Abstract

We study theoretically the linear and nonlinear propagation of light in one-dimensional bi-periodic arrays of fibers, with the propagation constant periodically modulated along the propagation direction. We predict analytically and observe numerically subdiffractive propagation along such fiber arrays, and characterize the light propagation properties. We also predict novel subdiffractive discrete solitons in the presence of Kerr nonlinearity, both of focusing and defocusing cases, which are essentially different from the usual discrete solitons in waveguide arrays.

© 2006 Optical Society of America

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  1. E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059 (1987).
    [CrossRef] [PubMed]
  2. S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486 (1987).
    [CrossRef] [PubMed]
  3. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato and S. Kawakami, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett. 74, 1212 (1999).
    [CrossRef]
  4. D. Chigrin, S. Enoch, C. Sotomayor Torres and G. Tayeb, "Self-guiding in two-dimensional photonic crystals," Opt. Express 11, 1203 (2003).
    [CrossRef] [PubMed]
  5. R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Fuchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tünnermann, "Diffractionless propagation of light in a low-index photonic-crystal film," Appl. Phys. Lett. 85, 5854 (2004).
    [CrossRef]
  6. D. W. Prather, S. Shi, D. M. Pustai, C. Chen, S. Venkataraman, A. Sharkawy, G. Schneider, and J. Murakowski, "Dispersion-based optical routing in photonic crystals," Opt. Lett. 29, 50-52 (2004).
    [CrossRef] [PubMed]
  7. H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchinson, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383 (1998).
    [CrossRef]
  8. R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel and J. S. Aitchison, "Self-focusing and defocusing in waveguide arrays," Phys. Rev. Lett. 86, 3296 (2001).
    [CrossRef] [PubMed]
  9. M. J. Ablowitz and Z. H. Musslimani, "Discrete diffraction managed spatial solitons," Phys. Rev. Lett. 87, 254102 (2001).
    [CrossRef] [PubMed]
  10. T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer and F. Lederer, "Anomalous refraction and diffraction in discrete optical systems," Phys. Rev. Lett. 88, 093901 (2002).
    [CrossRef] [PubMed]
  11. A. A. Sukhorukov, Y. S. Kivshar, H. S. Eisenberg, and Y. Silberberg, "Spatial optical solitons in waveguide arrays," IEEE J. Quantum Electron. 39,31-50 (2003).
    [CrossRef]
  12. J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchinson, "Experimental observation of discrete modulational instability," Phys. Rev. Lett. 92, 163902 (2004).
    [CrossRef] [PubMed]
  13. T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, "Optical bloch oscillations in temperature tuned waveguide arrays," Phys. Rev. Lett. 83, 4752 (1999).
    [CrossRef]
  14. H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchinson, "Diffraction management," Phys. Rev. Lett. 85, 1863 (2000).
    [CrossRef] [PubMed]
  15. U. Peschel and F. Lederer, "Oscillation and decay of discrete solitons in modulated waveguide array," J. Opt. Soc. Am. B 19, 544 (2002)
    [CrossRef]
  16. S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, "Observation of dynamic localization in periodically curved waveguide arrays," Phys. Rev. Lett. 96, 243901 (2006).
    [CrossRef] [PubMed]
  17. K. Staliunas and R. Herrero, Nondiffractive propagation of light in photonic crystals, Phys. Rev. E,  73, 016601 (2006).
    [CrossRef]
  18. K. Staliunas, R. Herrero and G. J. de Valcarcel, Sub-diffractive band-edge solitons in Bose-Einstein condensates in periodic potentials, Phys. Rev. E 73, 065603(R) (2006).
    [CrossRef]

2006 (2)

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, "Observation of dynamic localization in periodically curved waveguide arrays," Phys. Rev. Lett. 96, 243901 (2006).
[CrossRef] [PubMed]

K. Staliunas and R. Herrero, Nondiffractive propagation of light in photonic crystals, Phys. Rev. E,  73, 016601 (2006).
[CrossRef]

2004 (3)

J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchinson, "Experimental observation of discrete modulational instability," Phys. Rev. Lett. 92, 163902 (2004).
[CrossRef] [PubMed]

R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Fuchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tünnermann, "Diffractionless propagation of light in a low-index photonic-crystal film," Appl. Phys. Lett. 85, 5854 (2004).
[CrossRef]

