Abstract

A new type of waveguide lattice that relies on the effect of bandgap guidance, rather than total internal reflection, in the regions between the waveguide defects is proposed. Two different setting, for low index and high index defects are suggested. We analyze the linear bandgap and diffraction properties of such lattices. In the nonlinear regime the Kerr effect can counteract diffraction leading to the formation of gap lattice solitons. Interestingly enough, in the case of low index defects, stable soliton solutions are localized in the low index areas. This finding challenges the widely accepted idea that stable solitons can be sustained in high refractive index regions. In addition, in the case of high index defects, the coupling coefficient can become negative. Physical settings where the linear and nonlinear properties for bandgap lattices can be experimentally realized are presented.

© 2005 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 – 2062 ( 1987 ).
    [Crossref] [PubMed]
  2. S. John , “ Strong Localization of Photons in Certain Disordered Dielectric Superlattices ,” Phys. Rev. Lett.   58 , 2486 – 2489 ( 1987 ).
    [Crossref] [PubMed]
  3. J. Joannopoulos , R. Meade , and J. N. Winn , Photonic Crystals: Molding the Flow of Light ( Princeton University Press, Princeton, NJ , 1995 ).
  4. J. Knight , J. Broeng , T. A. Birks , and P. Russell , “ Photonic band gap guidance in optical fibers ,” Science   282 , 1476 – 1478 ( 1998 ).
    [Crossref] [PubMed]
  5. P. Russell , “ Photonic crystal fibers ,” Science   299 , 358 – 362 ( 2003 ).
    [Crossref] [PubMed]
  6. D. N. Christodoulides and R. I. Joseph , “ Discrete self-focusing in nonlinear arrays of coupled waveguides ,” Opt. Lett.   13 , 794 – 796 ( 1988 ).
    [Crossref] [PubMed]
  7. 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]
  8. D. N. Christodoulides , F. Lederer , and Y. Silberberg , “ Discretizing light behaviour in linear and nonlinear waveguide lattices ,” Nature   424 , 817 – 823 ( 2003 ).
    [Crossref] [PubMed]
  9. A. Mekis , J. C. Chen , I. Kurland , S. Fan , P. R. Villeneuve , and J. D. Joannopoulos , “ High Transmission through Sharp Bends in Photonic Crystal Waveguides ,” Phys. Rev. Lett.   77 , 3787 – 3790 ( 1996 ).
    [Crossref] [PubMed]
  10. 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 – 2020 ( 1991 ).
    [Crossref] [PubMed]
  11. E. Yablonovitch , T. J. Gmitter , R. D. Meade , A. M. Rappe , K. D. Brommer , and J. D. Joannopoulos , “ Donor and Acceptor Modes in Photonic Band Strucure ,” Phys. Rev. Lett.   67 , 3380 – 3383 ( 1991 ).
    [Crossref] [PubMed]
  12. N. Stefanou and A. Modinos , “ Impurity bands in photonic insulators ,” Phys. Rev. B   57 , 12, 127 –12, 133 ( 1998 ).
    [Crossref]
  13. A. Yariv , Y. Xu , R. K. Lee , and A. Scherer , “ Coupled-resonator optical waveguide: a proposal and analysis ,” Opt. Lett.   24 , 711 – 713 ( 1999 ).
    [Crossref]
  14. M. Bayindir , B. Temelkuran , and E. Ozbay , “ Tight-Binding Description of the Coupled Defect Modes in Three-Dimensional Photonic Crystals ,” Phys. Rev. Lett.   84 , 2140 – 2143 ( 2000 ).
    [Crossref] [PubMed]
  15. R. Morandotti , U. Peschel , J. S. Aitchison , H. S. Eisenberg , and Y. Silberberg , “ Dynamics of Discrete Solitons in Optical Waveguide Arrays ,” Phys. Rev. Lett. ( 1999 ).
    [Crossref]
  16. R. Iwanow , R. Schiek , G. I. Stegeman , T. Pertsch , F. ederer , Y. Min , and W. Sohler , “ Observation of Discrete Quadratic Solitons ,” Phys. Rev. Lett.   93 , 113 , 902 –1–4 ( 2004 ).
    [Crossref]
  17. T. Pertsch , P. Dannberg , W. Elflein , A. Bräuer , and F. Lederer , “ Optical Bloch Oscillations in Temperature Tuned Waveguide Arrays ,” Phys. Rev. Lett.   83 , 4752 – 4755 ( 1999 ).
    [Crossref]
  18. R. Morandotti , U. Peschel , J. S. Aitchison , H. S. Eisenberg , and Y. Silberberg , “ Experimental Observation of Linear and Nonlinear Optical Bloch Oscillations ,” Phys. Rev. Lett.   83 , 4756 – 4759 ( 1999 ).
    [Crossref]
  19. J. Meier , J. Hudock , D. Christodoulides , G. Stegeman , Y. Silberberg , R. Morandotti , and J. S. Aitchison , “ Discrete Vector Solitons in Kerr Nonlinear Waveguide Arrays ,” Phys. Rev. Lett.   91 , 143 , 907 –1–4 ( 2003 ).
    [Crossref]
  20. D. Mandelik , H. S. Eisenberg , Y. Silberberg , R. Morandotti , and J. S. Aitchison , “ Band-Gap Structure of Waveguide Arrays and Excitation of Floquet-Bloch Solitons ,” Phys. Rev. Lett.   90 , 053 , 902 –1–4 ( 2003 ).
    [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 , 023 , 902 –1–4 ( 2003 ).
    [Crossref]
  22. J. Feng , “ Alternative scheme for studying gap solitons in an infinite periodic Kerr medium ,” Opt. Lett.   18 , 1302 – 1304 ( 1993 ).
    [Crossref] [PubMed]
  23. D. D. Mandelik , R. Morandotti , J. S. Aitchison , and Y. Silberberg , “ Gap Solitons in Waveguide Arrays ,” Phys. Rev. Lett.   92 , 093 , 904 –1–4 ( 2004 ).
    [Crossref]
  24. D. Neshev , A. A. Sukhorukov , B. Hanna , W. Krolikowski , and Y. S. Kivshar , “ Controlled Generation and Steering of Spatial Gap Solitons ,” Phys. Rev. Lett.   93 , 083 , 905 –1–4 ( 2004 ).
    [Crossref]
  25. P. J. Y. Louis , E. A. Ostrovskaya , C. M. Savage , and Y. S. Kivshar , “ Bose-Einstein condensates in optical lattices: Band-gap structure and solitons ,” Phys. Rev. A   67 , 013 , 602 –1–9 ( 2003 ).
    [Crossref]
  26. N. K. Efremidis and D. N. Christodoulides , “ Lattice solitons in Bose-Einstein condensates ,” Phys. Rev. A   67 , 063 , 608 –1–9 ( 2003 ).
    [Crossref]
  27. Y. V. Kartashov , V. A. Vysloukh , and L. Torner , “ Soliton trains in photonic lattices ,” Opt. Express   12 , 2831 – 2837 ( 2004 ).
    [Crossref] [PubMed]
  28. J. Wang , F. Ye , L. Dong , T. Cai , and Y.-P. Li , “ Lattice solitons supported by competing cubic-quintic nonlinearity ,” Phys. Lett. A   339 , 74 – 82 ( 2005 ).
    [Crossref]
  29. P. Kevrekidis , B. Malomed , and Z. Musslimani , “ Discrete gap solitons in a diffraction-managed waveguide array ,” Eur. Phys. J. D   23 , 421 – 436 ( 2003 ).
    [Crossref]
  30. D. N. Christodoulides and R. I. Joseph , “ Slow Bragg Solitons in Nonlinear Periodic Structures ,” Phys. Rev. Lett.   62 , 1746 – 1749 ( 1989 ).
    [Crossref] [PubMed]
  31. A. B. Aceves and S. Wabnitz , “ Self-induced transparency solitons in nonlinear refractive periodic media ,” Phys. Lett. A   141 , 37 – 42 ( 1989 ).
    [Crossref]
  32. B. J. Eggleton , R. E. Slusher , C. M. de Sterke , P. A. Krug , and J. E. Sipe , “ Bragg Grating Solitons ,” Phys. Rev. Lett.   76 , 1627 – 1630 ( 1996 ).
    [Crossref] [PubMed]
  33. C. M. de Sterke and J. E. Sipe , “ Gap solitons ,” in Progress in Optics , E. Wolf , ed., vol. XXXIII, p. 203 ( North-Holland, Amsterdam , 1994 ).
  34. F. Fedele , J. Yang , and Z. Chen , “ Defect modes in one-dimensional photonic lattices ,” Opt. Lett.   30 , 1506 – 1508 ( 2005 ).
    [Crossref] [PubMed]
  35. Y. V. Kartashov , L. Torner , and V. A. Vysloukh , “ Diffraction management of focused light beams in optical lattices with a quadratic frequency modulation ,” Opt. Express   13 , 4244 – 4249 ( 2005 ).
    [Crossref] [PubMed]
  36. N. K. Efremidis , D. N. Christodoulides , S. Sears , J. W. Fleischer , and M. Segev , “ Discrete Solitons in Photorefractive Optically-Induced Photonic Lattices ,” Phys. Rev. E   66 , 046 , 602 –1–5 ( 2002 ).
    [Crossref]
  37. 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] [PubMed]
  38. 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 , 213 , 906 –1–4 ( 2003 ).
    [Crossref]
  39. J. Yang and Z. H. Musslimani , “ Fundamental and vortex solitons in a two-dimensional optical lattice ,” Opt. Lett.   21 , 2094 – 2096 ( 2003 ).
    [Crossref]
  40. B. A. Malomed and P. G. Kevrekidis , “ Discrete vortex solitons ,” Prys. Rev. E   64 , 026 , 601 –1–6 ( 2001 ).
  41. B. B. Baizakov , B. A. Malomed , and M. Salerno , “ Multidimensional solitons in periodic potentials ,” Europhys. Lett.   63 , 642 – 648 ( 2003 ).
    [Crossref]
  42. J. W. Fleischer , G. Bartal , O. Cohen , O. Manela , M. Segev , J. Hudock , and D. N. Christodoulides , “ Observation of Vortex-Ring “Discrete” Solitons in 2D Photonic Lattices ,” Phys. Rev. Lett.   92 , 123 , 904 –1–4 ( 2004 ).
    [Crossref]
  43. D. N. Neshev , T. J. Alexander , E. A. Ostrovskaya , Y. S. Kivshar , H. Martin , I. Makasyuk , and Z. Chen , “ Observation of Discrete Vortex Solitons in Optically Induced Photonic Lattices ,” Phys. Rev. Lett.   92 , 123 , 903 –1–4 ( 2004 ).
    [Crossref]
  44. Y. V. Kartashov , V. A. Vysloukh , and L. Torner , “ Rotary Solitons in Bessel Optical Lattices ,” Phys. Rev. Lett.   93 , 093 , 904 –1–4 ( 2004 ).
    [Crossref]
  45. Y. V. Kartashov , A. A. Egorov , L. Torner , and D. N. Christodoulides , “ Stable soliton complexes in two-dimensional photonic lattices ,” Opt. Lett.   29 , 1918 – 1920 ( 2004 ).
    [Crossref] [PubMed]
  46. J. W. Fleischer , G. Bartal , O. Cohen , T. Schwartz , O. Manela , B. Freeman , M. Segev , H. Buljan , and N. K. Efremidis , “ Spatial photonics in nonlinear waveguide arrays ,” Opt. Express   13 , 1780 – 1796 ( 2005 ).
    [Crossref] [PubMed]
  47. P. Yeh and A. Yariv , “ Bragg reflection waveguides ,” Opt. Commun.   19 , 427 – 430 ( 1976 ).
    [Crossref]
  48. A. Y. Cho , A. Yariv , and P. Yeh , “ Observation of confined propagation in Bragg waveguides ,” Appl. Phys. Lett.   30 , 471 ( 1977 ).
    [Crossref]
  49. A. Yariv , “ Coupled-wave formalism for optical waveguiding by transverse Bragg reflection ,” Opt. Lett.   27 , 936 – 938 ( 2002 ).
    [Crossref]
  50. S. Linden , J. P. Mondia , H. M. V. Driel , T. C. Kleckner , C. R. Stanley , D. Modotto , A. Locatelli , C. D. An-gelis , R. Morandotti , and J. S. Aitchison , “ Nonlinear transmission properties of a deep-etched microstructured waveguide ,” Appl. Phys. Lett.   84 , 5437 – 5439 ( 2004 ).
    [Crossref]
  51. 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 , 123 , 902 –1–4 ( 2004 ).
    [Crossref]
  52. T. M. Monro , D. J. Richardson , N. G. R. Broderick , and P. J. Bennett , “ Holey Optical Fibers: An Efficient Modal Model ,” J. Lightwave Technol.   17 , 1093 – 1102 ( 1999 ).
    [Crossref]
  53. R. d. L. Kronig and W. G. Penney , “ Quantum Mechanics of Electrons in Crystal Lattices ,” P. Roy. Soc. Lond. A Mat.   814 , 499 – 513 ( 1931 ).
    [Crossref]
  54. S. Theodorakis and E. Leontidis , “ Bound states in a nonlinear Kronig-Penney model ,” J. Phys. A   30 , 4835 – 4849 ( 1997 ).
    [Crossref]
  55. W. Li and A. Smerzi , “ Nonlinear Krönig-Penney model ,” Phys. Rev. E   70 , 016 , 605 –1–4 ( 2004 ).
    [Crossref]
  56. I. M. Merhasin , B. V. Gisin , R. Driben , and B. A. Malomed , “ Finite-band solitons in the Kronig-Penney model with the cubic-quintic nonlinearity ,” Phys. Rev. E   71 , 016 , 613 –1–12 ( 2005 ).
    [Crossref]
  57. C. Kittel , Introduction to Solid State Physics ( Wiley, New York , 1986 ).
  58. H. S. Eisenberg , Y. Silberberg , R. Morandotti , and J. S. Aitchison , “ Diffraction Management ,” Phys. Rev. Lett.   85 , 1863 – 1866 ( 2000 ).
    [Crossref] [PubMed]
  59. S. F. Mingaleev , R. A. Kivshar , S. Yuri , and Sammut , “ Long-range interaction and nonlinear localized modes in photonic crystal waveguides ,” Phys. Rev. E   62 , 5777 – 5782 ( 2000 ).
    [Crossref]
  60. J. Sipe and H. G. Winful , “ Nonlinear Schrödinger solitons in a periodic structure ,” Opt. Lett.   13 , 132 – 133 ( 1988 ).
    [Crossref] [PubMed]

