Izvestiya of Saratov University.

Physics

ISSN 1817-3020 (Print)
ISSN 2542-193X (Online)


For citation:

Davidovich M. V. Plasmon-polaritons Along the Asymmetric Hyperbolic Metamaterial. Izvestiya of Sarat. Univ. Physics. , 2019, vol. 19, iss. 4, pp. 288-303. DOI: 10.18500/1817-3020-2019-19-4-288-303

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
02.12.2019
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Russian
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Plasmon-polaritons Along the Asymmetric Hyperbolic Metamaterial

Autors: 
Davidovich Mikhail Vladimirovich, Saratov State University
Abstract: 

Background and Objectives: Plasmon-polaritons along a surface of bulk hyperbolic metamaterial and along a slab of such metamaterial with an arbitrary orientation of the crystallographic axis are considered (the axis in the polarization plane is an arbitrary angle with the direction of propagation). We use the rigorous approach based on Maxwell’s equations. The parameters of the hyperbolic metamaterial in the form of the effective dielectric constant tensor are determined by homogenization. The dielectric permittivity of metal layers is determined by the Drude–Lorentz model. The axis change is made using the rotation matrix of the coordinate system, and the effective permittivity tensor is transformed accordingly. The possibility of using graphene layers with the conductivity of a graphene sheet based on the Kubo model is considered. The conditions of existence of fast, slow, flowing, forward and backward plasmon-polaritons are found. Backward plasmon-polaritons correspond to a wave in which the phase velocity is opposite to the energy transfer velocity. Classification of waves is made both on the basis of calculation of Pointing vector, and by the solution of the dispersion equation and definition of signs of real and imaginary parts of a constant of propagation. The Fresnel formulas are also derived for the diffraction of a plane wave of arbitrary polarization on such a structure. Methods of analytical and numerical solution of dispersion equations are applied. Partial analytical solutions of dispersion equations are obtained. A new type of backward inverse plasmon-polaritons propagating along the flat boundary of a massive sample of a hyperbolic metamaterial with a vacuum, which does not exist for a solid metal sample, is found. The possibility of dispersion control by applying an external magnetic field is considered, as well as the possibility of plasmon-polariton amplification in waveguides from metamaterials with optically pumped graphene sheets, as well as in diffraction on plane-layered structures. Methods: We use the Maxwell equation, mode matching technique, the homogenization for hyperbolic metamaterials without spatial dispersion and construct the complex dispersion equation. We consider the asymmetric hyperbolic metamaterial with a rotated optical axis. The dispersion equation was solved analytically and numerically by the iterative method

