Abstract

We investigate the effects of the space-time coupling (STC) on the nonlinear formation and propagation of Light Bullets, spatiotemporal solitons in which dispersion and diffraction along all dimensions are balanced by nonlinearity, through periodic media with a weak transverse modulation of the refractive index, i.e. waveguide arrays. The STC arises from wavelength dependence of the strength of inter-waveguide coupling and can be tuned by variation of the array geometry. We show experimentally and numerically that the STC breaks the spectral symmetry of Light Bullets to a considerable degree and modifies their group velocity, leading to superluminal propagation when the Light Bullets decay.

© 2011 OSA

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  1. A. Dogariu, A. Kuzmich, and L. J. Wang, “Transparent anomalous dispersion and superluminal light-pulse propagation at a negative group velocity,” Phys. Rev. A 63(5), 053806 (2001).
    [CrossRef]
  2. A. Dogariu, A. Kuzmich, H. Cao, and L. Wang, “Superluminal light pulse propagation via rephasing in a transparent anomalously dispersive medium,” Opt. Express 8(6), 344–350 (2001).
    [CrossRef] [PubMed]
  3. A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Measurement of the single-photon tunneling time,” Phys. Rev. Lett. 71(5), 708–711 (1993).
    [CrossRef] [PubMed]
  4. A. Kuzmich, A. Dogariu, L. J. Wang, P. W. Milonni, and R. Y. Chiao, “Signal velocity, causality, and quantum noise in superluminal light pulse propagation,” Phys. Rev. Lett. 86(18), 3925–3929 (2001).
    [CrossRef] [PubMed]
  5. M. D. Stenner, D. J. Gauthier, and M. A. Neifeld, “The speed of information in a ‘fast-light’ optical medium,” Nature 425(6959), 695–698 (2003).
    [CrossRef] [PubMed]
  6. G. Nimtz, “Evanescent modes are not necessarily Einstein causal,” Eur. Phys. J. B 7(4), 523–525 (1999), doi:.
    [CrossRef]
  7. M. Nakazawa, T. Yamamoto, and K. Tamura, “1.28 tbit/s–70 km OTDM transmission using third- and fourth-order simultaneous dispersion compensation with a phase modulator,” Electron. Lett. 36(24), 2027–2029 (2000).
    [CrossRef]
  8. H. C. H. Mulvad, M. Galili, L. K. Oxenløwe, H. Hu, A. T. Clausen, J. B. Jensen, C. Peucheret, and P. Jeppesen, “Demonstration of 5.1 Tbit/s data capacity on a single-wavelength channel,” Opt. Express 18(2), 1438–1443 (2010).
    [CrossRef] [PubMed]
  9. T. D. Vo, H. Hu, M. Galili, E. Palushani, J. Xu, L. K. Oxenløwe, S. J. Madden, D.-Y. Choi, D. A. P. Bulla, M. D. Pelusi, J. Schröder, B. Luther-Davies, and B. J. Eggleton, “Photonic chip based transmitter optimization and receiver demultiplexing of a 1.28 Tbit/s OTDM signal,” Opt. Express 18(16), 17252–17261 (2010).
    [CrossRef] [PubMed]
  10. A. Stepanov, J. Kuhl, I. Kozma, E. Riedle, G. Almási, and J. Hebling, “Scaling up the energy of THz pulses created by optical rectification,” Opt. Express 13(15), 5762–5768 (2005).
    [CrossRef] [PubMed]
  11. R. Danielius, A. Piskarskas, P. Di Trapani, A. Andreoni, C. Solcia, and P. Foggi, “Matching of group velocities by spatial walk-off in collinear three-wave interaction with tilted pulses,” Opt. Lett. 21(13), 973–975 (1996).
    [CrossRef] [PubMed]
  12. D. Faccio, A. Averchi, A. Dubietis, P. Polesana, A. Piskarskas, P. D. Trapani, and A. Couairon, “Stimulated Raman X waves in ultrashort optical pulse filamentation,” Opt. Lett. 32(2), 184–186 (2007).
    [CrossRef] [PubMed]
  13. O. Martinez, “Achromatic phase matching for second harmonic generation of femtosecond pulses,” IEEE J. Quantum Electron. 25(12), 2464–2468 (1989).
    [CrossRef]
  14. P. Saari and K. Reivelt, “Evidence of x-shaped propagation-invariant localized light waves,” Phys. Rev. Lett. 79(21), 4135–4138 (1997).
    [CrossRef]
  15. A. V. Gorbach and D. V. Skryabin, “Cascaded generation of multiply charged optical vortices and spatiotemporal helical beams in a Raman medium,” Phys. Rev. Lett. 98(24), 243601 (2007).
    [CrossRef] [PubMed]
  16. P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated X-shaped light bullets,” Phys. Rev. Lett. 91(9), 093904 (2003).
    [CrossRef] [PubMed]
  17. D. Faccio, M. A. Porras, A. Dubietis, F. Bragheri, A. Couairon, and P. Di Trapani, “Conical emission, pulse splitting, and X-wave parametric amplification in nonlinear dynamics of ultrashort light pulses,” Phys. Rev. Lett. 96(19), 193901 (2006).
    [CrossRef] [PubMed]
  18. S. Minardi, A. Gopal, A. Couairon, G. Tamoašuskas, R. Piskarskas, A. Dubietis, and P. Di Trapani, “Accurate retrieval of pulse-splitting dynamics of a femtosecond filament in water by time-resolved shadowgraphy,” Opt. Lett. 34(19), 3020–3022 (2009).
    [CrossRef] [PubMed]
  19. I. Blonskyi, V. Kadan, O. Shpotyuk, and I. Dmitruk, “Manifestations of sub- and superluminality in filamented femtosecond laser pulse in fused silica,” Opt. Commun. 282(9), 1913–1917 (2009).
    [CrossRef]
  20. C. J. Benton and D. V. Skryabin, “Coupling induced anomalous group velocity dispersion in nonlinear arrays of silicon photonic wires,” Opt. Express 17(7), 5879–5884 (2009).
    [CrossRef] [PubMed]
  21. C. J. Benton, A. V. Gorbach, and D. V. Skryabin, “Spatiotemporal quasisolitons and resonant radiation in arrays of silicon-on-insulator photonic wires,” Phys. Rev. A 78(3), 033818 (2008).
    [CrossRef]
  22. A. V. Gorbach, W. Ding, O. K. Staines, C. E. de Nobriga, G. D. Hobbs, W. J. Wadsworth, J. C. Knight, D. V. Skryabin, A. Samarelli, M. Sorel, and R. M. De La Rue, “Spatiotemporal nonlinear optics in arrays of subwavelength waveguides,” Phys. Rev. A 82(4), 041802 (2010).
    [CrossRef]
  23. Y. Silberberg, “Collapse of optical pulses,” Opt. Lett. 15(22), 1282–1284 (1990).
    [CrossRef] [PubMed]
  24. S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Three-dimensional light bullets in arrays of waveguides,” Phys. Rev. Lett. 105(26), 263901 (2010).
    [CrossRef] [PubMed]
  25. Y. V. Kartashov, B. A. Malomed, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys. 83(1), 247–306 (2011).
    [CrossRef]
  26. Y. S. Kivshar and S. K. Turitsyn, “Spatiotemporal pulse collapse on periodic potentials,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 49(4), R2536–R2539 (1994).
    [CrossRef] [PubMed]
  27. A. B. Aceves and C. De Angelis, “Spatiotemporal pulse dynamics in a periodic nonlinear waveguide,” Opt. Lett. 18(2), 110–112 (1993).
    [CrossRef] [PubMed]
  28. D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424(6950), 817–823 (2003).
    [CrossRef] [PubMed]
  29. S. K. Turitsyn, “Collapse criterion for a pulse dynamics in a periodic nonlinear waveguide,” Opt. Lett. 18(18), 1493–1495 (1993).
    [CrossRef] [PubMed]
  30. F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1-3), 1–126 (2008).
    [CrossRef]
  31. Y. Kivshar and G. Agrawal, Optical Solitons (Academic Press, 2003).
  32. B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B: Quantum Semiclassical Opt. 7(5), R53–R72 (2005).
  33. J. E. Rothenberg, “Pulse splitting during self-focusing in normally dispersive media,” Opt. Lett. 17(8), 583–585 (1992).
    [CrossRef] [PubMed]
  34. A. Szameit, M. C. Rechtsman, O. Bahat-Treidel, and M. Segev, “Pt-symmetry in honeycomb photonic lattices,” Phys. Rev. A 84(2), 021806 (2011).
    [CrossRef]
  35. F. Bragheri, D. Faccio, F. Bonaretti, A. Lotti, M. Clerici, O. Jedrkiewicz, C. Liberale, S. Henin, L. Tartara, V. Degiorgio, and P. Di Trapani, “Complete retrieval of the field of ultrashort optical pulses using the angle-frequency spectrum,” Opt. Lett. 33(24), 2952–2954 (2008).
    [CrossRef] [PubMed]
  36. A. Zozulya and S. Diddams, “Dynamics of self-focused femtosecond laser pulses in the near and far fields,” Opt. Express 4(9), 336–343 (1999).
    [CrossRef] [PubMed]
  37. M. A. Porras, I. Gonzalo, and A. Mondello, “Pulsed light beams in vacuum with superluminal and negative group velocities,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(6), 066604 (2003).
    [CrossRef] [PubMed]
  38. S. Malaguti, G. Bellanca, and S. Trillo, “Two-dimensional envelope localized waves in the anomalous dispersion regime,” Opt. Lett. 33(10), 1117–1119 (2008).
    [CrossRef] [PubMed]
  39. A. Szameit, T. Pertsch, F. Dreisow, S. Nolte, A. Tünnermann, U. Peschel, and F. Lederer, “Light evolution in arbitrary two-dimensional waveguide arrays,” Phys. Rev. A 75(5), 053814 (2007).
    [CrossRef]
  40. A. Szameit, D. Blömer, J. Burghoff, T. Pertsch, S. Nolte, and A. Tünnermann, “Hexagonal waveguide arrays written with fs-laser pulses,” Appl. Phys. B 82(4), 507–512 (2006).
    [CrossRef]
  41. F. Eilenberger, S. Minardi, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Evolution dynamics of discrete-continuous light bullets,” Phys. Rev. A 84(1), 013836 (2011).
    [CrossRef]
  42. F. Eilenberger, A. Szameit, and T. Pertsch, “Transition from discrete to continuous townes solitons in periodic media,” Phys. Rev. A 82(4), 043802 (2010).
    [CrossRef]
  43. G. Agrawal, Nonlinear Fiber Optics (Academic Press, 2001).
  44. N. Vakhitov and A. Kolokolov, “Stationary solutions of the wave equation in a medium with nonlinearity saturation,” Radiophys. Quantum Electron. 16(7), 783–789 (1973).
    [CrossRef]
  45. N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, “Discrete solitons in photorefractive optically induced photonic lattices,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(4), 046602 (2002).
    [CrossRef] [PubMed]
  46. 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(6928), 147–150 (2003).
    [CrossRef] [PubMed]
  47. 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(2), 023902 (2003).
    [CrossRef] [PubMed]
  48. U. Röpke, H. Bartelt, S. Unger, K. Schuster, and J. Kobelke, “Fiber waveguide arrays as model system for discrete optics,” Appl. Phys. B 104(3), 481–486 (2011), doi:.
    [CrossRef]
  49. U. Röpke, H. Bartelt, S. Unger, K. Schuster, and J. Kobelke, “Two-dimensional high-precision fiber waveguide arrays for coherent light propagation,” Opt. Express 15(11), 6894–6899 (2007).
    [CrossRef] [PubMed]
  50. J. C. Knight, “Photonic crystal fibres,” Nature 424(6950), 847–851 (2003).
    [CrossRef] [PubMed]
  51. P. Russell, “Photonic crystal fibers,” Science 299(5605), 358–362 (2003).
    [CrossRef] [PubMed]
  52. T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tünnermann, and F. Lederer, “Nonlinearity and disorder in fiber arrays,” Phys. Rev. Lett. 93(5), 053901 (2004).
    [CrossRef] [PubMed]
  53. T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446(7131), 52–55 (2007).
    [CrossRef] [PubMed]
  54. M. Kolesik and J. V. Moloney, “Nonlinear optical pulse propagation simulation: from Maxwell’s to unidirectional equations,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(3), 036604 (2004).
    [CrossRef] [PubMed]
  55. I. Babushkin, A. Husakou, J. Herrmann, and Y. S. Kivshar, “Frequency-selective self-trapping and supercontinuum generation in arrays of coupled nonlinear waveguides,” Opt. Express 15(19), 11978–11983 (2007).
    [CrossRef] [PubMed]
  56. P. Kinsler, “Unidirectional optical pulse propagation equation for materials with both electric and magnetic responses,” Phys. Rev. A 81(2), 023808 (2010).
    [CrossRef]
  57. R. R. Alfano and S. L. Shapiro, “Emission in the region 4000 to 7000 å via four-photon coupling in glass,” Phys. Rev. Lett. 24(11), 584–587 (1970).
    [CrossRef]
  58. J. K. Ranka, R. S. Windeler, and A. J. Stentz, “Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm,” Opt. Lett. 25(1), 25–27 (2000).
    [CrossRef] [PubMed]
  59. J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
    [CrossRef]
  60. C. Conti, S. Trillo, P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, and J. Trull, “Nonlinear electromagnetic X waves,” Phys. Rev. Lett. 90(17), 170406 (2003).
    [CrossRef] [PubMed]
  61. M. Kolesik, E. M. Wright, and J. V. Moloney, “Dynamic nonlinear X waves for femtosecond pulse propagation in water,” Phys. Rev. Lett. 92(25), 253901 (2004).
    [CrossRef] [PubMed]
  62. M. Heinrich, A. Szameit, F. Dreisow, R. Keil, S. Minardi, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, “Observation of three-dimensional discrete-continuous x waves in photonic lattices,” Phys. Rev. Lett. 103(11), 113903 (2009).
    [CrossRef] [PubMed]
  63. M. A. C. Potenza, S. Minardi, J. Trull, G. Blasi, D. Salerno, A. Varanavicius, A. Piskarskas, and P. D. Trapani, “Three dimensional imaging of short pulses,” Opt. Commun. 229(1-6), 381–390 (2004).
    [CrossRef]
  64. S. Minardi, J. Trull, and M. A. C. Potenza, “Holographic properties of parametric image conversion for spatiotemporal imaging of ultrashort laser pulses,” J. Hologr. Speckle 5(1), 85–93 (2009).
    [CrossRef]