2005 (5)

2004 (11)

W. Li and A. Smerzi , “ Nonlinear Krönig-Penney model ,” Phys. Rev. E   70 , 016 , 605 –1–4 ( 2004 ).
[Crossref]

S. Linden , J. P. Mondia , H. M. V. Driel , T. C. Kleckner , C. R. Stanley , D. Modotto , A. Locatelli , C. D. An-gelis , R. Morandotti , and J. S. Aitchison , “ Nonlinear transmission properties of a deep-etched microstructured waveguide ,” Appl. Phys. Lett.   84 , 5437 – 5439 ( 2004 ).
[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 , 123 , 902 –1–4 ( 2004 ).
[Crossref]

J. W. Fleischer , G. Bartal , O. Cohen , O. Manela , M. Segev , J. Hudock , and D. N. Christodoulides , “ Observation of Vortex-Ring “Discrete” Solitons in 2D Photonic Lattices ,” Phys. Rev. Lett.   92 , 123 , 904 –1–4 ( 2004 ).
[Crossref]

D. N. Neshev , T. J. Alexander , E. A. Ostrovskaya , Y. S. Kivshar , H. Martin , I. Makasyuk , and Z. Chen , “ Observation of Discrete Vortex Solitons in Optically Induced Photonic Lattices ,” Phys. Rev. Lett.   92 , 123 , 903 –1–4 ( 2004 ).
[Crossref]

Y. V. Kartashov , V. A. Vysloukh , and L. Torner , “ Rotary Solitons in Bessel Optical Lattices ,” Phys. Rev. Lett.   93 , 093 , 904 –1–4 ( 2004 ).
[Crossref]

Y. V. Kartashov , A. A. Egorov , L. Torner , and D. N. Christodoulides , “ Stable soliton complexes in two-dimensional photonic lattices ,” Opt. Lett.   29 , 1918 – 1920 ( 2004 ).
[Crossref] [PubMed]

Y. V. Kartashov , V. A. Vysloukh , and L. Torner , “ Soliton trains in photonic lattices ,” Opt. Express   12 , 2831 – 2837 ( 2004 ).
[Crossref] [PubMed]

D. D. Mandelik , R. Morandotti , J. S. Aitchison , and Y. Silberberg , “ Gap Solitons in Waveguide Arrays ,” Phys. Rev. Lett.   92 , 093 , 904 –1–4 ( 2004 ).
[Crossref]

D. Neshev , A. A. Sukhorukov , B. Hanna , W. Krolikowski , and Y. S. Kivshar , “ Controlled Generation and Steering of Spatial Gap Solitons ,” Phys. Rev. Lett.   93 , 083 , 905 –1–4 ( 2004 ).
[Crossref]

R. Iwanow , R. Schiek , G. I. Stegeman , T. Pertsch , F. ederer , Y. Min , and W. Sohler , “ Observation of Discrete Quadratic Solitons ,” Phys. Rev. Lett.   93 , 113 , 902 –1–4 ( 2004 ).
[Crossref]

2003 (12)

P. Russell , “ Photonic crystal fibers ,” Science   299 , 358 – 362 ( 2003 ).
[Crossref] [PubMed]

D. N. Christodoulides , F. Lederer , and Y. Silberberg , “ Discretizing light behaviour in linear and nonlinear waveguide lattices ,” Nature   424 , 817 – 823 ( 2003 ).
[Crossref] [PubMed]

P. J. Y. Louis , E. A. Ostrovskaya , C. M. Savage , and Y. S. Kivshar , “ Bose-Einstein condensates in optical lattices: Band-gap structure and solitons ,” Phys. Rev. A   67 , 013 , 602 –1–9 ( 2003 ).
[Crossref]

N. K. Efremidis and D. N. Christodoulides , “ Lattice solitons in Bose-Einstein condensates ,” Phys. Rev. A   67 , 063 , 608 –1–9 ( 2003 ).
[Crossref]

J. Meier , J. Hudock , D. Christodoulides , G. Stegeman , Y. Silberberg , R. Morandotti , and J. S. Aitchison , “ Discrete Vector Solitons in Kerr Nonlinear Waveguide Arrays ,” Phys. Rev. Lett.   91 , 143 , 907 –1–4 ( 2003 ).
[Crossref]

D. Mandelik , H. S. Eisenberg , Y. Silberberg , R. Morandotti , and J. S. Aitchison , “ Band-Gap Structure of Waveguide Arrays and Excitation of Floquet-Bloch Solitons ,” Phys. Rev. Lett.   90 , 053 , 902 –1–4 ( 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 , 023 , 902 –1–4 ( 2003 ).
[Crossref]

P. Kevrekidis , B. Malomed , and Z. Musslimani , “ Discrete gap solitons in a diffraction-managed waveguide array ,” Eur. Phys. J. D   23 , 421 – 436 ( 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] [PubMed]

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 , 213 , 906 –1–4 ( 2003 ).
[Crossref]

J. Yang and Z. H. Musslimani , “ Fundamental and vortex solitons in a two-dimensional optical lattice ,” Opt. Lett.   21 , 2094 – 2096 ( 2003 ).
[Crossref]

B. B. Baizakov , B. A. Malomed , and M. Salerno , “ Multidimensional solitons in periodic potentials ,” Europhys. Lett.   63 , 642 – 648 ( 2003 ).
[Crossref]

2002 (2)

A. Yariv , “ Coupled-wave formalism for optical waveguiding by transverse Bragg reflection ,” Opt. Lett.   27 , 936 – 938 ( 2002 ).
[Crossref]

N. K. Efremidis , D. N. Christodoulides , S. Sears , J. W. Fleischer , and M. Segev , “ Discrete Solitons in Photorefractive Optically-Induced Photonic Lattices ,” Phys. Rev. E   66 , 046 , 602 –1–5 ( 2002 ).
[Crossref]

2001 (1)

B. A. Malomed and P. G. Kevrekidis , “ Discrete vortex solitons ,” Prys. Rev. E   64 , 026 , 601 –1–6 ( 2001 ).

2000 (3)

H. S. Eisenberg , Y. Silberberg , R. Morandotti , and J. S. Aitchison , “ Diffraction Management ,” Phys. Rev. Lett.   85 , 1863 – 1866 ( 2000 ).
[Crossref] [PubMed]

S. F. Mingaleev , R. A. Kivshar , S. Yuri , and Sammut , “ Long-range interaction and nonlinear localized modes in photonic crystal waveguides ,” Phys. Rev. E   62 , 5777 – 5782 ( 2000 ).
[Crossref]

M. Bayindir , B. Temelkuran , and E. Ozbay , “ Tight-Binding Description of the Coupled Defect Modes in Three-Dimensional Photonic Crystals ,” Phys. Rev. Lett.   84 , 2140 – 2143 ( 2000 ).
[Crossref] [PubMed]

1999 (5)

R. Morandotti , U. Peschel , J. S. Aitchison , H. S. Eisenberg , and Y. Silberberg , “ Dynamics of Discrete Solitons in Optical Waveguide Arrays ,” Phys. Rev. Lett. ( 1999 ).
[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 – 4755 ( 1999 ).
[Crossref]

R. Morandotti , U. Peschel , J. S. Aitchison , H. S. Eisenberg , and Y. Silberberg , “ Experimental Observation of Linear and Nonlinear Optical Bloch Oscillations ,” Phys. Rev. Lett.   83 , 4756 – 4759 ( 1999 ).
[Crossref]

A. Yariv , Y. Xu , R. K. Lee , and A. Scherer , “ Coupled-resonator optical waveguide: a proposal and analysis ,” Opt. Lett.   24 , 711 – 713 ( 1999 ).
[Crossref]

T. M. Monro , D. J. Richardson , N. G. R. Broderick , and P. J. Bennett , “ Holey Optical Fibers: An Efficient Modal Model ,” J. Lightwave Technol.   17 , 1093 – 1102 ( 1999 ).
[Crossref]

1998 (3)

N. Stefanou and A. Modinos , “ Impurity bands in photonic insulators ,” Phys. Rev. B   57 , 12, 127 –12, 133 ( 1998 ).
[Crossref]

J. Knight , J. Broeng , T. A. Birks , and P. Russell , “ Photonic band gap guidance in optical fibers ,” Science   282 , 1476 – 1478 ( 1998 ).
[Crossref] [PubMed]

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)

S. Theodorakis and E. Leontidis , “ Bound states in a nonlinear Kronig-Penney model ,” J. Phys. A   30 , 4835 – 4849 ( 1997 ).
[Crossref]

1996 (2)

A. Mekis , J. C. Chen , I. Kurland , S. Fan , P. R. Villeneuve , and J. D. Joannopoulos , “ High Transmission through Sharp Bends in Photonic Crystal Waveguides ,” Phys. Rev. Lett.   77 , 3787 – 3790 ( 1996 ).
[Crossref] [PubMed]

