Quantifying Information via Shannon Entropy in Spatially Structured Optical Beams

Abstract

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.

Prediction of the Number of Cumulative Pulses Based on the Photon Statistical Entropy Evaluation in Photon-Counting LiDAR

“…It is an important quantitative tool to evaluate the uncertainty of information generation, transmission, and reception. In recent years, many studies using entropy as an evaluation metric to improve performance have emerged in various fields, such as image quality assessment [ 24 , 25 ], beam complexity analysis [ 26 ], laser chaotic signal evaluation [ 27 , 28 ], fuzzy clustering [ 29 , 30 ], quantum communication [ 31 , 32 ], etc. In photon-counting LiDAR, the process of range measurement can be regarded as an information transmission model, and the uncertainty of the distribution of the signal and noise is completely different.…”

Free-space optical multiplexed orbital angular momentum beam identification system using Fourier optical convolutional layer based on 4f system

“…12,20 These beams with helical wavefront, which are generally called vortex beams, could be best described in terms of Laguerre-Gaussian (LG) modes which have an azimuthal phase term of exp(ilθ), representing an on-axis phase singularities of order l, where l is known as topological charge (TC) of the beam, which determines the number of times the phase should change by 2π on one single rotation around the beam axis. 21,22 Such vortex beams possess a well defined OAM of lh per photon. 23 So far, various state-of-the-art methods for the generation of LG beams have been successfully developed.…”

Continuity Scaling: A Rigorous Framework for Detecting and Quantifying Causality Accurately

“…The principle of Granger causality formalizes a paradigmatic framework [9][10][11], quantifying causality in terms of prediction improvements, but, because of its linear, multivariate, and statistical regression nature, the various derived methods require extensive data [12]. Entropy-based methods [13][14][15][16][17][18][19][20] face a similar difficulty. Another issue with the Granger causality is the fundamental requirement of separability of the underlying dynamical variables, which usually cannot be met in the real world systems.…”