2011

Y. V. Kartashov, B. A. Malomed, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys. 83(1), 247–306 (2011).
[CrossRef]

F. Eilenberger, S. Minardi, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Evolution dynamics of discrete-continuous light bullets,” Phys. Rev. A 84(1), 013836 (2011).
[CrossRef]

U. Röpke, H. Bartelt, S. Unger, K. Schuster, and J. Kobelke, “Fiber waveguide arrays as model system for discrete optics,” Appl. Phys. B 104(3), 481–486 (2011), doi:.
[CrossRef]

A. Szameit, M. C. Rechtsman, O. Bahat-Treidel, and M. Segev, “Pt-symmetry in honeycomb photonic lattices,” Phys. Rev. A 84(2), 021806 (2011).
[CrossRef]

2010

F. Eilenberger, A. Szameit, and T. Pertsch, “Transition from discrete to continuous townes solitons in periodic media,” Phys. Rev. A 82(4), 043802 (2010).
[CrossRef]

A. V. Gorbach, W. Ding, O. K. Staines, C. E. de Nobriga, G. D. Hobbs, W. J. Wadsworth, J. C. Knight, D. V. Skryabin, A. Samarelli, M. Sorel, and R. M. De La Rue, “Spatiotemporal nonlinear optics in arrays of subwavelength waveguides,” Phys. Rev. A 82(4), 041802 (2010).
[CrossRef]

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Three-dimensional light bullets in arrays of waveguides,” Phys. Rev. Lett. 105(26), 263901 (2010).
[CrossRef] [PubMed]

P. Kinsler, “Unidirectional optical pulse propagation equation for materials with both electric and magnetic responses,” Phys. Rev. A 81(2), 023808 (2010).
[CrossRef]

H. C. H. Mulvad, M. Galili, L. K. Oxenløwe, H. Hu, A. T. Clausen, J. B. Jensen, C. Peucheret, and P. Jeppesen, “Demonstration of 5.1 Tbit/s data capacity on a single-wavelength channel,” Opt. Express 18(2), 1438–1443 (2010).
[CrossRef] [PubMed]

T. D. Vo, H. Hu, M. Galili, E. Palushani, J. Xu, L. K. Oxenløwe, S. J. Madden, D.-Y. Choi, D. A. P. Bulla, M. D. Pelusi, J. Schröder, B. Luther-Davies, and B. J. Eggleton, “Photonic chip based transmitter optimization and receiver demultiplexing of a 1.28 Tbit/s OTDM signal,” Opt. Express 18(16), 17252–17261 (2010).
[CrossRef] [PubMed]

2009

C. J. Benton and D. V. Skryabin, “Coupling induced anomalous group velocity dispersion in nonlinear arrays of silicon photonic wires,” Opt. Express 17(7), 5879–5884 (2009).
[CrossRef] [PubMed]

S. Minardi, A. Gopal, A. Couairon, G. Tamoašuskas, R. Piskarskas, A. Dubietis, and P. Di Trapani, “Accurate retrieval of pulse-splitting dynamics of a femtosecond filament in water by time-resolved shadowgraphy,” Opt. Lett. 34(19), 3020–3022 (2009).
[CrossRef] [PubMed]

M. Heinrich, A. Szameit, F. Dreisow, R. Keil, S. Minardi, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, “Observation of three-dimensional discrete-continuous x waves in photonic lattices,” Phys. Rev. Lett. 103(11), 113903 (2009).
[CrossRef] [PubMed]

S. Minardi, J. Trull, and M. A. C. Potenza, “Holographic properties of parametric image conversion for spatiotemporal imaging of ultrashort laser pulses,” J. Hologr. Speckle 5(1), 85–93 (2009).
[CrossRef]

I. Blonskyi, V. Kadan, O. Shpotyuk, and I. Dmitruk, “Manifestations of sub- and superluminality in filamented femtosecond laser pulse in fused silica,” Opt. Commun. 282(9), 1913–1917 (2009).
[CrossRef]

2008

C. J. Benton, A. V. Gorbach, and D. V. Skryabin, “Spatiotemporal quasisolitons and resonant radiation in arrays of silicon-on-insulator photonic wires,” Phys. Rev. A 78(3), 033818 (2008).
[CrossRef]

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1-3), 1–126 (2008).
[CrossRef]

S. Malaguti, G. Bellanca, and S. Trillo, “Two-dimensional envelope localized waves in the anomalous dispersion regime,” Opt. Lett. 33(10), 1117–1119 (2008).
[CrossRef] [PubMed]

F. Bragheri, D. Faccio, F. Bonaretti, A. Lotti, M. Clerici, O. Jedrkiewicz, C. Liberale, S. Henin, L. Tartara, V. Degiorgio, and P. Di Trapani, “Complete retrieval of the field of ultrashort optical pulses using the angle-frequency spectrum,” Opt. Lett. 33(24), 2952–2954 (2008).
[CrossRef] [PubMed]

2007

D. Faccio, A. Averchi, A. Dubietis, P. Polesana, A. Piskarskas, P. D. Trapani, and A. Couairon, “Stimulated Raman X waves in ultrashort optical pulse filamentation,” Opt. Lett. 32(2), 184–186 (2007).
[CrossRef] [PubMed]

U. Röpke, H. Bartelt, S. Unger, K. Schuster, and J. Kobelke, “Two-dimensional high-precision fiber waveguide arrays for coherent light propagation,” Opt. Express 15(11), 6894–6899 (2007).
[CrossRef] [PubMed]

I. Babushkin, A. Husakou, J. Herrmann, and Y. S. Kivshar, “Frequency-selective self-trapping and supercontinuum generation in arrays of coupled nonlinear waveguides,” Opt. Express 15(19), 11978–11983 (2007).
[CrossRef] [PubMed]

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446(7131), 52–55 (2007).
[CrossRef] [PubMed]

A. Szameit, T. Pertsch, F. Dreisow, S. Nolte, A. Tünnermann, U. Peschel, and F. Lederer, “Light evolution in arbitrary two-dimensional waveguide arrays,” Phys. Rev. A 75(5), 053814 (2007).
[CrossRef]

A. V. Gorbach and D. V. Skryabin, “Cascaded generation of multiply charged optical vortices and spatiotemporal helical beams in a Raman medium,” Phys. Rev. Lett. 98(24), 243601 (2007).
[CrossRef] [PubMed]

2006

A. Szameit, D. Blömer, J. Burghoff, T. Pertsch, S. Nolte, and A. Tünnermann, “Hexagonal waveguide arrays written with fs-laser pulses,” Appl. Phys. B 82(4), 507–512 (2006).
[CrossRef]

D. Faccio, M. A. Porras, A. Dubietis, F. Bragheri, A. Couairon, and P. Di Trapani, “Conical emission, pulse splitting, and X-wave parametric amplification in nonlinear dynamics of ultrashort light pulses,” Phys. Rev. Lett. 96(19), 193901 (2006).
[CrossRef] [PubMed]

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
[CrossRef]

2005

A. Stepanov, J. Kuhl, I. Kozma, E. Riedle, G. Almási, and J. Hebling, “Scaling up the energy of THz pulses created by optical rectification,” Opt. Express 13(15), 5762–5768 (2005).
[CrossRef] [PubMed]

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B: Quantum Semiclassical Opt. 7(5), R53–R72 (2005).

