Abstract

We report on the experimental observation of Bloch oscillations of an optical wave packet in a lattice with second-order coupling. To this end, we employ zigzag waveguide arrays, in which the second-order coupling can be precisely tuned.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. F. Bloch, Z. Phys. 52, 555 (1928).
    [CrossRef]
  2. C. Waschke, H. Roskos, R. Schwedler, K. Leo, H. Kurz, and K. Koehler, Phys. Rev. Lett. 70, 3319 (1993).
    [CrossRef] [PubMed]
  3. M. B. Dahan, E. Peik, J. Reichel, Y. Castin, and C. Salomon, Phys. Rev. Lett. 76, 4508 (1996).
    [CrossRef] [PubMed]
  4. S. R. Wilkinson, C. F. Bharucha, K. W. Madison, Q. Niu, and M. G. Raizen, Phys. Rev. Lett. 76, 4512 (1996).
    [CrossRef] [PubMed]
  5. B. P. Anderson and M. A. Kasevich, Science 282, 1686(1998).
    [CrossRef] [PubMed]
  6. U. Peschel, T. Pertsch, and F. Lederer, Opt. Lett. 23, 1701(1998).
    [CrossRef]
  7. T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 83, 4752 (1999).
    [CrossRef]
  8. R. Morandotti, U. Peschel, J. Aitchinson, H. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 4756 (1999).
    [CrossRef]
  9. G. Wang, J. Ping Huang, and K. W. Yu, Opt. Lett. 35, 1908 (2010).
    [CrossRef] [PubMed]
  10. N. Efremidis and D. Christodoulides, Phys. Rev. E 65, 056607 (2002).
    [CrossRef]
  11. F. Dreisow, A. Szameit, M. Heinrich, T. Pertsch, S. Nolte, and A. Tünnermann, Opt. Lett. 33, 2689 (2008).
    [CrossRef] [PubMed]
  12. G. Lenz, I. Talanina, and M. de Sterke, Phys. Rev. Lett. 83, 963 (1999).
    [CrossRef]
  13. A. Szameit and S. Nolte, J. Phys. B 43, 163001 (2010).
    [CrossRef]
  14. A. Szameit, F. Dreisow, T. Pertsch, S. Nolte, and A. Tünnermann, Opt. Express 15, 1579 (2007).
    [CrossRef] [PubMed]
  15. A. Szameit, F. Dreisow, H. Hartung, S. Nolte, and A. Tünnermann, Appl. Phys. Lett. 90, 241113 (2007).
    [CrossRef]

2010 (2)

2008 (1)

2007 (2)

A. Szameit, F. Dreisow, T. Pertsch, S. Nolte, and A. Tünnermann, Opt. Express 15, 1579 (2007).
[CrossRef] [PubMed]

A. Szameit, F. Dreisow, H. Hartung, S. Nolte, and A. Tünnermann, Appl. Phys. Lett. 90, 241113 (2007).
[CrossRef]

2002 (1)

N. Efremidis and D. Christodoulides, Phys. Rev. E 65, 056607 (2002).
[CrossRef]

1999 (3)

G. Lenz, I. Talanina, and M. de Sterke, Phys. Rev. Lett. 83, 963 (1999).
[CrossRef]

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

R. Morandotti, U. Peschel, J. Aitchinson, H. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 4756 (1999).
[CrossRef]

1998 (2)

1996 (2)

M. B. Dahan, E. Peik, J. Reichel, Y. Castin, and C. Salomon, Phys. Rev. Lett. 76, 4508 (1996).
[CrossRef] [PubMed]

S. R. Wilkinson, C. F. Bharucha, K. W. Madison, Q. Niu, and M. G. Raizen, Phys. Rev. Lett. 76, 4512 (1996).
[CrossRef] [PubMed]

1993 (1)

C. Waschke, H. Roskos, R. Schwedler, K. Leo, H. Kurz, and K. Koehler, Phys. Rev. Lett. 70, 3319 (1993).
[CrossRef] [PubMed]

1928 (1)

F. Bloch, Z. Phys. 52, 555 (1928).
[CrossRef]

Aitchinson, J.

R. Morandotti, U. Peschel, J. Aitchinson, H. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 4756 (1999).
[CrossRef]

Anderson, B. P.

B. P. Anderson and M. A. Kasevich, Science 282, 1686(1998).
[CrossRef] [PubMed]

Bharucha, C. F.

