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A detailed statistical representation of the local structure of optical vortices in random wavefields

Lindgren, Georg LU (2012) In Journal of Optics 14(3).
Abstract
The statistical properties near phase singularities in a complex wave

field are here studied by means of the conditional distributions of the real and imaginary Gaussian components, given a common zero crossing point. The exact distribution is expressed as a Slepian model, where a regression term provides the main structure, with parameters given by the gradients of the Gaussian components at the singularity, and Gaussian non-stationary residuals that provide local variability. This technique differs from the linearisation (Taylor expansion) technique commonly used.



The empirically and theoretically verified elliptic eccentricity of the intensity contours in the vortex core is a property of the regression term,... (More)
The statistical properties near phase singularities in a complex wave

field are here studied by means of the conditional distributions of the real and imaginary Gaussian components, given a common zero crossing point. The exact distribution is expressed as a Slepian model, where a regression term provides the main structure, with parameters given by the gradients of the Gaussian components at the singularity, and Gaussian non-stationary residuals that provide local variability. This technique differs from the linearisation (Taylor expansion) technique commonly used.



The empirically and theoretically verified elliptic eccentricity of the intensity contours in the vortex core is a property of the regression term, but with different normalization compared to the classical theory. The residual term models the statistical variability around these ellipses. The radii of the circular contours of the current magnitude are similarly modified by the new regression expansion, and also here the random deviations are modelled by the residual field. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
crossing, dislocation, Gaussian waves, optical vorticity, phase singularity, Rice formula, Slepian model
in
Journal of Optics
volume
14
issue
3
publisher
IOP Publishing
external identifiers
  • wos:000300788400018
  • scopus:84857541947
ISSN
2040-8986
DOI
10.1088/2040-8978/14/3/035704
project
BECC
language
English
LU publication?
yes
id
a33225c1-7846-4b5a-8394-ef69ba8fba90 (old id 2343056)
date added to LUP
2012-04-19 11:08:40
date last changed
2017-03-26 03:02:19
@article{a33225c1-7846-4b5a-8394-ef69ba8fba90,
  abstract     = {The statistical properties near phase singularities in a complex wave<br/><br>
field are here studied by means of the conditional distributions of the real and imaginary Gaussian components, given a common zero crossing point. The exact distribution is expressed as a Slepian model, where a regression term provides the main structure, with parameters given by the gradients of the Gaussian components at the singularity, and Gaussian non-stationary residuals that provide local variability. This technique differs from the linearisation (Taylor expansion) technique commonly used.<br/><br>
<br/><br>
The empirically and theoretically verified elliptic eccentricity of the intensity contours in the vortex core is a property of the regression term, but with different normalization compared to the classical theory. The residual term models the statistical variability around these ellipses. The radii of the circular contours of the current magnitude are similarly modified by the new regression expansion, and also here the random deviations are modelled by the residual field.},
  articleno    = {035704},
  author       = {Lindgren, Georg},
  issn         = {2040-8986},
  keyword      = {crossing,dislocation,Gaussian waves,optical vorticity,phase singularity,Rice formula,Slepian model},
  language     = {eng},
  number       = {3},
  publisher    = {IOP Publishing},
  series       = {Journal of Optics},
  title        = {A detailed statistical representation of the local structure of optical vortices in random wavefields},
  url          = {http://dx.doi.org/10.1088/2040-8978/14/3/035704},
  volume       = {14},
  year         = {2012},
}