Reference: 
  1. Guo Y., Newman W., Cortes C. L., Jacob Z. Applications of hyperbolic metamaterial substrates. Advances in OptoElectronics, 2012, Article ID 452502 (9 p.). DOI: https://doi.org/10.1155/2012/452502
  2. Guo Y., Jakob Z. Thermal hyperbolic metamaterials. Opt. Express, 2013, vol. 21, pp. 15014–15019.
  3. Cortes C. L., Newman W., Molesky S., Jacob Z. Quantum nanophotonics using hyperbolic metamaterials. Journal of Optics, 2012, vol. 14, no. 15, 063001 (15 p.).
  4. Guo Y., Cortes C., Molesky S., Jakob Z. Broadband super-Planckian thermal emission from hyperbolic metamaterials. Appl. Phys. Lett., 2012, vol. 101, 131106 (15 p.).
  5. Poddubny А., Iorsh I., Belov P., Kivshar Yu. Hyperbolic metamaterials. Nat. Photonics, 2013, vol. 7, no. 12, pp. 948–957.
  6. Noginov M., Lapine M., Podolskiy V., Kivshar Yu. Focus issue: hyperbolic metamaterials. Optics Express, 2013, vol. 21, no. 12, pp. 14895–14897.
  7. Drachev V. P., Podolskiy V. A., Kildishev A. V. Hyperbolic metamaterials: new physics behind a classical problem. Optics Express, 2013, vol. 21, iss. 12, pp. 15048– 1564.
  8. Shekhar P., Atkinson J., Zubin J. Hyperbolic metamaterials: fundamentals and applications. Nano Convergence, 2014, vol. 1, no. 1, pp. 1–16.
  9. 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, 053842 (11 p.).
  10. Zhukovsky S. V., Kidwai O., Sipe J. E. Physical nature of volume plasmon polaritons in hyperbolic metamaterials. Optics Express, 2013, vol. 21, iss. 12, pp. 14982–14987.
  11. Zapata-Rodriguez C. J., Miret J. J., Vukovic S., Belic M. R. Engineered surface waves in hyperbolic metamaterials. Opt. Express, 2013, vol. 21, no. 16, pp. 19113–19127.
  12. Nefedov I. S., Valagiannopoulos C. A., Hashemi S. M., Nefedov E. I. Total absorption in asymmetric hyperbolic media. Scientifi c Reports, 2013, vol. 3, 2662 (4 p.).
  13. Nefedov I. S., Melnikov L. A. Super-Planckian far-zone thermal emission from asymmetric hyperbolic metamaterials. Appl. Phys. Lett., 2014, vol. 105, no. 16, 161902 (5 p.).
  14. Davidovich M. V., Nefedov I. S. Spatiotemporal Dispersion and Waveguide Properties of 2DPeriodic Metallic Rod Photonic Crystals. Journal of Experimental and Theoretical Physics, 2014, vol. 118, no. 5, pp. 673–686.
  15. Ferrari L., Wu C. H., Lepage D., Zhang X., Liu Z. W. Hyperbolic metamaterials and their applications. Prog. Quantum Electron., 2015, vol. 40, pp. 1–40. DOI: https://doi.org/10.1016/j.pquantelec.2014.10.001
  16. Davidovich M. V. Plasmon Analysis and Homogenization in Plane Layered Photonic Crystals and Hyperbolic Metamaterials // Journal of Experimental and Theoretical Physics, 2016, vol. 123, no. 6, pp. 928–941.
  17. Li T., Khurgin J. B. Hyperbolic metamaterials: beyond the effective medium theory. Optica, 2016, vol. 3, iss. 12, pp. 1388–1396.
  18. Kristina K. H., Sreekanth K. V., Strangl G. Dyeembedded and nanopatterned hyperbolic metamaterials for spontaneous emission rate enhancement. Journal of the Optical Society of America B, 2016, vol. 33, no. 6, 1038 (6 p.).
  19. Peragut F., Cerutti L., Baranov A., Hugonin J. P., Taliercio T., De Wilde Y., Greffet J. J. Hyperbolic metamaterials and surface plasmon polaritons. Optica, 2017, vol. 4, iss. 11, pp. 1409–1415.
  20. Ferrari L. , Smalley J. S. T., Fainman Y., Liu Z. Hyperbolic metamaterials for dispersion-assisted directional light emission. Nanoscale, 2017, vol. 9, no. 26, pp. 9034–9048.
  21. Davidovich M. V. Hyperbolic Medium of Finite-Length Wires. Journal of Experimental and Theoretical Physics, 2018, vol. 127, no. 1, pp. 1–19. DOI: https://doi.org/10.1134/S1063776118070178
  22. Boardman A. D., Alberucci A., Assanto G., Grimalsky V. V., Kibler B., McNiff J., Nefedov I. S., Rapoport Yu. G., Valagiannopoulos C. A. Waves in hyperbolic and double negative metamaterials including rogues and solitons. Nanotechnology, 2017, vol. 28, 444001 (41 p.).
  23. Alù A., Silveirinha M. G., Salandrino A., Engheta N. Epsilon-Near-Zero (ENZ) Metamaterials and Electromagnetic Sources: Tailoring the Radiation Phase Pattern. Phys. Rev. B, 2007, vol. 75, 155410 (13 p.).
  24.  Vainstein L. A. Elektromagnitnye volny [Electromagnetic waves]. Moscow, Radio i svyaz’ Publ., 1988. 440 p. (in Russian).
  25. Davidovich M. V. Plasmons in multilayered plan-layered structures. Quantum Electronics, 2017, vol. 47, no. 6, pp. 567‒579. DOI: https://doi.org/10.1070/QEL16272
  26. Davidovich M. V. Backward and forward plasmons in symmetric structures. Proc. SPIE, 2018, vol. 10717. 1071714 (6 p.).
  27. Davidovich M. V. On the Condition for Transformation of a Fast Surface Wave into a Slow Surface Wave. Journal of Communications Technology and Electronics, 2018, vol. 63, no. 6, pp. 497–504. DOI: https://doi.org/10.1134/S106422691806005
  28. Davidovich M. V. Backward plasmon-polaritons in multilayered dissipative structures. Proc. SPIE, 2019, vol. 11066, 110660V (6 p.).
  29. Davidovich M. V. Dispersion of surface plasmons in structures with a conductive fi lm. Optics and Spectroscopy, 2019, vol. 126, no. 3, pp. 279–289.
  30. Hanson G.W. Dyadic Green’s functions and guided surface waves for a surface conductivity model of graphene. J. Appl. Phys., 2008, vol. 103, 064302 (8 p.).
  31. Falkovsky L.A., Varlamov A.A. Space-time dispersion of graphene conductivity. Eur. Phys. J., 2007, vol. B 56, pp. 281‒284.
  32. Lovat G., Hanson G. W., Araneo R., Burghignoli P. Semiclassical spatially dispersive intraband conductivity tensor and quantum capacitance of graphene. Phys. Rev. B, 2013, vol. 87, 115429 (11 p.).
  33. Dubinov A. A., Aleshkin V. Y., Mitin V., Otsuji T., Ryzhii V. Terahertz surface plasmons in optically pumped graphene structures. J. Phys.: Condens. Matter., 2011, vol. 23, 145302 (8 p.).
  34. 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, 075416 (6 p.).
  35. Kozina O. N., Melnikov L. A. Optical Characteristics of Asymmetrical Hyperbolic Metamaterials. Izv. Saratov Univ. (N. S.), Ser. Physics, 2019, vol. 19, iss. 2, pp. 122– 131 (in Russian). DOI: https://doi.org/10.18500/1817-3020-2019-19-2-122-131
  36. Davidovich M. V. Amplifi cation of optical and THZ surface plasmon-polaritons by electron beams. Proc. SPIE, 2019, vol. 11066, 1106614 (11 p.). DOI: https://doi.org/10.1117/12.2521234
  37. Lyashko E. I., Maimistov A. I. Linear guided waves in a hyperbolic planar waveguide. Dispersion relations. Quantum Electronics, 2015, vol. 45, no. 11, pp. 1050–1054.
  38. Lyashko E. I., Maimistov A. I. Modes of a nonlinear planar waveguide with a dielectric layer immersed in a hyperbolic medium. Quantum Electronics, 2017, vol. 47, no. 11, pp. 1053–1063.