D. W. Prather, S. Shi, D. M. Pustai, C. Chen, S. Venkataraman, A. Sharkawy, G. Schneider, and J. Murakowski, "Dispersion-based optical routing in photonic crystals," Opt. Lett. 29, 50-52 (2004).
[CrossRef] [PubMed]

2003 (2)

D. Chigrin, S. Enoch, C. Sotomayor Torres and G. Tayeb, "Self-guiding in two-dimensional photonic crystals," Opt. Express 11, 1203 (2003).
[CrossRef] [PubMed]

A. A. Sukhorukov, Y. S. Kivshar, H. S. Eisenberg, and Y. Silberberg, "Spatial optical solitons in waveguide arrays," IEEE J. Quantum Electron. 39,31-50 (2003).
[CrossRef]

2002 (2)

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer and F. Lederer, "Anomalous refraction and diffraction in discrete optical systems," Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

U. Peschel and F. Lederer, "Oscillation and decay of discrete solitons in modulated waveguide array," J. Opt. Soc. Am. B 19, 544 (2002)
[CrossRef]

2001 (2)

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel and J. S. Aitchison, "Self-focusing and defocusing in waveguide arrays," Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef] [PubMed]

M. J. Ablowitz and Z. H. Musslimani, "Discrete diffraction managed spatial solitons," Phys. Rev. Lett. 87, 254102 (2001).
[CrossRef] [PubMed]

2000 (1)

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchinson, "Diffraction management," Phys. Rev. Lett. 85, 1863 (2000).
[CrossRef] [PubMed]

1999 (2)

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, "Optical bloch oscillations in temperature tuned waveguide arrays," Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato and S. Kawakami, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett. 74, 1212 (1999).
[CrossRef]

1998 (1)

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchinson, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

1987 (2)

E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486 (1987).
[CrossRef] [PubMed]

Ablowitz, M. J.

M. J. Ablowitz and Z. H. Musslimani, "Discrete diffraction managed spatial solitons," Phys. Rev. Lett. 87, 254102 (2001).
[CrossRef] [PubMed]

Aitchinson, J. S.

J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchinson, "Experimental observation of discrete modulational instability," Phys. Rev. Lett. 92, 163902 (2004).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchinson, "Diffraction management," Phys. Rev. Lett. 85, 1863 (2000).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchinson, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Aitchison, J. S.

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel and J. S. Aitchison, "Self-focusing and defocusing in waveguide arrays," Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef] [PubMed]

Augustin, M.

R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Fuchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tünnermann, "Diffractionless propagation of light in a low-index photonic-crystal film," Appl. Phys. Lett. 85, 5854 (2004).
[CrossRef]

Boyd, A. R.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchinson, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Brauer, A.

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer and F. Lederer, "Anomalous refraction and diffraction in discrete optical systems," Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

Bräuer, A.

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, "Optical bloch oscillations in temperature tuned waveguide arrays," Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

Chen, C.

Chigrin, D.

Christodoulides, D. N.

J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchinson, "Experimental observation of discrete modulational instability," Phys. Rev. Lett. 92, 163902 (2004).
[CrossRef] [PubMed]

Cianci, E.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, "Observation of dynamic localization in periodically curved waveguide arrays," Phys. Rev. Lett. 96, 243901 (2006).
[CrossRef] [PubMed]

Dannberg, P.

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, "Optical bloch oscillations in temperature tuned waveguide arrays," Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

Eisenberg, H. S.

A. A. Sukhorukov, Y. S. Kivshar, H. S. Eisenberg, and Y. Silberberg, "Spatial optical solitons in waveguide arrays," IEEE J. Quantum Electron. 39,31-50 (2003).
[CrossRef]

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel and J. S. Aitchison, "Self-focusing and defocusing in waveguide arrays," Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchinson, "Diffraction management," Phys. Rev. Lett. 85, 1863 (2000).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchinson, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Elflein, W.

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, "Optical bloch oscillations in temperature tuned waveguide arrays," Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

Enoch, S.

Etrich, C.

R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Fuchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tünnermann, "Diffractionless propagation of light in a low-index photonic-crystal film," Appl. Phys. Lett. 85, 5854 (2004).
[CrossRef]

Foglietti, V.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, "Observation of dynamic localization in periodically curved waveguide arrays," Phys. Rev. Lett. 96, 243901 (2006).
[CrossRef] [PubMed]

Fuchs, H.-J.

