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Translating this into optics, it has been understood that a monochromatic plane-wave photon in free space can carry a rather limited amount of distinctive features (i.e., polarization and wavelength), providing up to one bit of information per photon. The amount of information a human can transmit per unit sentence containing a fixed number of words is indirectly correlated with the amount of distinctive features the language can handle (i.e., language capacity). For instance, human speech can carry up to distinctive sounds (due to 14 binary distinctive features, e.g., ), only a small subset of which is realized in any particular known language. One way of defining information is associating it with the presence of distinctive features.
Out of the broad scope of studies where information theory has a potential to contribute, at this point, we exemplary explore its applications to electrical engineering and signal processing. Being a higher level of abstraction, it focuses on a configuration of a system under consideration in the context of its prehistory, similarly to thermodynamics, without attachment to a particular class of objects under study in its axiomatics. Information theory stands out from most of other approaches in physics. However, the fundamental challenge of rigorous qualification and quantification of information in EM waves still remains a topic of debate including both physical and even semi-philosophical notions. With relevance to this IT-driven age, the two longstanding goals in information processing are (i) achieving higher channel capacity (i.e., throughput) and (ii) (pre)processing of collected information. It is capable of reliably transmitting a modulated signal and collecting information about the propagation channel itself. IntroductionĪn electromagnetic field is a fundamental physical carrier of information.
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. 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. 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. 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. 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. Here, we propose a new definition of the classical Shannon information via the Wigner distribution function, while respecting the Heisenberg inequality. 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. A number of theoretical approaches based on, e.g., conditional Shannon entropy and Fisher information have been developed, along with some experimental validations. 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.
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