B. J. Eggleton , R. E. Slusher , C. M. de Sterke , P. A. Krug , and J. E. Sipe , “ Bragg Grating Solitons ,” Phys. Rev. Lett.   76 , 1627 – 1630 ( 1996 ).
[Crossref] [PubMed]

1993 (1)

1991 (2)

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 – 2020 ( 1991 ).
[Crossref] [PubMed]

E. Yablonovitch , T. J. Gmitter , R. D. Meade , A. M. Rappe , K. D. Brommer , and J. D. Joannopoulos , “ Donor and Acceptor Modes in Photonic Band Strucure ,” Phys. Rev. Lett.   67 , 3380 – 3383 ( 1991 ).
[Crossref] [PubMed]

1989 (2)

D. N. Christodoulides and R. I. Joseph , “ Slow Bragg Solitons in Nonlinear Periodic Structures ,” Phys. Rev. Lett.   62 , 1746 – 1749 ( 1989 ).
[Crossref] [PubMed]

A. B. Aceves and S. Wabnitz , “ Self-induced transparency solitons in nonlinear refractive periodic media ,” Phys. Lett. A   141 , 37 – 42 ( 1989 ).
[Crossref]

1988 (2)

1987 (2)

E. Yablonovitch , “ Inhibited Spontaneous Emission in Solid-State Physics and Electronics ,” Phys. Rev. Lett.   58 , 2059 – 2062 ( 1987 ).
[Crossref] [PubMed]

S. John , “ Strong Localization of Photons in Certain Disordered Dielectric Superlattices ,” Phys. Rev. Lett.   58 , 2486 – 2489 ( 1987 ).
[Crossref] [PubMed]

1977 (1)

A. 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 – 430 ( 1976 ).
[Crossref]

1931 (1)

R. d. L. Kronig and W. G. Penney , “ Quantum Mechanics of Electrons in Crystal Lattices ,” P. Roy. Soc. Lond. A Mat.   814 , 499 – 513 ( 1931 ).
[Crossref]

Aceves, A. B.

A. B. Aceves and S. Wabnitz , “ Self-induced transparency solitons in nonlinear refractive periodic media ,” Phys. Lett. A   141 , 37 – 42 ( 1989 ).
[Crossref]

Aitchison, J. S.

D. D. Mandelik , R. Morandotti , J. S. Aitchison , and Y. Silberberg , “ Gap Solitons in Waveguide Arrays ,” Phys. Rev. Lett.   92 , 093 , 904 –1–4 ( 2004 ).
[Crossref]

S. Linden , J. P. Mondia , H. M. V. Driel , T. C. Kleckner , C. R. Stanley , D. Modotto , A. Locatelli , C. D. An-gelis , R. Morandotti , and J. S. Aitchison , “ Nonlinear transmission properties of a deep-etched microstructured waveguide ,” Appl. Phys. Lett.   84 , 5437 – 5439 ( 2004 ).
[Crossref]

D. Mandelik , H. S. Eisenberg , Y. Silberberg , R. Morandotti , and J. S. Aitchison , “ Band-Gap Structure of Waveguide Arrays and Excitation of Floquet-Bloch Solitons ,” Phys. Rev. Lett.   90 , 053 , 902 –1–4 ( 2003 ).
[Crossref]

J. Meier , J. Hudock , D. Christodoulides , G. Stegeman , Y. Silberberg , R. Morandotti , and J. S. Aitchison , “ Discrete Vector Solitons in Kerr Nonlinear Waveguide Arrays ,” Phys. Rev. Lett.   91 , 143 , 907 –1–4 ( 2003 ).
[Crossref]

H. S. Eisenberg , Y. Silberberg , R. Morandotti , and J. S. Aitchison , “ Diffraction Management ,” Phys. Rev. Lett.   85 , 1863 – 1866 ( 2000 ).
[Crossref] [PubMed]

R. Morandotti , U. Peschel , J. S. Aitchison , H. S. Eisenberg , and Y. Silberberg , “ Experimental Observation of Linear and Nonlinear Optical Bloch Oscillations ,” Phys. Rev. Lett.   83 , 4756 – 4759 ( 1999 ).
[Crossref]

R. Morandotti , U. Peschel , J. S. Aitchison , H. S. Eisenberg , and Y. Silberberg , “ Dynamics of Discrete Solitons in Optical Waveguide Arrays ,” Phys. Rev. Lett. ( 1999 ).
[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]

Alexander, T. J.

D. N. Neshev , T. J. Alexander , E. A. Ostrovskaya , Y. S. Kivshar , H. Martin , I. Makasyuk , and Z. Chen , “ Observation of Discrete Vortex Solitons in Optically Induced Photonic Lattices ,” Phys. Rev. Lett.   92 , 123 , 903 –1–4 ( 2004 ).
[Crossref]

An-gelis, C. D.

S. Linden , J. P. Mondia , H. M. V. Driel , T. C. Kleckner , C. R. Stanley , D. Modotto , A. Locatelli , C. D. An-gelis , R. Morandotti , and J. S. Aitchison , “ Nonlinear transmission properties of a deep-etched microstructured waveguide ,” Appl. Phys. Lett.   84 , 5437 – 5439 ( 2004 ).
[Crossref]

Baizakov, B. B.

B. B. Baizakov , B. A. Malomed , and M. Salerno , “ Multidimensional solitons in periodic potentials ,” Europhys. Lett.   63 , 642 – 648 ( 2003 ).
[Crossref]

Bartal, G.

J. W. Fleischer , G. Bartal , O. Cohen , T. Schwartz , O. Manela , B. Freeman , M. Segev , H. Buljan , and N. K. Efremidis , “ Spatial photonics in nonlinear waveguide arrays ,” Opt. Express   13 , 1780 – 1796 ( 2005 ).
[Crossref] [PubMed]

J. W. Fleischer , G. Bartal , O. Cohen , O. Manela , M. Segev , J. Hudock , and D. N. Christodoulides , “ Observation of Vortex-Ring “Discrete” Solitons in 2D Photonic Lattices ,” Phys. Rev. Lett.   92 , 123 , 904 –1–4 ( 2004 ).
[Crossref]

Bayindir, M.

M. Bayindir , B. Temelkuran , and E. Ozbay , “ Tight-Binding Description of the Coupled Defect Modes in Three-Dimensional Photonic Crystals ,” Phys. Rev. Lett.   84 , 2140 – 2143 ( 2000 ).
[Crossref] [PubMed]

Bennett, P. J.

Birks, T. A.

J. Knight , J. Broeng , T. A. Birks , and P. Russell , “ Photonic band gap guidance in optical fibers ,” Science   282 , 1476 – 1478 ( 1998 ).
[Crossref] [PubMed]

Boyd, A. R.

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]

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 – 4755 ( 1999 ).
[Crossref]

Broderick, N. G. R.

Broeng, J.

J. Knight , J. Broeng , T. A. Birks , and P. Russell , “ Photonic band gap guidance in optical fibers ,” Science   282 , 1476 – 1478 ( 1998 ).
[Crossref] [PubMed]

Brommer, K. D.

E. Yablonovitch , T. J. Gmitter , R. D. Meade , A. M. Rappe , K. D. Brommer , and J. D. Joannopoulos , “ Donor and Acceptor Modes in Photonic Band Strucure ,” Phys. Rev. Lett.   67 , 3380 – 3383 ( 1991 ).
[Crossref] [PubMed]

Buljan, H.

Cai, T.

J. Wang , F. Ye , L. Dong , T. Cai , and Y.-P. Li , “ Lattice solitons supported by competing cubic-quintic nonlinearity ,” Phys. Lett. A   339 , 74 – 82 ( 2005 ).
[Crossref]

Carmon, T.

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 , 023 , 902 –1–4 ( 2003 ).
[Crossref]

Chen, J. C.

A. Mekis , J. C. Chen , I. Kurland , S. Fan , P. R. Villeneuve , and J. D. Joannopoulos , “ High Transmission through Sharp Bends in Photonic Crystal Waveguides ,” Phys. Rev. Lett.   77 , 3787 – 3790 ( 1996 ).
[Crossref] [PubMed]

Chen, Z.

F. Fedele , J. Yang , and Z. Chen , “ Defect modes in one-dimensional photonic lattices ,” Opt. Lett.   30 , 1506 – 1508 ( 2005 ).
[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 , 123 , 902 –1–4 ( 2004 ).
[Crossref]

D. N. Neshev , T. J. Alexander , E. A. Ostrovskaya , Y. S. Kivshar , H. Martin , I. Makasyuk , and Z. Chen , “ Observation of Discrete Vortex Solitons in Optically Induced Photonic Lattices ,” Phys. Rev. Lett.   92 , 123 , 903 –1–4 ( 2004 ).
[Crossref]

Cho, A. Y.

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

Christodoulides, D.

J. Meier , J. Hudock , D. Christodoulides , G. Stegeman , Y. Silberberg , R. Morandotti , and J. S. Aitchison , “ Discrete Vector Solitons in Kerr Nonlinear Waveguide Arrays ,” Phys. Rev. Lett.   91 , 143 , 907 –1–4 ( 2003 ).
[Crossref]

Christodoulides, D. N.

J. W. Fleischer , G. Bartal , O. Cohen , O. Manela , M. Segev , J. Hudock , and D. N. Christodoulides , “ Observation of Vortex-Ring “Discrete” Solitons in 2D Photonic Lattices ,” Phys. Rev. Lett.   92 , 123 , 904 –1–4 ( 2004 ).
[Crossref]

Y. V. Kartashov , A. A. Egorov , L. Torner , and D. N. Christodoulides , “ Stable soliton complexes in two-dimensional photonic lattices ,” Opt. Lett.   29 , 1918 – 1920 ( 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 , 123 , 902 –1–4 ( 2004 ).
[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] [PubMed]

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 , 213 , 906 –1–4 ( 2003 ).
[Crossref]

N. K. Efremidis and D. N. Christodoulides , “ Lattice solitons in Bose-Einstein condensates ,” Phys. Rev. A   67 , 063 , 608 –1–9 ( 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] [PubMed]

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 , 023 , 902 –1–4 ( 2003 ).
[Crossref]

N. K. Efremidis , D. N. Christodoulides , S. Sears , J. W. Fleischer , and M. Segev , “ Discrete Solitons in Photorefractive Optically-Induced Photonic Lattices ,” Phys. Rev. E   66 , 046 , 602 –1–5 ( 2002 ).
[Crossref]

D. N. Christodoulides and R. I. Joseph , “ Slow Bragg Solitons in Nonlinear Periodic Structures ,” Phys. Rev. Lett.   62 , 1746 – 1749 ( 1989 ).
[Crossref] [PubMed]

D. N. Christodoulides and R. I. Joseph , “ Discrete self-focusing in nonlinear arrays of coupled waveguides ,” Opt. Lett.   13 , 794 – 796 ( 1988 ).
[Crossref] [PubMed]

Cohen, O.

J. W. Fleischer , G. Bartal , O. Cohen , T. Schwartz , O. Manela , B. Freeman , M. Segev , H. Buljan , and N. K. Efremidis , “ Spatial photonics in nonlinear waveguide arrays ,” Opt. Express   13 , 1780 – 1796 ( 2005 ).
[Crossref] [PubMed]

J. W. Fleischer , G. Bartal , O. Cohen , O. Manela , M. Segev , J. Hudock , and D. N. Christodoulides , “ Observation of Vortex-Ring “Discrete” Solitons in 2D Photonic Lattices ,” Phys. Rev. Lett.   92 , 123 , 904 –1–4 ( 2004 ).
[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 , 213 , 906 –1–4 ( 2003 ).
[Crossref]

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 – 2020 ( 1991 ).
[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 – 4755 ( 1999 ).
[Crossref]

de Sterke, C. M.

