Abstract

The propagation of light in 5×5 and 7×7 cubic lattices of evanescently coupled waveguides is investigated for the first time, to the authors’ knowledge. The results reveal ideal discrete diffraction and demonstrate the excellent quality of the waveguide arrays, which were manufactured in fused silica by femtosecond-laser-induced refractive-index modifications.

© 2004 Optical Society of America

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  1. J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  8. T. Pertsch, U. Peschel, S. Nolte, A. Tünnermann, F. Lederer, J. Kobelke, K. Schuster, and H. Bartelt, in Conference on Quantum Electronics and Laser Science (QELS), Vol. 90 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2003), paper QThK5.
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  14. P. Oberson, B. Gisin, B. Huttner, and N. Gisin, Appl. Opt. 37, 7268 (1998).
    [CrossRef]

2003

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

S. Nolte, M. Will, J. Burghoff, and A. Tünnermann, Appl. Phys. A 77, 109 (2003).
[CrossRef]

2002

2001

E. D. Eugenieva, N. K. Efremidis, and D. N. Christodoulides, Opt. Lett. 26, 1978 (2001).
[CrossRef]

B. A. Malomed and P. G. Kevrekidis, Phys. Rev. E 64, 026601 (2001).
[CrossRef]

D. N. Christodoulides and E. D. Eugenieva, Phys. Rev. Lett. 87, 233901 (2001).
[CrossRef]

1998

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

P. Oberson, B. Gisin, B. Huttner, and N. Gisin, Appl. Opt. 37, 7268 (1998).
[CrossRef]

1997

K. Miura, J. Qiu, H. Inouye, T. Mitsuyu, and K. Hirao, Appl. Phys. Lett. 71, 3329 (1997).
[CrossRef]

1996

Aitchison, J. S.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Bartelt, H.

T. Pertsch, U. Peschel, S. Nolte, A. Tünnermann, F. Lederer, J. Kobelke, K. Schuster, and H. Bartelt, in Conference on Quantum Electronics and Laser Science (QELS), Vol. 90 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2003), paper QThK5.

Boyd, A. R.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Bräuner, A.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuner, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef]

Burghoff, J.

S. Nolte, M. Will, J. Burghoff, and A. Tünnermann, Appl. Phys. A 77, 109 (2003).
[CrossRef]

Cerullo, G.

Chichkov, B. N.

Christodoulides, D. N.

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

D. N. Christodoulides and E. D. Eugenieva, Phys. Rev. Lett. 87, 233901 (2001).
[CrossRef]

E. D. Eugenieva, N. K. Efremidis, and D. N. Christodoulides, Opt. Lett. 26, 1978 (2001).
[CrossRef]

Davis, K. M.

De Silvestri, S.

Efremidis, N. K.

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

E. D. Eugenieva, N. K. Efremidis, and D. N. Christodoulides, Opt. Lett. 26, 1978 (2001).
[CrossRef]

Eisenberg, H. S.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Eugenieva, E. D.

D. N. Christodoulides and E. D. Eugenieva, Phys. Rev. Lett. 87, 233901 (2001).
[CrossRef]

E. D. Eugenieva, N. K. Efremidis, and D. N. Christodoulides, Opt. Lett. 26, 1978 (2001).
[CrossRef]

Fleischer, J. W.

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

Gisin, B.

Gisin, N.

Hirao, K.

K. Miura, J. Qiu, H. Inouye, T. Mitsuyu, and K. Hirao, Appl. Phys. Lett. 71, 3329 (1997).
[CrossRef]

K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, Opt. Lett. 21, 1729 (1996).
[CrossRef] [PubMed]

Huttner, B.

Inouye, H.

K. Miura, J. Qiu, H. Inouye, T. Mitsuyu, and K. Hirao, Appl. Phys. Lett. 71, 3329 (1997).
[CrossRef]

Iwanow, R.

T. Pertsch, U. Peschel, F. Lederer, J. Meier, R. Schiek, R. Iwanow, G. Stegeman, Y. H. Min, and W. Sohler, presented at the Meeting on Nonlinear Guided Waves and Their Applications, Stresa, Italy (September 1–4, 2002).

Kevrekidis, P. G.

B. A. Malomed and P. G. Kevrekidis, Phys. Rev. E 64, 026601 (2001).
[CrossRef]

Kobelke, J.

T. Pertsch, U. Peschel, S. Nolte, A. Tünnermann, F. Lederer, J. Kobelke, K. Schuster, and H. Bartelt, in Conference on Quantum Electronics and Laser Science (QELS), Vol. 90 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2003), paper QThK5.

