Signal representation on the angular Poincare sphere, based on second-order moments
| dc.contributor.author | Bastiaans, Martin J. | |
| dc.contributor.author | Alieva Krasheninnikova, Tatiana | |
| dc.date.accessioned | 2023-06-20T03:46:26Z | |
| dc.date.available | 2023-06-20T03:46:26Z | |
| dc.date.issued | 2010-04 | |
| dc.description | © 2010 Optical Society of America. The financial support of the Spanish Ministry of Science and Innovation under project TEC2008-04105 and the Santander-Complutense project PR-34/07-15914 is acknowledged. | |
| dc.description.abstract | Based on the analysis of second-order moments, a generalized canonical representation of a two-dimensional optical signal is proposed, which is associated with the angular Poincare sphere. Vortex-free ( or zero-twist) optical beams arise on the equator of this sphere, while beams with a maximum vorticity ( or maximum twist) are located at the poles. An easy way is shown how the latitude on the sphere, which is a measure for the degree of vorticity, can be derived from the second-order moments. The latitude is invariant when the beam propagates through a first-order optical system between conjugate planes. To change the vorticity of a beam, a system that does not operate between conjugate planes is needed, with the gyrator as the prime representative of such a system. A direct way is derived to find an optical system ( consisting of a lens, a magnifier, a rotator, and a gyrator) that transforms a beam with an arbitrary moment matrix into its canonical form. | |
| dc.description.department | Depto. de Óptica | |
| dc.description.faculty | Fac. de Ciencias Físicas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | Spanish Ministry of Science and Innovation | |
| dc.description.sponsorship | Santander-Complutense | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/27489 | |
| dc.identifier.doi | 10.1364/JOSAA.27.000918 | |
| dc.identifier.issn | 1084-7529 | |
| dc.identifier.officialurl | http://dx.doi.org/10.1364/JOSAA.27.000918 | |
| dc.identifier.relatedurl | http://www.opticsinfobase.org/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/44417 | |
| dc.issue.number | 4 | |
| dc.journal.title | Journal of The Optical Society Of America A-Optics Image Science and Vision | |
| dc.language.iso | eng | |
| dc.page.final | 927 | |
| dc.page.initial | 918 | |
| dc.publisher | Optical Society of America | |
| dc.relation.projectID | PR-34/07-15914 | |
| dc.relation.projectID | TEC2008-04105 | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 535 | |
| dc.subject.keyword | Schell-model beams | |
| dc.subject.keyword | Wigner distribution function | |
| dc.subject.keyword | Partially coherent beams | |
| dc.subject.keyword | 1st-order optical-systems | |
| dc.subject.keyword | Light-beams | |
| dc.subject.keyword | Decomposition | |
| dc.subject.keyword | Vortex | |
| dc.subject.keyword | Transformation | |
| dc.subject.keyword | Propagation | |
| dc.subject.keyword | Spectrum | |
| dc.subject.ucm | Óptica (Física) | |
| dc.subject.unesco | 2209.19 Óptica Física | |
| dc.title | Signal representation on the angular Poincare sphere, based on second-order moments | |
| dc.type | journal article | |
| dc.volume.number | 27 | |
| dcterms.references | 1. M. Born and E. Wolf, Principles of Optics (Pergamon, 1980). 2. M. J. Padgett and J. Courtial, “Poincaré-sphere equivalent for light beams containing orbital angular momentum,” Opt. Lett. 24, 430–432 (1999). 3. G. S. Agarwal, “SU(2) structure of the Poincaré sphere for light beams with orbital angular momentum,” J. Opt. Soc. Am. A 16, 2914–2916 (1999). 4. G. F. Calvo, “Wigner representation and geometric transformations of optical orbital angular momentum spatial modes,” Opt. Lett. 30, 1207–1209 (2005). 5. T. Alieva and M. J. Bastiaans, “Orthonormal mode sets for the two-dimensional fractional Fourier transformation,” Opt. Lett. 32, 1226–1228 (2007). 