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Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Editor: Henry M. Van Driel
  • Vol. 24, Iss. 10 — Oct. 1, 2007
  • pp: 2632–2639

Optical Bloch oscillations in general waveguide lattices

Alexander Szameit, Thomas Pertsch, Stefan Nolte, Andreas Tünnermann, Ulf Peschel, and Falk Lederer  »View Author Affiliations


JOSA B, Vol. 24, Issue 10, pp. 2632-2639 (2007)
http://dx.doi.org/10.1364/JOSAB.24.002632


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Abstract

We study the dynamics of excitations in general two-dimensional (2D) lattices with an external spatial linear potential. Analytical expressions for the energy eigenspectrum (Wannier–Stark ladder) and the eigenstates (Wannier–Stark states) of the lattice Schrödinger equation are given, and the resulting periodic motion of localized excitations (Bloch oscillations) is investigated for arbitrary excitation, including single site and broad beam excitation.

© 2007 Optical Society of America

OCIS Codes
(130.3120) Integrated optics : Integrated optics devices
(230.7370) Optical devices : Waveguides

ToC Category:
Integrated Optics

History
Original Manuscript: June 14, 2007
Revised Manuscript: July 10, 2007
Manuscript Accepted: July 25, 2007
Published: September 19, 2007

Citation
Alexander Szameit, Thomas Pertsch, Stefan Nolte, Andreas Tünnermann, Ulf Peschel, and Falk Lederer, "Optical Bloch oscillations in general waveguide lattices," J. Opt. Soc. Am. B 24, 2632-2639 (2007)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-24-10-2632


