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Quantifying Information via Shannon Entropy in Spatially Structured Optical Beams.
Maria Solyanik-Gorgone1, Jiachi Ye1, Mario Miscuglio1
1Department of Electrical and Computer Engineering, The George Washington University, Washington, DC 20052, USA.
Research (Washington, D.C.)
|December 6, 2021
Summary
This study introduces a novel method to quantify information in optical channels using the Wigner distribution function. This approach accurately measures information in complex laser modes, advancing optical communication and sensing.
Area of Science:
- Quantum optics
- Information theory
- Laser physics
Background:
- Assessing information in noisy optical channels remains challenging.
- Existing methods using Shannon entropy or Fisher information have limitations with complex optical beam structures.
- There's a need for a generalized approach to quantify information in structured light.
Purpose of the Study:
- To propose a new definition of classical Shannon information using the Wigner distribution function.
- To calculate and experimentally validate information content in various laser modes (Gaussian, Hermite-Gaussian, Laguerre-Gaussian).
- To develop a method for inferring laser beam field structure and assessing contained information.
Main Methods:
- Definition of classical Shannon information via the Wigner distribution function, adhering to the Heisenberg inequality.
- Calculation of information in different laser modes.
- Experimental reconstruction of the Wigner distribution function from intensity distributions of structured laser beams.
Main Results:
- A new, alphabet-independent definition of classical Shannon information is presented.
- The method successfully quantifies information in Gaussian, Hermite-Gaussian, and Laguerre-Gaussian laser modes.
- Experimental validation confirms the technique's ability to infer field structure and assess information in singular optics.
Conclusions:
- The proposed Wigner distribution function-based information definition is general and applicable to laser modes of any topology.
- This approach scales with the structural complexity of the optical system, offering a universal measure of information.
- The synergy between Wigner distribution function analysis and information theory can enhance coherent detection and remote sensing.
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