Abstract

We investigate the influence of second-order coupling in femtosecond-laser-written zigzag waveguide arrays, where the ratio Δ between second- and first-order coupling constants is adjusted from Δ=0.0 to Δ=2.8. Propagation patterns are observed directly via color center fluorescence.

© 2008 Optical Society of America

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  1. D. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
    [CrossRef] [PubMed]
  2. S. F. Mingaleev, P. L. Christiansen, Y. B. Gaididei, M. Johansson, and K. Rasmussen, J. Biol. Phys. 25, 41 (1999).
    [CrossRef]
  3. D. Hennig, Eur. Phys. J. B 20, 419 (2001).
    [CrossRef]
  4. N. Efremidis and D. Christodoulides, Phys. Rev. E 65, 056607 (2002).
    [CrossRef]
  5. P. G. Kevrekidis, B. A. Malomed, A. Saxena, A. R. Bishop, and D. Frantzeskakis, Physica D 183, 87 (2003).
    [CrossRef]
  6. R. Iyer, J. Aitchison, J. Wan, M. Dignam, and M. de Sterke, Opt. Express 15, 3212 (2007).
    [CrossRef] [PubMed]
  7. K. Itoh, W. Watanabe, S. Nolte, and C. B. Schaffer, MRS Bull. 31, 620 (2006).
    [CrossRef]
  8. A. Szameit, F. Dreisow, H. Hartung, S. Nolte, A. Tuennermann, and F. Lederer, Appl. Phys. Lett. 90, 241113 (2007).
    [CrossRef]
  9. F. Dreisow, M. Heinrich, A. Szameit, S. Doering, S. Nolte, A. Tuennermann, S. Fahr, and F. Lederer, Opt. Express 16, 3474 (2008).
    [CrossRef] [PubMed]
  10. A. Szameit, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, Phys. Rev. A 77, 043804 (2008).
    [CrossRef]
  11. A. Szameit, F. Dreisow, T. Pertsch, S. Nolte, and A. Tuennermann, Opt. Express 15, 1579 (2007).
    [CrossRef] [PubMed]
  12. A. Szameit, T. Pertsch, F. Dreisow, S. Nolte, A. Tuennermann, U. Peschel, and F. Lederer, Phys. Rev. A 75, 053814 (2007).
    [CrossRef]

2008 (2)

2007 (4)

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

A. Szameit, T. Pertsch, F. Dreisow, S. Nolte, A. Tuennermann, U. Peschel, and F. Lederer, Phys. Rev. A 75, 053814 (2007).
[CrossRef]

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

R. Iyer, J. Aitchison, J. Wan, M. Dignam, and M. de Sterke, Opt. Express 15, 3212 (2007).
[CrossRef] [PubMed]

2006 (1)

K. Itoh, W. Watanabe, S. Nolte, and C. B. Schaffer, MRS Bull. 31, 620 (2006).
[CrossRef]

2003 (2)

P. G. Kevrekidis, B. A. Malomed, A. Saxena, A. R. Bishop, and D. Frantzeskakis, Physica D 183, 87 (2003).
[CrossRef]

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

2002 (1)

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

2001 (1)

D. Hennig, Eur. Phys. J. B 20, 419 (2001).
[CrossRef]

1999 (1)

S. F. Mingaleev, P. L. Christiansen, Y. B. Gaididei, M. Johansson, and K. Rasmussen, J. Biol. Phys. 25, 41 (1999).
[CrossRef]

Aitchison, J.

Bishop, A. R.

P. G. Kevrekidis, B. A. Malomed, A. Saxena, A. R. Bishop, and D. Frantzeskakis, Physica D 183, 87 (2003).
[CrossRef]

Christiansen, P. L.

S. F. Mingaleev, P. L. Christiansen, Y. B. Gaididei, M. Johansson, and K. Rasmussen, J. Biol. Phys. 25, 41 (1999).
[CrossRef]

Christodoulides, D.

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

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

de Sterke, M.

Dignam, M.

Doering, S.

Dreisow, F.