2004

T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tünnermann, and F. Lederer, “Nonlinearity and disorder in fiber arrays,” Phys. Rev. Lett. 93(5), 053901 (2004).
[CrossRef] [PubMed]

M. A. C. Potenza, S. Minardi, J. Trull, G. Blasi, D. Salerno, A. Varanavicius, A. Piskarskas, and P. D. Trapani, “Three dimensional imaging of short pulses,” Opt. Commun. 229(1-6), 381–390 (2004).
[CrossRef]

M. Kolesik and J. V. Moloney, “Nonlinear optical pulse propagation simulation: from Maxwell’s to unidirectional equations,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(3), 036604 (2004).
[CrossRef] [PubMed]

M. Kolesik, E. M. Wright, and J. V. Moloney, “Dynamic nonlinear X waves for femtosecond pulse propagation in water,” Phys. Rev. Lett. 92(25), 253901 (2004).
[CrossRef] [PubMed]

2003

M. A. Porras, I. Gonzalo, and A. Mondello, “Pulsed light beams in vacuum with superluminal and negative group velocities,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(6), 066604 (2003).
[CrossRef] [PubMed]

C. Conti, S. Trillo, P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, and J. Trull, “Nonlinear electromagnetic X waves,” Phys. Rev. Lett. 90(17), 170406 (2003).
[CrossRef] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature 422(6928), 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(2), 023902 (2003).
[CrossRef] [PubMed]

J. C. Knight, “Photonic crystal fibres,” Nature 424(6950), 847–851 (2003).
[CrossRef] [PubMed]

P. Russell, “Photonic crystal fibers,” Science 299(5605), 358–362 (2003).
[CrossRef] [PubMed]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424(6950), 817–823 (2003).
[CrossRef] [PubMed]

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated X-shaped light bullets,” Phys. Rev. Lett. 91(9), 093904 (2003).
[CrossRef] [PubMed]

M. D. Stenner, D. J. Gauthier, and M. A. Neifeld, “The speed of information in a ‘fast-light’ optical medium,” Nature 425(6959), 695–698 (2003).
[CrossRef] [PubMed]

2002

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, “Discrete solitons in photorefractive optically induced photonic lattices,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(4), 046602 (2002).
[CrossRef] [PubMed]

2001

A. Kuzmich, A. Dogariu, L. J. Wang, P. W. Milonni, and R. Y. Chiao, “Signal velocity, causality, and quantum noise in superluminal light pulse propagation,” Phys. Rev. Lett. 86(18), 3925–3929 (2001).
[CrossRef] [PubMed]

A. Dogariu, A. Kuzmich, and L. J. Wang, “Transparent anomalous dispersion and superluminal light-pulse propagation at a negative group velocity,” Phys. Rev. A 63(5), 053806 (2001).
[CrossRef]

A. Dogariu, A. Kuzmich, H. Cao, and L. Wang, “Superluminal light pulse propagation via rephasing in a transparent anomalously dispersive medium,” Opt. Express 8(6), 344–350 (2001).
[CrossRef] [PubMed]

2000

J. K. Ranka, R. S. Windeler, and A. J. Stentz, “Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm,” Opt. Lett. 25(1), 25–27 (2000).
[CrossRef] [PubMed]

M. Nakazawa, T. Yamamoto, and K. Tamura, “1.28 tbit/s–70 km OTDM transmission using third- and fourth-order simultaneous dispersion compensation with a phase modulator,” Electron. Lett. 36(24), 2027–2029 (2000).
[CrossRef]

1999

1997

P. Saari and K. Reivelt, “Evidence of x-shaped propagation-invariant localized light waves,” Phys. Rev. Lett. 79(21), 4135–4138 (1997).
[CrossRef]

1996

1994

Y. S. Kivshar and S. K. Turitsyn, “Spatiotemporal pulse collapse on periodic potentials,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 49(4), R2536–R2539 (1994).
[CrossRef] [PubMed]

1993

1992

1990

1989

O. Martinez, “Achromatic phase matching for second harmonic generation of femtosecond pulses,” IEEE J. Quantum Electron. 25(12), 2464–2468 (1989).
[CrossRef]

1973

N. Vakhitov and A. Kolokolov, “Stationary solutions of the wave equation in a medium with nonlinearity saturation,” Radiophys. Quantum Electron. 16(7), 783–789 (1973).
[CrossRef]

1970

R. R. Alfano and S. L. Shapiro, “Emission in the region 4000 to 7000 å via four-photon coupling in glass,” Phys. Rev. Lett. 24(11), 584–587 (1970).
[CrossRef]

Aceves, A. B.

Alfano, R. R.

R. R. Alfano and S. L. Shapiro, “Emission in the region 4000 to 7000 å via four-photon coupling in glass,” Phys. Rev. Lett. 24(11), 584–587 (1970).
[CrossRef]

Almási, G.

Andreoni, A.

Assanto, G.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1-3), 1–126 (2008).
[CrossRef]

Averchi, A.

Babushkin, I.

Bahat-Treidel, O.

A. Szameit, M. C. Rechtsman, O. Bahat-Treidel, and M. Segev, “Pt-symmetry in honeycomb photonic lattices,” Phys. Rev. A 84(2), 021806 (2011).
[CrossRef]

Bartal, G.

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446(7131), 52–55 (2007).
[CrossRef] [PubMed]

Bartelt, H.

U. Röpke, H. Bartelt, S. Unger, K. Schuster, and J. Kobelke, “Fiber waveguide arrays as model system for discrete optics,” Appl. Phys. B 104(3), 481–486 (2011), doi:.
[CrossRef]

F. Eilenberger, S. Minardi, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Evolution dynamics of discrete-continuous light bullets,” Phys. Rev. A 84(1), 013836 (2011).
[CrossRef]

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Three-dimensional light bullets in arrays of waveguides,” Phys. Rev. Lett. 105(26), 263901 (2010).
[CrossRef] [PubMed]

U. Röpke, H. Bartelt, S. Unger, K. Schuster, and J. Kobelke, “Two-dimensional high-precision fiber waveguide arrays for coherent light propagation,” Opt. Express 15(11), 6894–6899 (2007).
[CrossRef] [PubMed]

T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tünnermann, and F. Lederer, “Nonlinearity and disorder in fiber arrays,” Phys. Rev. Lett. 93(5), 053901 (2004).
[CrossRef] [PubMed]

Bellanca, G.

Benton, C. J.

C. J. Benton and D. V. Skryabin, “Coupling induced anomalous group velocity dispersion in nonlinear arrays of silicon photonic wires,” Opt. Express 17(7), 5879–5884 (2009).
[CrossRef] [PubMed]

C. J. Benton, A. V. Gorbach, and D. V. Skryabin, “Spatiotemporal quasisolitons and resonant radiation in arrays of silicon-on-insulator photonic wires,” Phys. Rev. A 78(3), 033818 (2008).
[CrossRef]

Blasi, G.

M. A. C. Potenza, S. Minardi, J. Trull, G. Blasi, D. Salerno, A. Varanavicius, A. Piskarskas, and P. D. Trapani, “Three dimensional imaging of short pulses,” Opt. Commun. 229(1-6), 381–390 (2004).
[CrossRef]

Blömer, D.

A. Szameit, D. Blömer, J. Burghoff, T. Pertsch, S. Nolte, and A. Tünnermann, “Hexagonal waveguide arrays written with fs-laser pulses,” Appl. Phys. B 82(4), 507–512 (2006).
[CrossRef]

Blonskyi, I.

I. Blonskyi, V. Kadan, O. Shpotyuk, and I. Dmitruk, “Manifestations of sub- and superluminality in filamented femtosecond laser pulse in fused silica,” Opt. Commun. 282(9), 1913–1917 (2009).
[CrossRef]

Bonaretti, F.

Bragheri, F.

F. Bragheri, D. Faccio, F. Bonaretti, A. Lotti, M. Clerici, O. Jedrkiewicz, C. Liberale, S. Henin, L. Tartara, V. Degiorgio, and P. Di Trapani, “Complete retrieval of the field of ultrashort optical pulses using the angle-frequency spectrum,” Opt. Lett. 33(24), 2952–2954 (2008).
[CrossRef] [PubMed]

D. Faccio, M. A. Porras, A. Dubietis, F. Bragheri, A. Couairon, and P. Di Trapani, “Conical emission, pulse splitting, and X-wave parametric amplification in nonlinear dynamics of ultrashort light pulses,” Phys. Rev. Lett. 96(19), 193901 (2006).
[CrossRef] [PubMed]

Bulla, D. A. P.

Burghoff, J.

A. Szameit, D. Blömer, J. Burghoff, T. Pertsch, S. Nolte, and A. Tünnermann, “Hexagonal waveguide arrays written with fs-laser pulses,” Appl. Phys. B 82(4), 507–512 (2006).
[CrossRef]

Cao, H.

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(2), 023902 (2003).
[CrossRef] [PubMed]

Chiao, R. Y.

A. Kuzmich, A. Dogariu, L. J. Wang, P. W. Milonni, and R. Y. Chiao, “Signal velocity, causality, and quantum noise in superluminal light pulse propagation,” Phys. Rev. Lett. 86(18), 3925–3929 (2001).
[CrossRef] [PubMed]

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Measurement of the single-photon tunneling time,” Phys. Rev. Lett. 71(5), 708–711 (1993).
[CrossRef] [PubMed]

Choi, D.-Y.

Christodoulides, D. N.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1-3), 1–126 (2008).
[CrossRef]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424(6950), 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(2), 023902 (2003).
[CrossRef] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature 422(6928), 147–150 (2003).
[CrossRef] [PubMed]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, “Discrete solitons in photorefractive optically induced photonic lattices,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(4), 046602 (2002).
[CrossRef] [PubMed]

Clausen, A. T.

Clerici, M.

Coen, S.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
[CrossRef]

Conti, C.

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated X-shaped light bullets,” Phys. Rev. Lett. 91(9), 093904 (2003).
[CrossRef] [PubMed]

C. Conti, S. Trillo, P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, and J. Trull, “Nonlinear electromagnetic X waves,” Phys. Rev. Lett. 90(17), 170406 (2003).
[CrossRef] [PubMed]

Couairon, A.

Danielius, R.

De Angelis, C.

De La Rue, R. M.

A. V. Gorbach, W. Ding, O. K. Staines, C. E. de Nobriga, G. D. Hobbs, W. J. Wadsworth, J. C. Knight, D. V. Skryabin, A. Samarelli, M. Sorel, and R. M. De La Rue, “Spatiotemporal nonlinear optics in arrays of subwavelength waveguides,” Phys. Rev. A 82(4), 041802 (2010).
[CrossRef]

de Nobriga, C. E.

A. V. Gorbach, W. Ding, O. K. Staines, C. E. de Nobriga, G. D. Hobbs, W. J. Wadsworth, J. C. Knight, D. V. Skryabin, A. Samarelli, M. Sorel, and R. M. De La Rue, “Spatiotemporal nonlinear optics in arrays of subwavelength waveguides,” Phys. Rev. A 82(4), 041802 (2010).
[CrossRef]

Degiorgio, V.

Di Trapani, P.

S. Minardi, A. Gopal, A. Couairon, G. Tamoašuskas, R. Piskarskas, A. Dubietis, and P. Di Trapani, “Accurate retrieval of pulse-splitting dynamics of a femtosecond filament in water by time-resolved shadowgraphy,” Opt. Lett. 34(19), 3020–3022 (2009).
[CrossRef] [PubMed]

F. Bragheri, D. Faccio, F. Bonaretti, A. Lotti, M. Clerici, O. Jedrkiewicz, C. Liberale, S. Henin, L. Tartara, V. Degiorgio, and P. Di Trapani, “Complete retrieval of the field of ultrashort optical pulses using the angle-frequency spectrum,” Opt. Lett. 33(24), 2952–2954 (2008).
[CrossRef] [PubMed]

D. Faccio, M. A. Porras, A. Dubietis, F. Bragheri, A. Couairon, and P. Di Trapani, “Conical emission, pulse splitting, and X-wave parametric amplification in nonlinear dynamics of ultrashort light pulses,” Phys. Rev. Lett. 96(19), 193901 (2006).
[CrossRef] [PubMed]

C. Conti, S. Trillo, P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, and J. Trull, “Nonlinear electromagnetic X waves,” Phys. Rev. Lett. 90(17), 170406 (2003).
[CrossRef] [PubMed]

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated X-shaped light bullets,” Phys. Rev. Lett. 91(9), 093904 (2003).
[CrossRef] [PubMed]

R. Danielius, A. Piskarskas, P. Di Trapani, A. Andreoni, C. Solcia, and P. Foggi, “Matching of group velocities by spatial walk-off in collinear three-wave interaction with tilted pulses,” Opt. Lett. 21(13), 973–975 (1996).
[CrossRef] [PubMed]

Diddams, S.