S. R. Wilkinson, C. F. Bharucha, K. W. Madison, Q. Niu, and M. G. Raizen, Phys. Rev. Lett. 76, 4512 (1996).
[CrossRef] [PubMed]

Bloch, F.

F. Bloch, Z. Phys. 52, 555 (1928).
[CrossRef]

Bräuer, A.

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

Castin, Y.

M. B. Dahan, E. Peik, J. Reichel, Y. Castin, and C. Salomon, Phys. Rev. Lett. 76, 4508 (1996).
[CrossRef] [PubMed]

Christodoulides, D.

N. Efremidis and D. Christodoulides, Phys. Rev. E 65, 056607 (2002).
[CrossRef]

Dahan, M. B.

M. B. Dahan, E. Peik, J. Reichel, Y. Castin, and C. Salomon, Phys. Rev. Lett. 76, 4508 (1996).
[CrossRef] [PubMed]

Dannberg, P.

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

de Sterke, M.

G. Lenz, I. Talanina, and M. de Sterke, Phys. Rev. Lett. 83, 963 (1999).
[CrossRef]

Dreisow, F.

Efremidis, N.

N. Efremidis and D. Christodoulides, Phys. Rev. E 65, 056607 (2002).
[CrossRef]

Eisenberg, H.

R. Morandotti, U. Peschel, J. Aitchinson, H. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 4756 (1999).
[CrossRef]

Elflein, W.

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

Hartung, H.

A. Szameit, F. Dreisow, H. Hartung, S. Nolte, and A. Tünnermann, Appl. Phys. Lett. 90, 241113 (2007).
[CrossRef]

Heinrich, M.

Kasevich, M. A.

B. P. Anderson and M. A. Kasevich, Science 282, 1686(1998).
[CrossRef] [PubMed]

Koehler, K.

C. Waschke, H. Roskos, R. Schwedler, K. Leo, H. Kurz, and K. Koehler, Phys. Rev. Lett. 70, 3319 (1993).
[CrossRef] [PubMed]

Kurz, H.

C. Waschke, H. Roskos, R. Schwedler, K. Leo, H. Kurz, and K. Koehler, Phys. Rev. Lett. 70, 3319 (1993).
[CrossRef] [PubMed]

Lederer, F.

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

U. Peschel, T. Pertsch, and F. Lederer, Opt. Lett. 23, 1701(1998).
[CrossRef]

Lenz, G.

G. Lenz, I. Talanina, and M. de Sterke, Phys. Rev. Lett. 83, 963 (1999).
[CrossRef]

Leo, K.

C. Waschke, H. Roskos, R. Schwedler, K. Leo, H. Kurz, and K. Koehler, Phys. Rev. Lett. 70, 3319 (1993).
[CrossRef] [PubMed]

Madison, K. W.

S. R. Wilkinson, C. F. Bharucha, K. W. Madison, Q. Niu, and M. G. Raizen, Phys. Rev. Lett. 76, 4512 (1996).
[CrossRef] [PubMed]

Morandotti, R.

R. Morandotti, U. Peschel, J. Aitchinson, H. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 4756 (1999).
[CrossRef]

Niu, Q.

S. R. Wilkinson, C. F. Bharucha, K. W. Madison, Q. Niu, and M. G. Raizen, Phys. Rev. Lett. 76, 4512 (1996).
[CrossRef] [PubMed]

Nolte, S.

Peik, E.

M. B. Dahan, E. Peik, J. Reichel, Y. Castin, and C. Salomon, Phys. Rev. Lett. 76, 4508 (1996).
[CrossRef] [PubMed]

Pertsch, T.

Peschel, U.

R. Morandotti, U. Peschel, J. Aitchinson, H. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 4756 (1999).
[CrossRef]

U. Peschel, T. Pertsch, and F. Lederer, Opt. Lett. 23, 1701(1998).
[CrossRef]

Ping Huang, J.

Raizen, M. G.

S. R. Wilkinson, C. F. Bharucha, K. W. Madison, Q. Niu, and M. G. Raizen, Phys. Rev. Lett. 76, 4512 (1996).
[CrossRef] [PubMed]

Reichel, J.

M. B. Dahan, E. Peik, J. Reichel, Y. Castin, and C. Salomon, Phys. Rev. Lett. 76, 4508 (1996).
[CrossRef] [PubMed]

Roskos, H.

