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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: Henry van Driel
  • Vol. 27, Iss. 1 — Jan. 1, 2010
  • pp: 112–117

Plasmonic Bloch oscillations in metal heterowaveguide superlattices and metal waveguide arrays with graded width of guiding regions

Weihua Lin and Lin Chen  »View Author Affiliations

JOSA B, Vol. 27, Issue 1, pp. 112-117 (2010)

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We study the propagation of surface plasmon polaritons (SPPs) in nanoscale metal heterowaveguide superlattices and metal waveguide arrays (MWGAs), both realized by gradually increasing the width of guiding regions. Theoretical analysis of the transmission properties of SPPs passing through the metal heterowaveguide superlattices by the transfer matrix method reveals that the SPPs minibands and minigaps in the frequency domain exhibit a spatial tilting, implying the appearance of plasmonic Wannier–Stark ladders and the existence of time-resolved plasmonic Bloch oscillations (BOs) in the superlattices. The analytic results of the coupled wave theory show that SPPs periodically oscillate transversely in the MWGAs under conditions of multiple waveguide excitation as the behavior of spatial BOs. Numerical simulations of the dynamic evolution of SPPs in the superlattices and MWGAs by the finite-difference time-domain method demonstrate the analytical predications well.

© 2009 Optical Society of America

OCIS Codes
(230.7370) Optical devices : Waveguides
(240.6680) Optics at surfaces : Surface plasmons

ToC Category:
Optics at Surfaces

Original Manuscript: July 29, 2009
Revised Manuscript: October 29, 2009
Manuscript Accepted: November 27, 2009
Published: December 24, 2009

Weihua Lin and Lin Chen, "Plasmonic Bloch oscillations in metal heterowaveguide superlattices and metal waveguide arrays with graded width of guiding regions," J. Opt. Soc. Am. B 27, 112-117 (2010)

