Journal of Radio Electronics. eISSN 1684-1719. 2025. ¹3

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DOI: https://doi.org/10.30898/1684-1719.2025.3.2

 

 

 

ON HOLONOMIC AND PIECEWISE HOLONOMIC SIGNALS

 

N.S. Bukhman

 

Samara State Technical University,
443100, Samara, Molodogvardeyskaya str., 244

 

The paper was received August 9, 2024.

 

Abstract. The properties of holomorphic and piecewise holomorphic signals during propagation in a dispersing medium are compared. It is shown that the status of the signal (holomorphic or piecewise holomorphic) cannot be changed by any physically realizable (that is, not violating the principle of causality) filter. It is shown that the properties of holomorphic and piecewise holomorphic signals are not only different, but usually directly opposite. For example, piecewise holomorphic signals (unlike holomorphic ones) necessarily have precursors, fade out in an absorbing medium according to a hyperbolic (rather than exponential) law, have an anthropogenic (rather than natural) origin, and transfer information (unlike holomorphic ones). Holomorphic signals (unlike piecewise holomorphic ones) are capable of propagating as a whole with a group velocity (and any one – sublight, superluminal, negative and complex).

Key words: holonomic signal, piecewise holonomic signal, holomorphic signal, piecewise holomorphic signal, information transmission, group velocity, superluminal velocity, signals of extraterrestrial civilizations.

Corresponding author: Bukhman Nikolay Sergeevich, nik3142@yandex.ru

References

1. Vinogradova M.B., Rudenko O.V., Suhorukov A.P. Teoriya voln. – 1979.

2. Vaĭnshteĭn L.A. Propagation of pulses //Soviet Physics Uspekhi. – 1976. – Ò. 19. – ¹. 2. – Ñ. 189. https://doi.org/10.1070/PU1976v019n02ABEH005138

3. Bukhman N.S. Absorption of a Narrow-Band Signal in a Dispersive Medium //Radiophysics and Quantum Electronics. – 2023. – Ò. 65. – ¹. 12. – Ñ. 897-910. https://doi.org/10.1007/s11141-023-10266-8

4. Bukhman N.S. On the principle of causality and superluminal signal propagation velocities //Journal of Communications Technology and Electronics. – 2021. – Ò. 66. – Ñ. 227-241. https://doi.org/10.1134/S1064226921030049

5. Bukhman N.S., Kulikova A.V. On the influence of the dispersion of absorption on the time dependence of a holonomic narrow-band signal in a dispersive medium far from the point of radiation. // Zhurnal radioelektroniki [Journal of Radio Electronics] [online]. 2023. ¹2. https://doi.org/10.30898/1684-1719.2023.2.5 (In Russian)

6. Bukhman N.S. On the distortion of the rising edge of a carrier-free signal //Journal of Communications Technology and Electronics. – 2016. – Ò. 61. – Ñ. 1327-1337.https://doi.org/10.7868/S0033849416120056

7. Bukhman N.S. On the distortion of the leading edge of a quasi-monochromatic signal in a resonantly absorbing medium //Journal of Communications Technology and Electronics. – 2019. – Ò. 64. – Ñ. 203-216. https://doi.org/10.1134/S0033849419030045

8. Landau L.D., Lífshíts E.M. Electrodynamics of continuous media. – Oxford : Pergamon Press, 1946. – Ñ. 1963.

9. Fedoryuk M.V. Asymptotics: integrals and series //Mathematical Reference Library. – 1987.

10. Macke B., Ségard B. Optical precursors with self-induced transparency //Physical Review A–Atomic, Molecular, and Optical Physics. – 2010. – Ò. 81. – ¹. 1. – Ñ. 015803.

11. Macke B., Ségard B. Optical precursors in transparent media //Physical Review A–Atomic, Molecular, and Optical Physics. – 2009. – Ò. 80. – ¹. 1. – Ñ. 011803.

