No Access Submitted: 02 December 2013 Accepted: 22 January 2014 Published Online: 25 February 2014
Journal of Applied Physics 115, 083104 (2014); https://doi.org/10.1063/1.4865435
The exact dispersion relations of the transverse magnetic surface plasmons (SPs) supported by a graphene parallel plate waveguide (PPWG), surrounded on one or both sides by Kerr-type nonlinear media, are obtained analytically. It is shown that if self-focusing nonlinear materials are chosen as the surrounding media, the SPs localization length (LL) is decreased, while their propagation length (PL) remains unchanged, as compared to those of a typical graphene PPWG. Moreover, PL and LL of the SPs are considerably affected by adjusting nonlinear parts of the dielectric permittivities of the nonlinear media. It is found that using an appropriate defocusing nonlinear material as a substrate of the graphene PPWG, which is surrounded on one side by the nonlinear medium, leads to noticeable enhancement of the propagation and localization characteristics of the surface plasmons. The results presented here can be useful for enhancing capabilities of plasmonic devices based on the graphene PPWG for sensing and waveguide applications.
  1. 1. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666 (2004). https://doi.org/10.1126/science.1102896 , Google ScholarCrossref, ISI
  2. 2. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, and S. V. Dubonos, Nature (London) 438, 197 (2005). https://doi.org/10.1038/nature04233 , Google ScholarCrossref, ISI
  3. 3. Y. Zhang, J. P. Small, W. V. Pontius, and P. Kim, Appl. Phys. Lett. 86, 073104 (2005). https://doi.org/10.1063/1.1862334 , Google ScholarScitation, ISI
  4. 4. Y. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim, Nature 438, 201 (2005). https://doi.org/10.1038/nature04235 , Google ScholarCrossref, ISI
  5. 5. K. S. Novoselov, Z. Jiang, Y. Zhang, S. V. Morozov, H. L. Stormer, U. Zeitler, J. C. Maan, G. S. Boebinger, P. Kim, and A. K. Geim, Science 315, 1379 (2007). https://doi.org/10.1126/science.1137201 , Google ScholarCrossref, ISI
  6. 6. A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, Rev. Mod. Phys. 81, 109 (2009). https://doi.org/10.1103/RevModPhys.81.109 , Google ScholarCrossref, ISI
  7. 7. F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, Nature Photon. 4, 611 (2010). https://doi.org/10.1038/nphoton.2010.186 , Google ScholarCrossref, ISI
  8. 8. A. Vakil and N. Engheta, Science 332, 1291 (2011). https://doi.org/10.1126/science.1202691 , Google ScholarCrossref, ISI
  9. 9. F. H. L. Koppens, D. E. Chang, and F. J. Garcia de Abajo, Nano Lett. 11, 3370 (2011). https://doi.org/10.1021/nl201771h , Google ScholarCrossref, ISI
  10. 10. A. N. Grigorenko, M. Polini, and K. S. Novoselov, Nature Photon. 6, 749 (2012). https://doi.org/10.1038/nphoton.2012.262 , Google ScholarCrossref, ISI
  11. 11. M. Tamagnone, J. S. Gomez-Diaz, J. R. Mosig, and J. Perruisseau-Carrier, J. Appl. Phys. Lett. 101, 214102 (2012). https://doi.org/10.1063/1.4767338 , Google ScholarScitation
  12. 12. F. J. Garcia de Abajo, Science 339, 917 (2013). https://doi.org/10.1126/science.1231119 , Google ScholarCrossref
  13. 13. S. A. Mikhailov and K. Ziegler, Phys. Rev. Lett. 99, 016803 (2007). https://doi.org/10.1103/PhysRevLett.99.016803 , Google ScholarCrossref, ISI
  14. 14. G. W. Hanson, J. Appl. Phys. 103, 064302 (2008). https://doi.org/10.1063/1.2891452 , Google ScholarScitation, ISI
  15. 15. G. W. Hanson, A. B. Yakovlev, and A. Mafi, J. Appl. Phys. 110, 114305 (2011). https://doi.org/10.1063/1.3662883 , Google ScholarScitation, ISI
  16. 16. M. Jablan, H. Buljan, and M. Soljacic, Opt. Express 19, 11236 (2011). https://doi.org/10.1364/OE.19.011236 , Google ScholarCrossref
  17. 17. G. W. Hanson, J. Appl. Phys. 104, 084314 (2008). https://doi.org/10.1063/1.3005881 , Google ScholarScitation, ISI
  18. 18. M. Jablan, H. Buljan, and M. Soljacic, Phys. Rev. B 80, 245435 (2009). https://doi.org/10.1103/PhysRevB.80.245435 , Google ScholarCrossref, ISI
  19. 19. C. H. Gan, H. S. Chu, and E. P. Li, Phys. Rev. B 85, 125431 (2012). https://doi.org/10.1103/PhysRevB.85.125431 , Google ScholarCrossref, ISI