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References

  1. C. Zener, "A theory of the electrical breakdown of solid dielectrics," Proc. R. Soc. London, Ser. A 145, 523-529 (1934). [CrossRef]
  2. D. Dunlap and V. Kenkre, "Dynamic localization of a charged particle moving under the influence of an electric field," Phys. Rev. B 34, 3625-3633 (1986). [CrossRef]
  3. G. Nenciu, "Dynamics of band electrons in electric and magnetic fields: rigorous justification of the effective Hamiltonians," Rev. Mod. Phys. 63, 92-127 (1991). [CrossRef]
  4. E. Mendez and G. Bastard, "Wannier-Stark ladders and Bloch oscillations in superlattices," Phys. Today 46, 34-42 (1993). [CrossRef]
  5. J. Feldmann, K. Leo, J. Shah, D. Miller, J. Cunningham, T. Meier, G. von 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]
  6. G. Wannier, "Wave functions and effective Hamiltonian for Bloch electrons in an electric field," Phys. Rev. 117, 432-439 (1960). [CrossRef]
  7. E. Mendez, F. Agull-Rueda, and J. Hong, "Stark localization in GaAs-GaAlAs superlattices under an electric field," Phys. Rev. Lett. 60, 2426-2429 (1988). [CrossRef] [PubMed]
  8. H. K. D. Witthaut, F. Keck, and S. Mossmann, "Bloch oscillations in two-dimensional lattices," New J. Phys. 6, 1-18 (2004). [CrossRef]
  9. J. Yellin, "Two exact lattice propagators," Phys. Rev. E 52, 2208-2215 (1995). [CrossRef]
  10. F. Keck and H. Korsch, "Infinite-variable Bessel functions in two-dimensional Wannier-Stark systems," J. Phys. A 35, 105-116 (2002). [CrossRef]
  11. D. W. S. Mossmann, A. Schulze, and H. Korsch, "Two-dimensional Bloch oscillations: a Lie-algebraic approach," J. Phys. A 38, 3381-3395 (2005). [CrossRef]
  12. M. Glueck, A. Kolovsky, and H. Korsch, "Wannier-Stark resonances in optical and semiconductor superlattices," Phys. Rep. 366, 103-182 (2002). [CrossRef]
  13. C. Waschke, H. Roskos, R. Schwedler, K. Leo, H. Kurz, and K. Koehler, "Coherent submillimeter-wave emission from Bloch oscillations in a semiconductor superlattice," Phys. Rev. Lett. 70, 3319-3322 (1993). [CrossRef] [PubMed]
  14. D. Cai, N. Gronbech-Jensen, A. Bishop, and M. Salerno, "Electric-field-induced nonlinear Bloch oscillations and dynamical localization," Phys. Rev. Lett. 74, 1186-1189 (1995). [CrossRef] [PubMed]
  15. M. B. Dahan, E. Peik, J. Reichel, Y. Castin, and C. Salomon, "Bloch oscillations of atoms in an optical potential," Phys. Rev. Lett. 76, 4508-4511 (1996). [CrossRef] [PubMed]
  16. M. Raizen, Q. Niu, and C. Salomon, "New light on quantum transport," Phys. Today 50, 30-34 (1997). [CrossRef]
  17. A. Kolovsky and H. Korsch, "Bloch oscillations of cold atoms in two-dimensional optical lattices," Int. J. Mod. Phys. B 18, 1235-1260 (2004). [CrossRef]
  18. A. Kolovsky and H. Korsch, "Bloch oscillations of cold atoms in two-dimensional optical lattices," Phys. Rev. A 67, 063601 (2003). [CrossRef]
  19. C. de Sterke, J. Bright, P. Krug, and T. Hammon, "Observation of an optical Wannier-Stark ladder," Phys. Rev. E 57, 2365-2370 (1998). [CrossRef]
  20. U. Peschel, T. Pertsch, and F. Lederer, "Optical Bloch oscillations in waveguide arrays," Opt. Lett. 23, 1701-1703 (1998). [CrossRef]
  21. R. Morandotti, U. Peschel, J. Aitchinson, H. Eisenberg, and Y. Silberberg, "Experimental observation of linear and nonlinear optical Bloch oscillations," Phys. Rev. Lett. 83, 4756-4759 (1999). [CrossRef]
  22. T. Pertsch, P. Dannberg, W. Elflein, A. Braeuer, and F. Lederer, "Optical Bloch oscillations in temperature tuned waveguide arrays," Phys. Rev. Lett. 83, 4753-4755 (2004).
  23. H. Trompeter, W. Krolikowski, D. Neshev, A. Desyatnikov, A. Sukhorukov, Y. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, "Bloch oscillations and Zener tunneling in two-dimensional photonic lattices," Phys. Rev. Lett. 96, 053903 (2006). [CrossRef] [PubMed]
  24. A. Yariv, Optical Electronics, 4th ed. (Saunders College Publishers, 1991).
  25. A. Szameit, T. Pertsch, F. Dreisow, S. Nolte, A. Tuennermann, U. Peschel, and F. Lederer, "Light evolution in arbitrary two-dimensional waveguide arrays," Phys. Rev. A 75, 053814 (2007). [CrossRef]
  26. S. Nolte, M. Will, J. Burghoff, and A. Tuennermann, "Femtosecond waveguide writing: a new avenue to three-dimensional integrated optics," Appl. Phys. A 77, 109-111 (2003). [CrossRef]
  27. T. Pertsch, U. Peschel, F. Lederer, J. Burghoff, M. Will, S. Nolte, and A. Tuennermann, "Discrete diffraction in two-dimensional arrays of coupled waveguides in silica," Opt. Lett. 29, 468-470 (2004). [CrossRef] [PubMed]
  28. A. Szameit, D. Bloemer, J. Burghoff, T. Pertsch, S. Nolte, and A. Tuennermann, "Hexagonal waveguide arrays written with fs-laser pulses," Appl. Phys. B . 82, 507-512 (2006). [CrossRef]
  29. N. Chiodo, G. D. Valle, R. Osellame, S. Longhi, G. Cerullo, R. Ramponi, P. Laporta, and U. Morgner, "Imaging of Bloch oscillations in erbium-doped curved waveguide arrays," Opt. Lett. 31, 1651-1653 (2006). [CrossRef] [PubMed]
  30. G. Lenz, I. Talanina, and M. de Sterke, "Bloch oscillations in an array of curved optical waveguides," Phys. Rev. Lett. 83, 963-966 (1999). [CrossRef]
  31. A. Szameit, F. Dreisow, T. Pertsch, S. Nolte, and A. Tuennermann, "Control of directional evanescent coupling in fs laser written waveguides," Opt. Express 15, 1579-1587 (2007). [CrossRef] [PubMed]

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