12. Boyd and R.W., Gauthier D.J. « Slow''and» fasf'light // Progress in Optics. – 2002. – V. 43. – P. 497.

13. Macke B., Ségard B. Simple asymptotic forms for Sommerfeld and Brillouin precursors //Physical Review A–Atomic, Molecular, and Optical Physics. – 2012. – Ò. 86. – ¹. 1. – Ñ. 013837. https://doi.org/10.1103/PhysRevA.86.013837

14. Sommerfeld A. Über die Fortpflanzung des Lichtes in dispergierenden Medien //Annalen der Physik. – 1914. – Ò. 349. – ¹. 10. – Ñ. 177-202.

15. Brillouin L. Über die Fortpflanzung des Lichtes in dispergierenden Medien //Annalen der Physik. – 1914. – Ò. 349. – ¹. 10. – Ñ. 203-240.

16. Aaviksoo J., Kuhl J., Ploog K. Observation of optical precursors at pulse propagation in GaAs //Physical Review A. – 1991. – Ò. 44. – ¹. 9. – Ñ. R5353. https://doi.org/10.1103/PhysRevA.44.R5353

17. Österberg U., Andersson D., Lisak M. On precursor propagation in linear dielectrics //Optics communications. – 2007. – Ò. 277. – ¹. 1. – Ñ. 5-13. https://doi.org/10.1016/j.optcom.2007.04.050

18. Du S. et al. Observation of optical precursors at the biphoton level //Optics letters. – 2008. – Ò. 33. – ¹. 18. – Ñ. 2149-2151. https://doi.org/10.1364/OL.33.002149

19. Macke B., Ségard B. Brillouin precursors in Debye media //Physical Review A. – 2015. – Ò. 91. – ¹. 5. – Ñ. 053814. https://doi.org/10.1103/PhysRevA.91.053814

20. Strel'NitskiĬ V.S. Cosmic masers //Soviet Physics Uspekhi. – 1975. – Ò. 17. – ¹. 4. – Ñ. 507. https://doi.org/10.1070/PU1975v017n04ABEH004424

21. Townes C.H. Astronomical masers and lasers //Quantum Electronics. – 1997. – Ò. 27. – ¹. 12. – Ñ. 1031. https://doi.org/10.1070/QE1997v027n12ABEH001104

22. Varshalovich D.A. Mazernyj effekt v kosmose // Fizika kosmosa: Malen'kaya enciklopediya / Pod red. R.A. Syunyaeva, Yu.N. Drozhzhina-Labinskogo, Ya.B. Zel'dovicha i dr.. – 2-e izd. – M.: Sovetskaya enciklopediya, 1986. – S. 376–378.

23. Dickinson D. F. Cosmic Masers// Scientific American. – 1978. – V. 238. – ¹ 6. – P. 68. https://doi.org/10.3367/UFNr.0128.197906e.0345

24. Wang L.J., Kuzmich A., Dogariu A. Gain-assisted superluminal light propagation //Nature. – 2000. – Ò. 406. – ¹. 6793. – Ñ. 277-279. https://doi.org/10.1038/35018520

25. Talukder M.A.I., Amagishi Y., Tomita M. Superluminal to subluminal transition in the pulse propagation in a resonantly absorbing medium //Physical Review Letters. – 2001. – Ò. 86. – ¹. 16. – Ñ. 3546. https://doi.org/10.1103/PhysRevLett.86.3546

26. Dogariu A., Kuzmich A., Wang L.J. Transparent anomalous dispersion and superluminal light-pulse propagation at a negative group velocity //Physical Review A. – 2001. – Ò. 63. – ¹. 5. – Ñ. 053806. https://doi.org/10.1103/PhysRevA.63.053806

27. Akulshin A.M., Cimmino A., Opat G.I. Negative group velocity of a light pulse in cesium vapour //Quantum Electronics. – 2002. – Ò. 32. – ¹. 7. – Ñ. 567. https://doi.org/10.1070/QE2002v032n07ABEH002249

28. Macke B., Ségard B. Propagation of light-pulses at a negative group-velocity //The European Physical Journal D-Atomic, Molecular, Optical and Plasma Physics. – 2003. – Ò. 23. – Ñ. 125-141. https://doi.org/10.1140/epjd/e2003-00022-0

29. Akulshin A.M. et al. Pulses of» fast light,» the signal velocity, and giant Kerr nonlinearity //LASER PHYSICS-LAWRENCE-. – 2005. – Ò. 15. – ¹. 9. – Ñ. 1252.