6. T. Alieva and M. J. Bastiaans, “Phase-space rotations and orbital Stokes parameters,” Opt. Lett. 34, 410–412 (2009). 7. M. J. Bastiaans, “Application of the Wigner distribution function to partially coherent light,” J. Opt. Soc. Am. A 3, 1227–1238 (1986). 8. M. J. Bastiaans, “Second-order moments of the Wigner distribution function in first-order optical systems,” Optik 88, 163–168 (1991). 9. J. Serna, R. Martínez-Herrero, and P. M. Mejías, “Parametric characterization of general partially coherent beams propagating through ABCD optical systems,” J. Opt. Soc. Am. A 8, 1094–1098 (1991). 10. K. Sundar, N. Mukunda, and R. Simon, “Coherent-mode decomposition of general anisotropic Gaussian Schell-model beams,” J. Opt. Soc. Am. A 12, 560–569 (1995). 11. J. Williamson, “On the algebraic problem concerning the normal forms of linear dynamical systems,” Am. J. Math. 58, 141–163 (1936). 12. R. K. Luneburg, Mathematical Theory of Optics (Univ. of California Press, 1966). 13. S. Helgason, Differential Geometry, Lie Groups and Symmetric Species (Academic, 1978), Chap. VI. 14. K. B. Wolf, Geometric Optics on Phase Space (Springer, 2004). 15. R. Simon and N. Mukunda, “Iwasawa decomposition in first-order optics: universal treatment of shape-invariant propagation for coherent and partially coherent beams,” J. Opt. Soc. Am. A 15, 2146–2155 (1998). 16. R. Simon and K. B. Wolf, “Structure of the set of paraxial optical systems,” J. Opt. Soc. Am. A 17, 342–355 (2000). 17. R. Simon and N. Mukunda, “Twisted Gaussian Schellmodel beams,” J. Opt. Soc. Am. A 10, 95–109 (1993). 18. R. Simon, K. Sundar, and N. Mukunda, “Twisted Gaussian Schell-model beams. I. Symmetry structure and normalmode spectrum,” J. Opt. Soc. Am. A 10, 2008–2016 (1993). 19. K. Sundar, R. Simon, and N. Mukunda, “Twisted Gaussian Schell-model beams. II. Spectrum analysis and propagation characteristics,” J. Opt. Soc. Am. A 10, 2017–2023 (1993). 20. A. T. Friberg, B. Tervonen, and J. Turunen, “Interpretation and experimental demonstration of twisted Gaussian Schell-model beams,” J. Opt. Soc. Am. A 11, 1818–1826 (1994). 21. D. Ambrosini, V. Bagini, F. Gori, and M. Santarsiero, “Twisted Gaussian Schell-model beams: a superposition model,” J. Mod. Opt. 41, 1391–1399 (1994). 22. R. Simon, A. T. Friberg, and E. Wolf, “Transfer of radiance by twisted Gaussian Schell-model beams in paraxial systems,” J. Eur. Opt. Soc. A: Pure Appl. Opt. 5, 331–343 (1996). 23. R. Simon and N. Mukunda, “Twist phase in Gaussian-beam optics,” J. Opt. Soc. Am. A 15, 2373–2382 (1998). 24. M. J. Bastiaans, “Wigner distribution function applied to twisted Gaussian light propagating in first-order optical systems,” J. Opt. Soc. Am. A 17, 2475–2480 (2000). 25. M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying vortices,” Phys. Rev. A 56, 163–165 (1997). 26. M. S. Soskin, M. V. Vasnetsov, “Singular optics,” Prog. Opt. 42, 219–276 (2001). 27. J. Serna and J. M. Movilla, “Orbital angular momentum of partially coherent beams,” Opt. Lett. 26, 405–407 (2001). 28. A. Ya. Bekshaev, M. V. Vasnetsov, V. G. Denisenko, and M. S. Soskin, “Transformation of the orbital angular momentum of a beam with optical vortex in a astigmatic optical system,” JETP Lett. 75, 127–130 (2002). 29. A. Ya. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, “Optical vortex symmetry breakdown and decomposition of the orbital angular momentum of the light beams,” J. Opt. Soc. Am. A 20, 1635–1643 (2003). 30. T. Alieva and M. J. Bastiaans, “Evolution of the vortex and the asymmetrical parts of orbital angular momentum in separable first-order optical systems,” Opt. Lett. 29, 1587–1589 (2004). 31. M. J. Bastiaans and T. Alieva, “Moments of the Wigner distribution of rotationally symmetric partially coherent light,” Opt. Lett. 28, 2443–2445 (2003). | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | f1512137-328a-4bb6-9714-45de778c1be4 | |
| relation.isAuthorOfPublication.latestForDiscovery | f1512137-328a-4bb6-9714-45de778c1be4 |
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