B. J. Eggleton , R. E. Slusher , C. M. de Sterke , P. A. Krug , and J. E. Sipe , “ Bragg Grating Solitons ,” Phys. Rev. Lett.   76 , 1627 – 1630 ( 1996 ).
[Crossref] [PubMed]

C. M. de Sterke and J. E. Sipe , “ Gap solitons ,” in Progress in Optics , E. Wolf , ed., vol. XXXIII, p. 203 ( North-Holland, Amsterdam , 1994 ).

Dong, L.

J. Wang , F. Ye , L. Dong , T. Cai , and Y.-P. Li , “ Lattice solitons supported by competing cubic-quintic nonlinearity ,” Phys. Lett. A   339 , 74 – 82 ( 2005 ).
[Crossref]

Driben, R.

I. M. Merhasin , B. V. Gisin , R. Driben , and B. A. Malomed , “ Finite-band solitons in the Kronig-Penney model with the cubic-quintic nonlinearity ,” Phys. Rev. E   71 , 016 , 613 –1–12 ( 2005 ).
[Crossref]

Driel, H. M. V.

S. Linden , J. P. Mondia , H. M. V. Driel , T. C. Kleckner , C. R. Stanley , D. Modotto , A. Locatelli , C. D. An-gelis , R. Morandotti , and J. S. Aitchison , “ Nonlinear transmission properties of a deep-etched microstructured waveguide ,” Appl. Phys. Lett.   84 , 5437 – 5439 ( 2004 ).
[Crossref]

ederer, F.

R. Iwanow , R. Schiek , G. I. Stegeman , T. Pertsch , F. ederer , Y. Min , and W. Sohler , “ Observation of Discrete Quadratic Solitons ,” Phys. Rev. Lett.   93 , 113 , 902 –1–4 ( 2004 ).
[Crossref]

Efremidis, N. K.

J. W. Fleischer , G. Bartal , O. Cohen , T. Schwartz , O. Manela , B. Freeman , M. Segev , H. Buljan , and N. K. Efremidis , “ Spatial photonics in nonlinear waveguide arrays ,” Opt. Express   13 , 1780 – 1796 ( 2005 ).
[Crossref] [PubMed]

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 , 023 , 902 –1–4 ( 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 , 213 , 906 –1–4 ( 2003 ).
[Crossref]

N. K. Efremidis and D. N. Christodoulides , “ Lattice solitons in Bose-Einstein condensates ,” Phys. Rev. A   67 , 063 , 608 –1–9 ( 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] [PubMed]

N. K. Efremidis , D. N. Christodoulides , S. Sears , J. W. Fleischer , and M. Segev , “ Discrete Solitons in Photorefractive Optically-Induced Photonic Lattices ,” Phys. Rev. E   66 , 046 , 602 –1–5 ( 2002 ).
[Crossref]

Eggleton, B. J.

B. J. Eggleton , R. E. Slusher , C. M. de Sterke , P. A. Krug , and J. E. Sipe , “ Bragg Grating Solitons ,” Phys. Rev. Lett.   76 , 1627 – 1630 ( 1996 ).
[Crossref] [PubMed]

Egorov, A. A.

Eisenberg, H. S.

D. Mandelik , H. S. Eisenberg , Y. Silberberg , R. Morandotti , and J. S. Aitchison , “ Band-Gap Structure of Waveguide Arrays and Excitation of Floquet-Bloch Solitons ,” Phys. Rev. Lett.   90 , 053 , 902 –1–4 ( 2003 ).
[Crossref]

H. S. Eisenberg , Y. Silberberg , R. Morandotti , and J. S. Aitchison , “ Diffraction Management ,” Phys. Rev. Lett.   85 , 1863 – 1866 ( 2000 ).
[Crossref] [PubMed]

R. Morandotti , U. Peschel , J. S. Aitchison , H. S. Eisenberg , and Y. Silberberg , “ Experimental Observation of Linear and Nonlinear Optical Bloch Oscillations ,” Phys. Rev. Lett.   83 , 4756 – 4759 ( 1999 ).
[Crossref]

R. Morandotti , U. Peschel , J. S. Aitchison , H. S. Eisenberg , and Y. Silberberg , “ Dynamics of Discrete Solitons in Optical Waveguide Arrays ,” Phys. Rev. Lett. ( 1999 ).
[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]

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 – 4755 ( 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 , 123 , 902 –1–4 ( 2004 ).
[Crossref]

Fan, S.

A. Mekis , J. C. Chen , I. Kurland , S. Fan , P. R. Villeneuve , and J. D. Joannopoulos , “ High Transmission through Sharp Bends in Photonic Crystal Waveguides ,” Phys. Rev. Lett.   77 , 3787 – 3790 ( 1996 ).
[Crossref] [PubMed]

Fedele, F.

Feng, J.

Fleischer, J. W.

J. W. Fleischer , G. Bartal , O. Cohen , T. Schwartz , O. Manela , B. Freeman , M. Segev , H. Buljan , and N. K. Efremidis , “ Spatial photonics in nonlinear waveguide arrays ,” Opt. Express   13 , 1780 – 1796 ( 2005 ).
[Crossref] [PubMed]

J. W. Fleischer , G. Bartal , O. Cohen , O. Manela , M. Segev , J. Hudock , and D. N. Christodoulides , “ Observation of Vortex-Ring “Discrete” Solitons in 2D Photonic Lattices ,” Phys. Rev. Lett.   92 , 123 , 904 –1–4 ( 2004 ).
[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] [PubMed]

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 , 213 , 906 –1–4 ( 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 , 023 , 902 –1–4 ( 2003 ).
[Crossref]

N. K. Efremidis , D. N. Christodoulides , S. Sears , J. W. Fleischer , and M. Segev , “ Discrete Solitons in Photorefractive Optically-Induced Photonic Lattices ,” Phys. Rev. E   66 , 046 , 602 –1–5 ( 2002 ).
[Crossref]

Freeman, B.

Gisin, B. V.

I. M. Merhasin , B. V. Gisin , R. Driben , and B. A. Malomed , “ Finite-band solitons in the Kronig-Penney model with the cubic-quintic nonlinearity ,” Phys. Rev. E   71 , 016 , 613 –1–12 ( 2005 ).
[Crossref]

Gmitter, T. J.

E. Yablonovitch , T. J. Gmitter , R. D. Meade , A. M. Rappe , K. D. Brommer , and J. D. Joannopoulos , “ Donor and Acceptor Modes in Photonic Band Strucure ,” Phys. Rev. Lett.   67 , 3380 – 3383 ( 1991 ).
[Crossref] [PubMed]

Hanna, B.

D. Neshev , A. A. Sukhorukov , B. Hanna , W. Krolikowski , and Y. S. Kivshar , “ Controlled Generation and Steering of Spatial Gap Solitons ,” Phys. Rev. Lett.   93 , 083 , 905 –1–4 ( 2004 ).
[Crossref]

Hudock, J.

J. W. Fleischer , G. Bartal , O. Cohen , O. Manela , M. Segev , J. Hudock , and D. N. Christodoulides , “ Observation of Vortex-Ring “Discrete” Solitons in 2D Photonic Lattices ,” Phys. Rev. Lett.   92 , 123 , 904 –1–4 ( 2004 ).
[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 , 213 , 906 –1–4 ( 2003 ).
[Crossref]

J. Meier , J. Hudock , D. Christodoulides , G. Stegeman , Y. Silberberg , R. Morandotti , and J. S. Aitchison , “ Discrete Vector Solitons in Kerr Nonlinear Waveguide Arrays ,” Phys. Rev. Lett.   91 , 143 , 907 –1–4 ( 2003 ).
[Crossref]

Iwanow, R.

R. Iwanow , R. Schiek , G. I. Stegeman , T. Pertsch , F. ederer , Y. Min , and W. Sohler , “ Observation of Discrete Quadratic Solitons ,” Phys. Rev. Lett.   93 , 113 , 902 –1–4 ( 2004 ).
[Crossref]

Joannopoulos, J.

J. Joannopoulos , R. Meade , and J. N. Winn , Photonic Crystals: Molding the Flow of Light ( Princeton University Press, Princeton, NJ , 1995 ).

Joannopoulos, J. D.

A. Mekis , J. C. Chen , I. Kurland , S. Fan , P. R. Villeneuve , and J. D. Joannopoulos , “ High Transmission through Sharp Bends in Photonic Crystal Waveguides ,” Phys. Rev. Lett.   77 , 3787 – 3790 ( 1996 ).
[Crossref] [PubMed]

E. Yablonovitch , T. J. Gmitter , R. D. Meade , A. M. Rappe , K. D. Brommer , and J. D. Joannopoulos , “ Donor and Acceptor Modes in Photonic Band Strucure ,” Phys. Rev. Lett.   67 , 3380 – 3383 ( 1991 ).
[Crossref] [PubMed]

John, S.

S. John , “ Strong Localization of Photons in Certain Disordered Dielectric Superlattices ,” Phys. Rev. Lett.   58 , 2486 – 2489 ( 1987 ).
[Crossref] [PubMed]

Joseph, R. I.

D. N. Christodoulides and R. I. Joseph , “ Slow Bragg Solitons in Nonlinear Periodic Structures ,” Phys. Rev. Lett.   62 , 1746 – 1749 ( 1989 ).
[Crossref] [PubMed]

D. N. Christodoulides and R. I. Joseph , “ Discrete self-focusing in nonlinear arrays of coupled waveguides ,” Opt. Lett.   13 , 794 – 796 ( 1988 ).
[Crossref] [PubMed]

Kartashov, Y. V.

Kevrekidis, P.

P. Kevrekidis , B. Malomed , and Z. Musslimani , “ Discrete gap solitons in a diffraction-managed waveguide array ,” Eur. Phys. J. D   23 , 421 – 436 ( 2003 ).
[Crossref]

Kevrekidis, P. G.

B. A. Malomed and P. G. Kevrekidis , “ Discrete vortex solitons ,” Prys. Rev. E   64 , 026 , 601 –1–6 ( 2001 ).

Kittel, C.

C. Kittel , Introduction to Solid State Physics ( Wiley, New York , 1986 ).

Kivshar, R. A.

S. F. Mingaleev , R. A. Kivshar , S. Yuri , and Sammut , “ Long-range interaction and nonlinear localized modes in photonic crystal waveguides ,” Phys. Rev. E   62 , 5777 – 5782 ( 2000 ).
[Crossref]

Kivshar, Y. S.

D. Neshev , A. A. Sukhorukov , B. Hanna , W. Krolikowski , and Y. S. Kivshar , “ Controlled Generation and Steering of Spatial Gap Solitons ,” Phys. Rev. Lett.   93 , 083 , 905 –1–4 ( 2004 ).
[Crossref]

D. N. Neshev , T. J. Alexander , E. A. Ostrovskaya , Y. S. Kivshar , H. Martin , I. Makasyuk , and Z. Chen , “ Observation of Discrete Vortex Solitons in Optically Induced Photonic Lattices ,” Phys. Rev. Lett.   92 , 123 , 903 –1–4 ( 2004 ).
[Crossref]

P. J. Y. Louis , E. A. Ostrovskaya , C. M. Savage , and Y. S. Kivshar , “ Bose-Einstein condensates in optical lattices: Band-gap structure and solitons ,” Phys. Rev. A   67 , 013 , 602 –1–9 ( 2003 ).
[Crossref]

Kleckner, T. C.

