Abstract

We study theoretically the dispersion properties of Bloch modes and nonlinearly-induced defect states in two-dimensional waveguide arrays. We define the conditions for achieving anomalous group-velocity dispersion and discuss possibilities for generation of spatiotemporal solitons.

© 2008 Optical Society of America

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  1. Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic Press, San Diego, 2003).
  2. G. I. Stegeman and M. Segev, "Optical spatial solitons and their interactions: Universality and diversity," Science 286, 1518-1523 (1999).
    [CrossRef]
  3. G. P. Agrawal, Nonlinear Fiber Optics, fourth ed. (Academic Press, New York, 2007).
  4. Y. Silberberg, "Collapse of optical pulses," Opt. Lett. 15, 1282-1284 (1990).
  5. A. B. Blagoeva, S. G. Dinev, A. A. Dreischuh, and A. Naidenov, "Light bullets formation in a bulk media," IEEE J. Quantum Electron. QE-27, 2060 (1991).
  6. F. Wise and P. Di Trapani, "The hunt for light bullets - spatiotemporal solitons," Opt. Photon. News 13, 28-32 (2002).
  7. B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, "Spatiotemporal optical solitons," J. Opt. B: Quantum Semicl. Opt. 7, R53-R72 (2005).
  8. H. S. Eisenberg, R. Morandotti, Y. Silberberg, S. Bar Ad, D. Ross, and J. S. Aitchison, "Kerr spatiotemporal self-focusing in a planar glass waveguide," Phys. Rev. Lett. 87, 043902-4 (2001).
    [CrossRef]
  9. D. Cheskis, S. Bar Ad, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, and D. Ross, "Strong spatiotemporal localization in a silica nonlinear waveguide array," Phys. Rev. Lett. 91, 223901-4 (2003).
    [CrossRef]
  10. N. I. Nikolov, D. Neshev, O. Bang, and W. Z. Krolikowski, "Quadratic solitons as nonlocal solitons," Phys. Rev. E 68, 036614-5 (2003).
    [CrossRef]
  11. X. Liu, L. J. Qian, and F. W. Wise, "Generation of optical spatiotemporal solitons," Phys. Rev. Lett. 82, 4631- 4634 (1999).
    [CrossRef]
  12. X. Liu, K. Beckwitt, and F. Wise, "Two-dimensional optical spatiotemporal solitons in quadratic media," Phys. Rev. E 62, 1328-1340 (2000).
    [CrossRef]
  13. A. B. Aceves, C. De Angelis, A. M. Rubenchik, and S. K. Turitsyn, "Multidimensional solitons in fiber arrays," Opt. Lett. 19, 329-331 (1994).
  14. E.W. Laedke, K. H. Spatschek, and S. K. Turitsyn, "Stability of discrete solitons and quasicollapse to intrinsically localized modes," Phys. Rev. Lett. 73, 1055-1059 (1994).
    [CrossRef]
  15. A. B. Aceves, G. G. Luther, C. De Angelis, A. M. Rubenchik, and S. K. Turitsyn, "Energy localization in nonlinear fiber arrays - collapse-effect compressor," Phys. Rev. Lett. 75, 73-76 (1995).
    [CrossRef]
  16. A. B. Aceves, M. Santagiustina, and C. De Angelis, "Analytical study of nonlinear-optical pulse dynamics in arrays of linearly coupled waveguides," J. Opt. Soc. Am. B 14, 1807-1815 (1997).
    [CrossRef]
  17. D. Mihalache, D. Mazilu, F. Lederer, and Yu. S. Kivshar, "Stable discrete surface light bullets," Opt. Express 15, 589-595 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-2-589.
  18. D. N. Christodoulides, F. Lederer, and Y. Silberberg, "Discretizing light behaviour in linear and nonlinear waveguide lattices," Nature 424, 817-823 (2003).
    [CrossRef]
  19. D. N. Christodoulides and R. I. Joseph, "Discrete self-focusing in nonlinear arrays of coupled wave-guides," Opt. Lett. 13, 794-796 (1988).
  20. H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383-3386 (1998).
    [CrossRef]
  21. J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of discrete solitons in optically induced real time waveguide arrays," Phys. Rev. Lett. 90, 023902-4 (2003).
    [CrossRef]
  22. D. Neshev, E. Ostrovskaya, Y. Kivshar, and W. Krolikowski, "Spatial solitons in optically induced gratings," Opt. Lett. 28, 710-712 (2003).
