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Experimental study of the spread of knotted electromagnetic wave induced in the antenna field knotted anechoic conditions


M.V. Smelov – Ph. D. (Eng.), Head of Department, Foundation for promising technologies and innovations (Moscow) E-mail:

The article describes the results of the dissemination knotted electromagnetic wave experiment induced in the antenna field knotted anechoic conditions. Knotted antenna is a linear phased array antenna (PAA), which consists of two elements in the form of knotted antennae, each in the form of cinquefoil. The purpose of the experiments show an abnormally low specific attenuation knotted electromagnetic waves induced by this PAR in the wave zone Fraunhofer long range radio communication of up to 48 wavelengths λ ~ 13 cm (up to 6 m). The experiment was conducted in field anechoic conditions with the transmitting and receiving phased array mounted on the dielectric masts, and the dielectric guide. Outside the reflected signal is less than −95 dBm. The theoretical aspect of the existence of a knotted electromagnetic field is as follows. The experiment is based on the findings of theoretical research of new nontrivial topological solutions of Maxwell\'s equations written in the second exterior differential forms. It is the very existence of the electromagnetic field described by these equations, due to the phenomenon of the Hopf bundle [1] in the hypersphere S3 physical space (vacuum), where the stereographic projection S3 parallels in each of its points on our observable 3 dimensional Euclidean space has the shape of knotted 3-D tori. The lines of the meridians of tori set orbit of U(1) symmetry of the interior of the electromagnetic field (ie layers of the principal bundle), these lines in the physical dimensions and determine the magnetic field lines and orthogonal electric field, and the connection of the principal bundle determines the intensity of the physical fields. Measurements of attenuation knotted EME conducted in the wave Fresnel zone of 3λ to 10λ and the wave zone of Fraunhofer 10λ to 48λ at intervals equal to L = 11 cm step spiral helix, forming a topological knotted braid radiation EMW. The measurements revealed that near the beginning of the wave zone Fraunhofer 12L−24L change in the average level of attenuation of less than 0.5 dB, but for the radio distance from 24L to 57L there is almost zero change in the average attenuation (attenuation tempo) and the rate of attenuation tends to zero with increasing distance communication along the meridian on the sphere S3 fiber space radius of ~ 53 billion. light-years. Radiation pattern knotted EMW shrinks with increasing distance radio communication. It should be recalled that the rate of decay of the transverse electromagnetic wave is equal to 6 dB when doubling the distance of communication and, on the contrary, expands directional diagram.


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  2. Nefjodov E.I., Ermolaev JU.M., Smelov M.V. EHksperimentalnoe issledovanie vozbuzhdenija i rasprostranenija zauzlennykh ehlektromagnitnykh voln v razlichnykh sredakh // Radiotekhnika. 2013. № 2. S. 31.
  3. Smelov M.V. EHksperimentalnoe issledovanie sverkhsvetovojj skorosti rasprostranenija zauzlennykh ehlektromagnitnykh voln v vakuume // Radiotekhnika. 2015. № 1. S. 70.
  4. Smelov M.V. EHksperimentalnoe issledovanie zauzlennykh antenn v forme trilistnika i pjatilistnika // Radiotekhnika. 2013. № 2. S. 23.
  5. Smelov M.V. EHksperimentalnoe issledovanie fazirovannojj antennojj reshetki iz chetyrekh zauzlennykh antenn v forme pjatnadcatilistnikov // Antenny. 2014. № 9(208). S. 18.


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