S. Linden , J. P. Mondia , H. M. V. Driel , T. C. Kleckner , C. R. Stanley , D. Modotto , A. Locatelli , C. D. An-gelis , R. Morandotti , and J. S. Aitchison , “ Nonlinear transmission properties of a deep-etched microstructured waveguide ,” Appl. Phys. Lett.   84 , 5437 – 5439 ( 2004 ).
[Crossref]

Knight, J.

J. Knight , J. Broeng , T. A. Birks , and P. Russell , “ Photonic band gap guidance in optical fibers ,” Science   282 , 1476 – 1478 ( 1998 ).
[Crossref] [PubMed]

Krolikowski, W.

D. Neshev , A. A. Sukhorukov , B. Hanna , W. Krolikowski , and Y. S. Kivshar , “ Controlled Generation and Steering of Spatial Gap Solitons ,” Phys. Rev. Lett.   93 , 083 , 905 –1–4 ( 2004 ).
[Crossref]

Kronig, R. d. L.

R. d. L. Kronig and W. G. Penney , “ Quantum Mechanics of Electrons in Crystal Lattices ,” P. Roy. Soc. Lond. A Mat.   814 , 499 – 513 ( 1931 ).
[Crossref]

Krug, P. A.

B. J. Eggleton , R. E. Slusher , C. M. de Sterke , P. A. Krug , and J. E. Sipe , “ Bragg Grating Solitons ,” Phys. Rev. Lett.   76 , 1627 – 1630 ( 1996 ).
[Crossref] [PubMed]

Kurland, I.

A. Mekis , J. C. Chen , I. Kurland , S. Fan , P. R. Villeneuve , and J. D. Joannopoulos , “ High Transmission through Sharp Bends in Photonic Crystal Waveguides ,” Phys. Rev. Lett.   77 , 3787 – 3790 ( 1996 ).
[Crossref] [PubMed]

Lederer, F.

D. N. Christodoulides , F. Lederer , and Y. Silberberg , “ Discretizing light behaviour in linear and nonlinear waveguide lattices ,” Nature   424 , 817 – 823 ( 2003 ).
[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 – 4755 ( 1999 ).
[Crossref]

Lee, R. K.

Leontidis, E.

S. Theodorakis and E. Leontidis , “ Bound states in a nonlinear Kronig-Penney model ,” J. Phys. A   30 , 4835 – 4849 ( 1997 ).
[Crossref]

Li, W.

W. Li and A. Smerzi , “ Nonlinear Krönig-Penney model ,” Phys. Rev. E   70 , 016 , 605 –1–4 ( 2004 ).
[Crossref]

Li, Y.-P.

J. Wang , F. Ye , L. Dong , T. Cai , and Y.-P. Li , “ Lattice solitons supported by competing cubic-quintic nonlinearity ,” Phys. Lett. A   339 , 74 – 82 ( 2005 ).
[Crossref]

Linden, S.

S. Linden , J. P. Mondia , H. M. V. Driel , T. C. Kleckner , C. R. Stanley , D. Modotto , A. Locatelli , C. D. An-gelis , R. Morandotti , and J. S. Aitchison , “ Nonlinear transmission properties of a deep-etched microstructured waveguide ,” Appl. Phys. Lett.   84 , 5437 – 5439 ( 2004 ).
[Crossref]

Locatelli, A.

S. Linden , J. P. Mondia , H. M. V. Driel , T. C. Kleckner , C. R. Stanley , D. Modotto , A. Locatelli , C. D. An-gelis , R. Morandotti , and J. S. Aitchison , “ Nonlinear transmission properties of a deep-etched microstructured waveguide ,” Appl. Phys. Lett.   84 , 5437 – 5439 ( 2004 ).
[Crossref]

Louis, P. J. Y.

P. J. Y. Louis , E. A. Ostrovskaya , C. M. Savage , and Y. S. Kivshar , “ Bose-Einstein condensates in optical lattices: Band-gap structure and solitons ,” Phys. Rev. A   67 , 013 , 602 –1–9 ( 2003 ).
[Crossref]

Makasyuk, I.

D. N. Neshev , T. J. Alexander , E. A. Ostrovskaya , Y. S. Kivshar , H. Martin , I. Makasyuk , and Z. Chen , “ Observation of Discrete Vortex Solitons in Optically Induced Photonic Lattices ,” Phys. Rev. Lett.   92 , 123 , 903 –1–4 ( 2004 ).
[Crossref]

Malomed, B.

P. Kevrekidis , B. Malomed , and Z. Musslimani , “ Discrete gap solitons in a diffraction-managed waveguide array ,” Eur. Phys. J. D   23 , 421 – 436 ( 2003 ).
[Crossref]

Malomed, B. A.

I. M. Merhasin , B. V. Gisin , R. Driben , and B. A. Malomed , “ Finite-band solitons in the Kronig-Penney model with the cubic-quintic nonlinearity ,” Phys. Rev. E   71 , 016 , 613 –1–12 ( 2005 ).
[Crossref]

B. B. Baizakov , B. A. Malomed , and M. Salerno , “ Multidimensional solitons in periodic potentials ,” Europhys. Lett.   63 , 642 – 648 ( 2003 ).
[Crossref]

B. A. Malomed and P. G. Kevrekidis , “ Discrete vortex solitons ,” Prys. Rev. E   64 , 026 , 601 –1–6 ( 2001 ).

Mandelik, D.

D. Mandelik , H. S. Eisenberg , Y. Silberberg , R. Morandotti , and J. S. Aitchison , “ Band-Gap Structure of Waveguide Arrays and Excitation of Floquet-Bloch Solitons ,” Phys. Rev. Lett.   90 , 053 , 902 –1–4 ( 2003 ).
[Crossref]

Mandelik, D. D.

D. D. Mandelik , R. Morandotti , J. S. Aitchison , and Y. Silberberg , “ Gap Solitons in Waveguide Arrays ,” Phys. Rev. Lett.   92 , 093 , 904 –1–4 ( 2004 ).
[Crossref]

Manela, O.

J. W. Fleischer , G. Bartal , O. Cohen , T. Schwartz , O. Manela , B. Freeman , M. Segev , H. Buljan , and N. K. Efremidis , “ Spatial photonics in nonlinear waveguide arrays ,” Opt. Express   13 , 1780 – 1796 ( 2005 ).
[Crossref] [PubMed]

J. W. Fleischer , G. Bartal , O. Cohen , O. Manela , M. Segev , J. Hudock , and D. N. Christodoulides , “ Observation of Vortex-Ring “Discrete” Solitons in 2D Photonic Lattices ,” Phys. Rev. Lett.   92 , 123 , 904 –1–4 ( 2004 ).
[Crossref]

Martin, H.

D. N. Neshev , T. J. Alexander , E. A. Ostrovskaya , Y. S. Kivshar , H. Martin , I. Makasyuk , and Z. Chen , “ Observation of Discrete Vortex Solitons in Optically Induced Photonic Lattices ,” Phys. Rev. Lett.   92 , 123 , 903 –1–4 ( 2004 ).
[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 , 123 , 902 –1–4 ( 2004 ).
[Crossref]

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 – 2020 ( 1991 ).
[Crossref] [PubMed]

Meade, R.

J. Joannopoulos , R. Meade , and J. N. Winn , Photonic Crystals: Molding the Flow of Light ( Princeton University Press, Princeton, NJ , 1995 ).

Meade, R. D.

E. Yablonovitch , T. J. Gmitter , R. D. Meade , A. M. Rappe , K. D. Brommer , and J. D. Joannopoulos , “ Donor and Acceptor Modes in Photonic Band Strucure ,” Phys. Rev. Lett.   67 , 3380 – 3383 ( 1991 ).
[Crossref] [PubMed]

Meier, J.

J. Meier , J. Hudock , D. Christodoulides , G. Stegeman , Y. Silberberg , R. Morandotti , and J. S. Aitchison , “ Discrete Vector Solitons in Kerr Nonlinear Waveguide Arrays ,” Phys. Rev. Lett.   91 , 143 , 907 –1–4 ( 2003 ).
[Crossref]

Mekis, A.

A. Mekis , J. C. Chen , I. Kurland , S. Fan , P. R. Villeneuve , and J. D. Joannopoulos , “ High Transmission through Sharp Bends in Photonic Crystal Waveguides ,” Phys. Rev. Lett.   77 , 3787 – 3790 ( 1996 ).
[Crossref] [PubMed]

Merhasin, I. M.

I. M. Merhasin , B. V. Gisin , R. Driben , and B. A. Malomed , “ Finite-band solitons in the Kronig-Penney model with the cubic-quintic nonlinearity ,” Phys. Rev. E   71 , 016 , 613 –1–12 ( 2005 ).
[Crossref]

Min, Y.

R. Iwanow , R. Schiek , G. I. Stegeman , T. Pertsch , F. ederer , Y. Min , and W. Sohler , “ Observation of Discrete Quadratic Solitons ,” Phys. Rev. Lett.   93 , 113 , 902 –1–4 ( 2004 ).
[Crossref]

Mingaleev, S. F.

S. F. Mingaleev , R. A. Kivshar , S. Yuri , and Sammut , “ Long-range interaction and nonlinear localized modes in photonic crystal waveguides ,” Phys. Rev. E   62 , 5777 – 5782 ( 2000 ).
[Crossref]

Modinos, A.

N. Stefanou and A. Modinos , “ Impurity bands in photonic insulators ,” Phys. Rev. B   57 , 12, 127 –12, 133 ( 1998 ).
[Crossref]

Modotto, D.

S. Linden , J. P. Mondia , H. M. V. Driel , T. C. Kleckner , C. R. Stanley , D. Modotto , A. Locatelli , C. D. An-gelis , R. Morandotti , and J. S. Aitchison , “ Nonlinear transmission properties of a deep-etched microstructured waveguide ,” Appl. Phys. Lett.   84 , 5437 – 5439 ( 2004 ).
[Crossref]

Mondia, J. P.

S. Linden , J. P. Mondia , H. M. V. Driel , T. C. Kleckner , C. R. Stanley , D. Modotto , A. Locatelli , C. D. An-gelis , R. Morandotti , and J. S. Aitchison , “ Nonlinear transmission properties of a deep-etched microstructured waveguide ,” Appl. Phys. Lett.   84 , 5437 – 5439 ( 2004 ).
[Crossref]

Monro, T. M.

Morandotti, R.

S. Linden , J. P. Mondia , H. M. V. Driel , T. C. Kleckner , C. R. Stanley , D. Modotto , A. Locatelli , C. D. An-gelis , R. Morandotti , and J. S. Aitchison , “ Nonlinear transmission properties of a deep-etched microstructured waveguide ,” Appl. Phys. Lett.   84 , 5437 – 5439 ( 2004 ).
[Crossref]

D. D. Mandelik , R. Morandotti , J. S. Aitchison , and Y. Silberberg , “ Gap Solitons in Waveguide Arrays ,” Phys. Rev. Lett.   92 , 093 , 904 –1–4 ( 2004 ).
[Crossref]

J. Meier , J. Hudock , D. Christodoulides , G. Stegeman , Y. Silberberg , R. Morandotti , and J. S. Aitchison , “ Discrete Vector Solitons in Kerr Nonlinear Waveguide Arrays ,” Phys. Rev. Lett.   91 , 143 , 907 –1–4 ( 2003 ).
[Crossref]

D. Mandelik , H. S. Eisenberg , Y. Silberberg , R. Morandotti , and J. S. Aitchison , “ Band-Gap Structure of Waveguide Arrays and Excitation of Floquet-Bloch Solitons ,” Phys. Rev. Lett.   90 , 053 , 902 –1–4 ( 2003 ).
[Crossref]

H. S. Eisenberg , Y. Silberberg , R. Morandotti , and J. S. Aitchison , “ Diffraction Management ,” Phys. Rev. Lett.   85 , 1863 – 1866 ( 2000 ).
[Crossref] [PubMed]

R. Morandotti , U. Peschel , J. S. Aitchison , H. S. Eisenberg , and Y. Silberberg , “ Experimental Observation of Linear and Nonlinear Optical Bloch Oscillations ,” Phys. Rev. Lett.   83 , 4756 – 4759 ( 1999 ).
[Crossref]

R. Morandotti , U. Peschel , J. S. Aitchison , H. S. Eisenberg , and Y. Silberberg , “ Dynamics of Discrete Solitons in Optical Waveguide Arrays ,” Phys. Rev. Lett. ( 1999 ).
[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]

Musslimani, Z.

