25.Ja
DESCARGAR ARTÍCULO EN FORMATO PDF
Referencias
1. G.F. Torres del Castillo, J. Phys. A: Math. Theor. 41 (2008) 115302. [ Links ]
2. W.T. Payne, Am. J. Phys. 20 (1952) 253. [ Links ]
]]>3. S. Pancharatnam, Proc. Ind. Acad. Sci. A 44 (1956) 247. Reprinted in Geometric Phases in Physics, edited by A. Shapere and F. Wilczek (World Scientific, Singapore, 1989). [ Links ]
4. M.V. Berry, J. Mod. Optics 34 (1987) 1401. Reprinted in Geometric Phases in Physics, edited by A. Shapere and F. Wilczek (World Scientific, Singapore, 1989). [ Links ]
5. B.-G. Englert, C. Kurtsiefer, and H. Weinfurter, Phys. Rev. A 63 (2001) 032303. [ Links ]
6. M. Born and E. Wolf, Principles of Optics, 6th ed. (Cambridge University Press, Cambridge, 1997). [ Links ]
7. R.D. Guenther, Modern Optics (Wiley, New York, 1990). Chap. 2. [ Links ]
]]>8. D.S. Kliger and J.W. Lewis, Polarized Light in Optics and Spectroscopy (Academic Press, New York, 1990). [ Links ]
9. R. Simon and N. Mukunda, Phys. Lett. A 143 (1990) 165. [ Links ]
10. D. Han, Y.S. Kim, and M.E. Noz, Phys. Rev. E56 (1997) 6065. [ Links ]
11. D. Han, Y.S. Kim, and M.E. Noz, J. Opt. Soc. Am. A 14 (1997) 2290. [ Links ]
12. T. Tudor, J. Phys. A: Math. Theor. 41 (2008) 415303. [ Links ]
]]>13. G.F. Torres del Castillo, 3-D Spinors, Spin-weighted Functions and their Applications (Birkhauser, Boston, 2003). [ Links ]
14. J.C. Loredo, O. Ortíz, R. Weingärtner, and F. De Zela, Phys. Rev. A 80 (2009)012113. [ Links ]
15. L.D. Landau, E.M. Lifshitz, and L.P. Pitaevskií, Electrodynamics of Continuous Media, 2nd ed. (Pergamon Press, Oxford, 1984), §101. [ Links ]
16. R. Penrose and W. Rindler, Spinors and space-time, Vol. 1 (Cambridge University Press, Cambridge, 1984), Sec. 1.3. [ Links ]
17. K. Gottfried and T.-M. Yan, Quantum Mechanics: Fundamentals, 2nd ed. (Springer-Verlag, New York, 2003), Sec. 2.2. [ Links ]
]]>18. T. Tudor and V. Manea, J. Opt. Soc. Am. B 28 (2011) 596. [ Links ]
19. J.J. Gil, Eur. Phys. J. Appl. Phys. 40 (2007) 1. [ Links ]
]]>