Abstract

We demonstrate an experimental method for the direct measurement of band structures of one-dimensional periodic optical media. With the help of a prism coupler that is used in a retroreflective scheme, the allowed bands of a waveguide array in lithium niobate are determined and the results are compared with numerical calculations. Furthermore, we demonstrate the suitability of this method to measure propagation constants of extended nonlinear modes inside the forbidden gap.

© 2006 Optical Society of America

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2006 (1)

2005 (2)

2004 (2)

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, Phys. Rev. Lett. 92, 93904 (2004).
[Crossref]

R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, Phys. Rev. Lett. 93, 113902 (2004).
[Crossref] [PubMed]

2003 (3)

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 90, 53902 (2003).
[Crossref]

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

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 23902 (2003).
[Crossref]

2001 (1)

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, Phys. Rev. Lett. 86, 3296 (2001).
[Crossref] [PubMed]

1999 (1)

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

1998 (1)

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

1995 (1)

1987 (1)

R. Zengerle, J. Mod. Opt. 34, 1589 (1987).
[Crossref]

1983 (1)

J. Vollmer, J. P. Nisius, P. Hertel, and E. Krätzig, Appl. Phys. A 32, 125 (1983).
[Crossref]

1970 (1)

Aitchison, J. S.

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, Phys. Rev. Lett. 92, 93904 (2004).
[Crossref]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 90, 53902 (2003).
[Crossref]

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, Phys. Rev. Lett. 86, 3296 (2001).
[Crossref] [PubMed]

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

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

Aulkemeyer, S.

Bartal, G.

Boyd, A. R.

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

Buljan, H.

Carmon, T.

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 23902 (2003).
[Crossref]

Chen, F.

Christodoulides, D. N.

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 23902 (2003).
[Crossref]

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

Cohen, O.

Efremidis, N. K.

Eisenberg, H. S.

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 90, 53902 (2003).
[Crossref]

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, Phys. Rev. Lett. 86, 3296 (2001).
[Crossref] [PubMed]

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

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

Fleischer, J. W.

Freedman, B.

Hertel, P.

J. Vollmer, J. P. Nisius, P. Hertel, and E. Krätzig, Appl. Phys. A 32, 125 (1983).
[Crossref]

Iwanow, R.

R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, Phys. Rev. Lett. 93, 113902 (2004).
[Crossref] [PubMed]

Kip, D.

Krätzig, E.

J. Vollmer, J. P. Nisius, P. Hertel, and E. Krätzig, Appl. Phys. A 32, 125 (1983).
[Crossref]

Lederer, F.

R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, Phys. Rev. Lett. 93, 113902 (2004).
[Crossref] [PubMed]

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

Mandelik, D.

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, Phys. Rev. Lett. 92, 93904 (2004).
[Crossref]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 90, 53902 (2003).
[Crossref]

Manela, O.

Min, Y.

R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, Phys. Rev. Lett. 93, 113902 (2004).
[Crossref] [PubMed]

Morandotti, R.

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, Phys. Rev. Lett. 92, 93904 (2004).
[Crossref]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 90, 53902 (2003).
[Crossref]

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, Phys. Rev. Lett. 86, 3296 (2001).
[Crossref] [PubMed]

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

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

Moretti, P.

Nisius, J. P.

J. Vollmer, J. P. Nisius, P. Hertel, and E. Krätzig, Appl. Phys. A 32, 125 (1983).
[Crossref]

Pertsch, T.

R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, Phys. Rev. Lett. 93, 113902 (2004).
[Crossref] [PubMed]

Peschel, U.

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

Runde, D.

Rüter, C. E.

Schiek, R.

R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, Phys. Rev. Lett. 93, 113902 (2004).
[Crossref] [PubMed]

Schwartz, T.

Segev, M.

Shandarov, V.

Silberberg, Y.

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, Phys. Rev. Lett. 92, 93904 (2004).
[Crossref]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 90, 53902 (2003).
[Crossref]

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

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, Phys. Rev. Lett. 86, 3296 (2001).
[Crossref] [PubMed]

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

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

Sohler, W.

R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, Phys. Rev. Lett. 93, 113902 (2004).
[Crossref] [PubMed]

Sorel, M.

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, Phys. Rev. Lett. 86, 3296 (2001).
[Crossref] [PubMed]

Stegeman, G. I.

R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, Phys. Rev. Lett. 93, 113902 (2004).
[Crossref] [PubMed]

Stepic, M.

Tien, P. K.

Ulrich, R.

Vollmer, J.

J. Vollmer, J. P. Nisius, P. Hertel, and E. Krätzig, Appl. Phys. A 32, 125 (1983).
[Crossref]

Wirth, C.

Zengerle, R.

R. Zengerle, J. Mod. Opt. 34, 1589 (1987).
[Crossref]

Appl. Phys. A (1)

J. Vollmer, J. P. Nisius, P. Hertel, and E. Krätzig, Appl. Phys. A 32, 125 (1983).
[Crossref]

J. Mod. Opt. (1)

R. Zengerle, J. Mod. Opt. 34, 1589 (1987).
[Crossref]

J. Opt. Soc. Am. (1)

Nature (1)

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

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev. Lett. (7)

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, Phys. Rev. Lett. 92, 93904 (2004).
[Crossref]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 90, 53902 (2003).
[Crossref]

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

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, Phys. Rev. Lett. 86, 3296 (2001).
[Crossref] [PubMed]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 23902 (2003).
[Crossref]

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

R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, Phys. Rev. Lett. 93, 113902 (2004).
[Crossref] [PubMed]

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Figures (5)

Fig. 1
Fig. 1

(a) Prism coupling method: AP, apertures; XY, x y -stage; RT, rotary stage; PD, photodiode; CCD, CCD camera. (b) Adjustment of k z by tilting the sample by an angle θ.

Fig. 2
Fig. 2

Measured output light intensity I versus incident angle α for three different values of angle θ corresponding to k z = 0 (solid curve), k z = π ( 2 Λ ) (dashed curve), and k z = π Λ (dotted curve).

Fig. 3
Fig. 3

Full spectrum of reflected light intensity I as a function of incident angle α and tilt angle θ.

Fig. 4
Fig. 4

Measured values (open symbols) and numerical modeling (solid curves) of the effective refractive indices n eff of (linear) FB modes versus transverse wave vector k z , relative to the substrate index n sub . The solid square inside the gap is the measured effective index of an extended nonlinear mode.

Fig. 5
Fig. 5

Measured (lower part) and calculated (upper part) intensity distributions of extended FB modes at the output face for (a) band 1 at k z = π Λ , (b) band 2 at k z = π Λ , (c) band 3 at k z = π Λ , and (d) band 3 at k z = 0 .

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