    [CrossRef]
  23. F. Chen, M. Stepi’c, C. R¨uter, D. Runde, D. Kip, V. Shandarov, O. Manela, and M. Segev, "Discrete diffraction and spatial gap solitons in photovoltaic LiNbO3 waveguide arrays," Opt. Express 13, 4314-4324 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-11-4314.
    [CrossRef]
  24. A. Fratalocchi, G. Assanto, K. A. Brzdakiewicz, and M. A. Karpierz, "Discrete propagation and spatial solitons in nematic liquid crystals," Opt. Lett. 29, 1530-1532 (2004).
    [CrossRef]
  25. 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 422, 147-150 (2003).
    [CrossRef]
  26. C. R. Rosberg, D. N. Neshev, A. A. Sukhorukov, W. Krolikowski, and Yu. S. Kivshar, "Observation of nonlinear self-trapping in triangular photonic lattices," Opt. Lett. 32, 397-399 (2007).
    [CrossRef]
  27. A. Szameit, D. Blomer, J. Burghoff, T. Schreiber, T. Pertsch, S. Nolte, A. Tunnermann, and F. Lederer, "Discrete nonlinear localization in femtosecond laser written waveguides in fused silica," Opt. Express 13, 10552-10557 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-26-10552.
    [CrossRef]
  28. F. Couny, F. Benabid, P. J. Roberts, M. T. Burnett, and S. A. Maier, "Identification of Blochmodes in hollow-core photonic crystal fiber cladding," Opt. Express 15, 325-338 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-2-325.
  29. C. R. Rosberg, F. H. Bennet, D. N. Neshev, P. D. Rasmussen, O. Bang, W. Krolikowski, A. Bjarklev, and Yu. S. Kivshar, "Tunable diffraction and self-defocusing in liquid-filled photonic crystal fibers," Opt. Express 15, 12145-12150 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-19-12145.
    [CrossRef]
  30. J. Jasapara, T. H. Her, R. Bise, R. Windeler, and D. J. DiGiovanni, "Group-velocity dispersion measurements in a photonic bandgap fiber," J. Opt. Soc. Am. B 20, 1611-1615 (2003).
    [CrossRef]
  31. P. Mach, M. Dolinski, K. W. Baldwin, J. A. Rogers, C. Kerbage, R. S. Windeler, and B. J. Eggleton, "Tunable microfluidic optical fiber," Appl. Phys. Lett. 80, 4294-4296 (2002).
    [CrossRef]
  32. F. Luan, A. K. George, T. D. Hedley, G. J. Pearce, D. M. Bird, J. C. Knight, and P. St. Russell, "All-solid photonic bandgap fiber," Opt. Lett. 29, 2369-2371 (2004).
    [CrossRef]
  33. T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tunnermann, and F. Lederer, "Nonlinearity and disorder in fiber arrays," Phys. Rev. Lett. 93, 053901-4 (2004).
    [CrossRef]
  34. U. Ropke, H. Bartelt, S. Unger, K. Schuster, and J. Kobelke, "Two-dimensional high-precision fiber waveguide arrays for coherent light propagation," Opt. Express 15, 6894-6899 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-11-6894.
    [CrossRef]
  35. S. G. Johnson and J. D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis," Opt. Express 8, 173-190 (2001), http://www.opticsinfobase.org/abstract.cfm?URI=oe-8-3-173.
  36. A. Samoc, "Dispersion of refractive properties of solvents: chloroform, toluene, benzene, and carbon disulfide in ultraviolet, visible, and near-infrared," J. Appl. Phys. 94, 6167-6174 (2003).
    [CrossRef]
  37. D. N. Nikogosyan, Properties of Optical and Laser-Related Materials: A Handbook (Wiley, Chichester, UK, 1997).
  38. K. Okamoto, Fundamentals of optical waveguides (Academic Press, San Diego, 2000).
  39. I. P. Nikolakakos, A. Major, J. S. Aitchison, and P. W. E. Smith, "Broadband characterization of the nonlinear optical properties of common reference materials," IEEE J. Sel. Top. Quantum Electron. 10, 1164-1170 (2004).
  40. COMSOL Multiphysics 3.3 (2007), COMSOL Inc. (http://www.comsol.com/).
  41. P. G. Kevrekidis, B. A. Malomed, and Y. B. Gaididei, "Solitons in triangular and honeycomb dynamical lattices with the cubic nonlinearity," Phys. Rev. E 66, 016609-10 (2002).
    [CrossRef]