P. Kevrekidis , B. Malomed , and Z. Musslimani , “ Discrete gap solitons in a diffraction-managed waveguide array ,” Eur. Phys. J. D   23 , 421 – 436 ( 2003 ).
[Crossref]

Musslimani, Z. H.

J. Yang and Z. H. Musslimani , “ Fundamental and vortex solitons in a two-dimensional optical lattice ,” Opt. Lett.   21 , 2094 – 2096 ( 2003 ).
[Crossref]

Neshev, D.

D. Neshev , A. A. Sukhorukov , B. Hanna , W. Krolikowski , and Y. S. Kivshar , “ Controlled Generation and Steering of Spatial Gap Solitons ,” Phys. Rev. Lett.   93 , 083 , 905 –1–4 ( 2004 ).
[Crossref]

Neshev, D. N.

D. N. Neshev , T. J. Alexander , E. A. Ostrovskaya , Y. S. Kivshar , H. Martin , I. Makasyuk , and Z. Chen , “ Observation of Discrete Vortex Solitons in Optically Induced Photonic Lattices ,” Phys. Rev. Lett.   92 , 123 , 903 –1–4 ( 2004 ).
[Crossref]

Ostrovskaya, E. A.

D. N. Neshev , T. J. Alexander , E. A. Ostrovskaya , Y. S. Kivshar , H. Martin , I. Makasyuk , and Z. Chen , “ Observation of Discrete Vortex Solitons in Optically Induced Photonic Lattices ,” Phys. Rev. Lett.   92 , 123 , 903 –1–4 ( 2004 ).
[Crossref]

P. J. Y. Louis , E. A. Ostrovskaya , C. M. Savage , and Y. S. Kivshar , “ Bose-Einstein condensates in optical lattices: Band-gap structure and solitons ,” Phys. Rev. A   67 , 013 , 602 –1–9 ( 2003 ).
[Crossref]

Ozbay, E.

M. Bayindir , B. Temelkuran , and E. Ozbay , “ Tight-Binding Description of the Coupled Defect Modes in Three-Dimensional Photonic Crystals ,” Phys. Rev. Lett.   84 , 2140 – 2143 ( 2000 ).
[Crossref] [PubMed]

Penney, W. G.

R. d. L. Kronig and W. G. Penney , “ Quantum Mechanics of Electrons in Crystal Lattices ,” P. Roy. Soc. Lond. A Mat.   814 , 499 – 513 ( 1931 ).
[Crossref]

Pertsch, T.

R. Iwanow , R. Schiek , G. I. Stegeman , T. Pertsch , F. ederer , Y. Min , and W. Sohler , “ Observation of Discrete Quadratic Solitons ,” Phys. Rev. Lett.   93 , 113 , 902 –1–4 ( 2004 ).
[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 – 4755 ( 1999 ).
[Crossref]

Peschel, U.

R. Morandotti , U. Peschel , J. S. Aitchison , H. S. Eisenberg , and Y. Silberberg , “ Experimental Observation of Linear and Nonlinear Optical Bloch Oscillations ,” Phys. Rev. Lett.   83 , 4756 – 4759 ( 1999 ).
[Crossref]

R. Morandotti , U. Peschel , J. S. Aitchison , H. S. Eisenberg , and Y. Silberberg , “ Dynamics of Discrete Solitons in Optical Waveguide Arrays ,” Phys. Rev. Lett. ( 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 – 2020 ( 1991 ).
[Crossref] [PubMed]

Rappe, A. M.

E. Yablonovitch , T. J. Gmitter , R. D. Meade , A. M. Rappe , K. D. Brommer , and J. D. Joannopoulos , “ Donor and Acceptor Modes in Photonic Band Strucure ,” Phys. Rev. Lett.   67 , 3380 – 3383 ( 1991 ).
[Crossref] [PubMed]

Richardson, D. J.

Russell, P.

P. Russell , “ Photonic crystal fibers ,” Science   299 , 358 – 362 ( 2003 ).
[Crossref] [PubMed]

J. Knight , J. Broeng , T. A. Birks , and P. Russell , “ Photonic band gap guidance in optical fibers ,” Science   282 , 1476 – 1478 ( 1998 ).
[Crossref] [PubMed]

Salerno, M.

B. B. Baizakov , B. A. Malomed , and M. Salerno , “ Multidimensional solitons in periodic potentials ,” Europhys. Lett.   63 , 642 – 648 ( 2003 ).
[Crossref]

Sammut,

S. F. Mingaleev , R. A. Kivshar , S. Yuri , and Sammut , “ Long-range interaction and nonlinear localized modes in photonic crystal waveguides ,” Phys. Rev. E   62 , 5777 – 5782 ( 2000 ).
[Crossref]

Savage, C. M.

P. J. Y. Louis , E. A. Ostrovskaya , C. M. Savage , and Y. S. Kivshar , “ Bose-Einstein condensates in optical lattices: Band-gap structure and solitons ,” Phys. Rev. A   67 , 013 , 602 –1–9 ( 2003 ).
[Crossref]

Scherer, A.

Schiek, R.

R. Iwanow , R. Schiek , G. I. Stegeman , T. Pertsch , F. ederer , Y. Min , and W. Sohler , “ Observation of Discrete Quadratic Solitons ,” Phys. Rev. Lett.   93 , 113 , 902 –1–4 ( 2004 ).
[Crossref]

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 – 2020 ( 1991 ).
[Crossref] [PubMed]

Schwartz, T.

Sears, S.

N. K. Efremidis , D. N. Christodoulides , S. Sears , J. W. Fleischer , and M. Segev , “ Discrete Solitons in Photorefractive Optically-Induced Photonic Lattices ,” Phys. Rev. E   66 , 046 , 602 –1–5 ( 2002 ).
[Crossref]

Segev, M.

J. W. Fleischer , G. Bartal , O. Cohen , T. Schwartz , O. Manela , B. Freeman , M. Segev , H. Buljan , and N. K. Efremidis , “ Spatial photonics in nonlinear waveguide arrays ,” Opt. Express   13 , 1780 – 1796 ( 2005 ).
[Crossref] [PubMed]

J. W. Fleischer , G. Bartal , O. Cohen , O. Manela , M. Segev , J. Hudock , and D. N. Christodoulides , “ Observation of Vortex-Ring “Discrete” Solitons in 2D Photonic Lattices ,” Phys. Rev. Lett.   92 , 123 , 904 –1–4 ( 2004 ).
[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 , 213 , 906 –1–4 ( 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] [PubMed]

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 , 023 , 902 –1–4 ( 2003 ).
[Crossref]

N. K. Efremidis , D. N. Christodoulides , S. Sears , J. W. Fleischer , and M. Segev , “ Discrete Solitons in Photorefractive Optically-Induced Photonic Lattices ,” Phys. Rev. E   66 , 046 , 602 –1–5 ( 2002 ).
[Crossref]

Silberberg, Y.

D. D. Mandelik , R. Morandotti , J. S. Aitchison , and Y. Silberberg , “ Gap Solitons in Waveguide Arrays ,” Phys. Rev. Lett.   92 , 093 , 904 –1–4 ( 2004 ).
[Crossref]

D. N. Christodoulides , F. Lederer , and Y. Silberberg , “ Discretizing light behaviour in linear and nonlinear waveguide lattices ,” Nature   424 , 817 – 823 ( 2003 ).
[Crossref] [PubMed]

D. Mandelik , H. S. Eisenberg , Y. Silberberg , R. Morandotti , and J. S. Aitchison , “ Band-Gap Structure of Waveguide Arrays and Excitation of Floquet-Bloch Solitons ,” Phys. Rev. Lett.   90 , 053 , 902 –1–4 ( 2003 ).
[Crossref]

J. Meier , J. Hudock , D. Christodoulides , G. Stegeman , Y. Silberberg , R. Morandotti , and J. S. Aitchison , “ Discrete Vector Solitons in Kerr Nonlinear Waveguide Arrays ,” Phys. Rev. Lett.   91 , 143 , 907 –1–4 ( 2003 ).
[Crossref]

H. S. Eisenberg , Y. Silberberg , R. Morandotti , and J. S. Aitchison , “ Diffraction Management ,” Phys. Rev. Lett.   85 , 1863 – 1866 ( 2000 ).
[Crossref] [PubMed]

R. Morandotti , U. Peschel , J. S. Aitchison , H. S. Eisenberg , and Y. Silberberg , “ Experimental Observation of Linear and Nonlinear Optical Bloch Oscillations ,” Phys. Rev. Lett.   83 , 4756 – 4759 ( 1999 ).
[Crossref]

R. Morandotti , U. Peschel , J. S. Aitchison , H. S. Eisenberg , and Y. Silberberg , “ Dynamics of Discrete Solitons in Optical Waveguide Arrays ,” Phys. Rev. Lett. ( 1999 ).
[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]

Sipe, J.

Sipe, J. E.

B. J. Eggleton , R. E. Slusher , C. M. de Sterke , P. A. Krug , and J. E. Sipe , “ Bragg Grating Solitons ,” Phys. Rev. Lett.   76 , 1627 – 1630 ( 1996 ).
[Crossref] [PubMed]

C. M. de Sterke and J. E. Sipe , “ Gap solitons ,” in Progress in Optics , E. Wolf , ed., vol. XXXIII, p. 203 ( North-Holland, Amsterdam , 1994 ).

Slusher, R. E.

B. J. Eggleton , R. E. Slusher , C. M. de Sterke , P. A. Krug , and J. E. Sipe , “ Bragg Grating Solitons ,” Phys. Rev. Lett.   76 , 1627 – 1630 ( 1996 ).
[Crossref] [PubMed]

Smerzi, A.

W. Li and A. Smerzi , “ Nonlinear Krönig-Penney model ,” Phys. Rev. E   70 , 016 , 605 –1–4 ( 2004 ).
[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 – 2020 ( 1991 ).
[Crossref] [PubMed]

Sohler, W.

R. Iwanow , R. Schiek , G. I. Stegeman , T. Pertsch , F. ederer , Y. Min , and W. Sohler , “ Observation of Discrete Quadratic Solitons ,” Phys. Rev. Lett.   93 , 113 , 902 –1–4 ( 2004 ).
[Crossref]

Stanley, C. R.

S. Linden , J. P. Mondia , H. M. V. Driel , T. C. Kleckner , C. R. Stanley , D. Modotto , A. Locatelli , C. D. An-gelis , R. Morandotti , and J. S. Aitchison , “ Nonlinear transmission properties of a deep-etched microstructured waveguide ,” Appl. Phys. Lett.   84 , 5437 – 5439 ( 2004 ).
[Crossref]

Stefanou, N.

N. Stefanou and A. Modinos , “ Impurity bands in photonic insulators ,” Phys. Rev. B   57 , 12, 127 –12, 133 ( 1998 ).
[Crossref]

Stegeman, G.

