M. V. Davidovich – Dr.Sc. (Phys.-Math.), Professor, Department of Radiotechnique and Electrodynamics, Saratov State University n.a. N.G. Chernyshevsky

E-mail: davidovichmv@info.sgu.ru

V. P. Meschanov – Dr.Sc. (Eng.), Professor, Director of “NIKA-Microwave”, Ltd. (Saratov) E-mail: nika373@bk.ru

The flat and non-planar configuration of complex (with complicated configuration) metasurfaces, the transverse size which is small compared to wavelength, described by the tensor of surface conductivity have been considered. We used the method of tensor electrodynamic Green’s functions, linking the fields and current densities, and the method of integral equations for forward and backward plasmons.

1. Yu N., Capasso F. Flat optics with designer metasurfaces // Nat. Mater. 2014. V. 13. № 2. P. 139‒150.
2. Li Z., Yao K., Xia F., Shen S., Tian J., Liu Y. Graphene plasmonic metasurfaces to steer infrared light // Scientific Rep. 2015. V. 5. 12423.
3. Lu F., Liu B., Shen S. Infrared wavefront control based on graphene metasurfaces // Adv. Opt. Mater. 2014. V. 2. № 8. P. 794‒799.
4. Kildishev A.V., Boltasseva A., Shalaev V.M. Planar photonics with metasurfaces // 2013. V. 339. 1232009.
5. Yao K., Liu Y. Plasmonic metamaterials // Nanotech. Rev. 2014. V. 3. P. 177–210.
6. Sun S., He Q., Xiao S., Xu Q., Li X., Zhou L. Gradient-index meta-surfaces as a bridge linking propagating waves and surface waves // 2012. V. 11. № 5. P. 426‒431.
7. Liu Y., Zhang X. Metasurfaces for manipulating surface plasmons // Appl. Phys. Lett. 2013. V. 103. 141101.
8. Huang L., Chen X., Bai B., Tan Q., Jin G., Zentgraf T., Zhang S. Helicity dependent directional surface plasmon polariton excitation using a metasurface with interfacial phase discontinuity // Light: Sci. and Appl. 2013. V. 2, e70.
9. Munk B.A. Frequency selective surfaces: theory and design. N.Y.: John Wiley & Sons, Inc. 2000.
10. Yin X., Ye Z., Rho J., Wang Y., Zhang X. Photonic spin Hall effect at metasurfaces // Science. 2013. V. 339. P. 1405–1407.
11. Chen X., Huang L., Mühlenbernd H., Li G., Bai B., Tan Q., Jin G., Qiu C.W., Zhang S., Zentgraf T. Reversible three-dimensional focusing of visible light with ultrathin plasmonic flat lens // Adv. Optical Mater. 2013. V. 1. P. 517–521.
12. Pors A., Nielsen M.G., Eriksen R.L., Bozhevolnyi S.I. Broadband focusing flat mirrors based on plasmonic gradient metasurfaces // Nano Lett. 2013. V. 13. P. 829–834.
13. Ni X., Kildishev A.V., Shalaev V.M. Metasurface holograms for visible light // Nat. Commun. 2013. V. 4. № 2807. P. 1–6.
14. Bao Q., Loh K.P. Graphene photonics, plasmonics, and broadband optoelectronic devices // ACS Nano. 2012. V. 6. P. 3677–3694.
15. Yan H.G., Li X.S., Chandra B., Tulevski G., Wu Y.Q., Freitag M., Zhu W.J., Avouris P., Xia F.N. Tunable infrared plasmonic devices using graphene/insulator stacks // Nat. Nanotech. 2012. V. 7. P. 330–334.
16. Gomez-Diaz J.S., Tymchenko M., Alù A. Hyperbolic metasurfaces: surface plasmons, light-matter interactions, and physical implementation using graphene strips // Opt. Mater. Express. 2015. V. 5. № 10. P. 2313‒2329.
17. Davidovich M.V. Fotonnye kristally: funkcii Grina, integrodifferencial'nye uravneniya, rezul'taty modelirovaniya // Izvestiya VUZov. Radiofizika. 2006. T. 49. № 2. S. 150‒163.
18. Fal'kovskij L.A. Dinamicheskie svojstva grafena // ZhE'TF. 2012. T. 142. № 3. S. 560‒573.
19. Slepyan G.Ya., Maksimenko S.A., Lakhtakia L., Yevtushenko O., Gusakov A.V. Electrodynamics of carbon nanotubes: Dynamic conductivity, impedance boundary conditions, and surface wave propagation // Phys. Rev. 1999. V. B 60. № 24. P. 17136–17149.
20. Hanson G.W. Dyadic Green’s functions and guided surface waves for a surface conductivity model of graphene // J. Applied Physics. 2008. V. 103. 064302.
21. Maksimenko S.A., Slepyan G.Ya. Electrodynamic properties of carbon nanotubes / In Electromagnetic Fields in Unconventional Structures and Materials. Ed. by O.N. Singh and A. Lakhtakia. New York: John Wiley & Sons, Inc. 2000. P. 217–255.
22. Maksimenko S., Slepyan G. Electrodynamics of carbon nanotubes // J. Commun. Technol. Electron. 2002. V. 47. № 3. P. 235–252.
23. Lovat G., Hanson G.W., Araneo R., Burghignoli P. Semiclassical spatially dispersive intraband conductivity tensor and quantum capacitance of graphene // Phys. Rev. 2013. V. B 87. № 11. 115429.
24. Economou E.N. Surface plasmons in thin films // Phys. Rev. 1969. V. 182. P. 539–554.
25. Stern F. Polarizability of two-dimensional electron gas // Phys. Rev. Letters. 1967. V. 18. P. 546–548.
26. Tournois P., Laud V. Negative group velocities in metal-film optical waveguides // Opt. Comm. 1997. V. 137. P. 41‒45.
27. Ritchie R.H. Plasma losses by fast electrons in thin films // Phys. Rev. 1957. V. 106. P. 874‒881.
28. Markov G.T., Chaplin A.F. Vozbuzhdenie e'lektromagnitnykh voln. M: Radio i svyaz'. 1983.
29. Mikhailov S.A., Ziegler K. New electromagnetic mode in graphene // Phys. Rev. Letters. 2007. V. 99. 016803.
30. Davidovich M.V. Vtekayushchie i vytekayushchie nesobstvennye mody ‒ analiz dissipativnykh dispersionnykh uravnenij i volna Cenneka. Saratov: Izd-vo Saratovskogo un-ta. 2014.
31. Nikol'skij V.V. Variacionnye metody dlya vnutrennikh zadach e'lektrodinamiki. M.: Nauka. 1967.