Laporta, P.

Lederer, F.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuner, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef]

T. Pertsch, U. Peschel, F. Lederer, J. Meier, R. Schiek, R. Iwanow, G. Stegeman, Y. H. Min, and W. Sohler, presented at the Meeting on Nonlinear Guided Waves and Their Applications, Stresa, Italy (September 1–4, 2002).

T. Pertsch, U. Peschel, S. Nolte, A. Tünnermann, F. Lederer, J. Kobelke, K. Schuster, and H. Bartelt, in Conference on Quantum Electronics and Laser Science (QELS), Vol. 90 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2003), paper QThK5.

Malomed, B. A.

B. A. Malomed and P. G. Kevrekidis, Phys. Rev. E 64, 026601 (2001).
[CrossRef]

Marangoni, M.

Meier, J.

T. Pertsch, U. Peschel, F. Lederer, J. Meier, R. Schiek, R. Iwanow, G. Stegeman, Y. H. Min, and W. Sohler, presented at the Meeting on Nonlinear Guided Waves and Their Applications, Stresa, Italy (September 1–4, 2002).

Min, Y. H.

T. Pertsch, U. Peschel, F. Lederer, J. Meier, R. Schiek, R. Iwanow, G. Stegeman, Y. H. Min, and W. Sohler, presented at the Meeting on Nonlinear Guided Waves and Their Applications, Stresa, Italy (September 1–4, 2002).

Mitsuyu, T.

K. Miura, J. Qiu, H. Inouye, T. Mitsuyu, and K. Hirao, Appl. Phys. Lett. 71, 3329 (1997).
[CrossRef]

Miura, K.

K. Miura, J. Qiu, H. Inouye, T. Mitsuyu, and K. Hirao, Appl. Phys. Lett. 71, 3329 (1997).
[CrossRef]

K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, Opt. Lett. 21, 1729 (1996).
[CrossRef] [PubMed]

Morandotti, R.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Nolte, S.

S. Nolte, M. Will, J. Burghoff, and A. Tünnermann, Appl. Phys. A 77, 109 (2003).
[CrossRef]

M. Will, S. Nolte, B. N. Chichkov, and A. Tünnermann, Appl. Opt. 41, 4360 (2002).
[CrossRef] [PubMed]

T. Pertsch, U. Peschel, S. Nolte, A. Tünnermann, F. Lederer, J. Kobelke, K. Schuster, and H. Bartelt, in Conference on Quantum Electronics and Laser Science (QELS), Vol. 90 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2003), paper QThK5.

Oberson, P.

Osellame, R.

Pertsch, T.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuner, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef]

T. Pertsch, U. Peschel, F. Lederer, J. Meier, R. Schiek, R. Iwanow, G. Stegeman, Y. H. Min, and W. Sohler, presented at the Meeting on Nonlinear Guided Waves and Their Applications, Stresa, Italy (September 1–4, 2002).

T. Pertsch, U. Peschel, S. Nolte, A. Tünnermann, F. Lederer, J. Kobelke, K. Schuster, and H. Bartelt, in Conference on Quantum Electronics and Laser Science (QELS), Vol. 90 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2003), paper QThK5.

Peschel, U.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuner, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef]

T. Pertsch, U. Peschel, S. Nolte, A. Tünnermann, F. Lederer, J. Kobelke, K. Schuster, and H. Bartelt, in Conference on Quantum Electronics and Laser Science (QELS), Vol. 90 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2003), paper QThK5.

T. Pertsch, U. Peschel, F. Lederer, J. Meier, R. Schiek, R. Iwanow, G. Stegeman, Y. H. Min, and W. Sohler, presented at the Meeting on Nonlinear Guided Waves and Their Applications, Stresa, Italy (September 1–4, 2002).

Polli, D.

Qiu, J.

K. Miura, J. Qiu, H. Inouye, T. Mitsuyu, and K. Hirao, Appl. Phys. Lett. 71, 3329 (1997).
[CrossRef]

Ramponi, R.

Schiek, R.

T. Pertsch, U. Peschel, F. Lederer, J. Meier, R. Schiek, R. Iwanow, G. Stegeman, Y. H. Min, and W. Sohler, presented at the Meeting on Nonlinear Guided Waves and Their Applications, Stresa, Italy (September 1–4, 2002).

Schuster, K.

T. Pertsch, U. Peschel, S. Nolte, A. Tünnermann, F. Lederer, J. Kobelke, K. Schuster, and H. Bartelt, in Conference on Quantum Electronics and Laser Science (QELS), Vol. 90 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2003), paper QThK5.

