M.V. Davidovich - Dr. Sc. (Phys.-Math.), Professor, Department of Radiotechnique and Electrodynamics, Saratov State University named after N.G. Chernyshevsky. E-mail: davidovichmv@info.sgu.ru

The types of equations written with respect to the electric fields, magnetic fields and vector potentials are given. The methods of conversion of some equations to others are introduces. The appropriate algorithms for problems of diffraction and tasks on eigenvalues based on iteration procedures for equations and functionals based on them have been considered. In the second part of the paper examines the quasi-static transition of the corresponding integral equation describing the localized plasmon in the metal particle. For the dielectric constant of the metal Drude-Lorentz formula is used. The equations are generalized to the periodic case of photonic and plasmonic crystals. For them the possibility of obtaining metamaterial with isotropic properties described by a scalar dielectric and magnetic permeability is analyzed. Some results for the resonant frequencies of localized plasmons and for the variance in the number of structures are obtained on the basis of such algorithms and presented.

 

1. Davidovich M.V. Analiz struktur fotoniki i nanoplazmoniki. CH. 1: Integralnye uravnenija // Radiotekhnika. 2016. № 7. S. 25−31.
2. Klimov V.V. Nanoplazmonika // UFN. 2008. T. 178. № 8. S. 875−880.
3. Klimov V.V. Nanoplazmonika. M.: Fizmatlit. 2009. 408 s.
4. Majjer S.A. Plazmonika. Teorija i prilozhenija. M.-Izhevsk: NIC Reguljarnaja i khaoticheskaja dinamika. 2011. 296 s.
5. Davidovich M.V. Fotonnye kristally: funkcii Grina. Integrodifferencialnye uravnenija, rezultaty modelirovanija // Izvestija VUZov. Radiofizika. 2006. T. 49. № 2. S. 150−163.
6. Davidovich M.V. Iteracionnye metody reshenija zadach ehlektrodinamiki. Saratov: Izd-vo Saratovskogo un-ta. 2014. 240 s.
7. Vinogradov A.P. EHlektrodinamika kompozitnykh materialov. M.: EHditorial URSS. 2001. 208 s.
8. Kamenetskii E.O., Sigalov M., Shavit R. Tellegen particles and magnetoelectric metamaterials // J. Appl. Phys. 2009. 105, 013537(1−15).
9. Belov P.A., Simovskijj K.R., Tretjakov S.A. Obratnye volny i otricatelnaja refrakcija v fotonnykh (ehlektromagnitnykh) kristallakh // Radiotekhnika i ehlektronika. 2004. T. 49. № 11. S. 1285−1294.
10. Davidovich M.V., Stefjuk JU.V. Iteracionnye metody i algoritmy dlja integralnykh uravnenijj diehlektricheskikh rezonatorov // Izvestija VUZov. Radiofizika. 2010. T. 53. № 4. S. 296−309.
11. Davidovich M.V. Vektornye ehlektricheskie i magnitnye potencialy v ehlektrodinamike sploshnykh sred // Radiotekhnika. 2014. № 10. S. 57−62.
12. Davidovich M.V. Iteracionnye metody reshenija zadach ehlektrodinamiki. Saratov: Izd-vo Saratovskogo un-ta. 2014. 240 s.
13. Davidovich M.V. Diehlektricheskie rezonatory: metod integralnykh i integrodifferencialnykh uravnenijj // Izvestija Saratovskogo universiteta. Novaja serija. Ser. Fizika. 2008. T. 8. № 1. S. 3−14.
14. Gastine M., Courtois L., Dormann J.L. Electromagnetic Resonances of Free Dielectric Spheres // IEEE Transactions on Microwave Theory and Techniques. 1967. V. 15. № 12. P. 694−700.