Signal representation on the angular Poincaré sphere, based on second-order moments

M.J. Bastiaans, T. Alieva

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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 Poincaré 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. © 2010 Optical Society of America
Original languageEnglish
Pages (from-to)918-927
Number of pages10
JournalJournal of the Optical Society of America A, Optics, Image Science and Vision
Volume27
Issue number4
DOIs
Publication statusPublished - 2010

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Vorticity
Gyrators
moments
Optical systems
gyrators
vorticity
Poles
Lenses
Vortex flow
canonical forms
equators
magnification
optical communication
poles
lenses
vortices

Cite this

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title = "Signal representation on the angular Poincar{\'e} sphere, based on second-order moments",
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 Poincar{\'e} 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. {\circledC} 2010 Optical Society of America",
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Signal representation on the angular Poincaré sphere, based on second-order moments. / Bastiaans, M.J.; Alieva, T.

In: Journal of the Optical Society of America A, Optics, Image Science and Vision, Vol. 27, No. 4, 2010, p. 918-927.

Research output: Contribution to journalArticleAcademicpeer-review

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T1 - Signal representation on the angular Poincaré sphere, based on second-order moments

AU - Bastiaans, M.J.

AU - Alieva, T.

PY - 2010

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AB - 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 Poincaré 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. © 2010 Optical Society of America

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