Izvestiya of Saratov University.


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ISSN 2542-193X (Online)

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Kozina O. N., Melnikov L. A. Optical Characteristics of Asymmetrical Hyperbolic Metamaterials. Izvestiya of Sarat. Univ. Physics. , 2019, vol. 19, iss. 2, pp. 122-131. DOI: 10.18500/1817-3020-2019-19-2-122-131

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Optical Characteristics of Asymmetrical Hyperbolic Metamaterials

Kozina Olga Nikolaevna, Saratov Branch of Kotel’nikov Institute of Radio Engineering and Electronics of the Russian Academy of Sciences
Melnikov Leonid Arkad'evich, Saratov State Technical University named after Yuri Gagarin

Background and Objectives: Metamaterials, which are artificial structures with specified properties, keep the interest to nest investigations and creation of new types of them due to their unusual properties. One of the promising variant of the metamaterials is hyperbolic metamaterials (HMM) which exhibit the hyperbolic-type dispersion in the space of wave-vectors and are described by the diagonal extremely anisotropic permittivity tensor. Here we investigated optical properties of asymmetrical hyperbolic metamaterial (AHMM) consisting of periodically arranged layers (or wires) in a host media, titled relatively to the outer boundary. The most important feature of AHMM is the possibility to excite a very slow wave in AHMM by a plane wave, incoming from free space, while a minimal reflection may be achieved. We calculated spectral characteristics of the AHMM at different values of parameters of the structure. Methods: We have used the algorithm for solving of the Maxwell equation based on the Berreman 4x4 matrix which is convenient for the investigation of the propagation of polarized light in anisotropic media. We have adopted this method for the system when active atoms or ions are embedded into the medium for the calculations of light propagation in AHMM slabs which is infinite in the x and y-direction and has a finite-thickness in the z direction. Anisotropy of the hyperbolic media slab was taken into account. We use the effective medium model. Results: The transmittance and reflectance were calculated for different orientation of optical axis, angles of incidence and THz field frequencies in the AHMM with graphene layers. Spectral characteristics of reflection and transmission are presented. We have shown that huge resonances in transmittance and reflectance observed near 5 THz for different values of the incident angles which characterized a huge amplification in the AHMM. The effects of changing in the structure parameters have been demonstrated.


1. Smolyaninov Igor I., Smolyaninova Vera N. Hyperbolic metamaterials: Novel physics and applications. Solid-State Electronics, 2017, vol. 136, pp. 102–112.

2. Fedorov F. I. Optica anisotropnih sred [Optics of the anisotropic medium]. Minsk, AS BSSR, 1958. 381 p. (in Russian).

3. Felsen L., Marcuvitz N. Radiation and Scattering of Waves. Englewood Cliffs, N. J., Prentice-Hall, USA, 1973. 888 p.

4. Cortes C. L., Newman W., Molesky S., Jacob Z. Quantum nanophotonics using hyperbolic metamaterials. J. Opt., 2012, vol. 14, pp. 063001–063016.

5. Poddubny Alexander, Iorsh Ivan, Belov Pavel, Kivshar Yuri. Hyperbolic metamaterials. Nature photonics, 2013, vol. 7, pp. 958–967.

6. Iorsh I. V., Mukhin I. S., Shadrivov I. V., Belov P. A., Kivshar Y. S. Hyperbolic metamaterials based on multilayer graphene structures. Phys. Rev. B., 2013, vol. 87, pp. 075416.

7. Simovski C. R., Belov P. A., Atrashchenko A. V., Kivshar Y. S. Wire Metamaterials: Physics and Applications. Adv. Mater., 2012, vol. 24, pp. 4229–4248.

8. Melnikov L. A., Kozina O. N., Zotkina A. S., Nefedov I. S. Optical characteristics of the metal-wire dielectric periodic structure: hyperbolic eigenwaves. Proc. SPIE 9031, 2014, pp. 903117–903122.

9. Nefedov I. S., Valaginnopoulos C. A., Melnikov L. A. Perfect absorption in graphene Multilayers. J. Opt., 2013, vol. 15, pp. 114003(6).

10. Nefedov I., Melnikov L. Plasmonic Terahertz Amplification in Graphene-Based Asymmetric Hyperbolic Metamaterial. Photonics, 2015, vol. 2, iss. 2, pp. 594–603.

11. Berreman D. W. Optics in stratifi ed and anisotropic media: 4 x 4-matrix formulation. Journal of the Optical Society of America, 1972, vol. 62, no. 4, pp. 1157–1160.

12. Palto S. P. An Algorithm for Solving the Optical Problem for Stratifi ed Anisotropic Media. Journal of Experimental & Theoretical Physics, 2001, vol. 92, no. 4, pp. 552.

13. Korn G., Korn T. Spravochnik po matematike dlya nauchnih rabotnikov i enzhenerov [Math Handbook for Scientists and Engineers]. Moscow, Nauka Publ., 1973. 720 p. (in Russian).

14. Forbeaux I., Themlin J. M., Debever J. M. Heteroepitaxial graphite on 6HSiC(0001): interface formation through conduction-band electronic structure. Phys. Rev. B, 1998, vol. 58, pp. 16396–16406.

15. Amjadipour M., MacLeod J., Lipton-Duffi n J., Iacopi F., Motta N. Epitaxial graphene growth on FIB patterned 3C-SiC nanostructures on Si (111): reducing milling damage. Nanotechnology, 2017, vol. 28, iss. 34, pp. 345602.

16. Kidwai O., Zhukovsky S. V., Sipe J. E. Effective-medium approach to planar multilayer hyperbolic metamaterials: Strengths and limitations. Phys. Rev. A., 2012, vol. 85, pp. 053842(13).

17. Ritov S. M. Electromagnitnie svoistva melkosloistoy sredi [Electromagnetic properties of a thin layer medium]. SZETV [Jornal of Experimental and Theoretical Physics], 1955, vol. 29, no. 5, pp. 605–616 (in Russian).

18. Dubinov A. A., Aleshkin V. Ya., Mitin V., Otsuji T., Ryzhii V. Terahertz surface plasmons in optically pumped graphene structures. J. Phys. Condens. Matter., 2011, vol. 23, pp.145302.

19. Popov V. V., Polischuk O. V., Davoyan A. R., Ryzhii V., Otsuji T., Shur M. S. Plasmonic terahertz lasing in an array of graphene nanocavities. Phys. Rev. B, 2012, vol. 86, pp. 195437.

20. Ryzhii V., Ryzhii M., Otsuji T. Negative dynamic conductivity of graphene with optical pumping. Journal of Applied Physics, 2007, vol. 101, pp. 083114.

21. Mutschke H., Andersen A. C., Clement D., Henning Th., Peiter G. Infrared properties of SiC particles. Astron. Astrophys, 1999, vol. 345, pp. 87–104.

22. Chen J., Levine Z. H., Wilkins J. W. Linear and nonlinear optical properties of four polytypes of SiC. Phys. Rev. B, 1994, vol. 50, iss. 16, pp. 11514.