Mathematical models of chirowaveguides
Matematičeskoe modelirovanie, Tome 19 (2007) no. 5, pp. 3-24.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, main methods of chirowaveguides mathematical modeling are described. The following methods are examined: finite difference method, Bubnov-Galerkin method, finite element method, vector circuit method and dyadic Green's functions method. The novel class of waveguides, filled with chiral medium, exhibits a number of interesting new modes features. The artificial chiral media have attained a particular interest due to the possibility of manufacturing such materials for the microwave domain. Primary attention was given to the brief methods review and analysis of numerical results.
@article{MM_2007_19_5_a0,
     author = {A. N. Bogolyubov and N. A. Mosunova and D. A. Petrov},
     title = {Mathematical models of chirowaveguides},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {3--24},
     publisher = {mathdoc},
     volume = {19},
     number = {5},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2007_19_5_a0/}
}
TY  - JOUR
AU  - A. N. Bogolyubov
AU  - N. A. Mosunova
AU  - D. A. Petrov
TI  - Mathematical models of chirowaveguides
JO  - Matematičeskoe modelirovanie
PY  - 2007
SP  - 3
EP  - 24
VL  - 19
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2007_19_5_a0/
LA  - ru
ID  - MM_2007_19_5_a0
ER  - 
%0 Journal Article
%A A. N. Bogolyubov
%A N. A. Mosunova
%A D. A. Petrov
%T Mathematical models of chirowaveguides
%J Matematičeskoe modelirovanie
%D 2007
%P 3-24
%V 19
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2007_19_5_a0/
%G ru
%F MM_2007_19_5_a0
A. N. Bogolyubov; N. A. Mosunova; D. A. Petrov. Mathematical models of chirowaveguides. Matematičeskoe modelirovanie, Tome 19 (2007) no. 5, pp. 3-24. http://geodesic.mathdoc.fr/item/MM_2007_19_5_a0/

[1] B. Z. Katsenelenbaum, E. N. Korshunova, A. N. Sivov, A. D. Shatrov, “Kiralnye elektrodinamicheskie ob'ekty”, Phys. Usp., 40 (1997), 1201 | DOI

[2] A. Sihvola, M. Oksanen, F. Hujanen, “Broadband microwave measurement and analysis of artificial chiral material”, Proc. 24th European Microwave Conf. (Cannes, France, Sept.), 1994, 378–383

[3] A. F. Bahr, K. R. Clausing, “An approximate model for artificial chiral material”, IEEE Transactions on Antennas and Propagation, 42:12 (1994) | DOI | Zbl

[4] A. P. Vinogradov, A. V. Aivazyan, “Ob oshibochnosti ucheta kvadrupolnogo momenta pri raschete faktora kiralnosti”, Radiotekhnika i elektronika, 47:2 (2002), 192–195

[5] A. P. Vinogradov, “Microscopic Properties of a Chiral Object”, Proc. Bi-Anisotripics-93, 1993, 22–26

[6] V. V. Shevchenko, “Difraktsiya na maloi kiralnoi chastitse”, Radiotekhnika i elektronika, 40:12 (1995), 177–1789

[7] M. V. Kostin, V. V. Shevchenko, “On Electromagnetic Theory of Artificial Nonchiral and Chiral Media with Resonant Particles”, Advances in Complex Electromagnetic Materials, eds. A. Priou et al., Kluwer Acad. Publ., Dordrecht, 1997, 261–270

[8] K. F. Lindman, “Rotation polarisation of electromagnetic waves generated by the isotropic system of spiral resonators”, Annalen der Physik, 63 (1920), 621–644 | DOI

[9] A. N. Bogolyubov, N. A. Mosunova, D. A. Petrov, “Matematicheskoe modelirovanie kiralnykh volnoveduschikh sistem”, Elektronnyi zhurnal Radioelektroniki RAN, matematicheskie metody v zadachakh radioelektroniki, 2005, no. 7