  20. 20. D. Svintsov, V. Vyurkov, V. Ryzhii, and T. Otsuji, J. Appl. Phys. 113, 053701 (2013). https://doi.org/10.1063/1.4789818 , Google ScholarScitation
  21. 21. P. I. Buslaev, I. V. Iorsh, I. V. Shadrivov, P. A. Belov, and Y. S. Kivshar, JETP Lett. 97, 535 (2013). https://doi.org/10.1134/S0021364013090063 , Google ScholarCrossref
  22. 22. H. Hajian, A. Soltani-Vala, and M. Kalafi, J. Appl. Phys. 114, 033102 (2013). https://doi.org/10.1063/1.4813415 , Google ScholarScitation, ISI
  23. 23. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Grating (Springer, Berlin, 1988). Google ScholarCrossref
  24. 24. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, Berlin, 2007). Google ScholarCrossref
  25. 25. Plasmonic Nanoguide and Circuits, edited by S. I. Bozhevolnyi (Pan Stanford, 2009). Google Scholar
  26. 26. V. M. Agranovich, V. S. Babichenko, and V. Y. Chernyak, JETP Lett. 32, 512 (1980). Available at: http://www.jetpletters.ac.ru/ps/1431/article_21789.shtml. Google Scholar
  27. 27. G. I. Stegeman, C. T. Seaton, J. Ariyasu, R. F. Wallis, and A. A. Maradudin, J. Appl. Phys. 58, 2453 (1985). https://doi.org/10.1063/1.335920 , Google ScholarScitation
  28. 28. J. Ariyasu, C. T. Seaton, G. I. Stegeman, A. A. Maradudin, and R. F. Wallis, J. Appl. Phys. 58, 2460 (1985). https://doi.org/10.1063/1.335921 , Google ScholarScitation
  29. 29. A. D. Boardman, A. A. Maradudin, G. I. Stegeman, T. Twardowski, and E. M. Wright, Phys. Rev. A 35, 1159 (1987). https://doi.org/10.1103/PhysRevA.35.1159 , Google ScholarCrossref
  30. 30. D. Mihalache, G. I. Stegeman, C. T. Seaton, E. M. Wright, R. Zanoni, A. D. Boardman, and T. Twardowski, Opt. Lett. 12, 187 (1987). https://doi.org/10.1364/OL.12.000187 , Google ScholarCrossref
  31. 31. Q. Chen and Z. H. Wang, Opt. Lett. 18, 260 (1993). https://doi.org/10.1364/OL.18.000260 , Google ScholarCrossref
  32. 32. J. H. Huang, R. Chang, P. T. Leung, and D. P. Tsai, Opt. Commun. 282, 1412 (2009). https://doi.org/10.1016/j.optcom.2008.12.025 , Google ScholarCrossref, ISI
  33. 33. A. R. Davoyan, I. V. Shadrivov, and Y. S. Kivshar, Opt. Express 16, 21209 (2008). https://doi.org/10.1364/OE.16.021209 , Google ScholarCrossref
  34. 34. A. R. Davoyan, I. V. Shadrivov, and Y. S. Kivshar, Opt. Express 17, 21732 (2009). https://doi.org/10.1364/OE.17.021732 , Google ScholarCrossref
  35. 35. A. R. Davoyan, I. V. Shadrivov, and Y. S. Kivshar, Opt. Lett. 36, 930 (2011). https://doi.org/10.1364/OL.36.000930 , Google ScholarCrossref
  36. 36. L. Wang, W. Cai, X. Zhang, and J. Xu, Opt. Lett. 37, 2730 (2012). https://doi.org/10.1364/OL.37.002730 , Google ScholarCrossref, ISI
  37. 37. A. Y. Nikitin, F. Guinea, F. J. Garcia-Vidal, and L. Martin-Moreno, Phys. Rev. B 84, 195446 (2011). https://doi.org/10.1103/PhysRevB.84.195446 , Google ScholarCrossref
  38. 38. D. A. Smirnova, A. V. Gorbach, I. V. Iorsh, I. V. Shadrivov, and Y. S. Kivshar, Phys. Rev. B 88, 045443 (2013). https://doi.org/10.1103/PhysRevB.88.045443 , Google ScholarCrossref, ISI
  39. 39. M. Liu, X. Yin, and X. Zhang, Nano Lett. 12, 1482 (2012). https://doi.org/10.1021/nl204202k , Google ScholarCrossref
  40. 40. V. Ryzhii, T. Otsuji, M. Ryzhii, V. G. Leiman, S. O. Yurchenko, V. Mitin, and M. S. Shur, J. Appl. Phys. 112, 104507 (2012). https://doi.org/10.1063/1.4766814 , Google ScholarScitation
  41. 41. L. A. Falkovsky and S. S. Pershoguba, Phys. Rev. B 76, 153410 (2007). https://doi.org/10.1103/PhysRevB.76.153410 , Google ScholarCrossref, ISI
  42. 42. L. A. Falkovsky, J. Phys.: Conf. Ser. 129, 012004 (2008) https://doi.org/10.1088/1742-6596/129/1/012004. Google ScholarCrossref
  43. 43. H. Hajian, A. Soltani-Vala, and M. Kalafi, Opt. Commun. 292, 149 (2013). https://doi.org/10.1016/j.optcom.2012.12.002 , Google ScholarCrossref
  44. 44. S. A. Mikhailov, Europhys. Lett. 79, 27002 (2007). https://doi.org/10.1209/0295-5075/79/27002 , Google ScholarCrossref
  45. 45. E. Hendry, P. J. Hale, J. Moger, A. K. Savchenko, and S. A. Mikhailov, Phys. Rev. Lett. 105, 097401 (2010). https://doi.org/10.1103/PhysRevLett.105.097401 , Google ScholarCrossref, ISI
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