R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Fuchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tünnermann, "Diffractionless propagation of light in a low-index photonic-crystal film," Appl. Phys. Lett. 85, 5854 (2004).
[CrossRef]

Herrero, R.

K. Staliunas and R. Herrero, Nondiffractive propagation of light in photonic crystals, Phys. Rev. E,  73, 016601 (2006).
[CrossRef]

Iliew, R.

R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Fuchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tünnermann, "Diffractionless propagation of light in a low-index photonic-crystal film," Appl. Phys. Lett. 85, 5854 (2004).
[CrossRef]

John, S.

S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486 (1987).
[CrossRef] [PubMed]

Kawakami, S.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato and S. Kawakami, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett. 74, 1212 (1999).
[CrossRef]

Kawashima, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato and S. Kawakami, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett. 74, 1212 (1999).
[CrossRef]

Kivshar, Y. S.

A. A. Sukhorukov, Y. S. Kivshar, H. S. Eisenberg, and Y. Silberberg, "Spatial optical solitons in waveguide arrays," IEEE J. Quantum Electron. 39,31-50 (2003).
[CrossRef]

Kley, E.-B.

R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Fuchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tünnermann, "Diffractionless propagation of light in a low-index photonic-crystal film," Appl. Phys. Lett. 85, 5854 (2004).
[CrossRef]

Kosaka, H.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato and S. Kawakami, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett. 74, 1212 (1999).
[CrossRef]

Laporta, P.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, "Observation of dynamic localization in periodically curved waveguide arrays," Phys. Rev. Lett. 96, 243901 (2006).
[CrossRef] [PubMed]

Lederer, F.

R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Fuchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tünnermann, "Diffractionless propagation of light in a low-index photonic-crystal film," Appl. Phys. Lett. 85, 5854 (2004).
[CrossRef]

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer and F. Lederer, "Anomalous refraction and diffraction in discrete optical systems," Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

U. Peschel and F. Lederer, "Oscillation and decay of discrete solitons in modulated waveguide array," J. Opt. Soc. Am. B 19, 544 (2002)
[CrossRef]

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, "Optical bloch oscillations in temperature tuned waveguide arrays," Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

Lobino, M.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, "Observation of dynamic localization in periodically curved waveguide arrays," Phys. Rev. Lett. 96, 243901 (2006).
[CrossRef] [PubMed]

Longhi, S.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, "Observation of dynamic localization in periodically curved waveguide arrays," Phys. Rev. Lett. 96, 243901 (2006).
[CrossRef] [PubMed]

Marangoni, M.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, "Observation of dynamic localization in periodically curved waveguide arrays," Phys. Rev. Lett. 96, 243901 (2006).
[CrossRef] [PubMed]

Meier, J.

J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchinson, "Experimental observation of discrete modulational instability," Phys. Rev. Lett. 92, 163902 (2004).
[CrossRef] [PubMed]

Morandotti, R.

J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchinson, "Experimental observation of discrete modulational instability," Phys. Rev. Lett. 92, 163902 (2004).
[CrossRef] [PubMed]

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel and J. S. Aitchison, "Self-focusing and defocusing in waveguide arrays," Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchinson, "Diffraction management," Phys. Rev. Lett. 85, 1863 (2000).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchinson, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Murakowski, J.

Musslimani, Z. H.

M. J. Ablowitz and Z. H. Musslimani, "Discrete diffraction managed spatial solitons," Phys. Rev. Lett. 87, 254102 (2001).
[CrossRef] [PubMed]

Nolte, S.

R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Fuchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tünnermann, "Diffractionless propagation of light in a low-index photonic-crystal film," Appl. Phys. Lett. 85, 5854 (2004).
[CrossRef]

Notomi, M.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato and S. Kawakami, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett. 74, 1212 (1999).
[CrossRef]

Pertsch, T.

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer and F. Lederer, "Anomalous refraction and diffraction in discrete optical systems," Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, "Optical bloch oscillations in temperature tuned waveguide arrays," Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

Peschel, U.