J. Meier , J. Hudock , D. Christodoulides , G. Stegeman , Y. Silberberg , R. Morandotti , and J. S. Aitchison , “ Discrete Vector Solitons in Kerr Nonlinear Waveguide Arrays ,” Phys. Rev. Lett.   91 , 143 , 907 –1–4 ( 2003 ).
[Crossref]

Stegeman, G. I.

R. Iwanow , R. Schiek , G. I. Stegeman , T. Pertsch , F. ederer , Y. Min , and W. Sohler , “ Observation of Discrete Quadratic Solitons ,” Phys. Rev. Lett.   93 , 113 , 902 –1–4 ( 2004 ).
[Crossref]

Sukhorukov, A. A.

D. Neshev , A. A. Sukhorukov , B. Hanna , W. Krolikowski , and Y. S. Kivshar , “ Controlled Generation and Steering of Spatial Gap Solitons ,” Phys. Rev. Lett.   93 , 083 , 905 –1–4 ( 2004 ).
[Crossref]

Temelkuran, B.

M. Bayindir , B. Temelkuran , and E. Ozbay , “ Tight-Binding Description of the Coupled Defect Modes in Three-Dimensional Photonic Crystals ,” Phys. Rev. Lett.   84 , 2140 – 2143 ( 2000 ).
[Crossref] [PubMed]

Theodorakis, S.

S. Theodorakis and E. Leontidis , “ Bound states in a nonlinear Kronig-Penney model ,” J. Phys. A   30 , 4835 – 4849 ( 1997 ).
[Crossref]

Torner, L.

Villeneuve, P. R.

A. Mekis , J. C. Chen , I. Kurland , S. Fan , P. R. Villeneuve , and J. D. Joannopoulos , “ High Transmission through Sharp Bends in Photonic Crystal Waveguides ,” Phys. Rev. Lett.   77 , 3787 – 3790 ( 1996 ).
[Crossref] [PubMed]

Vysloukh, V. A.

Wabnitz, S.

A. B. Aceves and S. Wabnitz , “ Self-induced transparency solitons in nonlinear refractive periodic media ,” Phys. Lett. A   141 , 37 – 42 ( 1989 ).
[Crossref]

Wang, J.

J. Wang , F. Ye , L. Dong , T. Cai , and Y.-P. Li , “ Lattice solitons supported by competing cubic-quintic nonlinearity ,” Phys. Lett. A   339 , 74 – 82 ( 2005 ).
[Crossref]

Winful, H. G.

Winn, J. N.

J. Joannopoulos , R. Meade , and J. N. Winn , Photonic Crystals: Molding the Flow of Light ( Princeton University Press, Princeton, NJ , 1995 ).

Xu, Y.

Yablonovitch, E.

E. Yablonovitch , T. J. Gmitter , R. D. Meade , A. M. Rappe , K. D. Brommer , and J. D. Joannopoulos , “ Donor and Acceptor Modes in Photonic Band Strucure ,” Phys. Rev. Lett.   67 , 3380 – 3383 ( 1991 ).
[Crossref] [PubMed]

E. Yablonovitch , “ Inhibited Spontaneous Emission in Solid-State Physics and Electronics ,” Phys. Rev. Lett.   58 , 2059 – 2062 ( 1987 ).
[Crossref] [PubMed]

Yang, J.

F. Fedele , J. Yang , and Z. Chen , “ Defect modes in one-dimensional photonic lattices ,” Opt. Lett.   30 , 1506 – 1508 ( 2005 ).
[Crossref] [PubMed]

J. Yang and Z. H. Musslimani , “ Fundamental and vortex solitons in a two-dimensional optical lattice ,” Opt. Lett.   21 , 2094 – 2096 ( 2003 ).
[Crossref]

Yariv, A.

A. Yariv , “ Coupled-wave formalism for optical waveguiding by transverse Bragg reflection ,” Opt. Lett.   27 , 936 – 938 ( 2002 ).
[Crossref]

A. Yariv , Y. Xu , R. K. Lee , and A. Scherer , “ Coupled-resonator optical waveguide: a proposal and analysis ,” Opt. Lett.   24 , 711 – 713 ( 1999 ).
[Crossref]

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

P. Yeh and A. Yariv , “ Bragg reflection waveguides ,” Opt. Commun.   19 , 427 – 430 ( 1976 ).
[Crossref]

Ye, F.

J. Wang , F. Ye , L. Dong , T. Cai , and Y.-P. Li , “ Lattice solitons supported by competing cubic-quintic nonlinearity ,” Phys. Lett. A   339 , 74 – 82 ( 2005 ).
[Crossref]

Yeh, P.

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

P. Yeh and A. Yariv , “ Bragg reflection waveguides ,” Opt. Commun.   19 , 427 – 430 ( 1976 ).
[Crossref]

Yuri, S.

S. F. Mingaleev , R. A. Kivshar , S. Yuri , and Sammut , “ Long-range interaction and nonlinear localized modes in photonic crystal waveguides ,” Phys. Rev. E   62 , 5777 – 5782 ( 2000 ).
[Crossref]

Appl. Phys. Lett. (2)

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

S. Linden , J. P. Mondia , H. M. V. Driel , T. C. Kleckner , C. R. Stanley , D. Modotto , A. Locatelli , C. D. An-gelis , R. Morandotti , and J. S. Aitchison , “ Nonlinear transmission properties of a deep-etched microstructured waveguide ,” Appl. Phys. Lett.   84 , 5437 – 5439 ( 2004 ).
[Crossref]

Eur. Phys. J. D (1)

P. Kevrekidis , B. Malomed , and Z. Musslimani , “ Discrete gap solitons in a diffraction-managed waveguide array ,” Eur. Phys. J. D   23 , 421 – 436 ( 2003 ).
[Crossref]

Europhys. Lett. (1)

B. B. Baizakov , B. A. Malomed , and M. Salerno , “ Multidimensional solitons in periodic potentials ,” Europhys. Lett.   63 , 642 – 648 ( 2003 ).
[Crossref]

J. Lightwave Technol. (1)

J. Phys. A (1)

S. Theodorakis and E. Leontidis , “ Bound states in a nonlinear Kronig-Penney model ,” J. Phys. A   30 , 4835 – 4849 ( 1997 ).
[Crossref]

Nature (2)

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] [PubMed]

D. N. Christodoulides , F. Lederer , and Y. Silberberg , “ Discretizing light behaviour in linear and nonlinear waveguide lattices ,” Nature   424 , 817 – 823 ( 2003 ).
[Crossref] [PubMed]

Opt. Commun. (1)

P. Yeh and A. Yariv , “ Bragg reflection waveguides ,” Opt. Commun.   19 , 427 – 430 ( 1976 ).
[Crossref]

Opt. Express (3)

Opt. Lett. (8)

P. Roy. Soc. Lond. A Mat. (1)

R. d. L. Kronig and W. G. Penney , “ Quantum Mechanics of Electrons in Crystal Lattices ,” P. Roy. Soc. Lond. A Mat.   814 , 499 – 513 ( 1931 ).
[Crossref]

Phys. Lett. A (2)

A. B. Aceves and S. Wabnitz , “ Self-induced transparency solitons in nonlinear refractive periodic media ,” Phys. Lett. A   141 , 37 – 42 ( 1989 ).
[Crossref]

J. Wang , F. Ye , L. Dong , T. Cai , and Y.-P. Li , “ Lattice solitons supported by competing cubic-quintic nonlinearity ,” Phys. Lett. A   339 , 74 – 82 ( 2005 ).
[Crossref]

Phys. Rev. A (2)

P. J. Y. Louis , E. A. Ostrovskaya , C. M. Savage , and Y. S. Kivshar , “ Bose-Einstein condensates in optical lattices: Band-gap structure and solitons ,” Phys. Rev. A   67 , 013 , 602 –1–9 ( 2003 ).
[Crossref]

N. K. Efremidis and D. N. Christodoulides , “ Lattice solitons in Bose-Einstein condensates ,” Phys. Rev. A   67 , 063 , 608 –1–9 ( 2003 ).
[Crossref]

Phys. Rev. B (1)

N. Stefanou and A. Modinos , “ Impurity bands in photonic insulators ,” Phys. Rev. B   57 , 12, 127 –12, 133 ( 1998 ).
[Crossref]

Phys. Rev. E (4)

N. K. Efremidis , D. N. Christodoulides , S. Sears , J. W. Fleischer , and M. Segev , “ Discrete Solitons in Photorefractive Optically-Induced Photonic Lattices ,” Phys. Rev. E   66 , 046 , 602 –1–5 ( 2002 ).
[Crossref]

S. F. Mingaleev , R. A. Kivshar , S. Yuri , and Sammut , “ Long-range interaction and nonlinear localized modes in photonic crystal waveguides ,” Phys. Rev. E   62 , 5777 – 5782 ( 2000 ).
[Crossref]

W. Li and A. Smerzi , “ Nonlinear Krönig-Penney model ,” Phys. Rev. E   70 , 016 , 605 –1–4 ( 2004 ).
[Crossref]

I. M. Merhasin , B. V. Gisin , R. Driben , and B. A. Malomed , “ Finite-band solitons in the Kronig-Penney model with the cubic-quintic nonlinearity ,” Phys. Rev. E   71 , 016 , 613 –1–12 ( 2005 ).
[Crossref]

Phys. Rev. Lett. (24)

H. S. Eisenberg , Y. Silberberg , R. Morandotti , and J. S. Aitchison , “ Diffraction Management ,” Phys. Rev. Lett.   85 , 1863 – 1866 ( 2000 ).
[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 , 123 , 902 –1–4 ( 2004 ).
[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 , 213 , 906 –1–4 ( 2003 ).
[Crossref]

J. W. Fleischer , G. Bartal , O. Cohen , O. Manela , M. Segev , J. Hudock , and D. N. Christodoulides , “ Observation of Vortex-Ring “Discrete” Solitons in 2D Photonic Lattices ,” Phys. Rev. Lett.   92 , 123 , 904 –1–4 ( 2004 ).
[Crossref]

D. N. Neshev , T. J. Alexander , E. A. Ostrovskaya , Y. S. Kivshar , H. Martin , I. Makasyuk , and Z. Chen , “ Observation of Discrete Vortex Solitons in Optically Induced Photonic Lattices ,” Phys. Rev. Lett.   92 , 123 , 903 –1–4 ( 2004 ).
[Crossref]

Y. V. Kartashov , V. A. Vysloukh , and L. Torner , “ Rotary Solitons in Bessel Optical Lattices ,” Phys. Rev. Lett.   93 , 093 , 904 –1–4 ( 2004 ).
[Crossref]

B. J. Eggleton , R. E. Slusher , C. M. de Sterke , P. A. Krug , and J. E. Sipe , “ Bragg Grating Solitons ,” Phys. Rev. Lett.   76 , 1627 – 1630 ( 1996 ).
[Crossref] [PubMed]

D. N. Christodoulides and R. I. Joseph , “ Slow Bragg Solitons in Nonlinear Periodic Structures ,” Phys. Rev. Lett.   62 , 1746 – 1749 ( 1989 ).
[Crossref] [PubMed]

D. D. Mandelik , R. Morandotti , J. S. Aitchison , and Y. Silberberg , “ Gap Solitons in Waveguide Arrays ,” Phys. Rev. Lett.   92 , 093 , 904 –1–4 ( 2004 ).
[Crossref]

D. Neshev , A. A. Sukhorukov , B. Hanna , W. Krolikowski , and Y. S. Kivshar , “ Controlled Generation and Steering of Spatial Gap Solitons ,” Phys. Rev. Lett.   93 , 083 , 905 –1–4 ( 2004 ).
[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]

