Abstract

We report a direct observation of Bloch-like dynamics of light in curved waveguide arrays manufactured in Er:Yb-doped phosphate glass by femtosecond laser writing. The green upconversion fluorescence emitted by excited erbium ions is exploited to image the flow of the guided pump light at 980nm along the array. Direct and clear evidence of periodic light breathing for single-waveguide excitation, closely related to Bloch oscillations, is reported.

© 2006 Optical Society of America

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  1. D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
    [CrossRef] [PubMed]
  2. For a recent review on BO see, e.g., M. Glück, A. R. Kolovsky, and H. J. Korsch, Phys. Rep. 366, 103 (2002).
  3. U. Peschel, T. Pertsch, and F. Lederer, Opt. Lett. 23, 1701 (1998).
    [CrossRef]
  4. R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 4756 (1999).
    [CrossRef]
  5. T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 83, 4752 (1999).
    [CrossRef]
  6. G. Lenz, I. Talanina, and C. M. de Sterke, Phys. Rev. Lett. 83, 963 (1999).
    [CrossRef]
  7. G. Monsivais, M. del Castillo-Mussot, and F. Claro, Phys. Rev. Lett. 64, 1433 (1990).
    [CrossRef] [PubMed]
  8. C. M. de Sterke, J. E. Sipe, and L. A. Weller-Brophy, Opt. Lett. 16, 1141 (1991).
    [CrossRef] [PubMed]
  9. B. A. Usievich, V. A. Sychugov, J. Kh Nirligareev, and K. M. Golant, Opt. Spectrosc. 97, 841 (2004).
    [CrossRef]
  10. H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Bräuer, and U. Peschel, Phys. Rev. Lett. 96, 023901 (2006).
    [CrossRef] [PubMed]
  11. K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, Opt. Lett. 21, 1729 (1996).
    [CrossRef] [PubMed]
  12. Fabrication of two-dimensional straight waveguide arrays based on the femtosecond writing technique was recently demonstrated in T. Pertsch, U. Peschel, F. Lederer, J. Burghoff, M. Will, S. Nolte, and A. Tünnermann, Opt. Lett. 29, 468 (2004).
    [PubMed]
  13. A. Killi, U. Morgner, M. J. Lederer, and D. Kopf, Opt. Lett. 29, 1288 (2004).
    [CrossRef] [PubMed]
  14. R. Osellame, N. Chiodo, G. Della Valle, S. Taccheo, R. Ramponi, G. Cerullo, A. Killi, U. Morgner, M. Lederer, and D. Kopf, Opt. Lett. 29, 1900 (2004).
    [CrossRef] [PubMed]
  15. P. Oberson, B. Gisin, B. Huttner, and N. Gisin, Appl. Opt. 37, 7272 (1998).
    [CrossRef]
  16. Y. Lu and N. Ming, J. Mater. Sci. 30, 5705 (1995).
    [CrossRef]
  17. S. Longhi, Opt. Lett. 30, 2137 (2005).
    [CrossRef] [PubMed]

2006

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Bräuer, and U. Peschel, Phys. Rev. Lett. 96, 023901 (2006).
[CrossRef] [PubMed]

2005

2004

2003

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
[CrossRef] [PubMed]

2002

For a recent review on BO see, e.g., M. Glück, A. R. Kolovsky, and H. J. Korsch, Phys. Rep. 366, 103 (2002).

1999

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

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

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

1998

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

P. Oberson, B. Gisin, B. Huttner, and N. Gisin, Appl. Opt. 37, 7272 (1998).
[CrossRef]

1996

1995

Y. Lu and N. Ming, J. Mater. Sci. 30, 5705 (1995).
[CrossRef]

1991

1990

G. Monsivais, M. del Castillo-Mussot, and F. Claro, Phys. Rev. Lett. 64, 1433 (1990).
[CrossRef] [PubMed]

Aitchison, J. S.

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

Bräuer, A.

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Bräuer, and U. Peschel, Phys. Rev. Lett. 96, 023901 (2006).
[CrossRef] [PubMed]

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

Burghoff, J.

Cerullo, G.

Chiodo, N.

Christodoulides, D. N.

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
[CrossRef] [PubMed]

Claro, F.

G. Monsivais, M. del Castillo-Mussot, and F. Claro, Phys. Rev. Lett. 64, 1433 (1990).
[CrossRef] [PubMed]

Dannberg, P.

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

Davis, K. M.

de Sterke, C. M.

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

C. M. de Sterke, J. E. Sipe, and L. A. Weller-Brophy, Opt. Lett. 16, 1141 (1991).
[CrossRef] [PubMed]

del Castillo-Mussot, M.

G. Monsivais, M. del Castillo-Mussot, and F. Claro, Phys. Rev. Lett. 64, 1433 (1990).
[CrossRef] [PubMed]

Della Valle, G.

Eisenberg, H. S.

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. 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]

Gisin, B.

P. Oberson, B. Gisin, B. Huttner, and N. Gisin, Appl. Opt. 37, 7272 (1998).
[CrossRef]

Gisin, N.

P. Oberson, B. Gisin, B. Huttner, and N. Gisin, Appl. Opt. 37, 7272 (1998).
[CrossRef]

Glück, M.

For a recent review on BO see, e.g., M. Glück, A. R. Kolovsky, and H. J. Korsch, Phys. Rep. 366, 103 (2002).

Golant, K. M.

B. A. Usievich, V. A. Sychugov, J. Kh Nirligareev, and K. M. Golant, Opt. Spectrosc. 97, 841 (2004).
[CrossRef]

Hirao, K.

Huttner, B.