R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Fuchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tünnermann, "Diffractionless propagation of light in a low-index photonic-crystal film," Appl. Phys. Lett. 85, 5854 (2004).
[CrossRef]

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer and F. Lederer, "Anomalous refraction and diffraction in discrete optical systems," Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

U. Peschel and F. Lederer, "Oscillation and decay of discrete solitons in modulated waveguide array," J. Opt. Soc. Am. B 19, 544 (2002)
[CrossRef]

Prather, D. W.

Pustai, D. M.

Ramponi, R.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, "Observation of dynamic localization in periodically curved waveguide arrays," Phys. Rev. Lett. 96, 243901 (2006).
[CrossRef] [PubMed]

Salamo, G.

J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchinson, "Experimental observation of discrete modulational instability," Phys. Rev. Lett. 92, 163902 (2004).
[CrossRef] [PubMed]

Sato, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato and S. Kawakami, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett. 74, 1212 (1999).
[CrossRef]

Schelle, D.

R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Fuchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tünnermann, "Diffractionless propagation of light in a low-index photonic-crystal film," Appl. Phys. Lett. 85, 5854 (2004).
[CrossRef]

Schneider, G.

Sharkawy, A.

Shi, S.

Silberberg, Y.

J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchinson, "Experimental observation of discrete modulational instability," Phys. Rev. Lett. 92, 163902 (2004).
[CrossRef] [PubMed]

A. A. Sukhorukov, Y. S. Kivshar, H. S. Eisenberg, and Y. Silberberg, "Spatial optical solitons in waveguide arrays," IEEE J. Quantum Electron. 39,31-50 (2003).
[CrossRef]

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel and J. S. Aitchison, "Self-focusing and defocusing in waveguide arrays," Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchinson, "Diffraction management," Phys. Rev. Lett. 85, 1863 (2000).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchinson, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Sorel, M.

J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchinson, "Experimental observation of discrete modulational instability," Phys. Rev. Lett. 92, 163902 (2004).
[CrossRef] [PubMed]

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel and J. S. Aitchison, "Self-focusing and defocusing in waveguide arrays," Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef] [PubMed]

Sotomayor Torres, C.

Staliunas, K.

K. Staliunas and R. Herrero, Nondiffractive propagation of light in photonic crystals, Phys. Rev. E,  73, 016601 (2006).
[CrossRef]

Stegeman, G. I.

J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchinson, "Experimental observation of discrete modulational instability," Phys. Rev. Lett. 92, 163902 (2004).
[CrossRef] [PubMed]

Sukhorukov, A. A.

A. A. Sukhorukov, Y. S. Kivshar, H. S. Eisenberg, and Y. Silberberg, "Spatial optical solitons in waveguide arrays," IEEE J. Quantum Electron. 39,31-50 (2003).
[CrossRef]

Tamamura, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato and S. Kawakami, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett. 74, 1212 (1999).
[CrossRef]

Tayeb, G.

Tomita, A.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato and S. Kawakami, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett. 74, 1212 (1999).
[CrossRef]

Tünnermann, A.

R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Fuchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tünnermann, "Diffractionless propagation of light in a low-index photonic-crystal film," Appl. Phys. Lett. 85, 5854 (2004).
[CrossRef]

Venkataraman, S.

Yablonovitch, E.

E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

Yang, H.

J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchinson, "Experimental observation of discrete modulational instability," Phys. Rev. Lett. 92, 163902 (2004).
[CrossRef] [PubMed]

Zentgraf, T.

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer and F. Lederer, "Anomalous refraction and diffraction in discrete optical systems," Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

Appl. Phys. Lett. (2)

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato and S. Kawakami, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett. 74, 1212 (1999).
[CrossRef]

R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Fuchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tünnermann, "Diffractionless propagation of light in a low-index photonic-crystal film," Appl. Phys. Lett. 85, 5854 (2004).
[CrossRef]

IEEE J. Quantum Electron. (1)

A. A. Sukhorukov, Y. S. Kivshar, H. S. Eisenberg, and Y. Silberberg, "Spatial optical solitons in waveguide arrays," IEEE J. Quantum Electron. 39,31-50 (2003).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. E (1)

K. Staliunas and R. Herrero, Nondiffractive propagation of light in photonic crystals, Phys. Rev. E,  73, 016601 (2006).
[CrossRef]

Phys. Rev. Lett. (10)

