Abstract

We demonstrate one-dimensional optically-induced photonic lattices with a negative defect and observe linear bandgap guidance in such a defect. We show that a defect mode moves from the first bandgap to a higher bandgap as the lattice potential is increased. Our experimental results are in good agreement with the theoretical analysis of these effects.

© 2006 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  7. X. Wu, A. Yamilov, X. Liu, S. Li, V. P. Dravid, R. P. H. Chang, and H. Cao, "Ultraviolet photonic crystal laser," Appl. Phys. Lett. 85, 3657 (2004).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  22. . P. Yeh, and A. Yariv, "Bragg reflection waveguides," Opt. Commun. 19, 427 (1976).
    [CrossRef]
  23. Y. Cho, A. Yariv, and P. Yeh, "Observation of confined propagation in Bragg waveguides," Appl. Phys. Lett. 30, 471 (1977).
    [CrossRef]
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    [CrossRef]
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2006 (3)

2005 (3)

2004 (4)

F. Luan, A. K. George, T. D. Hedley, G. J. Pearce, D. M. Bird, J. C. Knight, and P. St. J. Russell, "All-solid photonic bandgap fiber," Opt. Lett. 29, 2369 (2004).
[CrossRef] [PubMed]

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, "Discrete solitons and soliton-induced dislocations in partially-coherent photonic lattices," Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef] [PubMed]

X. Wu, A. Yamilov, X. Liu, S. Li, V. P. Dravid, R. P. H. Chang, and H. Cao, "Ultraviolet photonic crystal laser," Appl. Phys. Lett. 85, 3657 (2004).
[CrossRef]

A. A. Sukhorukov, D. Neshev, W. Krolikowski, and Y. S. Kivshar, "Nonlinear Bloch-wave interaction and Bragg scattering in optically induced lattices," Phys. Rev. Lett. 92, 093901 (2004).
[CrossRef] [PubMed]

2003 (8)

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Band structure of waveguide arrays and excitation of Floquet-Bloch solitons," Phys. Rev. Lett. 90, 53902 (2003).
[CrossRef]

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, "Two-dimensional optical lattice solitons," Phys. Rev. Lett. 91, 213906 (2003).
[CrossRef] [PubMed]

J. Schmidtke, W. Stille, and H. Finkelmann, "Defect mode emission of a dye doped cholesteric polymer network," Phys. Rev. Lett. 90, 083902 (2003).
[CrossRef] [PubMed]

P. Russell, "Photonic crystal fibers," Science 299, 358 (2003).
[CrossRef] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature (London) 422, 147 (2003).
[CrossRef]

D. Neshev, E. Ostrovskaya, Y. Kivshar, and W. Krolikowski, "Spatial solitons in optically induced gratings," Opt. Lett. 28, 710 (2003).
[CrossRef] [PubMed]

R. Morandotti, H. S. Eisenberg, D. Mandelik, Y. Silberberg, D. Modotto, M. Sorel, C. R. Stanley, and J. S. Aitchison, "Interactions of discrete solitons with structural defects," Opt. Lett. 28, 834 (2003).
[CrossRef] [PubMed]

H. Trompeter, U. Peschel, T. Pertsch, F. Lederer, U. Streppel, D. Michaelis, and A. Bräuer, "Tailoring guided modes in waveguide arrays," Opt. Express 11, 3404 (2003).
[CrossRef]

2002 (1)

1999 (1)

U. Peschel, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, "Nonlinearly induced escape from a defect state in waveguide arrays," Appl. Phys. Lett. 75, 1348 (1999).
[CrossRef]

1991 (1)

S. L. McCall, P. M. Platzman, R. Dalichaouch, D. Smith, and S. Schultz, "Microwave propagation in two-dimensional dielectric lattices," Phys. Rev. Lett. 67, 2017 (1991).
[CrossRef] [PubMed]

1988 (1)

1977 (1)

Y. Cho, A. Yariv, and P. Yeh, "Observation of confined propagation in Bragg waveguides," Appl. Phys. Lett. 30, 471 (1977).
[CrossRef]

1976 (1)

. P. Yeh, and A. Yariv, "Bragg reflection waveguides," Opt. Commun. 19, 427 (1976).
[CrossRef]

Aitchison, J. S.

