Zhurnal Radioelektroniki - Journal of Radio Electronics. eISSN 1684-1719. 2023. №5
ContentsFull text in Russian (pdf)
DOI: https://doi.org/10.30898/1684-1719.2023.5.5
FOR CALCULATION REFLECTION AND PASSAGE OF WAVES
THROUGH MULTI-LAYER STRUCTURE.
PART 4. CRITERION OF APPLICABILITY
OF STEPPED APPROXIMATION OF NONUNIFORM MEDIUM
I.V. Antonets 1, V.G. Shavrov 2, V.I. Shcheglov 2
1 Syktyvkar State University
167001, Russia, Syktyvkar, Oktyabr'skij pr-t, 55
2 Kotelnikov IRE RAS, 125009, Russia, Moscow, Mokhovaya, 11, b. 7
The paper was received March 28, 2023.
Abstract. The correctness of applicability of stepped approximation for calculation the reflection, propagation and dissipation coefficients by falling the wave to multi-layer structure is investigated. The starting distribution is the linear increasing of wave number from initial to final points of structure. As an approach it is employed the presentation of structure as a combination from layers in each if it’s the wave number is constant but from one layer to other increases by stepped manner. It is formed 12 distributions with increasing fractional of distribution of structure to steps. It is shown that the dependence of reflection coefficient from the fractional distribution of structure with constant of its length has powerfully indented resonance character. It is shown that for expulsion the possibility of resonances excitation the half of minimum wave length must be more then whole length of structure. From this demand it is found the critical as so maximum value of wave number which is equal to ratio of number “pi” to the whole length of structure. It is found that the correct approximation of linear increasing by stepped is the so as which maximum of wave number is less than critical. It is found that in practice near the critical value for the achieve the correction (near 5%) it is enough the distribution of structure on seven steps which have equal high and length. When the maximum of wave number is more than critical number the anyone increasing of distribution (so as increasing of steps quantity) for increasing of approximation precision of linear structure by stepped does not achieved.
Key words: wave propagation, multi-layers structure, impedance.
Financing: The work was carried out as part of the state task of the V.A. Kotelnikov Institute of Radio Engineering and Electronics of the Russian Academy of Sciences
Corresponding author: Shcheglov Vladimir Ignatyevich, vshcheg@cplire.ru
1. Khvolson O.D. Kurs fiziki, T.2. [Corse of physics, Part 2]. Berlin, Gosizdat RSFSR. 1923. 776 p. (In Russian)
2. Brekhovsky L.M. Volny v sloistykh sredakh [Waves in layer media]. Moscow, Nauka. 1973. 501 p. (In Russian)
3. Born M., Wolf E. Principles of optics. Oxford, London, Edinburgh, New York, Paris, Frankfurt, Pergamon Press. 1964. 325 p.
4. Landsberg G.S. Optika [Optics]. Moscow, Nauka. 1976. 928 p. (In Russian)
5. Kizel V.A. Otrazhenie sveta [Reflection of light]. Moscow, Nauka. 1973. 352 p. (In Russian)
6. Brekhovsky L.M., Godin O.A. Akustika sloistykh sred [Acoustic of layer media]. Moscow, Nauka. 1989. 416 p. (In Russian)
7. Oksanen M.I., Hanninen J., Tretyakov S.A. Vector circuit method for calculating reflection and transmission of electromagnetic waves in multilayered chiral structures. IEEE Proceedings. H. 1991. V.138. №7. P.513-520.
8. Sarychev A.K., Bergman D.J., Yagil Y. Theory of the optical and microwave properties of metal-dielectric films. Phys. Rev. B. 1995. V.51. №8. P.5366-5385.
