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...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Association for the Advancement of Science (AAAS)
2021-01-01
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| Series: | Research |
| Online Access: | http://dx.doi.org/10.34133/2021/9780760 |
| _version_ | 1797282562724331520 |
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| 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 |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-03-07T17:14:53Z |
| format | Article |
| id | doaj.art-729ceb88b4eb4740aef6c8058560c7f1 |
| institution | Directory Open Access Journal |
| issn | 2639-5274 |
| language | English |
| last_indexed | 2024-03-07T17:14:53Z |
| publishDate | 2021-01-01 |
| publisher | American Association for the Advancement of Science (AAAS) |
| record_format | Article |
| series | Research |
| spelling | doaj.art-729ceb88b4eb4740aef6c8058560c7f12024-03-02T23:14:57ZengAmerican Association for the Advancement of Science (AAAS)Research2639-52742021-01-01202110.34133/2021/9780760Quantifying Information via Shannon Entropy in Spatially Structured Optical BeamsMaria Solyanik-Gorgone0Jiachi Ye1Mario Miscuglio2Andrei Afanasev3Alan E. Willner4Volker J. Sorger5Department of Electrical and Computer Engineering, The George Washington University, Washington, DC 20052, USADepartment of Electrical and Computer Engineering, The George Washington University, Washington, DC 20052, USADepartment of Electrical and Computer Engineering, The George Washington University, Washington, DC 20052, USADepartment of Physics, The George Washington University, Washington, DC 20052, USADepartment of Electrical Engineering at University of Southern California, Los Angeles, California 90089, USADepartment of Electrical and Computer Engineering, The George Washington University, Washington, DC 20052, USAWhile 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.http://dx.doi.org/10.34133/2021/9780760 |
| spellingShingle | 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 Research |
| title | 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_short | Quantifying Information via Shannon Entropy in Spatially Structured Optical Beams |
| title_sort | quantifying information via shannon entropy in spatially structured optical beams |
| url | http://dx.doi.org/10.34133/2021/9780760 |
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