30. Zolotovskiĭ I.O., Sementsov D.I. Velocity of the Maximum of the Envelope of a Frequency-Modulated Gaussian Pulse in an Amplifying Nonlinear Medium // Optics and Spectroscopy . – 2005. – V. 99. – No 1. – P. 81.          https://doi.org/10.1134/1.1999897

31. Zolotovskiĭ I.O., Sementsov D.I. Velocity of the pulse envelope in tunnel-coupled optical waveguides with strongly differing parameters //Optics and spectroscopy. – 2006. – Ò. 101. – Ñ. 114-117. https://doi.org/10.1134/S0030400X06070204

32. Macke B., Ségard B. From fast to slow light in a resonantly driven absorbing medium //Physical Review A–Atomic, Molecular, and Optical Physics. – 2010. – Ò. 82. – ¹. 2. – Ñ. 023816. https://doi.org/10.1103/PhysRevA.82.023816

33. Akulshin A.M., McLean R.J. Fast light in atomic media //Journal of Optics. – 2010. – Ò. 12. – ¹. 10. – Ñ. 104001. https://doi.org/10.1088/2040-8978/12/10/104001

34. Malykin G.B., Romanets E.A. Superluminal motion //Optics and Spectroscopy. – 2012. – Ò. 112. – Ñ. 920-934. https://doi.org/10.1134/S0030400X12040145

35. Zolotovskii I.O., Minvaliev R.N., Sementsov D.I. Dynamics of frequency-modulated wave packets in optical guides with complex-valued material parameters //Physics-Uspekhi. – 2013. – Ò. 56. – ¹. 12. – Ñ. 1245.. https://doi.org/10.3367/UFNe.0183.201312e.1353

36. Macke B., Ségard B. Simultaneous slow and fast light involving the Faraday effect //Physical Review A. – 2016. – Ò. 94. – ¹. 4. – Ñ. 043801. https://doi.org/10.1103/PhysRevA.94.043801

37. Ravelo B. Investigation on microwave negative group delay circuit //Electromagnetics. – 2011. – Ò. 31. – ¹. 8. – Ñ. 537-549. https://doi.org/10.1080/02726343.2011.621106

38. Macke B., Ségard B. // Opt. Commun. 2008. V. 281. ¹ 1. P. 12-17. https://doi.org/10.1016/j.optcom.2007.09.007

39. Tanaka H. et al. Propagation of optical pulses in a resonantly absorbing medium: Observation of negative velocity in Rb vapor //Physical Review A. – 2003. – Ò. 68. – ¹. 5. – Ñ. 053801. https://doi.org/10.1103/PhysRevA.68.053801

40. Macke B., Ségard B. On-resonance material fast light //Physical Review A. – 2018. – Ò. 97. – ¹. 6. – Ñ. 063830. https://doi.org/10.1103/PhysRevA.80.011803.

41. Bukhman N.S. On the velocity of propagation of a frequency-modulated wave packet in a dispersive absorbing medium //Optics and spectroscopy. – 2004. – Ò. 97. – Ñ. 114-121.https://doi.org/10.1134/1.1781291

42. Smirnov V.I. A Course of Higher Mathematics: International Series of Monographs in Pure and Applied Mathematics, Volume 62: A Course of Higher Mathematics. – Elsevier, 2014.

For citation:

Bukhman N.S. On holomorphic and piecewise holomorphic signals. // Journal of Radio Electronics. – 2025 – ¹ 3. https://doi.org/10.30898/1684-1719.2025.3.2 (In Russian)