[10] D. A. Petrov, “Kiralnye sredy, ikh svoistva i primenenie v sistemakh svyazi”, Mezhdunarodnyi forum informatizatsii (MFI-2004), Mezhdunarodnyi kongress (STN-2004), Telekommunikatsionnye i vychislitelnye sistemy, Trudy konferentsii, M., 2004, 238–239

[11] V. P. Modenov, I. V. Tsvetkov, “O prokhozhdenii elektromagnitnoi volny cherez kiralnyi sloi”, Elektrodinamika i tekhnika SVCh i KVCh, 7:3 (1999), 10

[12] V. K. Varadan, V. V. Varadan, A. Lakhtakia, “On the possibility of designing anti-reflection coatings using chiral composites”, J. Wave-Material Interaction, 2:1 (1987), 71–81

[13] H. Cory, I. Rosenhouse, “Minimisation of reflection coefficient at feed of radome-covered reflection an-tenna by chiral device”, Electron. Lett., 27:25 (1990), 2345–2347 | DOI

[14] D. L. Jaggard, J. C. Lui, A. Grot, P. Pelet, “Thin wire antennas in chiral media”, Electron. Lett., 27 (1991), 234–244 | DOI

[15] V. Ostroverkhov, O. Ostroverkhova, R. G. Petschek, K. D. Singer, L. Sukhomlinova, R. J. Twieg, “Prospects for chiral nonlinear optical media”, Selected Topics in Quantum Electronics IEEE Journal, 7:5 (2001), 781–792 | DOI

[16] V. I. Kopp, V. M. Churikov, J. Singer, N. Chao, D. Neugroschi, A. Z. Genack, “Chiral gratings in optical fiber”, Lasers and Electro-Optics Society, The 17th Annual Meeting of the IEEE (Leos, 2004), 2, 2004, 715–716 | MR

[17] S. A. Tretyakov, “Elektrodinamika slozhnykh sred: kiralnye, biizotropnye i nekotorye bianizotropnye materialy”, Radiotekhnika i elektronika, 39:10 (1994) | MR | Zbl

[18] A. Sihvola, M. Oksanen, F. Hujanen, “Broadband microwave measurement and analysis of artificial chiral material”, Proc. 24th European Microwave Conf. (Cannes, France, Sept.), 1994, 378–383

[19] F. Bahr, K. R. Clausing, “An approximate model for artificial chiral material”, IEEE Transactions on Antennas and Propagation, 42:12 (1994), 1592–1599 | DOI

[20] R. Brewitty-Taylor, P. G. Ledered, F. C. Smith, S. Haq., “Measurement and prediction of helix-loaded composites”, IEEE Transactions on Antennas and Propagation, 47:4 (1999) | DOI

[21] G. Busse, J. Reinent, A. F. Jacob, “Waveguide characterization of chiral material experiments”, IEEE Transactions on Microwave Theory and Technique, 47:3 (1999)

[22] Z. L. Liu, G. C. Sun, Q. L. Huang, K. L. Yao, “Circular waveguide method for measuring the electromagnetic parameters of chiral materials at microwave frequencies”, Meas. Sci. Technol., 10 (1999), 374–379 | DOI

[23] P. Pelet, N. Engheta, “The theory of chirowaveguides”, IEEE Trans. Antennas Propogat., 38 (1990), 90–98 | DOI | MR | Zbl

[24] Jianguo Xiao, Keqian Zhang, “Analysis of circular chiral dielectric waveguides”, International Journal of Infrared and Millimeter Waves, 19:3 (1998), 511–527 | DOI

[25] V. V. Fisanov, “O spektre voln ploskoparallelnogo kirovolnovoda”, Izvestiya vuzov, Radiofizika, 12:5 (2002), 406–410

[26] John Lekner, “Properties of a chiral slab waveguide”, Pure Appl. Opt., 6 (1997), 373–384 | DOI

[27] Haixin Zhou, Keqian Zhang, Jianguo Xiao, “Field analysis of a metal coated planar waveguide with chiral core”, International Journal of Infrared and Millimeter Waves, 20:8 (1999), 1549–1562 | DOI