Ding, W.

A. V. Gorbach, W. Ding, O. K. Staines, C. E. de Nobriga, G. D. Hobbs, W. J. Wadsworth, J. C. Knight, D. V. Skryabin, A. Samarelli, M. Sorel, and R. M. De La Rue, “Spatiotemporal nonlinear optics in arrays of subwavelength waveguides,” Phys. Rev. A 82(4), 041802 (2010).
[CrossRef]

Dmitruk, I.

I. Blonskyi, V. Kadan, O. Shpotyuk, and I. Dmitruk, “Manifestations of sub- and superluminality in filamented femtosecond laser pulse in fused silica,” Opt. Commun. 282(9), 1913–1917 (2009).
[CrossRef]

Dogariu, A.

A. Dogariu, A. Kuzmich, and L. J. Wang, “Transparent anomalous dispersion and superluminal light-pulse propagation at a negative group velocity,” Phys. Rev. A 63(5), 053806 (2001).
[CrossRef]

A. Dogariu, A. Kuzmich, H. Cao, and L. Wang, “Superluminal light pulse propagation via rephasing in a transparent anomalously dispersive medium,” Opt. Express 8(6), 344–350 (2001).
[CrossRef] [PubMed]

A. Kuzmich, A. Dogariu, L. J. Wang, P. W. Milonni, and R. Y. Chiao, “Signal velocity, causality, and quantum noise in superluminal light pulse propagation,” Phys. Rev. Lett. 86(18), 3925–3929 (2001).
[CrossRef] [PubMed]

Dreisow, F.

M. Heinrich, A. Szameit, F. Dreisow, R. Keil, S. Minardi, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, “Observation of three-dimensional discrete-continuous x waves in photonic lattices,” Phys. Rev. Lett. 103(11), 113903 (2009).
[CrossRef] [PubMed]

A. Szameit, T. Pertsch, F. Dreisow, S. Nolte, A. Tünnermann, U. Peschel, and F. Lederer, “Light evolution in arbitrary two-dimensional waveguide arrays,” Phys. Rev. A 75(5), 053814 (2007).
[CrossRef]

Dubietis, A.

Dudley, J. M.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
[CrossRef]

Efremidis, N. K.

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(6928), 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(2), 023902 (2003).
[CrossRef] [PubMed]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, “Discrete solitons in photorefractive optically induced photonic lattices,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(4), 046602 (2002).
[CrossRef] [PubMed]

Eggleton, B. J.

Eilenberger, F.

F. Eilenberger, S. Minardi, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Evolution dynamics of discrete-continuous light bullets,” Phys. Rev. A 84(1), 013836 (2011).
[CrossRef]

F. Eilenberger, A. Szameit, and T. Pertsch, “Transition from discrete to continuous townes solitons in periodic media,” Phys. Rev. A 82(4), 043802 (2010).
[CrossRef]

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Three-dimensional light bullets in arrays of waveguides,” Phys. Rev. Lett. 105(26), 263901 (2010).
[CrossRef] [PubMed]

Faccio, D.

Fishman, S.

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446(7131), 52–55 (2007).
[CrossRef] [PubMed]

Fleischer, J. W.

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(6928), 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(2), 023902 (2003).
[CrossRef] [PubMed]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, “Discrete solitons in photorefractive optically induced photonic lattices,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(4), 046602 (2002).
[CrossRef] [PubMed]

Foggi, P.

Galili, M.

Gauthier, D. J.

M. D. Stenner, D. J. Gauthier, and M. A. Neifeld, “The speed of information in a ‘fast-light’ optical medium,” Nature 425(6959), 695–698 (2003).
[CrossRef] [PubMed]

Genty, G.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
[CrossRef]

Gonzalo, I.

M. A. Porras, I. Gonzalo, and A. Mondello, “Pulsed light beams in vacuum with superluminal and negative group velocities,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(6), 066604 (2003).
[CrossRef] [PubMed]

Gopal, A.

Gorbach, A. V.

A. V. Gorbach, W. Ding, O. K. Staines, C. E. de Nobriga, G. D. Hobbs, W. J. Wadsworth, J. C. Knight, D. V. Skryabin, A. Samarelli, M. Sorel, and R. M. De La Rue, “Spatiotemporal nonlinear optics in arrays of subwavelength waveguides,” Phys. Rev. A 82(4), 041802 (2010).
[CrossRef]

C. J. Benton, A. V. Gorbach, and D. V. Skryabin, “Spatiotemporal quasisolitons and resonant radiation in arrays of silicon-on-insulator photonic wires,” Phys. Rev. A 78(3), 033818 (2008).
[CrossRef]

A. V. Gorbach and D. V. Skryabin, “Cascaded generation of multiply charged optical vortices and spatiotemporal helical beams in a Raman medium,” Phys. Rev. Lett. 98(24), 243601 (2007).
[CrossRef] [PubMed]

Hebling, J.

Heinrich, M.

M. Heinrich, A. Szameit, F. Dreisow, R. Keil, S. Minardi, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, “Observation of three-dimensional discrete-continuous x waves in photonic lattices,” Phys. Rev. Lett. 103(11), 113903 (2009).
[CrossRef] [PubMed]

Henin, S.

Herrmann, J.

Hobbs, G. D.

A. V. Gorbach, W. Ding, O. K. Staines, C. E. de Nobriga, G. D. Hobbs, W. J. Wadsworth, J. C. Knight, D. V. Skryabin, A. Samarelli, M. Sorel, and R. M. De La Rue, “Spatiotemporal nonlinear optics in arrays of subwavelength waveguides,” Phys. Rev. A 82(4), 041802 (2010).
[CrossRef]

Hu, H.

Husakou, A.

Jedrkiewicz, O.

F. Bragheri, D. Faccio, F. Bonaretti, A. Lotti, M. Clerici, O. Jedrkiewicz, C. Liberale, S. Henin, L. Tartara, V. Degiorgio, and P. Di Trapani, “Complete retrieval of the field of ultrashort optical pulses using the angle-frequency spectrum,” Opt. Lett. 33(24), 2952–2954 (2008).
[CrossRef] [PubMed]

C. Conti, S. Trillo, P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, and J. Trull, “Nonlinear electromagnetic X waves,” Phys. Rev. Lett. 90(17), 170406 (2003).
[CrossRef] [PubMed]

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated X-shaped light bullets,” Phys. Rev. Lett. 91(9), 093904 (2003).
[CrossRef] [PubMed]

Jensen, J. B.

Jeppesen, P.

Kadan, V.

I. Blonskyi, V. Kadan, O. Shpotyuk, and I. Dmitruk, “Manifestations of sub- and superluminality in filamented femtosecond laser pulse in fused silica,” Opt. Commun. 282(9), 1913–1917 (2009).
[CrossRef]

Kartashov, Y. V.

Y. V. Kartashov, B. A. Malomed, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys. 83(1), 247–306 (2011).
[CrossRef]

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Three-dimensional light bullets in arrays of waveguides,” Phys. Rev. Lett. 105(26), 263901 (2010).
[CrossRef] [PubMed]

Keil, R.

M. Heinrich, A. Szameit, F. Dreisow, R. Keil, S. Minardi, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, “Observation of three-dimensional discrete-continuous x waves in photonic lattices,” Phys. Rev. Lett. 103(11), 113903 (2009).
[CrossRef] [PubMed]

Kinsler, P.

P. Kinsler, “Unidirectional optical pulse propagation equation for materials with both electric and magnetic responses,” Phys. Rev. A 81(2), 023808 (2010).
[CrossRef]

Kivshar, Y. S.

I. Babushkin, A. Husakou, J. Herrmann, and Y. S. Kivshar, “Frequency-selective self-trapping and supercontinuum generation in arrays of coupled nonlinear waveguides,” Opt. Express 15(19), 11978–11983 (2007).
[CrossRef] [PubMed]

Y. S. Kivshar and S. K. Turitsyn, “Spatiotemporal pulse collapse on periodic potentials,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 49(4), R2536–R2539 (1994).
[CrossRef] [PubMed]

Knight, J. C.

A. V. Gorbach, W. Ding, O. K. Staines, C. E. de Nobriga, G. D. Hobbs, W. J. Wadsworth, J. C. Knight, D. V. Skryabin, A. Samarelli, M. Sorel, and R. M. De La Rue, “Spatiotemporal nonlinear optics in arrays of subwavelength waveguides,” Phys. Rev. A 82(4), 041802 (2010).
[CrossRef]

J. C. Knight, “Photonic crystal fibres,” Nature 424(6950), 847–851 (2003).
[CrossRef] [PubMed]

Kobelke, J.

U. Röpke, H. Bartelt, S. Unger, K. Schuster, and J. Kobelke, “Fiber waveguide arrays as model system for discrete optics,” Appl. Phys. B 104(3), 481–486 (2011), doi:.
[CrossRef]

F. Eilenberger, S. Minardi, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Evolution dynamics of discrete-continuous light bullets,” Phys. Rev. A 84(1), 013836 (2011).
[CrossRef]

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Three-dimensional light bullets in arrays of waveguides,” Phys. Rev. Lett. 105(26), 263901 (2010).
[CrossRef] [PubMed]

U. Röpke, H. Bartelt, S. Unger, K. Schuster, and J. Kobelke, “Two-dimensional high-precision fiber waveguide arrays for coherent light propagation,” Opt. Express 15(11), 6894–6899 (2007).
[CrossRef] [PubMed]

T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tünnermann, and F. Lederer, “Nonlinearity and disorder in fiber arrays,” Phys. Rev. Lett. 93(5), 053901 (2004).
[CrossRef] [PubMed]

Kolesik, M.

M. Kolesik, E. M. Wright, and J. V. Moloney, “Dynamic nonlinear X waves for femtosecond pulse propagation in water,” Phys. Rev. Lett. 92(25), 253901 (2004).
[CrossRef] [PubMed]

M. Kolesik and J. V. Moloney, “Nonlinear optical pulse propagation simulation: from Maxwell’s to unidirectional equations,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(3), 036604 (2004).
[CrossRef] [PubMed]

Kolokolov, A.

N. Vakhitov and A. Kolokolov, “Stationary solutions of the wave equation in a medium with nonlinearity saturation,” Radiophys. Quantum Electron. 16(7), 783–789 (1973).
[CrossRef]

Kozma, I.

Kuhl, J.

Kuzmich, A.

A. Dogariu, A. Kuzmich, H. Cao, and L. Wang, “Superluminal light pulse propagation via rephasing in a transparent anomalously dispersive medium,” Opt. Express 8(6), 344–350 (2001).
[CrossRef] [PubMed]

A. Dogariu, A. Kuzmich, and L. J. Wang, “Transparent anomalous dispersion and superluminal light-pulse propagation at a negative group velocity,” Phys. Rev. A 63(5), 053806 (2001).
[CrossRef]

A. Kuzmich, A. Dogariu, L. J. Wang, P. W. Milonni, and R. Y. Chiao, “Signal velocity, causality, and quantum noise in superluminal light pulse propagation,” Phys. Rev. Lett. 86(18), 3925–3929 (2001).
[CrossRef] [PubMed]

Kwiat, P. G.

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Measurement of the single-photon tunneling time,” Phys. Rev. Lett. 71(5), 708–711 (1993).
[CrossRef] [PubMed]

Lederer, F.