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Band structure of waveguide arrays and excitation of Floquet-Bloch solitons," Phys. Rev. Lett. 90, 53902 (2003).
[CrossRef]

R. Morandotti, H. S. Eisenberg, D. Mandelik, Y. Silberberg, D. Modotto, M. Sorel, C. R. Stanley, and J. S. Aitchison, "Interactions of discrete solitons with structural defects," Opt. Lett. 28, 834 (2003).
[CrossRef] [PubMed]

U. Peschel, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, "Nonlinearly induced escape from a defect state in waveguide arrays," Appl. Phys. Lett. 75, 1348 (1999).
[CrossRef]

Argyros, A.

Bird, D. M.

Birks, T. A.

Bräuer, A.

Cao, H.

X. Wu, A. Yamilov, X. Liu, S. Li, V. P. Dravid, R. P. H. Chang, and H. Cao, "Ultraviolet photonic crystal laser," Appl. Phys. Lett. 85, 3657 (2004).
[CrossRef]

Chang, R. P. H.

X. Wu, A. Yamilov, X. Liu, S. Li, V. P. Dravid, R. P. H. Chang, and H. Cao, "Ultraviolet photonic crystal laser," Appl. Phys. Lett. 85, 3657 (2004).
[CrossRef]

Chen, Z.

X. Wang, Z. Chen, and J. Yang, "Guiding light in optically-induced ring lattices with a low refractive index core," Opt. Lett. 31, 1887 (2006).
[CrossRef] [PubMed]

I. Makasyuk, Z. Chen, and J. Yang, "Band-gap guidance in optically induced photonic lattices with a negative defect," Phys. Rev. Lett.,  96, 223903 (2006).
[CrossRef]

F. Fedele, J. Yang, and Z. Chen, "Defect modes in 1D photonic lattices," Opt. Lett. 30, 1506 (2005).
[CrossRef] [PubMed]

F. Fedele, J. Yang, and Z. Chen, "Properties of defect modes in one-dimensional optically-induced photonic lattices," Stud. Appl. Math.,  115279 (2005).
[CrossRef]

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, "Discrete solitons and soliton-induced dislocations in partially-coherent photonic lattices," Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef] [PubMed]

Z. Chen and K. McCarthy, "Spatial soliton pixles from partially coherent light," Opt. Lett. 27, 2019 (2002).
[CrossRef]

Cho, Y.

Y. Cho, A. Yariv, and P. Yeh, "Observation of confined propagation in Bragg waveguides," Appl. Phys. Lett. 30, 471 (1977).
[CrossRef]

Christodoulides, D.

Christodoulides, D. N.

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, "Discrete solitons and soliton-induced dislocations in partially-coherent photonic lattices," Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature (London) 422, 147 (2003).
[CrossRef]

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, "Two-dimensional optical lattice solitons," Phys. Rev. Lett. 91, 213906 (2003).
[CrossRef] [PubMed]

Cohen, O.

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, "Two-dimensional optical lattice solitons," Phys. Rev. Lett. 91, 213906 (2003).
[CrossRef] [PubMed]

Cordeiro, C. B.

Dalichaouch, R.

S. L. McCall, P. M. Platzman, R. Dalichaouch, D. Smith, and S. Schultz, "Microwave propagation in two-dimensional dielectric lattices," Phys. Rev. Lett. 67, 2017 (1991).
[CrossRef] [PubMed]

Dravid, V. P.

X. Wu, A. Yamilov, X. Liu, S. Li, V. P. Dravid, R. P. H. Chang, and H. Cao, "Ultraviolet photonic crystal laser," Appl. Phys. Lett. 85, 3657 (2004).
[CrossRef]

Efremidis, N. K.