P. Oberson, B. Gisin, B. Huttner, and N. Gisin, Appl. Opt. 37, 7272 (1998).
[CrossRef]

Kh Nirligareev, J.

B. A. Usievich, V. A. Sychugov, J. Kh Nirligareev, and K. M. Golant, Opt. Spectrosc. 97, 841 (2004).
[CrossRef]

Killi, A.

Kolovsky, A. R.

For a recent review on BO see, e.g., M. Glück, A. R. Kolovsky, and H. J. Korsch, Phys. Rep. 366, 103 (2002).

Kopf, D.

Korsch, H. J.

For a recent review on BO see, e.g., M. Glück, A. R. Kolovsky, and H. J. Korsch, Phys. Rep. 366, 103 (2002).

Lederer, F.

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Bräuer, and U. Peschel, Phys. Rev. Lett. 96, 023901 (2006).
[CrossRef] [PubMed]

Fabrication of two-dimensional straight waveguide arrays based on the femtosecond writing technique was recently demonstrated in T. Pertsch, U. Peschel, F. Lederer, J. Burghoff, M. Will, S. Nolte, and A. Tünnermann, Opt. Lett. 29, 468 (2004).
[PubMed]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
[CrossRef] [PubMed]

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]

Lederer, M.

Lederer, M. J.

Lenz, G.

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

Longhi, S.

Lu, Y.

Y. Lu and N. Ming, J. Mater. Sci. 30, 5705 (1995).
[CrossRef]

Michaelis, D.

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Bräuer, and U. Peschel, Phys. Rev. Lett. 96, 023901 (2006).
[CrossRef] [PubMed]

Ming, N.

Y. Lu and N. Ming, J. Mater. Sci. 30, 5705 (1995).
[CrossRef]

Miura, K.

Monsivais, G.

G. Monsivais, M. del Castillo-Mussot, and F. Claro, Phys. Rev. Lett. 64, 1433 (1990).
[CrossRef] [PubMed]

Morandotti, R.

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

Morgner, U.

Nolte, S.

Oberson, P.

P. Oberson, B. Gisin, B. Huttner, and N. Gisin, Appl. Opt. 37, 7272 (1998).
[CrossRef]

Osellame, R.

Pertsch, T.

Peschel, U.

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Bräuer, and U. Peschel, Phys. Rev. Lett. 96, 023901 (2006).
[CrossRef] [PubMed]

Fabrication of two-dimensional straight waveguide arrays based on the femtosecond writing technique was recently demonstrated in T. Pertsch, U. Peschel, F. Lederer, J. Burghoff, M. Will, S. Nolte, and A. Tünnermann, Opt. Lett. 29, 468 (2004).
[PubMed]

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

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

Ramponi, R.

Silberberg, Y.

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
[CrossRef] [PubMed]

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

Sipe, J. E.

Streppel, U.

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Bräuer, and U. Peschel, Phys. Rev. Lett. 96, 023901 (2006).
[CrossRef] [PubMed]

Sugimoto, N.

Sychugov, V. A.

B. A. Usievich, V. A. Sychugov, J. Kh Nirligareev, and K. M. Golant, Opt. Spectrosc. 97, 841 (2004).
[CrossRef]

Taccheo, S.

Talanina, I.

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

Trompeter, H.

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Bräuer, and U. Peschel, Phys. Rev. Lett. 96, 023901 (2006).
[CrossRef] [PubMed]

Tünnermann, A.

Usievich, B. A.

B. A. Usievich, V. A. Sychugov, J. Kh Nirligareev, and K. M. Golant, Opt. Spectrosc. 97, 841 (2004).
[CrossRef]

Weller-Brophy, L. A.

Will, M.

Appl. Opt.

P. Oberson, B. Gisin, B. Huttner, and N. Gisin, Appl. Opt. 37, 7272 (1998).
[CrossRef]

J. Mater. Sci.

Y. Lu and N. Ming, J. Mater. Sci. 30, 5705 (1995).
[CrossRef]

Nature

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
[CrossRef] [PubMed]

Opt. Lett.

Opt. Spectrosc.

B. A. Usievich, V. A. Sychugov, J. Kh Nirligareev, and K. M. Golant, Opt. Spectrosc. 97, 841 (2004).
[CrossRef]

Phys. Rep.

For a recent review on BO see, e.g., M. Glück, A. R. Kolovsky, and H. J. Korsch, Phys. Rep. 366, 103 (2002).

Phys. Rev. Lett.

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Bräuer, and U. Peschel, Phys. Rev. Lett. 96, 023901 (2006).
[CrossRef] [PubMed]

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

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

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

G. Monsivais, M. del Castillo-Mussot, and F. Claro, Phys. Rev. Lett. 64, 1433 (1990).
[CrossRef] [PubMed]

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Figures (3)

Fig. 1
Fig. 1

(a) Schematic of an array of circularly curved waveguides for the observation of BO. (b) Measured 2D refractive index profile ( a = 10 μ m array). (c) Microscope image (top view) of the arrays showing the fiber coupling geometry for single-waveguide excitation.

Fig. 2
Fig. 2

Measured fluorescence pattern corresponding to the central waveguide excitation of (a) straight array with period a = 10 μ m , (b) curved array with radius of curvature R = 7.7 cm and a = 10 μ m , (c) curved array with R = 7.7 cm and a = 8 μ m .

Fig. 3
Fig. 3

Measured spatial refocusing period (Bloch period) for a few values of radius of curvature R (points) and corresponding theoretical curve (solid line). The curved arrays have the same waveguide separation a = 10 μ m .

Equations (2)

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c ̇ n = i Δ ( c n + 1 + c n 1 ) ( α 2 + i δ n ) c n .
s B = 2 π δ = λ 0 R n s a .

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