F. Eilenberger, S. Minardi, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Evolution dynamics of discrete-continuous light bullets,” Phys. Rev. A 84(1), 013836 (2011).
[CrossRef]

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Three-dimensional light bullets in arrays of waveguides,” Phys. Rev. Lett. 105(26), 263901 (2010).
[CrossRef] [PubMed]

M. Heinrich, A. Szameit, F. Dreisow, R. Keil, S. Minardi, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, “Observation of three-dimensional discrete-continuous x waves in photonic lattices,” Phys. Rev. Lett. 103(11), 113903 (2009).
[CrossRef] [PubMed]

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1-3), 1–126 (2008).
[CrossRef]

A. Szameit, T. Pertsch, F. Dreisow, S. Nolte, A. Tünnermann, U. Peschel, and F. Lederer, “Light evolution in arbitrary two-dimensional waveguide arrays,” Phys. Rev. A 75(5), 053814 (2007).
[CrossRef]

T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tünnermann, and F. Lederer, “Nonlinearity and disorder in fiber arrays,” Phys. Rev. Lett. 93(5), 053901 (2004).
[CrossRef] [PubMed]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424(6950), 817–823 (2003).
[CrossRef] [PubMed]

Liberale, C.

Lotti, A.

Luther-Davies, B.

Madden, S. J.

Malaguti, S.

Malomed, B. A.

Y. V. Kartashov, B. A. Malomed, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys. 83(1), 247–306 (2011).
[CrossRef]

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B: Quantum Semiclassical Opt. 7(5), R53–R72 (2005).

Martinez, O.

O. Martinez, “Achromatic phase matching for second harmonic generation of femtosecond pulses,” IEEE J. Quantum Electron. 25(12), 2464–2468 (1989).
[CrossRef]

Mihalache, D.

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B: Quantum Semiclassical Opt. 7(5), R53–R72 (2005).

Milonni, P. W.

A. Kuzmich, A. Dogariu, L. J. Wang, P. W. Milonni, and R. Y. Chiao, “Signal velocity, causality, and quantum noise in superluminal light pulse propagation,” Phys. Rev. Lett. 86(18), 3925–3929 (2001).
[CrossRef] [PubMed]

Minardi, S.

F. Eilenberger, S. Minardi, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Evolution dynamics of discrete-continuous light bullets,” Phys. Rev. A 84(1), 013836 (2011).
[CrossRef]

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Three-dimensional light bullets in arrays of waveguides,” Phys. Rev. Lett. 105(26), 263901 (2010).
[CrossRef] [PubMed]

M. Heinrich, A. Szameit, F. Dreisow, R. Keil, S. Minardi, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, “Observation of three-dimensional discrete-continuous x waves in photonic lattices,” Phys. Rev. Lett. 103(11), 113903 (2009).
[CrossRef] [PubMed]

S. Minardi, A. Gopal, A. Couairon, G. Tamoašuskas, R. Piskarskas, A. Dubietis, and P. Di Trapani, “Accurate retrieval of pulse-splitting dynamics of a femtosecond filament in water by time-resolved shadowgraphy,” Opt. Lett. 34(19), 3020–3022 (2009).
[CrossRef] [PubMed]

S. Minardi, J. Trull, and M. A. C. Potenza, “Holographic properties of parametric image conversion for spatiotemporal imaging of ultrashort laser pulses,” J. Hologr. Speckle 5(1), 85–93 (2009).
[CrossRef]

M. A. C. Potenza, S. Minardi, J. Trull, G. Blasi, D. Salerno, A. Varanavicius, A. Piskarskas, and P. D. Trapani, “Three dimensional imaging of short pulses,” Opt. Commun. 229(1-6), 381–390 (2004).
[CrossRef]

Moloney, J. V.

M. Kolesik, E. M. Wright, and J. V. Moloney, “Dynamic nonlinear X waves for femtosecond pulse propagation in water,” Phys. Rev. Lett. 92(25), 253901 (2004).
[CrossRef] [PubMed]

M. Kolesik and J. V. Moloney, “Nonlinear optical pulse propagation simulation: from Maxwell’s to unidirectional equations,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(3), 036604 (2004).
[CrossRef] [PubMed]

Mondello, A.

M. A. Porras, I. Gonzalo, and A. Mondello, “Pulsed light beams in vacuum with superluminal and negative group velocities,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(6), 066604 (2003).
[CrossRef] [PubMed]

Mulvad, H. C. H.

Nakazawa, M.

M. Nakazawa, T. Yamamoto, and K. Tamura, “1.28 tbit/s–70 km OTDM transmission using third- and fourth-order simultaneous dispersion compensation with a phase modulator,” Electron. Lett. 36(24), 2027–2029 (2000).
[CrossRef]

Neifeld, M. A.

M. D. Stenner, D. J. Gauthier, and M. A. Neifeld, “The speed of information in a ‘fast-light’ optical medium,” Nature 425(6959), 695–698 (2003).
[CrossRef] [PubMed]

Nimtz, G.

G. Nimtz, “Evanescent modes are not necessarily Einstein causal,” Eur. Phys. J. B 7(4), 523–525 (1999), doi:.
[CrossRef]

Nolte, S.

F. Eilenberger, S. Minardi, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Evolution dynamics of discrete-continuous light bullets,” Phys. Rev. A 84(1), 013836 (2011).
[CrossRef]

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Three-dimensional light bullets in arrays of waveguides,” Phys. Rev. Lett. 105(26), 263901 (2010).
[CrossRef] [PubMed]

M. Heinrich, A. Szameit, F. Dreisow, R. Keil, S. Minardi, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, “Observation of three-dimensional discrete-continuous x waves in photonic lattices,” Phys. Rev. Lett. 103(11), 113903 (2009).
[CrossRef] [PubMed]

A. Szameit, T. Pertsch, F. Dreisow, S. Nolte, A. Tünnermann, U. Peschel, and F. Lederer, “Light evolution in arbitrary two-dimensional waveguide arrays,” Phys. Rev. A 75(5), 053814 (2007).
[CrossRef]

A. Szameit, D. Blömer, J. Burghoff, T. Pertsch, S. Nolte, and A. Tünnermann, “Hexagonal waveguide arrays written with fs-laser pulses,” Appl. Phys. B 82(4), 507–512 (2006).
[CrossRef]

T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tünnermann, and F. Lederer, “Nonlinearity and disorder in fiber arrays,” Phys. Rev. Lett. 93(5), 053901 (2004).
[CrossRef] [PubMed]

Oxenløwe, L. K.

Palushani, E.

Pelusi, M. D.

Pertsch, T.

F. Eilenberger, S. Minardi, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Evolution dynamics of discrete-continuous light bullets,” Phys. Rev. A 84(1), 013836 (2011).
[CrossRef]

F. Eilenberger, A. Szameit, and T. Pertsch, “Transition from discrete to continuous townes solitons in periodic media,” Phys. Rev. A 82(4), 043802 (2010).
[CrossRef]

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Three-dimensional light bullets in arrays of waveguides,” Phys. Rev. Lett. 105(26), 263901 (2010).
[CrossRef] [PubMed]

M. Heinrich, A. Szameit, F. Dreisow, R. Keil, S. Minardi, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, “Observation of three-dimensional discrete-continuous x waves in photonic lattices,” Phys. Rev. Lett. 103(11), 113903 (2009).
[CrossRef] [PubMed]

A. Szameit, T. Pertsch, F. Dreisow, S. Nolte, A. Tünnermann, U. Peschel, and F. Lederer, “Light evolution in arbitrary two-dimensional waveguide arrays,” Phys. Rev. A 75(5), 053814 (2007).
[CrossRef]

A. Szameit, D. Blömer, J. Burghoff, T. Pertsch, S. Nolte, and A. Tünnermann, “Hexagonal waveguide arrays written with fs-laser pulses,” Appl. Phys. B 82(4), 507–512 (2006).
[CrossRef]

T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tünnermann, and F. Lederer, “Nonlinearity and disorder in fiber arrays,” Phys. Rev. Lett. 93(5), 053901 (2004).
[CrossRef] [PubMed]

Peschel, U.

A. Szameit, T. Pertsch, F. Dreisow, S. Nolte, A. Tünnermann, U. Peschel, and F. Lederer, “Light evolution in arbitrary two-dimensional waveguide arrays,” Phys. Rev. A 75(5), 053814 (2007).
[CrossRef]

T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tünnermann, and F. Lederer, “Nonlinearity and disorder in fiber arrays,” Phys. Rev. Lett. 93(5), 053901 (2004).
[CrossRef] [PubMed]

Peucheret, C.

Piskarskas, A.

D. Faccio, A. Averchi, A. Dubietis, P. Polesana, A. Piskarskas, P. D. Trapani, and A. Couairon, “Stimulated Raman X waves in ultrashort optical pulse filamentation,” Opt. Lett. 32(2), 184–186 (2007).
[CrossRef] [PubMed]

M. A. C. Potenza, S. Minardi, J. Trull, G. Blasi, D. Salerno, A. Varanavicius, A. Piskarskas, and P. D. Trapani, “Three dimensional imaging of short pulses,” Opt. Commun. 229(1-6), 381–390 (2004).
[CrossRef]

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated X-shaped light bullets,” Phys. Rev. Lett. 91(9), 093904 (2003).
[CrossRef] [PubMed]

C. Conti, S. Trillo, P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, and J. Trull, “Nonlinear electromagnetic X waves,” Phys. Rev. Lett. 90(17), 170406 (2003).
[CrossRef] [PubMed]

R. Danielius, A. Piskarskas, P. Di Trapani, A. Andreoni, C. Solcia, and P. Foggi, “Matching of group velocities by spatial walk-off in collinear three-wave interaction with tilted pulses,” Opt. Lett. 21(13), 973–975 (1996).
[CrossRef] [PubMed]

Piskarskas, R.

Polesana, P.

Porras, M. A.

D. Faccio, M. A. Porras, A. Dubietis, F. Bragheri, A. Couairon, and P. Di Trapani, “Conical emission, pulse splitting, and X-wave parametric amplification in nonlinear dynamics of ultrashort light pulses,” Phys. Rev. Lett. 96(19), 193901 (2006).
[CrossRef] [PubMed]

M. A. Porras, I. Gonzalo, and A. Mondello, “Pulsed light beams in vacuum with superluminal and negative group velocities,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(6), 066604 (2003).
[CrossRef] [PubMed]

Potenza, M. A. C.

S. Minardi, J. Trull, and M. A. C. Potenza, “Holographic properties of parametric image conversion for spatiotemporal imaging of ultrashort laser pulses,” J. Hologr. Speckle 5(1), 85–93 (2009).
[CrossRef]

M. A. C. Potenza, S. Minardi, J. Trull, G. Blasi, D. Salerno, A. Varanavicius, A. Piskarskas, and P. D. Trapani, “Three dimensional imaging of short pulses,” Opt. Commun. 229(1-6), 381–390 (2004).
[CrossRef]

Ranka, J. K.

Rechtsman, M. C.

A. Szameit, M. C. Rechtsman, O. Bahat-Treidel, and M. Segev, “Pt-symmetry in honeycomb photonic lattices,” Phys. Rev. A 84(2), 021806 (2011).
[CrossRef]

Reivelt, K.

P. Saari and K. Reivelt, “Evidence of x-shaped propagation-invariant localized light waves,” Phys. Rev. Lett. 79(21), 4135–4138 (1997).
[CrossRef]

Riedle, E.

Röpke, U.