Segev, M.

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

Silberberg, Y.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Sohler, W.

T. Pertsch, U. Peschel, F. Lederer, J. Meier, R. Schiek, R. Iwanow, G. Stegeman, Y. H. Min, and W. Sohler, presented at the Meeting on Nonlinear Guided Waves and Their Applications, Stresa, Italy (September 1–4, 2002).

Stegeman, G.

T. Pertsch, U. Peschel, F. Lederer, J. Meier, R. Schiek, R. Iwanow, G. Stegeman, Y. H. Min, and W. Sohler, presented at the Meeting on Nonlinear Guided Waves and Their Applications, Stresa, Italy (September 1–4, 2002).

Sugimoto, N.

Taccheo, S.

Tünnermann, A.

S. Nolte, M. Will, J. Burghoff, and A. Tünnermann, Appl. Phys. A 77, 109 (2003).
[CrossRef]

M. Will, S. Nolte, B. N. Chichkov, and A. Tünnermann, Appl. Opt. 41, 4360 (2002).
[CrossRef] [PubMed]

T. Pertsch, U. Peschel, S. Nolte, A. Tünnermann, F. Lederer, J. Kobelke, K. Schuster, and H. Bartelt, in Conference on Quantum Electronics and Laser Science (QELS), Vol. 90 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2003), paper QThK5.

Will, M.

S. Nolte, M. Will, J. Burghoff, and A. Tünnermann, Appl. Phys. A 77, 109 (2003).
[CrossRef]

M. Will, S. Nolte, B. N. Chichkov, and A. Tünnermann, Appl. Opt. 41, 4360 (2002).
[CrossRef] [PubMed]

Zentgraf, T.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuner, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef]

Appl. Opt.

Appl. Phys. A

S. Nolte, M. Will, J. Burghoff, and A. Tünnermann, Appl. Phys. A 77, 109 (2003).
[CrossRef]

Appl. Phys. Lett.

K. Miura, J. Qiu, H. Inouye, T. Mitsuyu, and K. Hirao, Appl. Phys. Lett. 71, 3329 (1997).
[CrossRef]

Nature

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

Opt. Lett.

OSA Trends in Optics and Photonics Series

T. Pertsch, U. Peschel, S. Nolte, A. Tünnermann, F. Lederer, J. Kobelke, K. Schuster, and H. Bartelt, in Conference on Quantum Electronics and Laser Science (QELS), Vol. 90 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2003), paper QThK5.

Phys. Rev. E

B. A. Malomed and P. G. Kevrekidis, Phys. Rev. E 64, 026601 (2001).
[CrossRef]

Phys. Rev. Lett.

D. N. Christodoulides and E. D. Eugenieva, Phys. Rev. Lett. 87, 233901 (2001).
[CrossRef]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuner, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef]

Other

T. Pertsch, U. Peschel, F. Lederer, J. Meier, R. Schiek, R. Iwanow, G. Stegeman, Y. H. Min, and W. Sohler, presented at the Meeting on Nonlinear Guided Waves and Their Applications, Stresa, Italy (September 1–4, 2002).

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Figures (6)

Fig. 1
Fig. 1

Schematic of the writing of a waveguide array in a transparent bulk material with femtosecond light pulses. Inset, microscopic image of the end facet of the 5×5 array.

Fig. 2
Fig. 2

(a) Refracted near-field measurement of the refractive-index profile of a single waveguide. (b) Measured mode profile at λ=740 nm.

Fig. 3
Fig. 3

Simulation of discrete light propagation by excitation of the center waveguide of a 7×7 matrix.

Fig. 4
Fig. 4

Output intensity distribution for excitation of several waveguides of a 7×7 waveguide matrix: (a) measurement for central excitation, (b) simulation of (a), (c) measurement for excitation at the edge, (d) simulation of (c), (e) measurement for excitation next to the edge, (f) simulation of (e). We obtained (b), (d), and (e) by multiplying the modal field of the individual guides by the amplitudes from Eq. (1).

Fig. 5
Fig. 5

Output intensity distribution for excitation of the center of a 5×5 waveguide matrix: (a) measurement, (b) simulation.

Fig. 6
Fig. 6

Dependence of the horizontal and vertical coupling ch/v on (a) the waveguide separation and (b) the wavelength for a separation of 25 µm.

Equations (3)

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

iddzamn+chamn+1+amn-1+cvam+1n+am-1n=0,
ch=205×exp-0.086×Δ/µm×m-1,
cv=56.7×exp-0.033×Δ/µm×m-1.

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