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, "Observation of dynamic localization in periodically curved waveguide arrays," Phys. Rev. Lett. 96, 243901 (2006).
[CrossRef] [PubMed]

J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchinson, "Experimental observation of discrete modulational instability," Phys. Rev. Lett. 92, 163902 (2004).
[CrossRef] [PubMed]

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, "Optical bloch oscillations in temperature tuned waveguide arrays," Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchinson, "Diffraction management," Phys. Rev. Lett. 85, 1863 (2000).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchinson, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel and J. S. Aitchison, "Self-focusing and defocusing in waveguide arrays," Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef] [PubMed]

M. J. Ablowitz and Z. H. Musslimani, "Discrete diffraction managed spatial solitons," Phys. Rev. Lett. 87, 254102 (2001).
[CrossRef] [PubMed]

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer and F. Lederer, "Anomalous refraction and diffraction in discrete optical systems," Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486 (1987).
[CrossRef] [PubMed]

Other (1)

K. Staliunas, R. Herrero and G. J. de Valcarcel, Sub-diffractive band-edge solitons in Bose-Einstein condensates in periodic potentials, Phys. Rev. E 73, 065603(R) (2006).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

Qualitative representation of the modulated fiber array. The grey regions indicate the thickness of the fibers. Notice the alternating periodic variation of the thickness along the z-direction: for values of z such that the thickness of the fiber j is maximum, the thickness of the neighboring fibers, j-1 and j+1, is minimum. It can be also observed that the distance between the cores of the fibers is constant along the z-direction.

Fig. 2.
Fig. 2.

Spatial dispersion curve obtained by solving Eq. (4) truncated to three modes. The wavenumber is plotted vs. the tilt of the Bloch modes. The dotted curves correspond to the limit of small modulation, Δβ → 0, when the three equations become uncoupled. The parameters are c = 0.25, Δβ = 0.2 (dashed) and Δβ = 0.4 (solid), and correspond to the case when the uncoupled curves just touch one another. In this situation, an increase of the modulation depth Δβ broadens the subdiffractive plateau.

Fig. 3.
Fig. 3.

The width of the beam in the parameter space (c, Δβ) as obtained by numerical integration of (2) over propagation distance of L=100, and starting from initial Gaussian beam. The color scale is such that the red regions correspond to large-, and the blue- to small final width of the beam.

Fig. 4.
Fig. 4.

Sub-diffractive propagating of beams, as obtained by numerical integration of (2) with c=0.25 and Δβ = 0.1. The top row displays the initial condition, the second row displays the density plots of the beam propagation, the third row displays the evolution of the intensity in the central fiber, and the bottom row - the Fourier power spectra of the intensity evolution. Different columns correspond to different initial conditions: left column – envelope of the (1,1) Bloch mode; Middle column – envelope of (−1,1) Bloch mode. Right column – Gaussian beam, with eigenvector (1,0), which can be considered as a combination of the Bloch modes: (1,0) = ((1,1)−(−1,1))/2

Fig. 5.
Fig. 5.

Sub-diffractive propagation in the presence of positive and negative nonlinearities (γ = 0.1 in the top row, γ = - 0.1 in the bottom row, other parameters and initial conditions as in Fig. 4).

Equations (8)

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β j ( z ) = β 0 + 2 Δ β ( 1 ) j cos ( qz ) ,
d A j dz = i · 2 Δ β ( 1 ) j cos ( z ) A j + ic ( A j 1 + A j + 1 ) + A j 2 A j ,
A j = e ikz e i · j Δ φ n = ( 1 ) j · n a n e izn ,
i ( k + n ) a n = i Δ β ( a n 1 + a n + 1 ) + 2 ic ( 1 ) n cos ( Δ φ ) a n
ik a 0 = i Δ β a 1 + 2 ic cos ( Δ φ ) a 0 ,
i ( k 1 ) a 1 = i Δ β a 0 2 ic cos ( Δ φ ) a 1 .
k ( Δ φ ) = 1 2 ± 1 2 4 Δ β 2 + ( 1 4 c · cos ( Δ φ ) ) 2 ,
( 1 + 4 c · cos ( Δ φ ) ± 4 Δ β 2 + ( 1 4 c · cos ( Δ φ ) ) 2 , 2 Δ β ) .

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