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NORMAL AND ANOMALOUS DISPERSION OF WEAKLY NONLINEAR LOCALIZED MODES IN PLATE OF LAYERED SUPERCONDUCTOR

heading: 
SOLID-STATE AND PLASMA RADIOPHYSICS
Apostolov, SS, Kadygrob, DV, Маizelis, ZA, Nikolaenko, AА, Shmat'ko, AA, Yampol’sk, ii, VA
Organization: 

O. Ya. Usikov Institute for Radiophysics and Electronics of the National Academy of Sciences of Ukraine
12, Proskura st., Kharkov, 61085, Ukraine

V. N. Karazin Kharkiv National University
4 Svobody Sq., Kharkiv, 61022, Ukraine
E-mail: yam@ire.kharkov.ua
https://doi.org/10.15407/rej2017.04.031
Language: Russian
Abstract: 

Weakly nonlinear localized electromagnetic modes in a plate of layered superconductor are theoretically studied. It is assumed that the plate is embedded in the uniform dielectric environment, the superconducting layers are perpendicular to the surface of the plate, and the modes propagate across the layers. Due to the strong anisotropy of the Josephson plasma in layered superconductors, localized modes can possess unusual dispersion properties.
The electromagnetic field in a layered superconductor is determined by the distribution of the gauge-invariant phase difference of the order parameter, which satisfies the system of coupled sin-Gordon equations. Based on the solution of these equations, as well as the Maxwell equations in the dielectric environment, dispersion relations can be obtained for localized electromagnetic modes.
It is established that the dispersion of such localized modes turns out to be anomalous in a certain range of parameters. In addition, the points on the dispersion curves are found, at which the group velocity of the modes can vanish. In addition, the nonlinearity leads to the fact that the dispersion relations contain the amplitude of the localized mode.
Due to the fact that in the nonlinear case the dispersion relations contain the amplitude of the localized mode, it is possible to observe the stop-light phenomenon for the localized modes in the layered superconductor plate.
Keywords: anomalous dispersion, layered superconductor, localized modes