2007 (5)

2005 (3)

2004 (4)

T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tunnermann, and F. Lederer, "Nonlinearity and disorder in fiber arrays," Phys. Rev. Lett. 93, 053901-4 (2004).
[CrossRef]

A. Fratalocchi, G. Assanto, K. A. Brzdakiewicz, and M. A. Karpierz, "Discrete propagation and spatial solitons in nematic liquid crystals," Opt. Lett. 29, 1530-1532 (2004).
[CrossRef]

F. Luan, A. K. George, T. D. Hedley, G. J. Pearce, D. M. Bird, J. C. Knight, and P. St. Russell, "All-solid photonic bandgap fiber," Opt. Lett. 29, 2369-2371 (2004).
[CrossRef]

I. P. Nikolakakos, A. Major, J. S. Aitchison, and P. W. E. Smith, "Broadband characterization of the nonlinear optical properties of common reference materials," IEEE J. Sel. Top. Quantum Electron. 10, 1164-1170 (2004).

2003 (8)

D. Neshev, E. Ostrovskaya, Y. Kivshar, and W. Krolikowski, "Spatial solitons in optically induced gratings," Opt. Lett. 28, 710-712 (2003).
[CrossRef]

J. Jasapara, T. H. Her, R. Bise, R. Windeler, and D. J. DiGiovanni, "Group-velocity dispersion measurements in a photonic bandgap fiber," J. Opt. Soc. Am. B 20, 1611-1615 (2003).
[CrossRef]

A. Samoc, "Dispersion of refractive properties of solvents: chloroform, toluene, benzene, and carbon disulfide in ultraviolet, visible, and near-infrared," J. Appl. Phys. 94, 6167-6174 (2003).
[CrossRef]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of discrete solitons in optically induced real time waveguide arrays," Phys. Rev. Lett. 90, 023902-4 (2003).
[CrossRef]

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 422, 147-150 (2003).
[CrossRef]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, "Discretizing light behaviour in linear and nonlinear waveguide lattices," Nature 424, 817-823 (2003).
[CrossRef]

D. Cheskis, S. Bar Ad, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, and D. Ross, "Strong spatiotemporal localization in a silica nonlinear waveguide array," Phys. Rev. Lett. 91, 223901-4 (2003).
[CrossRef]

N. I. Nikolov, D. Neshev, O. Bang, and W. Z. Krolikowski, "Quadratic solitons as nonlocal solitons," Phys. Rev. E 68, 036614-5 (2003).
[CrossRef]

2002 (3)

F. Wise and P. Di Trapani, "The hunt for light bullets - spatiotemporal solitons," Opt. Photon. News 13, 28-32 (2002).

P. Mach, M. Dolinski, K. W. Baldwin, J. A. Rogers, C. Kerbage, R. S. Windeler, and B. J. Eggleton, "Tunable microfluidic optical fiber," Appl. Phys. Lett. 80, 4294-4296 (2002).
[CrossRef]

P. G. Kevrekidis, B. A. Malomed, and Y. B. Gaididei, "Solitons in triangular and honeycomb dynamical lattices with the cubic nonlinearity," Phys. Rev. E 66, 016609-10 (2002).
[CrossRef]

2001 (2)

S. G. Johnson and J. D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis," Opt. Express 8, 173-190 (2001), http://www.opticsinfobase.org/abstract.cfm?URI=oe-8-3-173.

