Propagation of spatial correlation vortices

I. D. Maleev; G. A. Swartzlander, Jr.

doi:10.1364/JOSAB.25.000915

Journal of the Optical Society of America B
Vol. 25,
Issue 6,
pp. 915-922
(2008)
•https://doi.org/10.1364/JOSAB.25.000915

Propagation of spatial correlation vortices

I. D. Maleev and G. A. Swartzlander

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I. D. Maleev and G. A. Swartzlander, Jr., "Propagation of spatial correlation vortices," J. Opt. Soc. Am. B 25, 915-922 (2008)

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Related Topics
Table of Contents Category
- Coherence and Statistical Optics
Optics & Photonics Topics
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The topics in this list come from the Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Coherence (030.1640)
- Coherent optical effects (030.1670)
- Correlators (100.4550)
- Phase (350.5030)
- Physical optics (260.0260)

About this Article
History
- Original Manuscript: February 29, 2008
- Manuscript Accepted: March 17, 2008
- Published: May 14, 2008

Abstract

The propagating four-dimensional mutual coherence function of a partially coherent Gaussian beam containing an arbitrarily positioned optical vortex is analytically determined. The dark intensity core becomes diffuse under low coherence and the vortex is only detectable by examining the cross-correlation function. This function contains a vortex dipole or a ring dislocation depending on the vortex position in the beam. The position of these robust propagating correlation phase singularities is described.

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	Condition
Parameter	Noncoherent $l_{c} ∕ w_{0} = 0$	Partially Coherent $l_{c} ∕ w_{0} = \sqrt{2}$	Fully Coherent $l_{c} ∕ w_{0} \to \infty$
$σ = l_{C}^{2} + 2 w_{0}^{2}$	$2 w_{0}^{2}$	$4 w_{0}^{2}$	$l_{c}^{2}$
$α = w_{0}^{2} (w_{0}^{2} + l_{C}^{2}) ∕ 4 σ$	$w_{0}^{2} ∕ 8$	$(3 ∕ 16) w_{0}^{2}$	$w_{0}^{2} ∕ 4$
$δ = w_{0}^{4} ∕ 4 σ$	$w_{0}^{2} ∕ 8$	$w_{0}^{2} ∕ 16$	0
$p = l_{C}^{2} ∕ σ$	0	1/2	1
$k_{c}^{2} = w_{0}^{- 2} + 2 l_{C}^{- 2} = 1 ∕ p w_{0}^{2}$	∞	$2 w_{0}^{- 2}$	$w_{0}^{- 2}$
Ring dislocation radius (k space) $k_{R} = 2 (k_{C} l_{C} w_{0})^{- 1} = 2 σ^{- 1 ∕ 2}$	$2^{1 ∕ 2} ∕ w_{0}$	$1 ∕ w_{0}$	0
Vortex separation (k space) $k_{V} = (k_{R}^{2} + 4 s^{2} ∕ w_{0}^{4})^{1 ∕ 2}$	$w_{0}^{- 1} (2 + 4 s^{2} ∕ w_{0}^{2})^{1 ∕ 2}$	$w_{0}^{- 1} (1 + 4 s^{2} ∕ w_{0}^{2})^{1 ∕ 2}$	$2 s ∕ w_{0}^{2}$
Beam spread $Δ = w_{0} [1 + q^{2} ∕ p]^{1 ∕ 2}$	∞	$w_{0} [1 + 2 q^{2}]^{1 ∕ 2}$	$w_{0} [1 + q^{2}]^{1 ∕ 2}$

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