U. Röpke, H. Bartelt, S. Unger, K. Schuster, and J. Kobelke, “Fiber waveguide arrays as model system for discrete optics,” Appl. Phys. B 104(3), 481–486 (2011), doi:.
[CrossRef]

F. Eilenberger, S. Minardi, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Evolution dynamics of discrete-continuous light bullets,” Phys. Rev. A 84(1), 013836 (2011).
[CrossRef]

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Three-dimensional light bullets in arrays of waveguides,” Phys. Rev. Lett. 105(26), 263901 (2010).
[CrossRef] [PubMed]

U. Röpke, H. Bartelt, S. Unger, K. Schuster, and J. Kobelke, “Two-dimensional high-precision fiber waveguide arrays for coherent light propagation,” Opt. Express 15(11), 6894–6899 (2007).
[CrossRef] [PubMed]

Rothenberg, J. E.

Russell, P.

P. Russell, “Photonic crystal fibers,” Science 299(5605), 358–362 (2003).
[CrossRef] [PubMed]

Saari, P.

P. Saari and K. Reivelt, “Evidence of x-shaped propagation-invariant localized light waves,” Phys. Rev. Lett. 79(21), 4135–4138 (1997).
[CrossRef]

Salerno, D.

M. A. C. Potenza, S. Minardi, J. Trull, G. Blasi, D. Salerno, A. Varanavicius, A. Piskarskas, and P. D. Trapani, “Three dimensional imaging of short pulses,” Opt. Commun. 229(1-6), 381–390 (2004).
[CrossRef]

Samarelli, A.

A. V. Gorbach, W. Ding, O. K. Staines, C. E. de Nobriga, G. D. Hobbs, W. J. Wadsworth, J. C. Knight, D. V. Skryabin, A. Samarelli, M. Sorel, and R. M. De La Rue, “Spatiotemporal nonlinear optics in arrays of subwavelength waveguides,” Phys. Rev. A 82(4), 041802 (2010).
[CrossRef]

Schröder, J.

Schuster, K.

U. Röpke, H. Bartelt, S. Unger, K. Schuster, and J. Kobelke, “Fiber waveguide arrays as model system for discrete optics,” Appl. Phys. B 104(3), 481–486 (2011), doi:.
[CrossRef]

F. Eilenberger, S. Minardi, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Evolution dynamics of discrete-continuous light bullets,” Phys. Rev. A 84(1), 013836 (2011).
[CrossRef]

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Three-dimensional light bullets in arrays of waveguides,” Phys. Rev. Lett. 105(26), 263901 (2010).
[CrossRef] [PubMed]

U. Röpke, H. Bartelt, S. Unger, K. Schuster, and J. Kobelke, “Two-dimensional high-precision fiber waveguide arrays for coherent light propagation,” Opt. Express 15(11), 6894–6899 (2007).
[CrossRef] [PubMed]

T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tünnermann, and F. Lederer, “Nonlinearity and disorder in fiber arrays,” Phys. Rev. Lett. 93(5), 053901 (2004).
[CrossRef] [PubMed]

Schwartz, T.

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446(7131), 52–55 (2007).
[CrossRef] [PubMed]

Sears, S.

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, “Discrete solitons in photorefractive optically induced photonic lattices,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(4), 046602 (2002).
[CrossRef] [PubMed]

Segev, M.

A. Szameit, M. C. Rechtsman, O. Bahat-Treidel, and M. Segev, “Pt-symmetry in honeycomb photonic lattices,” Phys. Rev. A 84(2), 021806 (2011).
[CrossRef]

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1-3), 1–126 (2008).
[CrossRef]

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446(7131), 52–55 (2007).
[CrossRef] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature 422(6928), 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(2), 023902 (2003).
[CrossRef] [PubMed]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, “Discrete solitons in photorefractive optically induced photonic lattices,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(4), 046602 (2002).
[CrossRef] [PubMed]

Shapiro, S. L.

R. R. Alfano and S. L. Shapiro, “Emission in the region 4000 to 7000 å via four-photon coupling in glass,” Phys. Rev. Lett. 24(11), 584–587 (1970).
[CrossRef]

Shpotyuk, O.

I. Blonskyi, V. Kadan, O. Shpotyuk, and I. Dmitruk, “Manifestations of sub- and superluminality in filamented femtosecond laser pulse in fused silica,” Opt. Commun. 282(9), 1913–1917 (2009).
[CrossRef]

Silberberg, Y.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1-3), 1–126 (2008).
[CrossRef]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424(6950), 817–823 (2003).
[CrossRef] [PubMed]

Y. Silberberg, “Collapse of optical pulses,” Opt. Lett. 15(22), 1282–1284 (1990).
[CrossRef] [PubMed]

Skryabin, D. V.

A. V. Gorbach, W. Ding, O. K. Staines, C. E. de Nobriga, G. D. Hobbs, W. J. Wadsworth, J. C. Knight, D. V. Skryabin, A. Samarelli, M. Sorel, and R. M. De La Rue, “Spatiotemporal nonlinear optics in arrays of subwavelength waveguides,” Phys. Rev. A 82(4), 041802 (2010).
[CrossRef]

C. J. Benton and D. V. Skryabin, “Coupling induced anomalous group velocity dispersion in nonlinear arrays of silicon photonic wires,” Opt. Express 17(7), 5879–5884 (2009).
[CrossRef] [PubMed]

C. J. Benton, A. V. Gorbach, and D. V. Skryabin, “Spatiotemporal quasisolitons and resonant radiation in arrays of silicon-on-insulator photonic wires,” Phys. Rev. A 78(3), 033818 (2008).
[CrossRef]

A. V. Gorbach and D. V. Skryabin, “Cascaded generation of multiply charged optical vortices and spatiotemporal helical beams in a Raman medium,” Phys. Rev. Lett. 98(24), 243601 (2007).
[CrossRef] [PubMed]

Solcia, C.

Sorel, M.

A. V. Gorbach, W. Ding, O. K. Staines, C. E. de Nobriga, G. D. Hobbs, W. J. Wadsworth, J. C. Knight, D. V. Skryabin, A. Samarelli, M. Sorel, and R. M. De La Rue, “Spatiotemporal nonlinear optics in arrays of subwavelength waveguides,” Phys. Rev. A 82(4), 041802 (2010).
[CrossRef]

Staines, O. K.

A. V. Gorbach, W. Ding, O. K. Staines, C. E. de Nobriga, G. D. Hobbs, W. J. Wadsworth, J. C. Knight, D. V. Skryabin, A. Samarelli, M. Sorel, and R. M. De La Rue, “Spatiotemporal nonlinear optics in arrays of subwavelength waveguides,” Phys. Rev. A 82(4), 041802 (2010).
[CrossRef]

Stegeman, G. I.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1-3), 1–126 (2008).
[CrossRef]

Steinberg, A. M.

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Measurement of the single-photon tunneling time,” Phys. Rev. Lett. 71(5), 708–711 (1993).
[CrossRef] [PubMed]

Stenner, M. D.

M. D. Stenner, D. J. Gauthier, and M. A. Neifeld, “The speed of information in a ‘fast-light’ optical medium,” Nature 425(6959), 695–698 (2003).
[CrossRef] [PubMed]

Stentz, A. J.

Stepanov, A.

Szameit, A.

F. Eilenberger, S. Minardi, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Evolution dynamics of discrete-continuous light bullets,” Phys. Rev. A 84(1), 013836 (2011).
[CrossRef]

A. Szameit, M. C. Rechtsman, O. Bahat-Treidel, and M. Segev, “Pt-symmetry in honeycomb photonic lattices,” Phys. Rev. A 84(2), 021806 (2011).
[CrossRef]

F. Eilenberger, A. Szameit, and T. Pertsch, “Transition from discrete to continuous townes solitons in periodic media,” Phys. Rev. A 82(4), 043802 (2010).
[CrossRef]

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Three-dimensional light bullets in arrays of waveguides,” Phys. Rev. Lett. 105(26), 263901 (2010).
[CrossRef] [PubMed]

M. Heinrich, A. Szameit, F. Dreisow, R. Keil, S. Minardi, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, “Observation of three-dimensional discrete-continuous x waves in photonic lattices,” Phys. Rev. Lett. 103(11), 113903 (2009).
[CrossRef] [PubMed]

A. Szameit, T. Pertsch, F. Dreisow, S. Nolte, A. Tünnermann, U. Peschel, and F. Lederer, “Light evolution in arbitrary two-dimensional waveguide arrays,” Phys. Rev. A 75(5), 053814 (2007).
[CrossRef]

A. Szameit, D. Blömer, J. Burghoff, T. Pertsch, S. Nolte, and A. Tünnermann, “Hexagonal waveguide arrays written with fs-laser pulses,” Appl. Phys. B 82(4), 507–512 (2006).
[CrossRef]

Tamoašuskas, G.

Tamura, K.

M. Nakazawa, T. Yamamoto, and K. Tamura, “1.28 tbit/s–70 km OTDM transmission using third- and fourth-order simultaneous dispersion compensation with a phase modulator,” Electron. Lett. 36(24), 2027–2029 (2000).
[CrossRef]

Tartara, L.

Torner, L.

Y. V. Kartashov, B. A. Malomed, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys. 83(1), 247–306 (2011).
[CrossRef]

F. Eilenberger, S. Minardi, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Evolution dynamics of discrete-continuous light bullets,” Phys. Rev. A 84(1), 013836 (2011).
[CrossRef]

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Three-dimensional light bullets in arrays of waveguides,” Phys. Rev. Lett. 105(26), 263901 (2010).
[CrossRef] [PubMed]

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B: Quantum Semiclassical Opt. 7(5), R53–R72 (2005).

Trapani, P. D.

D. Faccio, A. Averchi, A. Dubietis, P. Polesana, A. Piskarskas, P. D. Trapani, and A. Couairon, “Stimulated Raman X waves in ultrashort optical pulse filamentation,” Opt. Lett. 32(2), 184–186 (2007).
[CrossRef] [PubMed]

M. A. C. Potenza, S. Minardi, J. Trull, G. Blasi, D. Salerno, A. Varanavicius, A. Piskarskas, and P. D. Trapani, “Three dimensional imaging of short pulses,” Opt. Commun. 229(1-6), 381–390 (2004).
[CrossRef]

Trillo, S.

S. Malaguti, G. Bellanca, and S. Trillo, “Two-dimensional envelope localized waves in the anomalous dispersion regime,” Opt. Lett. 33(10), 1117–1119 (2008).
[CrossRef] [PubMed]

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated X-shaped light bullets,” Phys. Rev. Lett. 91(9), 093904 (2003).
[CrossRef] [PubMed]

C. Conti, S. Trillo, P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, and J. Trull, “Nonlinear electromagnetic X waves,” Phys. Rev. Lett. 90(17), 170406 (2003).
[CrossRef] [PubMed]

Trull, J.

S. Minardi, J. Trull, and M. A. C. Potenza, “Holographic properties of parametric image conversion for spatiotemporal imaging of ultrashort laser pulses,” J. Hologr. Speckle 5(1), 85–93 (2009).
[CrossRef]

M. A. C. Potenza, S. Minardi, J. Trull, G. Blasi, D. Salerno, A. Varanavicius, A. Piskarskas, and P. D. Trapani, “Three dimensional imaging of short pulses,” Opt. Commun. 229(1-6), 381–390 (2004).
[CrossRef]

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated X-shaped light bullets,” Phys. Rev. Lett. 91(9), 093904 (2003).
[CrossRef] [PubMed]

C. Conti, S. Trillo, P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, and J. Trull, “Nonlinear electromagnetic X waves,” Phys. Rev. Lett. 90(17), 170406 (2003).
[CrossRef] [PubMed]

Tünnermann, A.