H. S. Eisenberg, R. Morandotti, Y. Silberberg, S. Bar Ad, D. Ross, and J. S. Aitchison, "Kerr spatiotemporal self-focusing in a planar glass waveguide," Phys. Rev. Lett. 87, 043902-4 (2001).
[CrossRef]

2000 (1)

X. Liu, K. Beckwitt, and F. Wise, "Two-dimensional optical spatiotemporal solitons in quadratic media," Phys. Rev. E 62, 1328-1340 (2000).
[CrossRef]

1999 (2)

X. Liu, L. J. Qian, and F. W. Wise, "Generation of optical spatiotemporal solitons," Phys. Rev. Lett. 82, 4631- 4634 (1999).
[CrossRef]

G. I. Stegeman and M. Segev, "Optical spatial solitons and their interactions: Universality and diversity," Science 286, 1518-1523 (1999).
[CrossRef]

1998 (1)

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383-3386 (1998).
[CrossRef]

1997 (1)

1995 (1)

A. B. Aceves, G. G. Luther, C. De Angelis, A. M. Rubenchik, and S. K. Turitsyn, "Energy localization in nonlinear fiber arrays - collapse-effect compressor," Phys. Rev. Lett. 75, 73-76 (1995).
[CrossRef]

1994 (2)

E.W. Laedke, K. H. Spatschek, and S. K. Turitsyn, "Stability of discrete solitons and quasicollapse to intrinsically localized modes," Phys. Rev. Lett. 73, 1055-1059 (1994).
[CrossRef]

A. B. Aceves, C. De Angelis, A. M. Rubenchik, and S. K. Turitsyn, "Multidimensional solitons in fiber arrays," Opt. Lett. 19, 329-331 (1994).

1991 (1)

A. B. Blagoeva, S. G. Dinev, A. A. Dreischuh, and A. Naidenov, "Light bullets formation in a bulk media," IEEE J. Quantum Electron. QE-27, 2060 (1991).

1990 (1)

1988 (1)

Appl. Phys. Lett. (1)

P. Mach, M. Dolinski, K. W. Baldwin, J. A. Rogers, C. Kerbage, R. S. Windeler, and B. J. Eggleton, "Tunable microfluidic optical fiber," Appl. Phys. Lett. 80, 4294-4296 (2002).
[CrossRef]

IEEE J. Quantum Electron. (1)

A. B. Blagoeva, S. G. Dinev, A. A. Dreischuh, and A. Naidenov, "Light bullets formation in a bulk media," IEEE J. Quantum Electron. QE-27, 2060 (1991).

IEEE J. Sel. Top. Quantum Electron. (1)

I. P. Nikolakakos, A. Major, J. S. Aitchison, and P. W. E. Smith, "Broadband characterization of the nonlinear optical properties of common reference materials," IEEE J. Sel. Top. Quantum Electron. 10, 1164-1170 (2004).

J. Appl. Phys. (1)

A. Samoc, "Dispersion of refractive properties of solvents: chloroform, toluene, benzene, and carbon disulfide in ultraviolet, visible, and near-infrared," J. Appl. Phys. 94, 6167-6174 (2003).
[CrossRef]

J. Opt. B: Quantum Semicl. Opt. (1)

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, "Spatiotemporal optical solitons," J. Opt. B: Quantum Semicl. Opt. 7, R53-R72 (2005).

J. Opt. Soc. Am. B (2)

Nature (2)

D. N. Christodoulides, F. Lederer, and Y. Silberberg, "Discretizing light behaviour in linear and nonlinear waveguide lattices," Nature 424, 817-823 (2003).
[CrossRef]

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 422, 147-150 (2003).
[CrossRef]

Opt. Express (7)

S. G. Johnson and J. D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis," Opt. Express 8, 173-190 (2001), http://www.opticsinfobase.org/abstract.cfm?URI=oe-8-3-173.

F. Chen, M. Stepi’c, C. R¨uter, D. Runde, D. Kip, V. Shandarov, O. Manela, and M. Segev, "Discrete diffraction and spatial gap solitons in photovoltaic LiNbO3 waveguide arrays," Opt. Express 13, 4314-4324 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-11-4314.
[CrossRef]

A. Szameit, D. Blomer, J. Burghoff, T. Schreiber, T. Pertsch, S. Nolte, A. Tunnermann, and F. Lederer, "Discrete nonlinear localization in femtosecond laser written waveguides in fused silica," Opt. Express 13, 10552-10557 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-26-10552.
[CrossRef]

F. Couny, F. Benabid, P. J. Roberts, M. T. Burnett, and S. A. Maier, "Identification of Blochmodes in hollow-core photonic crystal fiber cladding," Opt. Express 15, 325-338 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-2-325.