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  1. F. Bloch, “Uber die quantenmechanik der elektronen in kristallgittern,” Z. Phys. 52, 555-600 (1928).
  2. J. Feldmann, K. Leo, J. Shah, D. A. B. Miller, J. E. Cunningham, T. Meier, G. V. Plessen, A. Schulze, P. Thomas, and S. Schmitt-Rink, “Optical investigation of Bloch oscillations in a semiconductor superlattice,” Phys. Rev. B 46, 7252-7255 (1992). [CrossRef]
  3. V. G. Lyssenko, G. Valusis, F. Loser, T. Hasche, K. Leo, M. M. Dignam, and K. Kohler, “Direct measurement of the spatial displacement of bloch-oscillating electrons in semiconductor superlattices,” Phys. Rev. Lett. 79, 301-304 (1997). [CrossRef]
  4. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic crystals: Molding the Flow of Light, 2nd ed. (Princeton Univ., 2008).
  5. D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390, 671-673 (1997). [CrossRef]
  6. V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1, 41-48 (2007), and references therein. [CrossRef]
  7. C. M. de Sterke, J. E. Sipe, and L. A. W. Brophy, “Electromagnetic Stark ladders in waveguide geometries,” Opt. Lett. 16, 1141-1143 (1991). [CrossRef] [PubMed]
  8. U. Peschel, T. Pertsch, and F. Lederer, “Optical Bloch oscillations in waveguide arrays,” Opt. Lett. 23, 1701-1703 (1998). [CrossRef]
  9. G. Lenz, I. Talanina, and C. M. de Sterke, “Bloch oscillations in an array of curved optical waveguides,” Phys. Rev. Lett. 83, 963-966 (1999). [CrossRef]
  10. A. Kavokin, G. Malpuech, A. D. Carlo, P. Lugli, and F. Rossi, “Photonic Bloch oscillations in laterally confined Bragg mirrors,” Phys. Rev. B 61, 4413-4416 (2000). [CrossRef]
  11. G. Malpuech, A. Kavokin, G. Panzarini, and A. D. Carlo, “Theory of photon Bloch oscillations in photonic crystals,” Phys. Rev. B 63, 035108 (2001). [CrossRef]
  12. A. R. Davoyan, I. V. Shadrivov, A. A. Sukhorukov, and Yu. S. Kivshar, “Beam oscillations and curling in chirped periodic structures with metamaterials,” Phys. Rev. A 79, 013820 (2009). [CrossRef]
  13. C. M. de Sterke, J. N. Bright, P. A. Krug, and T. E. Hammon, “Observation of an optical Wannier-Stark ladder,” Phys. Rev. E 57, 2365-2369 (1998). [CrossRef]
  14. T. Pertsch, P. Dannberg, W. Elflein, A. Brauer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett. 83, 4752-4755 (1999). [CrossRef]
  15. R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillations,” Phys. Rev. Lett. 83, 4756-4759 (1999). [CrossRef]
  16. R. Sapienza, P. Costantino, D. Wiersma, M. Ghulinyan, C. J. Oton, and L. Pavesi, “Optical analogue of electronic Bloch oscillations,” Phys. Rev. Lett. 91, 263902 (2003). [CrossRef]
  17. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824-830 (2003), and references therein. [CrossRef] [PubMed]
  18. E. Ozbay, “Plasmonics: merging photonics and electronics nanoscale dimensions,” Science 311, 189-193 (2006), and references therein. [CrossRef] [PubMed]
  19. W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic nanolithography,” Nano Lett. 4, 1085-1088 (2004). [CrossRef]
  20. E. Altewischer, M. P. van Exter, and J. P. Woerdman, “Plasmon-assisted transmission of entangled photons,” Nature 418, 304-306 (2002). [CrossRef] [PubMed]
  21. B. Wang and G. P. Wang, “Surface plasmon polariton propagation in nanoscale metal gap waveguides,” Opt. Lett. 29, 1992-1994 (2004). [CrossRef] [PubMed]
  22. X. Fan and G. P. Wang, “Nanoscale metal waveguide arrays as Plasmon lenses,” Opt. Lett. 31, 1322-1324 (2006). [CrossRef] [PubMed]
  23. X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, “All-angle broadband negative refraction of metal waveguide arrays in the visible range: theoretical analysis and numerical demonstration,” Phys. Rev. Lett. 97, 073901 (2006). [CrossRef] [PubMed]
  24. W. Lin and G. P. Wang, “Metal heterowaveguide superlattices for a plasmonic analog to electronic Bloch oscillations,” Appl. Phys. Lett. 91, 143121 (2007). [CrossRef]
  25. W. Lin, X. Zhou, G. P. Wang, and C. T. Chan, “Spatial Bloch oscillations of plasmons in nanoscale metal waveguide arrays,” Appl. Phys. Lett. 91, 243113 (2007). [CrossRef]
  26. A. R. Davoyan, I. V. Shadrivov, A. A. Sukhorukov, and Yu. S. Kivshar, “Plasmonic Bloch oscillations in chirped metal-dielectric structures,” Appl. Phys. Lett. 94, 161105 (2009). [CrossRef]
  27. I. P. Kaminow, W. L. Mammel, and H. P. Weber, “Metal-clad optical waveguides: analytical and experimental study,” Appl. Opt. 13, 396-405 (1974). [CrossRef] [PubMed]
  28. B. Wang and G. P. Wang, “Plasmon Bragg reflectors and nanocavities on flat metallic surfaces,” Appl. Phys. Lett. 87, 013107 (2005). [CrossRef]
  29. G. P. Wang and B. Wang, “Metal heterostructure-based nanophotonic devices: finite-difference time-domain numerical simulations,” J. Opt. Soc. Am. B 23, 1660-1665 (2006). [CrossRef]
  30. A. Hosseini and Y. Massoud, “A low-loss metal-insulator-metal plasmonic bragg reflector,” Opt. Express 14, 11318-11323 (2006). [CrossRef]
  31. W. Lin, Y. Gu, and G. P. Wang, “Zener tunneling in plasmonic metal gap waveguide supplattices,” Appl. Phys. Lett. 93, 133118 (2008). [CrossRef]
  32. G. Mur, “Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagenic field equation,” IEEE Trans. Electromagn. Compat. 23, 377-382 (1981). [CrossRef]
  33. X. Wang and K. Kempa, “Negative refraction and subwavelength lensing in a polaritonic crystal,” Phys. Rev. B 71, 233101 (2005). [CrossRef]
  34. E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182, 539-554 (1969). [CrossRef]
  35. H. Raether, Surface Plasmons (Springer-Verlag, 1988), Chap. 2, p. 6.
  36. E.D.Palik, ed., Handbook of Optical Constants of Solids (Academic, 1985), Part 2, Chap. 1, p. 356.
  37. F. Y. Ye, T. Tian, and X. Q. Yang, Higher Mathematics, 2nd ed. (Higher Education Press, 1990), Chap. 11, p. 284.

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