• Українська
  • English
  • Русский
ISSN 2415-3400 (Online)
ISSN 1028-821X (Print)

Localized modes in the layered superconductor samples

Apostolov, SS, Kadygrob, DV, Маizelis, ZA, Rokhmanova, TN, Shmat’ko, AA, Yampol’sk, ii, VA

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

E-mail: stapos@ukr.net, yam@ire.kharkov.ua 

V. N. Karazin Kharkiv National University
4 Svobody Sq., Kharkiv, 61022, Ukraine

Language: russian

Subject and purpose. In this review the propagation of electromagnetic waves localized near the boundary of a sample of a layered superconductor with layers either parallel or perpendicular to its surface is discussed. The results obtained in a number of papers studying the dispersion law for such waves are generalized, classified and supplemented. Due to the strong anisotropy and nonlinearity of the Josephson plasma in layered superconductors, localized waves can have unusual dispersion properties, and their excitation can be accompanied by unusual resonance phenomena.

Methods and methodology. 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.

Results. In samples of a layered superconductor, whose layers are parallel to its boundary, both surface waves and waveguide modes with normal dispersion can propagate. For samples, the layers in which are perpendicular to the boundary, the dispersion law depends on the angle of propagation of the waves relative to the superconducting layers. In this paper it is shown for the first time that waves localized in a layered superconductor plate have an anomalous dispersion for all directions of propagation, except propagation strictly along the layers. Dispersion curves for such waves can have points of maximum and/or minimum, which can lead to nontrivial effects (e.g., stopping of light or internal reflection). Also, the excitation of localized waves and the unusual resonant phenomena are discussed in the work.

Conclusions. Due to the strong anisotropy and nonlinearity of the layered superconductor, the dispersion laws for waves, localized both in semi-infinite samples and in plates have a number of interesting features that lead to new phenomena important for using in the physics of the terahertz range.

Keywords: anomalous dispersion, layered superconductor, localized waves

Manuscript submitted 01.10.2018
PACS: 52.35.Mw, 73.20.Mf, 74.72.-h
Radiofiz. elektron. 2018, 23(4): 55-66
Full text  (PDF)

  1. Kamihara, Y., Hiramatsu, H., Hirano, M., Kawamura, R., Ya-nagi, H., Kamiya, T., Hosono, H., 2006. Iron-based layered supercon-ductor: LaOFeP. J. Am. Chem. Soc., 128(31), pp. 10012–10013. DOI: https://dx.doi.org/10.1021/ ja063355c
  2. 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
  3. Wait, J. R., 1985. Electromagnetic Wave Theory. New York, Harper and Row. 
  4. Mills, D. L., 1998. Nonlinear optics: basic concepts. Berlin: Springer.
  5. Rajaraman, R., 1987. Solitons and Instantons: An Introduction to Solitons and Instantons in Quantum Field Theory. Amsterdam: North-Holland.
  6. Tonouchi, M., 2007. Cutting-edge terahertz technology. Nat. Photonics, 1(2), pp. 97–105. https://doi.org/10.1038/ nphoton.2007.3
  7. 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
  8. 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
  9. Kleiner, R., 2007. Filling the Terahertz Gap. Science, 318(5854), pp. 1254–1255. DOI:https://dx.doi.org/10.1126/ science.1151373
  10. 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(2), pp. 026501 (9 p.). DOI: https://doi.org/10.1088/0034-4885/73/2/026501
  11. Yampol’skii, V. A., Kats, A. V., Nesterov, M. L., Nikitin, A. Yu., Slipchenko, T. M., Savel’ev, S., Nori, F., 2009. Resonance effects due to the excitation of surface Josephson plasma waves in layered superconductors. Phys. Rev. B., 79(21), pp. 214501 (8 p.). DOI:https:// doi.org/10.1103/PhysRevB.79.214501
  12. 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
  13. Slipchenko, T. M., Kadygrob, D. V., Bogdanis D., Yampol'skii, V. A., Krokhin, A. A., 2011. Surface and waveguide Josephson plasma waves in slabs of layered superconductors. Phys. Rev. B, 84(22), pp. 224512(8 p.). DOI: https://doi.org/10.1103/PhysRevB.84.224512
  14. Apostolov, S. S., Maizelis, Z. A., Sorokina, M.A., Yampol'skii, V. A., 2010. Nonlinear wood anomalies in the reflectivity of layered superconductors. Low Temp. Phys., 36(3), pp. 255–261. DOI: https://doi.org/10.1063/ 1.3331418
  15. Averkov, Yu. O., Yakovenko, V. M., Yampol’skii, V. A., Nori, F., 2012. Conversion of Terahertz Wave Polarization at the Boundary of a Layered Supercondutor due to the Resonance Excitation of Oblique Surface Waves. Phys. Rev. Lett., 109(2), pp. 027005 (5 p.). DOI:https:// doi.org/10.1103/PhysRevLett.109.027005
  16. 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
  17. Yampol'skii, V. A., Gulevich, D. R., Savel'ev, S., Nori, F., 2008. Surface plasma waves across the layers of intrinsic Josephson junctions, Phys. Rev. B, 78(5), pp. 054502 (4 p.). DOI:https://doi.org/10.1103/PhysRevB. 78.054502
  18. Kadygrob, D. V., Golick, V. A., Yampol'skii, V. A., Slipchenko, T. M., Gulevich, D. R., Savel'ev, S., 2009. Excitation of surface plasma waves across the layers of intrinsic Josephson junctions, Phys. Rev. B, 80(18), pp. 184512 (10 p.). DOI:https://doi.org/10.1103/PhysRevB. 80.184512
  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. Apostolov, S. S., Kadygrob, D.V., Maizelis, Z. A., Nikolaenko, A. A., Shmat'ko, A. A., Yampol’skii, V. A., 2017. Normal and anomalous dispersion of weakly nonlinear localized modes in plate of layered superconductor. Radiofiz. elektron.22(4), pp. 31–38. DOI: https://doi.org/10.15407/rej2017.04.031
  21. Apostolov, S. S., Kadygrob, D. V., Maizelis, Z. A., Nikolaenko, A. A., Yampol’skii, V. A., 2018. Nonlinear localized modes in a plate of a layered superconductor. Low Temp. Phys., 44(3), pp. 238–246. DOI: https:// doi.org/10.1063/1.5024544
  22. Rokhmanova, T., Apostolov, S. S., Kvitka, N.,
    Yampol’skii, V. A., 2018. Effect of a dc magnetic field on the anomalous dispersion of localized josephson plasma modes in layered superconductors. Low Temp. Phys., 44(6), pp. 552–560. DOI:https://doi.org/10.1063/ 1.5037558
  23. Apostolov, S. S., Makarov, N. M., Yampol’skii, V. A., 2018. Excitation of terahertz modes localized on a layered superconductor: Anomalous dispersion and resonant transmission. Phys. Rev. B, 97(2), pp. 024510(11 p.). DOI: https://doi.org/10.1103/PhysRevB.97.024510
  24. 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 
  25. 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