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, "Two-dimensional optical lattice solitons," Phys. Rev. Lett. 91, 213906 (2003).
[CrossRef] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature (London) 422, 147 (2003).
[CrossRef]

Eisenberg, H. S.

R. Morandotti, H. S. Eisenberg, D. Mandelik, Y. Silberberg, D. Modotto, M. Sorel, C. R. Stanley, and J. S. Aitchison, "Interactions of discrete solitons with structural defects," Opt. Lett. 28, 834 (2003).
[CrossRef] [PubMed]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Band structure of waveguide arrays and excitation of Floquet-Bloch solitons," Phys. Rev. Lett. 90, 53902 (2003).
[CrossRef]

U. Peschel, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, "Nonlinearly induced escape from a defect state in waveguide arrays," Appl. Phys. Lett. 75, 1348 (1999).
[CrossRef]

Eugenieva, E. D.

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, "Discrete solitons and soliton-induced dislocations in partially-coherent photonic lattices," Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef] [PubMed]

Fedele, F.

F. Fedele, J. Yang, and Z. Chen, "Properties of defect modes in one-dimensional optically-induced photonic lattices," Stud. Appl. Math.,  115279 (2005).
[CrossRef]

F. Fedele, J. Yang, and Z. Chen, "Defect modes in 1D photonic lattices," Opt. Lett. 30, 1506 (2005).
[CrossRef] [PubMed]

Finkelmann, H.

J. Schmidtke, W. Stille, and H. Finkelmann, "Defect mode emission of a dye doped cholesteric polymer network," Phys. Rev. Lett. 90, 083902 (2003).
[CrossRef] [PubMed]

Fleischer, J. W.

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, "Two-dimensional optical lattice solitons," Phys. Rev. Lett. 91, 213906 (2003).
[CrossRef] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature (London) 422, 147 (2003).
[CrossRef]

George, A. K.

Hedley, T. D.

Hudock, J.

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, "Two-dimensional optical lattice solitons," Phys. Rev. Lett. 91, 213906 (2003).
[CrossRef] [PubMed]

Joseph, R.

Kivshar, Y.

Kivshar, Y. S.

A. A. Sukhorukov, D. Neshev, W. Krolikowski, and Y. S. Kivshar, "Nonlinear Bloch-wave interaction and Bragg scattering in optically induced lattices," Phys. Rev. Lett. 92, 093901 (2004).
[CrossRef] [PubMed]

Knight, J. C.

Krolikowski, W.

A. A. Sukhorukov, D. Neshev, W. Krolikowski, and Y. S. Kivshar, "Nonlinear Bloch-wave interaction and Bragg scattering in optically induced lattices," Phys. Rev. Lett. 92, 093901 (2004).
[CrossRef] [PubMed]

D. Neshev, E. Ostrovskaya, Y. Kivshar, and W. Krolikowski, "Spatial solitons in optically induced gratings," Opt. Lett. 28, 710 (2003).
[CrossRef] [PubMed]

Lederer, F.

Leon-Saval, S. G.

Li, S.

X. Wu, A. Yamilov, X. Liu, S. Li, V. P. Dravid, R. P. H. Chang, and H. Cao, "Ultraviolet photonic crystal laser," Appl. Phys. Lett. 85, 3657 (2004).
[CrossRef]

Liu, X.

X. Wu, A. Yamilov, X. Liu, S. Li, V. P. Dravid, R. P. H. Chang, and H. Cao, "Ultraviolet photonic crystal laser," Appl. Phys. Lett. 85, 3657 (2004).
[CrossRef]

Luan, F.

Makasyuk, I.

I. Makasyuk, Z. Chen, and J. Yang, "Band-gap guidance in optically induced photonic lattices with a negative defect," Phys. Rev. Lett.,  96, 223903 (2006).
[CrossRef]

Mandelik, D.

