Spherical Bessel solutions of Maxwell’s equations in inhomogeneous rotationally symmetric media

  • Andrey V. Novitsky Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus https://orcid.org/0000-0001-9553-7318
  • Richard Jose Alvarez Rodriguez Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus
  • Vladimir M. Galynsky Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

Abstract

Matrix approach applied earlier for description of electromagnetic waves in homogeneous rotationally symmetric media is generalized to inhomogeneous bianisotropic media. We propose the general method to determine material parameters of inhomogeneous media depending on the electromagnetic wave’s profile. We consider an inverse problem which is the search of the material tensors of inhomogeneous rotationally symmetric media with predetermined electric and magnetic wave’s fields in the form of spherical Bessel functions. Functioning of the approach is demonstrated with a particular example. The approach can be applied to create the required response of the artificial medium (metamaterial) on the external radiation.

Author Biographies

Andrey V. Novitsky, Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

doctor of science (physics and mathematics), docent; professor at the department of theoretical physics and astrophysics, faculty of physics

Richard Jose Alvarez Rodriguez, Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

postgraduate student at the department of theoretical physics and astrophysics, faculty of physics

Vladimir M. Galynsky, Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

PhD (physics and mathematics); associate professor at the department of theoretical physics and astrophysics, faculty of physics

References

  1. Sarychev A. K., Shalaev V. M. Electrodynamics of metamaterials. Singapore, 2007.
  2. Smith D. R., Padilla W. J., Vier D. C., et al. Composite medium with simultaneously negative permeability and permittivity. Phys. Rev. Lett. 2000. Vol. 84, issue 18. P. 4184–4187.
  3. Veselago V. G. Elektrodinamika veshchestv s odnovremenno otritsatelʼnymi znacheniyami e i m [The electrodynamics of substances with simultaneously negative values of e and m]. Usp. f iz. nauk. 1967. Vol. 92. P. 517–526 (in Russ.).
  4. Fedotov V. A., Mladyonov P. L., Prosvirnin S. L., et al. Asymmetric propagation of electromagnetic waves through a planar chiral structure. Phys. Rev. Lett. 2006. Vol. 97, issue 16. Article ID 167401. DOI: 10.1103/PhysRevLett.97.167401.
  5. Pendry J. B., Schurig D., Smith D. R. Controlling electromagnetic fields. Science. 2006. Vol. 312, issue 5781. P. 1780–1782.
  6. Leonhardt U. Optical conformal mapping. Science. 2006. Vol. 312, issue 5781. P. 1777–1780.
  7. Pendry J. B., Fernández-Domínguez A. I., Luo Y., et al. Capturing photons with transformation optics. Nat. Phys. 2013. Vol. 9. P. 518–522.
  8. Fedorov V. Yu., Chanal M., Grojo D., et al. Accessing extreme spatiotemporal localization of high-power laser radiation through transformation optics and scalar wave equations. Phys. Rev. Lett. 2016. Vol. 117, issue 4. Article ID 043902.
  9. Yu N., Genevet P., Kats M. A., et al. Light propagation with phase discontinuities: generalized laws of reflection and refraction. Science. 2011. Vol. 334, issue 6054. P. 333–337.
  10. Chen H.-T., Taylor A. J., Yu N. A review of metasurfaces: physics and applications. Rep. Prog. Phys. 2016. Vol. 79, No. 7. Article ID 076401.
  11. Poddubny A., Iorsh I., Belov P., et al. Hyperbolic metamaterials. Nat. Photonics. 2013. Vol. 7. P. 958–967. DOI: 10.1038/nphoton.2013.243.
  12. Repan T., Lavrinenko A. V., Zhukovsky S. V. Dark-field hyperlens: Super-resolution imaging of weakly scattering objects. Opt. Express. 2015. Vol. 23, issue 19. P. 25350–25364. DOI: 10.1364/OE.23.025350.
  13. Kruk S. S., Wong Z. J., Pshenay-Severin E., et al. Magnetic hyperbolic optical metamaterials. Nat. Commun. 2016. Vol. 7. Article ID 11329. DOI: 10.1038/ncomms11329.
  14. Mirmoosa M. S., Kosulnikov S. Yu., Simovski C. R. Magnetic hyperbolic metamaterial of high-index nanowires. Phys. Rev. B. 2016. Vol. 94, issue 7. Article ID 075138. DOI: 10.1103/PhysRevB.94.075138.
  15. Slobozhanyuk A. P., Ginzburg P., Powell D. A., et al. Purcell effect in hyperbolic metamaterial resonators. Phys. Rev. B. 2015. Vol. 92, issue 19. Article ID 195127. DOI: 10.1103/PhysRevB.92.195127.
  16. Biehs S.-A., Lang S., Petrov A. Yu., et al. Blackbody theory for hyperbolic materials. Phys. Rev. Lett. 2015. Vol. 115, issue 17. Article ID 174301. DOI: 10.1103/PhysRevLett.115.174301.
  17. Javani M. H., Stockman M. I. Real and imaginary properties of epsilon-near-zero materials. Phys. Rev. Lett. 2016. Vol. 117, issue 10. Article ID 107404. DOI: 10.1103/PhysRevLett.117.107404.
  18. Frazer L. N. Use of the spherical layer matrix in inhomogeneous media. Geophys. J. Int. 1977. Vol. 50, No. 3. P. 743–749. DOI:10.1111/j.1365-246X.1977.tb01345.x.
  19. Babenko V. A., Astagyeva L. G., Kuzmin V. N. Electromagnetic scattering in disperse media: Inhomogeneous and anisotropic particles. Chichester, 2003.
  20. Kravtsov Yu. A., Kravtsov Yu. I. Geometricheskaya optika neodnorodnykh sred. Mosc., 1980 (in Russ.).
  21. Leonhardt U., Philbin T. G. Transformation optics and the geometry of light. Prog. Opt. 2009. Vol. 53. P. 69–152.
  22. Barkovskii L. M., Borzdov G. N., Lavrinenko A. V. Fresnel’s reflection and transmission operators for stratified gyroanisotropic media. J. Phys. A: Math. Gen. 1987. Vol. 20, No. 5. P. 1095–1106.
  23. Novitsky A. V., Barkovskii L. M. Operator matrices for describing guiding propagation in circular bianisotropic fibres. J. Phys. A: Math. Gen. 2005. Vol. 38, No. 2. P. 391– 404.
  24. Novitsky A. V., Barkovsky L. M. Matrix approach for light scattering from a multilayered rotationally symmetric bianisotropic sphere. Phys. Rev. A. 2008. Vol. 77, No. 2. Article ID 033849.
  25. Qiu C.-W., Li L.-W., Yeo T.-S., et al. Scattering by rotationally symmetric anisotropic spheres: Potential formulation and parametric studies. Phys. Rev. E. 2007. Vol. 75, issue 2. Article ID 026609.
  26. Fedorov F. I. Teoriya girotropii. Minsk, 1976 (in Russ.).
Published
2017-01-23
Keywords: anisotropic medium, metamaterials, propagation of electromagnetic waves
How to Cite
Novitsky, A. V., Rodriguez, R. J. A., & Galynsky, V. M. (2017). Spherical Bessel solutions of Maxwell’s equations in inhomogeneous rotationally symmetric media. Journal of the Belarusian State University. Physics, 1, 52-60. Retrieved from https://journals.bsu.by/index.php/physics/article/view/424
Section
Physics of Electromagnetic Phenomena