Quantifying Information via Shannon Entropy in Spatially Structured Optical Beams

While information is ubiquitously generated, shared, and analyzed in a modern-day life, there is still some controversy around the ways to assess the amount and quality of information inside a noisy optical channel. A number of theoretical approaches based on, e.g., conditional Shannon entropy and F...

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Autores principales:	Maria Solyanik-Gorgone, Jiachi Ye, Mario Miscuglio, Andrei Afanasev, Alan E. Willner, Volker J. Sorger
Formato:	article
Lenguaje:	EN
Publicado:	American Association for the Advancement of Science 2021
Materias:	Science Q
Acceso en línea:	https://doaj.org/article/729ceb88b4eb4740aef6c8058560c7f1
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id	oai:doaj.org-article:729ceb88b4eb4740aef6c8058560c7f1
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spelling	oai:doaj.org-article:729ceb88b4eb4740aef6c8058560c7f12021-11-22T08:31:11ZQuantifying Information via Shannon Entropy in Spatially Structured Optical Beams2639-527410.34133/2021/9780760https://doaj.org/article/729ceb88b4eb4740aef6c8058560c7f12021-01-01T00:00:00Zhttp://dx.doi.org/10.34133/2021/9780760https://doaj.org/toc/2639-5274While information is ubiquitously generated, shared, and analyzed in a modern-day life, there is still some controversy around the ways to assess the amount and quality of information inside a noisy optical channel. A number of theoretical approaches based on, e.g., conditional Shannon entropy and Fisher information have been developed, along with some experimental validations. Some of these approaches are limited to a certain alphabet, while others tend to fall short when considering optical beams with a nontrivial structure, such as Hermite-Gauss, Laguerre-Gauss, and other modes with a nontrivial structure. Here, we propose a new definition of the classical Shannon information via the Wigner distribution function, while respecting the Heisenberg inequality. Following this definition, we calculate the amount of information in Gaussian, Hermite-Gaussian, and Laguerre-Gaussian laser modes in juxtaposition and experimentally validate it by reconstruction of the Wigner distribution function from the intensity distribution of structured laser beams. We experimentally demonstrate the technique that allows to infer field structure of the laser beams in singular optics to assess the amount of contained information. Given the generality, this approach of defining information via analyzing the beam complexity is applicable to laser modes of any topology that can be described by well-behaved functions. Classical Shannon information, defined in this way, is detached from a particular alphabet, i.e., communication scheme, and scales with the structural complexity of the system. Such a synergy between the Wigner distribution function encompassing the information in both real and reciprocal space and information being a measure of disorder can contribute into future coherent detection algorithms and remote sensing.Maria Solyanik-GorgoneJiachi YeMario MiscuglioAndrei AfanasevAlan E. WillnerVolker J. SorgerAmerican Association for the Advancement of SciencearticleScienceQENResearch, Vol 2021 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Science Q
spellingShingle	Science Q Maria Solyanik-Gorgone Jiachi Ye Mario Miscuglio Andrei Afanasev Alan E. Willner Volker J. Sorger Quantifying Information via Shannon Entropy in Spatially Structured Optical Beams
description	While information is ubiquitously generated, shared, and analyzed in a modern-day life, there is still some controversy around the ways to assess the amount and quality of information inside a noisy optical channel. A number of theoretical approaches based on, e.g., conditional Shannon entropy and Fisher information have been developed, along with some experimental validations. Some of these approaches are limited to a certain alphabet, while others tend to fall short when considering optical beams with a nontrivial structure, such as Hermite-Gauss, Laguerre-Gauss, and other modes with a nontrivial structure. Here, we propose a new definition of the classical Shannon information via the Wigner distribution function, while respecting the Heisenberg inequality. Following this definition, we calculate the amount of information in Gaussian, Hermite-Gaussian, and Laguerre-Gaussian laser modes in juxtaposition and experimentally validate it by reconstruction of the Wigner distribution function from the intensity distribution of structured laser beams. We experimentally demonstrate the technique that allows to infer field structure of the laser beams in singular optics to assess the amount of contained information. Given the generality, this approach of defining information via analyzing the beam complexity is applicable to laser modes of any topology that can be described by well-behaved functions. Classical Shannon information, defined in this way, is detached from a particular alphabet, i.e., communication scheme, and scales with the structural complexity of the system. Such a synergy between the Wigner distribution function encompassing the information in both real and reciprocal space and information being a measure of disorder can contribute into future coherent detection algorithms and remote sensing.
format	article
author	Maria Solyanik-Gorgone Jiachi Ye Mario Miscuglio Andrei Afanasev Alan E. Willner Volker J. Sorger
author_facet	Maria Solyanik-Gorgone Jiachi Ye Mario Miscuglio Andrei Afanasev Alan E. Willner Volker J. Sorger
author_sort	Maria Solyanik-Gorgone
title	Quantifying Information via Shannon Entropy in Spatially Structured Optical Beams
title_short	Quantifying Information via Shannon Entropy in Spatially Structured Optical Beams
title_full	Quantifying Information via Shannon Entropy in Spatially Structured Optical Beams
title_fullStr	Quantifying Information via Shannon Entropy in Spatially Structured Optical Beams
title_full_unstemmed	Quantifying Information via Shannon Entropy in Spatially Structured Optical Beams
title_sort	quantifying information via shannon entropy in spatially structured optical beams
publisher	American Association for the Advancement of Science
publishDate	2021
url	https://doaj.org/article/729ceb88b4eb4740aef6c8058560c7f1
work_keys_str_mv	AT mariasolyanikgorgone quantifyinginformationviashannonentropyinspatiallystructuredopticalbeams AT jiachiye quantifyinginformationviashannonentropyinspatiallystructuredopticalbeams AT mariomiscuglio quantifyinginformationviashannonentropyinspatiallystructuredopticalbeams AT andreiafanasev quantifyinginformationviashannonentropyinspatiallystructuredopticalbeams AT alanewillner quantifyinginformationviashannonentropyinspatiallystructuredopticalbeams AT volkerjsorger quantifyinginformationviashannonentropyinspatiallystructuredopticalbeams
_version_	1718417801702539264

Quantifying Information via Shannon Entropy in Spatially Structured Optical Beams

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