F. Eilenberger, S. Minardi, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Evolution dynamics of discrete-continuous light bullets,” Phys. Rev. A 84(1), 013836 (2011).
[CrossRef]

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Three-dimensional light bullets in arrays of waveguides,” Phys. Rev. Lett. 105(26), 263901 (2010).
[CrossRef] [PubMed]

M. Heinrich, A. Szameit, F. Dreisow, R. Keil, S. Minardi, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, “Observation of three-dimensional discrete-continuous x waves in photonic lattices,” Phys. Rev. Lett. 103(11), 113903 (2009).
[CrossRef] [PubMed]

A. Szameit, T. Pertsch, F. Dreisow, S. Nolte, A. Tünnermann, U. Peschel, and F. Lederer, “Light evolution in arbitrary two-dimensional waveguide arrays,” Phys. Rev. A 75(5), 053814 (2007).
[CrossRef]

A. Szameit, D. Blömer, J. Burghoff, T. Pertsch, S. Nolte, and A. Tünnermann, “Hexagonal waveguide arrays written with fs-laser pulses,” Appl. Phys. B 82(4), 507–512 (2006).
[CrossRef]

T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tünnermann, and F. Lederer, “Nonlinearity and disorder in fiber arrays,” Phys. Rev. Lett. 93(5), 053901 (2004).
[CrossRef] [PubMed]

Turitsyn, S. K.

Y. S. Kivshar and S. K. Turitsyn, “Spatiotemporal pulse collapse on periodic potentials,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 49(4), R2536–R2539 (1994).
[CrossRef] [PubMed]

S. K. Turitsyn, “Collapse criterion for a pulse dynamics in a periodic nonlinear waveguide,” Opt. Lett. 18(18), 1493–1495 (1993).
[CrossRef] [PubMed]

Unger, S.

U. Röpke, H. Bartelt, S. Unger, K. Schuster, and J. Kobelke, “Fiber waveguide arrays as model system for discrete optics,” Appl. Phys. B 104(3), 481–486 (2011), doi:.
[CrossRef]

U. Röpke, H. Bartelt, S. Unger, K. Schuster, and J. Kobelke, “Two-dimensional high-precision fiber waveguide arrays for coherent light propagation,” Opt. Express 15(11), 6894–6899 (2007).
[CrossRef] [PubMed]

Vakhitov, N.

N. Vakhitov and A. Kolokolov, “Stationary solutions of the wave equation in a medium with nonlinearity saturation,” Radiophys. Quantum Electron. 16(7), 783–789 (1973).
[CrossRef]

Valiulis, G.

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated X-shaped light bullets,” Phys. Rev. Lett. 91(9), 093904 (2003).
[CrossRef] [PubMed]

C. Conti, S. Trillo, P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, and J. Trull, “Nonlinear electromagnetic X waves,” Phys. Rev. Lett. 90(17), 170406 (2003).
[CrossRef] [PubMed]

Varanavicius, A.

M. A. C. Potenza, S. Minardi, J. Trull, G. Blasi, D. Salerno, A. Varanavicius, A. Piskarskas, and P. D. Trapani, “Three dimensional imaging of short pulses,” Opt. Commun. 229(1-6), 381–390 (2004).
[CrossRef]

Vo, T. D.

Wadsworth, W. J.

A. V. Gorbach, W. Ding, O. K. Staines, C. E. de Nobriga, G. D. Hobbs, W. J. Wadsworth, J. C. Knight, D. V. Skryabin, A. Samarelli, M. Sorel, and R. M. De La Rue, “Spatiotemporal nonlinear optics in arrays of subwavelength waveguides,” Phys. Rev. A 82(4), 041802 (2010).
[CrossRef]

Wang, L.

Wang, L. J.

A. Dogariu, A. Kuzmich, and L. J. Wang, “Transparent anomalous dispersion and superluminal light-pulse propagation at a negative group velocity,” Phys. Rev. A 63(5), 053806 (2001).
[CrossRef]

A. Kuzmich, A. Dogariu, L. J. Wang, P. W. Milonni, and R. Y. Chiao, “Signal velocity, causality, and quantum noise in superluminal light pulse propagation,” Phys. Rev. Lett. 86(18), 3925–3929 (2001).
[CrossRef] [PubMed]

Windeler, R. S.

Wise, F.

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B: Quantum Semiclassical Opt. 7(5), R53–R72 (2005).

Wright, E. M.

M. Kolesik, E. M. Wright, and J. V. Moloney, “Dynamic nonlinear X waves for femtosecond pulse propagation in water,” Phys. Rev. Lett. 92(25), 253901 (2004).
[CrossRef] [PubMed]

Xu, J.

Yamamoto, T.

M. Nakazawa, T. Yamamoto, and K. Tamura, “1.28 tbit/s–70 km OTDM transmission using third- and fourth-order simultaneous dispersion compensation with a phase modulator,” Electron. Lett. 36(24), 2027–2029 (2000).
[CrossRef]

Zozulya, A.

Appl. Phys. B

A. Szameit, D. Blömer, J. Burghoff, T. Pertsch, S. Nolte, and A. Tünnermann, “Hexagonal waveguide arrays written with fs-laser pulses,” Appl. Phys. B 82(4), 507–512 (2006).
[CrossRef]

U. Röpke, H. Bartelt, S. Unger, K. Schuster, and J. Kobelke, “Fiber waveguide arrays as model system for discrete optics,” Appl. Phys. B 104(3), 481–486 (2011), doi:.
[CrossRef]

Electron. Lett.

M. Nakazawa, T. Yamamoto, and K. Tamura, “1.28 tbit/s–70 km OTDM transmission using third- and fourth-order simultaneous dispersion compensation with a phase modulator,” Electron. Lett. 36(24), 2027–2029 (2000).
[CrossRef]

Eur. Phys. J. B

G. Nimtz, “Evanescent modes are not necessarily Einstein causal,” Eur. Phys. J. B 7(4), 523–525 (1999), doi:.
[CrossRef]

IEEE J. Quantum Electron.

O. Martinez, “Achromatic phase matching for second harmonic generation of femtosecond pulses,” IEEE J. Quantum Electron. 25(12), 2464–2468 (1989).
[CrossRef]

J. Hologr. Speckle

S. Minardi, J. Trull, and M. A. C. Potenza, “Holographic properties of parametric image conversion for spatiotemporal imaging of ultrashort laser pulses,” J. Hologr. Speckle 5(1), 85–93 (2009).
[CrossRef]

J. Opt. B: Quantum Semiclassical Opt.

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B: Quantum Semiclassical Opt. 7(5), R53–R72 (2005).

Nature

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424(6950), 817–823 (2003).
[CrossRef] [PubMed]

J. C. Knight, “Photonic crystal fibres,” Nature 424(6950), 847–851 (2003).
[CrossRef] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature 422(6928), 147–150 (2003).
[CrossRef] [PubMed]

M. D. Stenner, D. J. Gauthier, and M. A. Neifeld, “The speed of information in a ‘fast-light’ optical medium,” Nature 425(6959), 695–698 (2003).
[CrossRef] [PubMed]

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446(7131), 52–55 (2007).
[CrossRef] [PubMed]

Opt. Commun.

M. A. C. Potenza, S. Minardi, J. Trull, G. Blasi, D. Salerno, A. Varanavicius, A. Piskarskas, and P. D. Trapani, “Three dimensional imaging of short pulses,” Opt. Commun. 229(1-6), 381–390 (2004).
[CrossRef]

I. Blonskyi, V. Kadan, O. Shpotyuk, and I. Dmitruk, “Manifestations of sub- and superluminality in filamented femtosecond laser pulse in fused silica,” Opt. Commun. 282(9), 1913–1917 (2009).
[CrossRef]

Opt. Express

A. Zozulya and S. Diddams, “Dynamics of self-focused femtosecond laser pulses in the near and far fields,” Opt. Express 4(9), 336–343 (1999).
[CrossRef] [PubMed]

A. Dogariu, A. Kuzmich, H. Cao, and L. Wang, “Superluminal light pulse propagation via rephasing in a transparent anomalously dispersive medium,” Opt. Express 8(6), 344–350 (2001).
[CrossRef] [PubMed]

A. Stepanov, J. Kuhl, I. Kozma, E. Riedle, G. Almási, and J. Hebling, “Scaling up the energy of THz pulses created by optical rectification,” Opt. Express 13(15), 5762–5768 (2005).
[CrossRef] [PubMed]

U. Röpke, H. Bartelt, S. Unger, K. Schuster, and J. Kobelke, “Two-dimensional high-precision fiber waveguide arrays for coherent light propagation,” Opt. Express 15(11), 6894–6899 (2007).
[CrossRef] [PubMed]

I. Babushkin, A. Husakou, J. Herrmann, and Y. S. Kivshar, “Frequency-selective self-trapping and supercontinuum generation in arrays of coupled nonlinear waveguides,” Opt. Express 15(19), 11978–11983 (2007).
[CrossRef] [PubMed]

C. J. Benton and D. V. Skryabin, “Coupling induced anomalous group velocity dispersion in nonlinear arrays of silicon photonic wires,” Opt. Express 17(7), 5879–5884 (2009).
[CrossRef] [PubMed]

H. C. H. Mulvad, M. Galili, L. K. Oxenløwe, H. Hu, A. T. Clausen, J. B. Jensen, C. Peucheret, and P. Jeppesen, “Demonstration of 5.1 Tbit/s data capacity on a single-wavelength channel,” Opt. Express 18(2), 1438–1443 (2010).
[CrossRef] [PubMed]

T. D. Vo, H. Hu, M. Galili, E. Palushani, J. Xu, L. K. Oxenløwe, S. J. Madden, D.-Y. Choi, D. A. P. Bulla, M. D. Pelusi, J. Schröder, B. Luther-Davies, and B. J. Eggleton, “Photonic chip based transmitter optimization and receiver demultiplexing of a 1.28 Tbit/s OTDM signal,” Opt. Express 18(16), 17252–17261 (2010).
[CrossRef] [PubMed]

Opt. Lett.