M. Bayindir , B. Temelkuran , and E. Ozbay , “ Tight-Binding Description of the Coupled Defect Modes in Three-Dimensional Photonic Crystals ,” Phys. Rev. Lett.   84 , 2140 – 2143 ( 2000 ).
[Crossref] [PubMed]

R. Morandotti , U. Peschel , J. S. Aitchison , H. S. Eisenberg , and Y. Silberberg , “ Dynamics of Discrete Solitons in Optical Waveguide Arrays ,” Phys. Rev. Lett. ( 1999 ).
[Crossref]

R. Iwanow , R. Schiek , G. I. Stegeman , T. Pertsch , F. ederer , Y. Min , and W. Sohler , “ Observation of Discrete Quadratic Solitons ,” Phys. Rev. Lett.   93 , 113 , 902 –1–4 ( 2004 ).
[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 – 4755 ( 1999 ).
[Crossref]

R. Morandotti , U. Peschel , J. S. Aitchison , H. S. Eisenberg , and Y. Silberberg , “ Experimental Observation of Linear and Nonlinear Optical Bloch Oscillations ,” Phys. Rev. Lett.   83 , 4756 – 4759 ( 1999 ).
[Crossref]

J. Meier , J. Hudock , D. Christodoulides , G. Stegeman , Y. Silberberg , R. Morandotti , and J. S. Aitchison , “ Discrete Vector Solitons in Kerr Nonlinear Waveguide Arrays ,” Phys. Rev. Lett.   91 , 143 , 907 –1–4 ( 2003 ).
[Crossref]

D. Mandelik , H. S. Eisenberg , Y. Silberberg , R. Morandotti , and J. S. Aitchison , “ Band-Gap Structure of Waveguide Arrays and Excitation of Floquet-Bloch Solitons ,” Phys. Rev. Lett.   90 , 053 , 902 –1–4 ( 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 , 023 , 902 –1–4 ( 2003 ).
[Crossref]

A. Mekis , J. C. Chen , I. Kurland , S. Fan , P. R. Villeneuve , and J. D. Joannopoulos , “ High Transmission through Sharp Bends in Photonic Crystal Waveguides ,” Phys. Rev. Lett.   77 , 3787 – 3790 ( 1996 ).
[Crossref] [PubMed]

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 – 2020 ( 1991 ).
[Crossref] [PubMed]

E. Yablonovitch , T. J. Gmitter , R. D. Meade , A. M. Rappe , K. D. Brommer , and J. D. Joannopoulos , “ Donor and Acceptor Modes in Photonic Band Strucure ,” Phys. Rev. Lett.   67 , 3380 – 3383 ( 1991 ).
[Crossref] [PubMed]

E. Yablonovitch , “ Inhibited Spontaneous Emission in Solid-State Physics and Electronics ,” Phys. Rev. Lett.   58 , 2059 – 2062 ( 1987 ).
[Crossref] [PubMed]

S. John , “ Strong Localization of Photons in Certain Disordered Dielectric Superlattices ,” Phys. Rev. Lett.   58 , 2486 – 2489 ( 1987 ).
[Crossref] [PubMed]

Prys. Rev. E (1)

B. A. Malomed and P. G. Kevrekidis , “ Discrete vortex solitons ,” Prys. Rev. E   64 , 026 , 601 –1–6 ( 2001 ).

Science (2)

J. Knight , J. Broeng , T. A. Birks , and P. Russell , “ Photonic band gap guidance in optical fibers ,” Science   282 , 1476 – 1478 ( 1998 ).
[Crossref] [PubMed]

P. Russell , “ Photonic crystal fibers ,” Science   299 , 358 – 362 ( 2003 ).
[Crossref] [PubMed]

Other (3)

J. Joannopoulos , R. Meade , and J. N. Winn , Photonic Crystals: Molding the Flow of Light ( Princeton University Press, Princeton, NJ , 1995 ).

C. M. de Sterke and J. E. Sipe , “ Gap solitons ,” in Progress in Optics , E. Wolf , ed., vol. XXXIII, p. 203 ( North-Holland, Amsterdam , 1994 ).

C. Kittel , Introduction to Solid State Physics ( Wiley, New York , 1986 ).

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Figures (10)

Fig. 1.
Fig. 1.

Different physical settings where BGL can be implemented. These settings can be (a) photonic crystal fiber arrays, (b) optically induced lattices, and (c) waveguide arrays. Notice that higher index areas are shown in darker colors. In these configurations the intensity of light is expected to be localized in the low refractive index defects of the lattice.

Fig. 2.
Fig. 2.

Different physical settings where bandgap lattices can be implemented. These settings can be (a) photonic crystal fiber arrays, (b) an optically induced lattices, and (c) waveguide arrays. Notice that higher index areas are shown in darker colors. In these configurations the intensity of light is expected to be localized in the high refractive index defects of the lattice.

Fig. 3.
Fig. 3.

On the left panel the band structure corresponding to the potential of Eq. (8) is shown. The period of this potential is L = 1 and its depth is V 0 = 9. The discrete spectrum is depicted with dots and the arrow indicates the band from which this mode bifurcates. The inset shows an enlarged view of the bifurcation. The first two bands of the spectrum have eigenvalues in the domains [2.62 5.31] and [-14.99 - 3.05], respectively. The eigenvalue of the first defect mode is q = -1.59. On the right panel the amplitude of the defect mode and a schematic illustration of the refractive index contrast across the lattice are shown.

Fig. 4.
Fig. 4.

The exact band structure (left panel) of a periodic superlattice as described by Eq. (10) for V 0 = 9 and L = 5. The inset shows an expanded view of the defect band. This band extends in the region [-1.68 - 1.51] while the bands above and bellow have spatial frequencies [3.04 3.09] and [-4.38 -3.32], respectively. On the right panel the Bloch modes at the base and the edge of the Brillouin zone are depicted. On the bottom of the figure a schematic illustration of the refractive index modulation along the lattice is presented.

Fig. 5.
Fig. 5.

Numerical simulations of low power (linear) beams propagating according to Eq. (1) where the lattice is given by Eq. (10). In (a) only two defects are involved, thus, forming a directional bandgap coupler, (b) diffraction of a single waveguide excitation, and (c) propagation with minimum diffraction when the beam is launched with a Bloch momentum k = π/2L that corresponds to the middle of the Brillouin zone. (a) and (b) the initial condition is the localized mode of a single low index defect and in (c) it is a Gaussian superposition of single defect modes having the proper phase difference. The propagation length is normalized to the coupling length zc = π/κ. Because the maximum beam intensity reduces rapidly as it diffracts, a highly nonlinear scheme in the color range (b) able to capture the diffraction pattern for several diffraction lengths is utilized.

Fig. 6.
Fig. 6.

On the left panel we can see the dependence of the width of the defect band from the spacing between the defects. On the right panel we plot the same data in a logarithmic scale for the width of the defect band. The data are presented with dots and the solid curve show the fitting function.

Fig. 7.
Fig. 7.

Self-focusing soliton solutions of the low index defect lattice given by Eq. (10) with period L = 5 and index contrast V 0 = 9. In the top left panel the existence curve of this family of soliton solutions (total power vs. the eigenvalue) is presented. The bandgaps are shown in gray color and the bands in white. The two defect modes corresponding to points (a) and (b) of the existence curve, with eigenvalues q = -1.33 and q = 1.61 respectively, are depicted in the bottom panel. The stable evolution of mode (a) over 5 diffraction lengths is presented in the top right panel.

Fig. 8.
Fig. 8.

Self-defocusing soliton solutions of the low index defect lattice given by Eq. (10) with period L = 5 and index contrast V 0 = 9. In the top left panel the existence curve of this family of soliton solution (total power vs. the eigenvalue) is presented. The bandgaps are show in gray color and the bands in white. The two defect mode corresponding to points (a) and (b) of the existence curve, and with eigenvalues q = 1.77 and q = -2.51 respectively, are depicted in the bottom panel. The stable evolution of mode (a) over 5 diffraction lengths is presented in the top right panel.

Fig. 9.
Fig. 9.

On the top left panel the band structure corresponding to the potential which is expressed by Eq. (22) is shown. The continuous part of the spectrum (the bands) of this potential is exactly the same as that of Eq. (10) (shown in Fig. 4). The period of this potential outside the defect is L = 1 and its depth is V 0 = 9. The first two modes of the discrete spectrum (which are associated with the defect) are depicted with dots, and the arrows indicate the bifurcations of these modes from the continuous bands. The top right panel shows enlarged views of these bifurcations. On the bottom panel the first two defect modes [(a) and (b)] are shown. The first two bands of the spectrum have eigenvalues in the regions [2.62 5.31] and [-14.99 - 3.05], respectively. The eigenvalue of the first defect mode (located in the TIR region) is q = 6.84 and of the second mode (located in the first bandgap between the first two bands) is q = 0.53.

Fig. 10.
Fig. 10.

Expanded view of the first two defect bands [(a) and (b)] inside the band structure (left panel) of a periodic superlattice as described by Eq. (23) for V 0 = 9 and L = 5.5. Bands (a) and (b) originate from the corresponding defect modes of Fig. 9. The narrow defect band (a) spans the region [6.8425 6.8429] while the band bellow has spatial frequencies in the domain [5.11 5.16]. Defect band (b) spans the region [0.49 0.57] while the bands above and bellow have spatial frequencies in the domains [3 3.16] and [-3.35 -4], respectively. On the right panel the Bloch modes of bands (a) and (b) at the base of the Brillouin zone are shown.

Equations (24)

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i ψ z + 1 2 ψ xx + V ( x ) ψ + γ ψ 2 = 0 .
ψ ( x , z ) = u ( x ) e iqz
qu + 1 2 u xx + V ( x ) u + γ u 3 = 0 .
u ( x ) = g ( x ) exp ( ikx )
V g ( x ; V 0 ) = { V 0 x < 1 4 0 1 4 < x 1 2 V 0 2 x = 1 4
V g ( x ) = V g ( x = x n )
i ψ z + 1 2 ψ x x + V ( x ; V 0 ) ψ + γ ψ 2 ψ = 0 .
V t ( x ) = V t ( x ; V 0 ) = V g ( x ; V 0 ) V d ( x , V 0 )
V d ( x ; V 0 ) = { V 0 x < 1 4 V 0 2 x = 1 4 0 otherwise
V ( x ; V 0 ) = { V g ( x ; V 0 ) V d ( x ; V 0 ) x L 2 V g ( x = x n L ) V d ( x = x n L ) x > L 2 and x L 2
q ϕ + 1 2 ϕ xx + V t ( x ) ϕ = 0 .
ψ ( x , z ) = e iqz n c n ( z ) ϕ n ( x ) .
i d c n d z + Δ q c n + κ ( c n + 1 + c n 1 ) + λ c n 2 c n = 0
κ = 1 2 ϕ n * d 2 ϕ n + 1 d x 2 dx + ϕ n * ϕ n + 1 V ( x ) dx
Δ q = ϕ n 2 ( V ( x ) V t ( x ) ) dx
λ = γ ϕ n 4 dx
q = Δ q + 2 κ cos k .
c n ( z ) = J n ( 2 κ z ) exp ( i π n 2 + i Δ q z )
ψ ( x , z = 0 ) = n ϕ n ( x ) e ( n A ) 2 e i k n ,
P = ψ 2 dx ,
H = [ ψ x 2 2 V ( x ) ψ 2 ψ 4 ] .
ψ ( x , z ) = u ( x ) exp ( iqz )
V t ( x ) = V t ( x ; V 0 ) = V g ( x 1 4 )
V ( x ) = V ( x ; V 0 ) = V t ( x = x Ln ; V 0 ) ,

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