F. Dreisow, M. Heinrich, A. Szameit, S. Doering, S. Nolte, A. Tuennermann, S. Fahr, and F. Lederer, Opt. Express 16, 3474 (2008).
[CrossRef] [PubMed]

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

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

A. Szameit, T. Pertsch, F. Dreisow, S. Nolte, A. Tuennermann, U. Peschel, and F. Lederer, Phys. Rev. A 75, 053814 (2007).
[CrossRef]

Efremidis, N.

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

Fahr, S.

Frantzeskakis, D.

P. G. Kevrekidis, B. A. Malomed, A. Saxena, A. R. Bishop, and D. Frantzeskakis, Physica D 183, 87 (2003).
[CrossRef]

Gaididei, Y. B.

S. F. Mingaleev, P. L. Christiansen, Y. B. Gaididei, M. Johansson, and K. Rasmussen, J. Biol. Phys. 25, 41 (1999).
[CrossRef]

Hartung, H.

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

Heinrich, M.

Hennig, D.

D. Hennig, Eur. Phys. J. B 20, 419 (2001).
[CrossRef]

Itoh, K.

K. Itoh, W. Watanabe, S. Nolte, and C. B. Schaffer, MRS Bull. 31, 620 (2006).
[CrossRef]

Iyer, R.

Johansson, M.

S. F. Mingaleev, P. L. Christiansen, Y. B. Gaididei, M. Johansson, and K. Rasmussen, J. Biol. Phys. 25, 41 (1999).
[CrossRef]

Kevrekidis, P. G.

P. G. Kevrekidis, B. A. Malomed, A. Saxena, A. R. Bishop, and D. Frantzeskakis, Physica D 183, 87 (2003).
[CrossRef]

Lederer, F.

F. Dreisow, M. Heinrich, A. Szameit, S. Doering, S. Nolte, A. Tuennermann, S. Fahr, and F. Lederer, Opt. Express 16, 3474 (2008).
[CrossRef] [PubMed]

A. Szameit, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, Phys. Rev. A 77, 043804 (2008).
[CrossRef]

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

A. Szameit, T. Pertsch, F. Dreisow, S. Nolte, A. Tuennermann, U. Peschel, and F. Lederer, Phys. Rev. A 75, 053814 (2007).
[CrossRef]

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

Malomed, B. A.

P. G. Kevrekidis, B. A. Malomed, A. Saxena, A. R. Bishop, and D. Frantzeskakis, Physica D 183, 87 (2003).
[CrossRef]

Mingaleev, S. F.

S. F. Mingaleev, P. L. Christiansen, Y. B. Gaididei, M. Johansson, and K. Rasmussen, J. Biol. Phys. 25, 41 (1999).
[CrossRef]

Nolte, S.

F. Dreisow, M. Heinrich, A. Szameit, S. Doering, S. Nolte, A. Tuennermann, S. Fahr, and F. Lederer, Opt. Express 16, 3474 (2008).
[CrossRef] [PubMed]

A. Szameit, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, Phys. Rev. A 77, 043804 (2008).
[CrossRef]

A. Szameit, T. Pertsch, F. Dreisow, S. Nolte, A. Tuennermann, U. Peschel, and F. Lederer, Phys. Rev. A 75, 053814 (2007).
[CrossRef]

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

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

K. Itoh, W. Watanabe, S. Nolte, and C. B. Schaffer, MRS Bull. 31, 620 (2006).
[CrossRef]

Pertsch, T.

A. Szameit, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, Phys. Rev. A 77, 043804 (2008).
[CrossRef]

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

A. Szameit, T. Pertsch, F. Dreisow, S. Nolte, A. Tuennermann, U. Peschel, and F. Lederer, Phys. Rev. A 75, 053814 (2007).
[CrossRef]

Peschel, U.

A. Szameit, T. Pertsch, F. Dreisow, S. Nolte, A. Tuennermann, U. Peschel, and F. Lederer, Phys. Rev. A 75, 053814 (2007).
[CrossRef]

Rasmussen, K.

S. F. Mingaleev, P. L. Christiansen, Y. B. Gaididei, M. Johansson, and K. Rasmussen, J. Biol. Phys. 25, 41 (1999).
[CrossRef]

Saxena, A.