D. Mihalache, D. Mazilu, F. Lederer, and Yu. S. Kivshar, "Stable discrete surface light bullets," Opt. Express 15, 589-595 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-2-589.

U. Ropke, H. Bartelt, S. Unger, K. Schuster, and J. Kobelke, "Two-dimensional high-precision fiber waveguide arrays for coherent light propagation," Opt. Express 15, 6894-6899 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-11-6894.
[CrossRef]

C. R. Rosberg, F. H. Bennet, D. N. Neshev, P. D. Rasmussen, O. Bang, W. Krolikowski, A. Bjarklev, and Yu. S. Kivshar, "Tunable diffraction and self-defocusing in liquid-filled photonic crystal fibers," Opt. Express 15, 12145-12150 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-19-12145.
[CrossRef]

Opt. Lett. (7)

Opt. Photon. News (1)

F. Wise and P. Di Trapani, "The hunt for light bullets - spatiotemporal solitons," Opt. Photon. News 13, 28-32 (2002).

Phys. Rev. E (3)

N. I. Nikolov, D. Neshev, O. Bang, and W. Z. Krolikowski, "Quadratic solitons as nonlocal solitons," Phys. Rev. E 68, 036614-5 (2003).
[CrossRef]

X. Liu, K. Beckwitt, and F. Wise, "Two-dimensional optical spatiotemporal solitons in quadratic media," Phys. Rev. E 62, 1328-1340 (2000).
[CrossRef]

P. G. Kevrekidis, B. A. Malomed, and Y. B. Gaididei, "Solitons in triangular and honeycomb dynamical lattices with the cubic nonlinearity," Phys. Rev. E 66, 016609-10 (2002).
[CrossRef]

Phys. Rev. Lett. (8)

X. Liu, L. J. Qian, and F. W. Wise, "Generation of optical spatiotemporal solitons," Phys. Rev. Lett. 82, 4631- 4634 (1999).
[CrossRef]

H. S. Eisenberg, R. Morandotti, Y. Silberberg, S. Bar Ad, D. Ross, and J. S. Aitchison, "Kerr spatiotemporal self-focusing in a planar glass waveguide," Phys. Rev. Lett. 87, 043902-4 (2001).
[CrossRef]

D. Cheskis, S. Bar Ad, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, and D. Ross, "Strong spatiotemporal localization in a silica nonlinear waveguide array," Phys. Rev. Lett. 91, 223901-4 (2003).
[CrossRef]

E.W. Laedke, K. H. Spatschek, and S. K. Turitsyn, "Stability of discrete solitons and quasicollapse to intrinsically localized modes," Phys. Rev. Lett. 73, 1055-1059 (1994).
[CrossRef]

A. B. Aceves, G. G. Luther, C. De Angelis, A. M. Rubenchik, and S. K. Turitsyn, "Energy localization in nonlinear fiber arrays - collapse-effect compressor," Phys. Rev. Lett. 75, 73-76 (1995).
[CrossRef]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383-3386 (1998).
[CrossRef]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of discrete solitons in optically induced real time waveguide arrays," Phys. Rev. Lett. 90, 023902-4 (2003).
[CrossRef]

T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tunnermann, and F. Lederer, "Nonlinearity and disorder in fiber arrays," Phys. Rev. Lett. 93, 053901-4 (2004).
[CrossRef]

Science (1)

G. I. Stegeman and M. Segev, "Optical spatial solitons and their interactions: Universality and diversity," Science 286, 1518-1523 (1999).
[CrossRef]

Other (5)

G. P. Agrawal, Nonlinear Fiber Optics, fourth ed. (Academic Press, New York, 2007).

Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic Press, San Diego, 2003).

D. N. Nikogosyan, Properties of Optical and Laser-Related Materials: A Handbook (Wiley, Chichester, UK, 1997).

K. Okamoto, Fundamentals of optical waveguides (Academic Press, San Diego, 2000).

COMSOL Multiphysics 3.3 (2007), COMSOL Inc. (http://www.comsol.com/).

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