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Band structure of waveguide arrays and excitation of Floquet-Bloch solitons," Phys. Rev. Lett. 90, 53902 (2003).
[CrossRef]

R. Morandotti, H. S. Eisenberg, D. Mandelik, Y. Silberberg, D. Modotto, M. Sorel, C. R. Stanley, and J. S. Aitchison, "Interactions of discrete solitons with structural defects," Opt. Lett. 28, 834 (2003).
[CrossRef] [PubMed]

Martin, H.

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, "Discrete solitons and soliton-induced dislocations in partially-coherent photonic lattices," Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef] [PubMed]

McCall, S. L.

S. L. McCall, P. M. Platzman, R. Dalichaouch, D. Smith, and S. Schultz, "Microwave propagation in two-dimensional dielectric lattices," Phys. Rev. Lett. 67, 2017 (1991).
[CrossRef] [PubMed]

McCarthy, K.

Michaelis, D.

Modotto, D.

Morales-Molina, L.

Morandotti, R.

R. Morandotti, H. S. Eisenberg, D. Mandelik, Y. Silberberg, D. Modotto, M. Sorel, C. R. Stanley, and J. S. Aitchison, "Interactions of discrete solitons with structural defects," Opt. Lett. 28, 834 (2003).
[CrossRef] [PubMed]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Band structure of waveguide arrays and excitation of Floquet-Bloch solitons," Phys. Rev. Lett. 90, 53902 (2003).
[CrossRef]

U. Peschel, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, "Nonlinearly induced escape from a defect state in waveguide arrays," Appl. Phys. Lett. 75, 1348 (1999).
[CrossRef]

Neshev, D.

A. A. Sukhorukov, D. Neshev, W. Krolikowski, and Y. S. Kivshar, "Nonlinear Bloch-wave interaction and Bragg scattering in optically induced lattices," Phys. Rev. Lett. 92, 093901 (2004).
[CrossRef] [PubMed]

D. Neshev, E. Ostrovskaya, Y. Kivshar, and W. Krolikowski, "Spatial solitons in optically induced gratings," Opt. Lett. 28, 710 (2003).
[CrossRef] [PubMed]

Ostrovskaya, E.

Pearce, G. J.

Pertsch, T.

Peschel, U.

H. Trompeter, U. Peschel, T. Pertsch, F. Lederer, U. Streppel, D. Michaelis, and A. Bräuer, "Tailoring guided modes in waveguide arrays," Opt. Express 11, 3404 (2003).
[CrossRef]

U. Peschel, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, "Nonlinearly induced escape from a defect state in waveguide arrays," Appl. Phys. Lett. 75, 1348 (1999).
[CrossRef]

Platzman, P. M.

S. L. McCall, P. M. Platzman, R. Dalichaouch, D. Smith, and S. Schultz, "Microwave propagation in two-dimensional dielectric lattices," Phys. Rev. Lett. 67, 2017 (1991).
[CrossRef] [PubMed]

Russell, P.

P. Russell, "Photonic crystal fibers," Science 299, 358 (2003).
[CrossRef] [PubMed]

Russell, P. St. J.

Schmidtke, J.

J. Schmidtke, W. Stille, and H. Finkelmann, "Defect mode emission of a dye doped cholesteric polymer network," Phys. Rev. Lett. 90, 083902 (2003).
[CrossRef] [PubMed]

Schultz, S.

S. L. McCall, P. M. Platzman, R. Dalichaouch, D. Smith, and S. Schultz, "Microwave propagation in two-dimensional dielectric lattices," Phys. Rev. Lett. 67, 2017 (1991).
[CrossRef] [PubMed]

Segev, M.

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, "Two-dimensional optical lattice solitons," Phys. Rev. Lett. 91, 213906 (2003).
[CrossRef] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature (London) 422, 147 (2003).
[CrossRef]

Silberberg, Y.