P. G. Kevrekidis, B. A. Malomed, A. Saxena, A. R. Bishop, and D. Frantzeskakis, Physica D 183, 87 (2003).
[CrossRef]

Schaffer, C. B.

K. Itoh, W. Watanabe, S. Nolte, and C. B. Schaffer, MRS Bull. 31, 620 (2006).
[CrossRef]

Silberberg, Y.

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

Szameit, A.

F. Dreisow, M. Heinrich, A. Szameit, S. Doering, S. Nolte, A. Tuennermann, S. Fahr, and F. Lederer, Opt. Express 16, 3474 (2008).
[CrossRef] [PubMed]

A. Szameit, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, Phys. Rev. A 77, 043804 (2008).
[CrossRef]

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

A. Szameit, T. Pertsch, F. Dreisow, S. Nolte, A. Tuennermann, U. Peschel, and F. Lederer, Phys. Rev. A 75, 053814 (2007).
[CrossRef]

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

Tuennermann, A.

F. Dreisow, M. Heinrich, A. Szameit, S. Doering, S. Nolte, A. Tuennermann, S. Fahr, and F. Lederer, Opt. Express 16, 3474 (2008).
[CrossRef] [PubMed]

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

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

A. Szameit, T. Pertsch, F. Dreisow, S. Nolte, A. Tuennermann, U. Peschel, and F. Lederer, Phys. Rev. A 75, 053814 (2007).
[CrossRef]

Tünnermann, A.

A. Szameit, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, Phys. Rev. A 77, 043804 (2008).
[CrossRef]

Wan, J.

Watanabe, W.

K. Itoh, W. Watanabe, S. Nolte, and C. B. Schaffer, MRS Bull. 31, 620 (2006).
[CrossRef]

Appl. Phys. Lett. (1)

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

Eur. Phys. J. B (1)

D. Hennig, Eur. Phys. J. B 20, 419 (2001).
[CrossRef]

J. Biol. Phys. (1)

S. F. Mingaleev, P. L. Christiansen, Y. B. Gaididei, M. Johansson, and K. Rasmussen, J. Biol. Phys. 25, 41 (1999).
[CrossRef]

MRS Bull. (1)

K. Itoh, W. Watanabe, S. Nolte, and C. B. Schaffer, MRS Bull. 31, 620 (2006).
[CrossRef]

Nature (1)

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

Opt. Express (3)

Phys. Rev. A (2)

A. Szameit, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, Phys. Rev. A 77, 043804 (2008).
[CrossRef]

A. Szameit, T. Pertsch, F. Dreisow, S. Nolte, A. Tuennermann, U. Peschel, and F. Lederer, Phys. Rev. A 75, 053814 (2007).
[CrossRef]

Phys. Rev. E (1)

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

Physica D (1)

P. G. Kevrekidis, B. A. Malomed, A. Saxena, A. R. Bishop, and D. Frantzeskakis, Physica D 183, 87 (2003).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Zigzag arrangement of a waveguide array with SOC. The distances between the waveguides and the layers are denoted with d W and d L , respectively, and the coupling strengths to first and second neighbors are given by c 1 and c 2 .

Fig. 2
Fig. 2

(a) Simulation of the SOC influence on the beam width; the first order coupling is fixed to 1.4 coupling lengths. (b)–(d) Selected experimental propagation images for small, medium, and high SOC: (b) I, Δ = 0.0 ; (c) III, Δ = 1.0 ; (d) IV, Δ = 2.8 (cf. Table 1).

Fig. 3
Fig. 3

Zigzag arrays with different SOC. Propagation images and simulations are fixed to the propagation width of w = 17 ; (a) and (b) I, Δ = 0.0 ; (c) and (d) II, Δ = 0.3 ; (e) and (f) IV, Δ = 2.8 ; (g) corresponding band structure and (h) diffraction strength.

Tables (1)

Tables Icon

Table 1 Summary of Waveguide and Layer Separations d W , d L with Corresponding Coupling Constants c 1 and Relative SOC Δ a

Equations (2)

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

i d a n d z = c 1 ( a n + 1 + a n 1 ) + c 2 ( a n + 2 + a n 2 ) .
a n ( z ) = m = i n m J n 2 m ( 2 c 1 z ) J m ( 2 c 2 z ) .

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