C. Waschke, H. Roskos, R. Schwedler, K. Leo, H. Kurz, and K. Koehler, Phys. Rev. Lett. 70, 3319 (1993).
[CrossRef] [PubMed]

Salomon, C.

M. B. Dahan, E. Peik, J. Reichel, Y. Castin, and C. Salomon, Phys. Rev. Lett. 76, 4508 (1996).
[CrossRef] [PubMed]

Schwedler, R.

C. Waschke, H. Roskos, R. Schwedler, K. Leo, H. Kurz, and K. Koehler, Phys. Rev. Lett. 70, 3319 (1993).
[CrossRef] [PubMed]

Silberberg, Y.

R. Morandotti, U. Peschel, J. Aitchinson, H. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 4756 (1999).
[CrossRef]

Szameit, A.

Talanina, I.

G. Lenz, I. Talanina, and M. de Sterke, Phys. Rev. Lett. 83, 963 (1999).
[CrossRef]

Tünnermann, A.

Wang, G.

Waschke, C.

C. Waschke, H. Roskos, R. Schwedler, K. Leo, H. Kurz, and K. Koehler, Phys. Rev. Lett. 70, 3319 (1993).
[CrossRef] [PubMed]

Wilkinson, S. R.

S. R. Wilkinson, C. F. Bharucha, K. W. Madison, Q. Niu, and M. G. Raizen, Phys. Rev. Lett. 76, 4512 (1996).
[CrossRef] [PubMed]

Yu, K. W.

Appl. Phys. Lett. (1)

A. Szameit, F. Dreisow, H. Hartung, S. Nolte, and A. Tünnermann, Appl. Phys. Lett. 90, 241113 (2007).
[CrossRef]

J. Phys. B (1)

A. Szameit and S. Nolte, J. Phys. B 43, 163001 (2010).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Phys. Rev. E (1)

N. Efremidis and D. Christodoulides, Phys. Rev. E 65, 056607 (2002).
[CrossRef]

Phys. Rev. Lett. (6)

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

R. Morandotti, U. Peschel, J. Aitchinson, H. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 4756 (1999).
[CrossRef]

C. Waschke, H. Roskos, R. Schwedler, K. Leo, H. Kurz, and K. Koehler, Phys. Rev. Lett. 70, 3319 (1993).
[CrossRef] [PubMed]

M. B. Dahan, E. Peik, J. Reichel, Y. Castin, and C. Salomon, Phys. Rev. Lett. 76, 4508 (1996).
[CrossRef] [PubMed]

S. R. Wilkinson, C. F. Bharucha, K. W. Madison, Q. Niu, and M. G. Raizen, Phys. Rev. Lett. 76, 4512 (1996).
[CrossRef] [PubMed]

G. Lenz, I. Talanina, and M. de Sterke, Phys. Rev. Lett. 83, 963 (1999).
[CrossRef]

Science (1)

B. P. Anderson and M. A. Kasevich, Science 282, 1686(1998).
[CrossRef] [PubMed]

Z. Phys. (1)

F. Bloch, Z. Phys. 52, 555 (1928).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

(a) A sketch of the zigzag waveguide lattice. The interaction between adjacent lattice sites is illustrated by the red solid line, whereas the lattice angle α determines the interaction strength between the next-nearest neighbors (blue dotted line). (b) Corresponding quantum-mechanical potential, formed by the individual potential wells and a linear potential gradient that results from a curvature of the waveguides along the propagation direction.

Fig. 2
Fig. 2

(Upper row) Experimentally observed trajectory of the wave packet motion as a function of the lattice angle α and, therefore, the relative second-order coupling Δ. (Second row) Numerical simulations of the light evolution insider our samples, using Eq. (1). (Lower row) Dispersion relation between β and κ of the underlying lattices, as given by Eq. (2).

Fig. 3
Fig. 3

(Upper row) Experimentally observed breathing of the excited wave packet when only a single lattice site is excited as a function of the lattice angle α and, therefore, the relative second-order coupling Δ. (Second row) Numerical simulations of the light evolution insider our samples, using Eq. (1).

Equations (2)

Equations on this page are rendered with MathJax. Learn more.

( i d d Z + m F ) φ m + ( φ m + 1 + φ m 1 ) + Δ ( φ m + 2 + φ m 2 ) = 0 .
β = 2 c 1 cos ( κ ) + 2 c 2 cos ( 2 κ ) ,

Metrics