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

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DOI: https://doi.org/10.30898/1684-1719.2025.3.1

 

 

 

ON THE GROUP VELOCITY OF A VIDEO SIGNAL IN A DIELECTRIC

 

N.S. Bukhman

 

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

 

The paper was received September 3, 2024.

 

Abstract. It is shown that holomorphic video signals of sufficient duration are capable (as well as holomorphic radio signals of sufficient duration) of propagating in a dielectric without significant distortion at a certain group velocity different from both the speed of light in a vacuum and the group velocity of a radio signal at radio frequencies. It is shown that this group velocity of the video signal coincides with its phase velocity. It is lower than the vacuum speed of light in media dominated by absorption at low frequencies and higher than the vacuum speed of light in media dominated by amplification at low frequencies. The group speed of the video signal in a normal atmosphere is calculated. It is shown that this group velocity is much closer to the vacuum velocity of light than the group velocity of a radio signal at radio frequencies. Therefore, at distances of less than 100 km, it can be assumed that any (including discontinuous) video signal with a duration of more than 10-10 seconds propagates "as in a vacuum" – without attenuation, as a whole and practically at the speed of light in a vacuum.

Key words: video signal, group speed, normal atmosphere, holomorphic signal, piecewise holomorphic signal, information transmission, ball lightning.

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. Proxorov A.M. Fizicheskaya e`nciklopediya. – Ripol Klassik, 1988. – T. 1.

4. Proxorov A.M. i dr. (red.). Fizicheskij e`nciklopedicheskij slovar`. – Sovetskaya e`nciklopediya, 1983.

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

6. 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.

7. 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   

8.  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  

9.  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  

10.  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  

11.  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  

12.  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.

13.  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  

14. 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  

15.  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  

16.  Akulshin A.M., McLean R.J. Fast light in atomic media //Journal of Optics. – 2010. – Ò. 12. – ¹. 10. – Ñ. 104001.

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

18.  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  

19.  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  

20.  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.

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

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

23.  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  

24.  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  

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

26. 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  

27.  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   

28.  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  

29.  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  

30.  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  

31.  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  

32. Atmosfera. Spravochnik (spravochny`e danny`e, modeli) //L.: Gidrometeoizdat. – 1991.

33. Zrazhevskij A.Yu., Titov S.V. Molekulyarnoe pogloshhenie v atmosferny`x parax vody` v 0-1 Tgcz chastotnom diapazone //Zhurnal radioe`lektroniki. – 2012. – ¹. 10. – S. 1-1.

34. Nikol`skij V.V. Nikol`skaya T.I. E`lektrodinamika i rasprostranenie radiovoln. – Nauka, 1989.

35. 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.

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

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

38. 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  

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

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

41. 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  

42. 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  

43. 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  

44. 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  

 

For citation:

Bukhman N.S. On the group velocity of a video signal in a dielectric. // Journal of Radio Electronics. – 2025 – ¹ 3. https://doi.org/10.30898/1684-1719.2025.3.1 (In Russian)