R. Morandotti, H. S. Eisenberg, D. Mandelik, Y. Silberberg, D. Modotto, M. Sorel, C. R. Stanley, and J. S. Aitchison, "Interactions of discrete solitons with structural defects," Opt. Lett. 28, 834 (2003).
[CrossRef] [PubMed]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Band structure of waveguide arrays and excitation of Floquet-Bloch solitons," Phys. Rev. Lett. 90, 53902 (2003).
[CrossRef]

U. Peschel, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, "Nonlinearly induced escape from a defect state in waveguide arrays," Appl. Phys. Lett. 75, 1348 (1999).
[CrossRef]

Smith, D.

S. L. McCall, P. M. Platzman, R. Dalichaouch, D. Smith, and S. Schultz, "Microwave propagation in two-dimensional dielectric lattices," Phys. Rev. Lett. 67, 2017 (1991).
[CrossRef] [PubMed]

Sorel, M.

Stanley, C. R.

Stille, W.

J. Schmidtke, W. Stille, and H. Finkelmann, "Defect mode emission of a dye doped cholesteric polymer network," Phys. Rev. Lett. 90, 083902 (2003).
[CrossRef] [PubMed]

Streppel, U.

Sukhorukov, A. A.

A. A. Sukhorukov, D. Neshev, W. Krolikowski, and Y. S. Kivshar, "Nonlinear Bloch-wave interaction and Bragg scattering in optically induced lattices," Phys. Rev. Lett. 92, 093901 (2004).
[CrossRef] [PubMed]

Trompeter, H.

Vicencio, R. A.

Wang, X.

Wu, X.

X. Wu, A. Yamilov, X. Liu, S. Li, V. P. Dravid, R. P. H. Chang, and H. Cao, "Ultraviolet photonic crystal laser," Appl. Phys. Lett. 85, 3657 (2004).
[CrossRef]

Yamilov, A.

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I. Makasyuk, Z. Chen, and J. Yang, "Band-gap guidance in optically induced photonic lattices with a negative defect," Phys. Rev. Lett.,  96, 223903 (2006).
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Appl. Phys. Lett. (3)

X. Wu, A. Yamilov, X. Liu, S. Li, V. P. Dravid, R. P. H. Chang, and H. Cao, "Ultraviolet photonic crystal laser," Appl. Phys. Lett. 85, 3657 (2004).
[CrossRef]

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J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature (London) 422, 147 (2003).
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Opt. Express (2)

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Figures (5)

Fig. 1.
Fig. 1.

Experimental setup. PBS: polarizing beam splitter; SBN: Strontium Barium Niobate.

Fig. 2.
Fig. 2.

Transverse intensity patterns of the lattice beam at crystal input (a) and output (b) with a single-site defect, and those of probe beam at input (c) and output (d) after 20-mm of propagation through the defect channel. (Bias field: 1.1 kV/cm).

Fig. 3.
Fig. 3.

Top: output lattice pattern with defect site marked by red arrow. Bottom: output probe beam. (a) and (c) correspond to DM in first and second bandgap, respectively. From left to right: bias field is 0.7, 1.1, 1.5, and 2.3 kV/cm for normalized lattice intensity of 0.28. (Lattice spacing is the same as in Fig. 2, but more lattice sites are shown in this figure.)

Fig. 4.
Fig. 4.

(a) Bandgap diagram. (b-d) Defect mode solutions at I 0 = 0.5 for E 0 = 4, 11 and 19, also marked by circles in (a). Shaded stripes correspond to lattice sites. (e-g) Numerical simulations of the evolution of a Gaussian beam through defect for E 0 = 4, 11 and 19. Propagation distance: z=40 mm. TIR gap indicates the total internal reflection gap or semi-infinite gap.

Fig. 5.
Fig. 5.

Top: output probe beam. Bottom: interferogram of the probe beam with a plane wave. From left to right: bias field is 0.5, 1.1, 1.7, and 2.3 kV/cm for normalized lattice intensity of 0.25.

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