Manuscript submitted 18.10.2017
PACS 52.35.Mw, 73.20.Mf, 74.72.-h​
Radiofiz. elektron. 2017, 22(4): 31-38
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References: 
  1. Kleiner, R., Steinmeyer, F., Kunkel, G., Muller, P., 1992. Intrinsic Josephson effects in Bi2Sr2CaCu2O8+d single crystals. Phys. Rev. Lett., 68(15), pp. 2394–2397. DOI:https://doi.org/10.1103/PhysRevLett.68.2394
  2. Brandt, E. H., 1995. The flux-line lattice in superconductors. Rep. Prog. Phys., 58(11), pp. 1465–1594. DOI:https://doi.org/10.1088/0034-4885/58/11/003
  3. Savel'ev, S., Yampol'skii, V. A., Rakhmanov, A. L., Nori, F., 2010. Terahertz Josephson plasma waves in layered superconductors: spectrum, generation, nonlinear and quantum phenomena. Rep. Prog. Phys., 73, pp. 026501 (49 p.). DOI:https://doi.org/10.1088/0034-4885/73/2/026501
  4.  Tonouchi, M., 2007. Cutting-edge terahertz technology. Nat. Photonics, 1(2), pp. 97–105. DOI:https://doi.org/10.1038/nphoton.2007.3
  5. Capasso, F., Gmachl, C., Sivco, D. L., Cho, A. Y., 2002. Quantum Cascade Lasers. Phys. Today, 55(5), pp. 34–40. DOI: https://doi.org/10.1063/1.1485582
  6.  Koshelets, V. P., Shitov, S.V., 2000. Integrated superconducting receivers. Supercond. Sci. Technol. 13(5), pp. R53–R69. DOI: https://doi.org/10.1088/0953-2048/13/5/201
  7. Kleiner, R., 2007. Filling the Terahertz Gap. Science. 318(5854), pp. 1254–1255. DOI:https://doi.org/10.1126/science.1151373
  8. Mills, D. L., 1998. Nonlinear optics: basic concepts. Berlin: Springer. DOI: https://doi.org/10.1007/978-3-642-58937-9
  9. Rajaraman, R., 1987. Solitons and Instantons: An Introduction to Solitons and Instantons in Quantum Field Theory. Amsterdam: North-Holland.
  10. Savel'ev, S., Rakhmanov, A. L., Yampol'skii, V. A., Nori, F., 2006. Analogs of nonlinear optics using Tera-Hertz Josephson plasma waves in layered superconductors. Nat. Physics, 2(8), pp. 521–525. DOI: https://doi.org/10.1038/nphys358
  11. Yampol'skii, V. A., Savel'ev, S., Slipchenko, T. M., Rakhmanov, A. L., Nori, F., 2008. Nonlinear Josephson plasma waves in slabs of layered superconductors. Physica C, 468(7), pp. 499–502. DOI: https://doi.org/10.1016/j.physc.2007.11.017
  12. Yampol'skii, V. A., Slipchenko, T. M., Mayzelis, Z. A., Kadygrob, D. V., Apostolov, S. S., Savel'ev, S. E., Nori, F., 2008. Hysteretic jumps in the response of layered superconductors to electromagnetic fields. Phys. Rev. B, 78(18), pp. 184504(1)–184504(6). DOI: https://doi.org/10.1103/PhysRevB.78.184504
  13. Savel'ev, S. E., Yampol'skii, V. A., Nori, F., 2007. Layered superconductors as nonlinear waveguides for terahertz waves. Phys. Rev. B, 75(18), pp. 184503 (8 p.). DOI: https://doi.org/10.1103/PhysRevB.75.184503
  14. Pendry, J. B., 2000. Negative Refraction Makes a Perfect Lens. Phys. Rev. Lett., 85(18), pp. 3966–3969. DOI:https://doi.org/10.1103/PhysRevLett.85.3966
  15. Shelby, R. A., Smith, D. R., Schultz, S., 2001. Experimental Verification of a Negative Index of Refraction. Science, 292(5514), pp. 77–79. DOI:https://doi.org/10.1126/science.1058847
  16. Veselago, V. G., 2003. Electrodynamics of materials with negative refractive index. Usp. fiz. nauk, 173(7), pp. 790–794 (in Russian).
  17. Rakhmanov, A. L., Yampol'skii, V. A., Fan, J. A., Capasso, F., Nori, F., 2010. Layered superconductors as negative-refractive-index metamaterials. Phys. Rev. B, 81(17), pp. 075101 (6 p.). DOI: 
    https://doi.org/10.1103/PhysRevB.81.075101
  18. Golick, V.A., Kadygrob, D. V., Yampol'skii, V. A., Rakhmanov, A. L., Ivanov, B. A., Nori, F., 2010. Surface Josephson Plasma Waves in Layered Superconductors above the Plasma Frequency: Evidence for a Negative Index of Refraction. Phys. Rev. Lett., 104(18), pp. 187003 (4 p.). DOI: https://doi.org/10.1103/PhysRevLett.104.187003
  19. Apostolov, S. S., Maizelis, Z. A., Yampol'skii, V. A., Havrilenko, V. I., 2017. Anomalous dispersion of surface and waveguide modes in layered superconductor slabs. Low Temp. Phys., 43(2), pp. 296–302. DOI: https://doi.org/10.1063/1.4977740
  20. Averkov, Yu. O., Yakovenko, V. M., Yampol'skii, V. A., Nori, F., 2013. Oblique surface Josephson plasma waves in layered superconductors. Phys. Rev. B, 87(5), pp. 054505 (8 p.). DOI: https://doi.org/10.1103/PhysRevB.87.054505
  21. Artemenko, S. N., Remizov, S. V., 2001. Stability, collective modes and radiation from sliding Josephson vortex lattice in layered superconductors. Physica C. 362(1–4), pp. 200–204. DOI: https://doi.org/10.1016/S0921-4534(01)00670-0
  22. Helm, Ch., Bulaevskii, L. N., 2002. Optical properties of layered superconductors near the Josephson plasma resonance. Phys. Rev. B. 66(9), pp. 094514 (23 p.). DOI: https://doi.org/10.1103/PhysRevB.66.094514
  23. Schmidt, V. V., 2000. Introduction to physics of superconductors. 2nd ed. Moscow: MCNMO (in Russian).
  24. Kosevich, А. М., Kovalev, А. S., 1989. Introduction to non-linear physical mechanics. Kyev: Nauk. dumka Publ. (in Russian).
  25. Landau, L. D., Lifshits, E. M., 2004. Theoretical physics. V. 1, Mechanics. 5th ed. Moscow: Fizmatlit Publ. (in Russian).