9. Kozar’ A.V. Optical properties of aperiodic thin layer structures: effective refraction index. Vestnik Moskovskogo Universiteta. Seriya 3. Fizika. Astronomiya [Moscow University Physics Bulletin. Series 3. Physics. Astronomy]. 2009. V.64. №3. P.54-56. (In Russian)
10. Kozar’ A.V. Optical properties of aperiodic thin-layer structures: The effective optical thickness. Vestnik Moskovskogo Universiteta. Seriya 3. Fizika. Astronomiya [Moscow University Physics Bulletin. Series 3. Physics. Astronomy]. 2018. V.73. №6. P.61-66. (In Russian)
11. Brillouin L., Parodi M. Rasprostranenie voln v periodicheskikh strukturakh [Wave propagation in periodic structure]. Moscow, Izdatel'stvo inostrannoj literatury. 1959. 457 p. (In Russian)
12. Shavrov V.G., Shcheglov V.I. Magnitostaticheskie i ehlektromagnitnye volny v slozhnykh strukturakh [Magnetostatic and electromagnetic waves in complex structures]. Moscow, Fizmatlit. 2017. 358 p. (In Russian)
13. Antonets I.V., Shcheglov V.I. Rasprostranenie voln cherez tonkie sloi i plenki [Propagation of waves through thin layers and films]. Syktivkar, SyktSU. 2010. 132 p. (In Russian)
14. Antonets I.V., Shcheglov V.I. Rasprostranenie voln cherez mnogoslojnye struktury. Chast' pervaya. Pryamoj metod [Propagation of waves through multi-layer structure. Part first. Direct method]. Syktivkar, SyktSU. 2011. 134 p. (In Russian)
15. Antonets I.V., Shavrov V.G., Shcheglov V.I. Volny v mnogosloinykh strukturakh. Chast' 1. Metody rascheta: pryamoi, usredneniya, matritsy [Waves in multi-layer structures. Part first. Methods of calculation: direct, middle-value, matrix]. Moscow, Fizmatlit. 2022. 424 p. (In Russian)
16. Antonets I.V., Shcheglov V.I. Rasprostranenie voln cherez mnogoslojnye struktury Chast' vtoraya. Metod matricy [Propagation of waves through multi-layer structure. Part second. Matrix method]. Syktivkar, SyktSU. 2012. 123 p. (In Russian)
17. Antonets I.V., Shcheglov V.I. Rasprostranenie voln cherez mnogoslojnye struktury Chast' tret'ya. Metod impedansa [Propagation of waves through multi-layer structure. Part third. Impedance method]. Syktivkar, SyktSU. 2012. 139 p. (In Russian)
18. Antonets I.V., Shavrov V.G., Shcheglov V.I. Matrix Algorithm for Calculation of the Reflection and Transmission Coefficients for the Incidence of Two Counterpropagation Waves on a Multilayer Structure. Journal of Communications Technology and Electronics. 2022. V.67. №9. P.1113-1119.
19. Antonets I.V., Shavrov V.G., Shcheglov V.I. Algorithmic calculation method of wave reflection and passage through multi-layer structure. Part 1. Matrix algorithm. Zhurnal radioelektroniki [Journal of Radio Electronics] [online]. 2022. №8. https://doi.org/10.30898/1684-1719.2022.8.8 (In Russian)
20. Antonets I.V., Shavrov V.G., Shcheglov V.I. Algorithmic calculation method of wave reflection and passage through multi-layer structure. Part 2. Incidence of wave on the inclined barrier. Zhurnal radioelektroniki [Journal of Radio Electronics] [online]. 2022. №8. https://doi.org/10.30898/1684-1719.2022.8.9 (In Russian)
21. Antonets I.V., Shavrov V.G., Shcheglov V.I. Generalized impedance method for calculation reflection and passage of waves through multi-layer structure. Part 1. Successive calculation of impedances and amplitudes. Zhurnal radioelektroniki [Journal of Radio Electronics] [online]. 2023. №1. https://doi.org/10.30898/1684-1719.2023.1.1 (In Russian)
22. Antonets I.V., Shavrov V.G., Shcheglov V.I. Generalized impedance method for calculation reflection and passage of waves through multi-layer structure. Part 2. Incidence of wave on rectangular barrier. Zhurnal radioelektroniki [Journal of Radio Electronics] [online]. 2023. №1. https://doi.org/10.30898/1684-1719.2023.1.2 (In Russian)
23. Antonets I.V., Shavrov V.G., Shcheglov V.I. Generalized impedance method for calculation reflection and passage of waves through multi-layer structure. Part 3. Incidence of wave on the step by step increased barrier. Zhurnal radioelektroniki [Journal of Radio Electronics] [online]. 2023. №1. https://doi.org/10.30898/1684-1719.2023.1.3 (In Russian)
For citation:
Antonets I.V., Shavrov V.G., Shcheglov V.I. Generalized impedance method for calculation reflection and passage of waves through multi-layer structure. Part 4. Criterion of applicability of stepped approximation of nonuniform medium. Zhurnal radioelektroniki [Journal of Radio Electronics] [online]. 2023. №5. https://doi.org/10.30898/1684-1719.2023.5.5 (In Russian)