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:
https://lup.lub.lu.se/record/2343056
- author
- Lindgren, Georg
LU
- organization
- publishing date
- 2012
- 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
- article number
- 035704
- publisher
- IOP Publishing
- external identifiers
-
- wos:000300788400018
- scopus:84857541947
- ISSN
- 2040-8986
- DOI
- 10.1088/2040-8978/14/3/035704
- language
- English
- LU publication?
- yes
- id
- a33225c1-7846-4b5a-8394-ef69ba8fba90 (old id 2343056)
- date added to LUP
- 2016-04-01 09:55:39
- date last changed
- 2022-06-21 14:50:44
@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.}},
author = {{Lindgren, Georg}},
issn = {{2040-8986}},
keywords = {{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}},
doi = {{10.1088/2040-8978/14/3/035704}},
volume = {{14}},
year = {{2012}},
}