[28] Keqian Zhang, Jianguo Xiao, Lian Gong, “Analysis of planar dielectric waveguide with chiral cladding”, International Journal of Infrared and Millimeter Waves, 19:9 (1998), 1275–1284 | DOI

[29] A. A. Samarskii, Teoriya raznostnykh skhem, Nauka, M., 1983 | MR

[30] A. N. Bogolyubov, A. V. Krasilnikova, D. V. Minaev, A. G. Sveshnikov, “Metod konechnykh raznostei dlya resheniya zadach sinteza volnoveduschikh sistem”, Matem. modelirovanie, 12:1 (2000), 13–24 | Zbl

[31] A. N. Bogolyubov, A. L. Delitsyn, A. V. Krasilnikova, D. V. Minaev, A. G. Sveshnikov, “Matematicheskoe modelirovanie volnoveduschikh sistem na osnove metoda konechnykh raznostei”, Zarubezhnaya radioelektronika. Uspekhi sovremennoi radioelektroniki, 1998, no. 5, 39–54 | MR

[32] S. G. Mikhlin, Chislennaya realizatsiya variatsionnykh metodov, Nauka, M., 1966 | MR

[33] V. P. Modenov, A. V. Romashin, “Skhema metoda Galerkina v zadache difraktsii dlya pryamougolnogo volnovoda s biizotropnoi vstavkoi. Prilozh. k zhurn.”, Fizika volnovykh protsessov i radiotekhnicheskie sistemy, 2004, 148–149

[34] V. P. Moodenov, “Waveguide filled with chiral medium calculation”, Proc VIII-th. International Conference on microwaves (MICON-2000) (Poland, Warsaw, 2000, May 22-24), 51–53

[35] V. P. Modenov, “O raschete metodom Galerkina postoyannykh rasprostraneniya v kiralnom volnovode s ferritovym sterzhnem”, Vych. metody i programmirovanie, 20 (1973), 50–56

[36] V. P. Modenov, “Binarnyi iteratsionnyi korrektor-protsess vychisleniya kompleksnykh kornei transtsendentnykh uravnenii”, Vestnik Moskovskogo Universiteta, Ser. 15, Vychislitelnaya matematika i kibernetika, 1985, no. 2, 63–65 | MR

[37] V. P. Modenov, A. V. Romashin, “Metod Galerkina v zadache na sobstvennye znacheniya dlya volnovoda s biizotropnym zapolneniem”, Elektrodinamika i tekhnika SVCh, KVCh i opticheskikh chastot, 12:3–4(40) (2004), 84–93

[38] V. P. Modenov, A. V. Romashin, I. V. Tsvetkov, “Raschet tsilindricheskikh volnovodov, zapolnennykh kiralnoi sredoi”, Fizika volnovykh protsessov i radiotekhnicheskie sistemy, 5:2 (2002), 56–58

[39] V. P. Modenov, A. V. Romashin, I. V. Tsvetkov, “Elektrodinamicheskii raschet volnovodov, zapolnennykh kiralnoi sredoi”, Elektrodinamika SVCh, KVCh i opticheskikh chastot, 10:2(34) (2002), 66–70

[40] G. I. Marchuk, V. I. Agoshkov, Vvedenie v proektsionno-setochnye metody, Nauka, M., 1981 | MR

[41] A. N. Bogolyubov, A. L. Delitsyn, A. V. Lavrenova, “Metod konechnykh elementov v zadachakh volnovodnoi difraktsii”, Elektromagnitnye volny, 9:8 (2004), 22–25

[42] A. N. Bogolyubov, I. A. Butkarev, D. V. Minaev, I. E. Mogilevskii, “Matematicheskoe modelirovanie volnoveduschikh sistem na osnove metoda konechnykh raznostei i metoda konechnykh elementov”, Radiotekhnika i elektronika, 50:2 (2005), 140–151