S. Minardi, A. Gopal, A. Couairon, G. Tamoašuskas, R. Piskarskas, A. Dubietis, and P. Di Trapani, “Accurate retrieval of pulse-splitting dynamics of a femtosecond filament in water by time-resolved shadowgraphy,” Opt. Lett. 34(19), 3020–3022 (2009).
[CrossRef] [PubMed]

S. Malaguti, G. Bellanca, and S. Trillo, “Two-dimensional envelope localized waves in the anomalous dispersion regime,” Opt. Lett. 33(10), 1117–1119 (2008).
[CrossRef] [PubMed]

F. Bragheri, D. Faccio, F. Bonaretti, A. Lotti, M. Clerici, O. Jedrkiewicz, C. Liberale, S. Henin, L. Tartara, V. Degiorgio, and P. Di Trapani, “Complete retrieval of the field of ultrashort optical pulses using the angle-frequency spectrum,” Opt. Lett. 33(24), 2952–2954 (2008).
[CrossRef] [PubMed]

D. Faccio, A. Averchi, A. Dubietis, P. Polesana, A. Piskarskas, P. D. Trapani, and A. Couairon, “Stimulated Raman X waves in ultrashort optical pulse filamentation,” Opt. Lett. 32(2), 184–186 (2007).
[CrossRef] [PubMed]

J. K. Ranka, R. S. Windeler, and A. J. Stentz, “Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm,” Opt. Lett. 25(1), 25–27 (2000).
[CrossRef] [PubMed]

Y. Silberberg, “Collapse of optical pulses,” Opt. Lett. 15(22), 1282–1284 (1990).
[CrossRef] [PubMed]

J. E. Rothenberg, “Pulse splitting during self-focusing in normally dispersive media,” Opt. Lett. 17(8), 583–585 (1992).
[CrossRef] [PubMed]

A. B. Aceves and C. De Angelis, “Spatiotemporal pulse dynamics in a periodic nonlinear waveguide,” Opt. Lett. 18(2), 110–112 (1993).
[CrossRef] [PubMed]

S. K. Turitsyn, “Collapse criterion for a pulse dynamics in a periodic nonlinear waveguide,” Opt. Lett. 18(18), 1493–1495 (1993).
[CrossRef] [PubMed]

R. Danielius, A. Piskarskas, P. Di Trapani, A. Andreoni, C. Solcia, and P. Foggi, “Matching of group velocities by spatial walk-off in collinear three-wave interaction with tilted pulses,” Opt. Lett. 21(13), 973–975 (1996).
[CrossRef] [PubMed]

Phys. Rep.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1-3), 1–126 (2008).
[CrossRef]

Phys. Rev. A

A. Dogariu, A. Kuzmich, and L. J. Wang, “Transparent anomalous dispersion and superluminal light-pulse propagation at a negative group velocity,” Phys. Rev. A 63(5), 053806 (2001).
[CrossRef]

C. J. Benton, A. V. Gorbach, and D. V. Skryabin, “Spatiotemporal quasisolitons and resonant radiation in arrays of silicon-on-insulator photonic wires,” Phys. Rev. A 78(3), 033818 (2008).
[CrossRef]

A. V. Gorbach, W. Ding, O. K. Staines, C. E. de Nobriga, G. D. Hobbs, W. J. Wadsworth, J. C. Knight, D. V. Skryabin, A. Samarelli, M. Sorel, and R. M. De La Rue, “Spatiotemporal nonlinear optics in arrays of subwavelength waveguides,” Phys. Rev. A 82(4), 041802 (2010).
[CrossRef]

A. Szameit, T. Pertsch, F. Dreisow, S. Nolte, A. Tünnermann, U. Peschel, and F. Lederer, “Light evolution in arbitrary two-dimensional waveguide arrays,” Phys. Rev. A 75(5), 053814 (2007).
[CrossRef]

A. Szameit, M. C. Rechtsman, O. Bahat-Treidel, and M. Segev, “Pt-symmetry in honeycomb photonic lattices,” Phys. Rev. A 84(2), 021806 (2011).
[CrossRef]

F. Eilenberger, S. Minardi, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Evolution dynamics of discrete-continuous light bullets,” Phys. Rev. A 84(1), 013836 (2011).
[CrossRef]

F. Eilenberger, A. Szameit, and T. Pertsch, “Transition from discrete to continuous townes solitons in periodic media,” Phys. Rev. A 82(4), 043802 (2010).
[CrossRef]

P. Kinsler, “Unidirectional optical pulse propagation equation for materials with both electric and magnetic responses,” Phys. Rev. A 81(2), 023808 (2010).
[CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys.

M. Kolesik and J. V. Moloney, “Nonlinear optical pulse propagation simulation: from Maxwell’s to unidirectional equations,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(3), 036604 (2004).
[CrossRef] [PubMed]

M. A. Porras, I. Gonzalo, and A. Mondello, “Pulsed light beams in vacuum with superluminal and negative group velocities,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(6), 066604 (2003).
[CrossRef] [PubMed]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, “Discrete solitons in photorefractive optically induced photonic lattices,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(4), 046602 (2002).
[CrossRef] [PubMed]

Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics

Y. S. Kivshar and S. K. Turitsyn, “Spatiotemporal pulse collapse on periodic potentials,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 49(4), R2536–R2539 (1994).
[CrossRef] [PubMed]

Phys. Rev. Lett.

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(2), 023902 (2003).
[CrossRef] [PubMed]

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Three-dimensional light bullets in arrays of waveguides,” Phys. Rev. Lett. 105(26), 263901 (2010).
[CrossRef] [PubMed]

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Measurement of the single-photon tunneling time,” Phys. Rev. Lett. 71(5), 708–711 (1993).
[CrossRef] [PubMed]

A. Kuzmich, A. Dogariu, L. J. Wang, P. W. Milonni, and R. Y. Chiao, “Signal velocity, causality, and quantum noise in superluminal light pulse propagation,” Phys. Rev. Lett. 86(18), 3925–3929 (2001).
[CrossRef] [PubMed]

P. Saari and K. Reivelt, “Evidence of x-shaped propagation-invariant localized light waves,” Phys. Rev. Lett. 79(21), 4135–4138 (1997).
[CrossRef]

A. V. Gorbach and D. V. Skryabin, “Cascaded generation of multiply charged optical vortices and spatiotemporal helical beams in a Raman medium,” Phys. Rev. Lett. 98(24), 243601 (2007).
[CrossRef] [PubMed]

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated X-shaped light bullets,” Phys. Rev. Lett. 91(9), 093904 (2003).
[CrossRef] [PubMed]

D. Faccio, M. A. Porras, A. Dubietis, F. Bragheri, A. Couairon, and P. Di Trapani, “Conical emission, pulse splitting, and X-wave parametric amplification in nonlinear dynamics of ultrashort light pulses,” Phys. Rev. Lett. 96(19), 193901 (2006).
[CrossRef] [PubMed]

C. Conti, S. Trillo, P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, and J. Trull, “Nonlinear electromagnetic X waves,” Phys. Rev. Lett. 90(17), 170406 (2003).
[CrossRef] [PubMed]

M. Kolesik, E. M. Wright, and J. V. Moloney, “Dynamic nonlinear X waves for femtosecond pulse propagation in water,” Phys. Rev. Lett. 92(25), 253901 (2004).
[CrossRef] [PubMed]

M. Heinrich, A. Szameit, F. Dreisow, R. Keil, S. Minardi, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, “Observation of three-dimensional discrete-continuous x waves in photonic lattices,” Phys. Rev. Lett. 103(11), 113903 (2009).
[CrossRef] [PubMed]

R. R. Alfano and S. L. Shapiro, “Emission in the region 4000 to 7000 å via four-photon coupling in glass,” Phys. Rev. Lett. 24(11), 584–587 (1970).
[CrossRef]

T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tünnermann, and F. Lederer, “Nonlinearity and disorder in fiber arrays,” Phys. Rev. Lett. 93(5), 053901 (2004).
[CrossRef] [PubMed]

Radiophys. Quantum Electron.

N. Vakhitov and A. Kolokolov, “Stationary solutions of the wave equation in a medium with nonlinearity saturation,” Radiophys. Quantum Electron. 16(7), 783–789 (1973).
[CrossRef]

Rev. Mod. Phys.

Y. V. Kartashov, B. A. Malomed, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys. 83(1), 247–306 (2011).
[CrossRef]

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
[CrossRef]

Science

P. Russell, “Photonic crystal fibers,” Science 299(5605), 358–362 (2003).
[CrossRef] [PubMed]

Other

G. Agrawal, Nonlinear Fiber Optics (Academic Press, 2001).

Y. Kivshar and G. Agrawal, Optical Solitons (Academic Press, 2003).

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Figures (9)

Fig. 1
Fig. 1

(a) Front facet of a typical fibre array with 91 cores. Core to core distance Λ = 34.8 µm or 29.7 µm, Core radius r = 9.7 µm or 8.3 µm, refractive index step Δn = 1.2·10−3. (b) Linear diffraction properties of the fibre array. (blue/left) Wavelength dependence of the diffraction length LDiff = π/(61/22c) and (red/right) normalized dispersion of the coupling constant α1 for the array with (solid) r = 9.7 µm and LDiff(1550 nm) = 22 mm and (dashed) r = 8.3 µm and LDiff(1550 nm) = 9.6 mm.

Fig. 2
Fig. 2

LB family properties for extended NLSE as a function of the nonlinear phase shift b for different values of the dispersion of the coupling constant α1. Plotted are (a) the LB energy, (b) the full width at half-maximum in the central waveguide, (c) the LB’s peak power, (d) the ratio of energy bound in the central waveguide, (e) the frequency shift in the central waveguide and (e) the frequency shift in the nearest neighbours of the central waveguide. All solutions to the right of the corresponding energy-minimum are stable, whereas those to the left are not.

Fig. 3
Fig. 3

(a) LB spacetime spectra for b = 15 and a fibre array with LDiff = 9.6 mm at a carrier wavelength of λ = 1550 nm for various strengths of the dispersion of the coupling α1. (white lines) Spectral centre of mass ΔSF(ν). (b) The spectral asymmetry ΔSF(b,α1) as a function of the nonlinear parameter b for various levels of α1. (c) Average ΔSF (dots) as a function of the dispersion of the coupling α1, with (gray line) a linear fit.

Fig. 4
Fig. 4

Schematic of the experimental setup. A LB is created in the fibre array and imaged onto a BBO crystal, where a time slice containing the LB is extracted by sum frequency cross correlation with a short pulse, thus separating it from the leading linear background. Using a 2-f setup the spatial spectrum of the LB is generated, of which a 1-D centred slice is imaged onto an imaging spectrograph, recording the spatiotemporal spectrum.

Fig. 5
Fig. 5

Experimental spacetime spectra of L = 25 mm fibre array with LDiff = 9.6 mm at various power levels. Delay was chosen such as to coincide with peak power of cross-correlation trace. (white lines) Spectral centre of mass Ω(ν). (red lines) Borders of the 1st Brillouin zone. (1st) Excitation of multiple LBs at high input power. (2nd, 3rd) Excitation of a single LB. Measured spectral asymmetry ΔSF = max(Ω)−min(Ω) ~2.8 nm at 96 nJ and 4.0 nm at 60 nJ. (4th) Insufficient power for LB excitation at low input power levels.

Fig. 6
Fig. 6

Evolution of the spectral asymmetry ΔSF of a LB for z < 80 mm for various input energies. The LB was generated in a simulation with input energys of 50 nJ < E < 350 nJ for a fibre geometry with LDiff(λ = 1550 nm) = 22 mm. Displayed are simulations with (left) a realistic level of STC, i.e. and strong spectral asymmetry (see Fig. 1) and (right) no STC, i.e. α 1 =0 , and thus no spectral asymmetry. The colorbar is the same for both graphs.

Fig. 7
Fig. 7

Simulation of LB decay and speedup with α1 = −0.1 induced by artificial loss. The initial energy is E = 11.05 at b = 15. The predicted point of decay zDecay = 2.65 is marked in (a) and (b) with the grey line. (a) Evolution of the power in the central waveguide. Overlaid is the position of the temporal centre of gravity <T>. (b) Relative speed of the LB. (blue circles) Measured from the slope of the white line in (a) and (red line) calculated using Eq. (12). (Dashed black line) Limit of maximum speedup at 12α1. (c) Evolution of the LBs effective energy E, together with (dashed line) the properties of the LB family with α1 = −0.1, taken from Fig. 2. The wavepacket remains a LB as long as its effective energy is sufficient to support a LB. If it drops below the energy threshold after z > zDecay rapid decay is observed.

Fig. 8
Fig. 8

Measured delay of arrival <ΔT> of pulse in central waveguide and nearest neighbour for a fibre array with LDiff = 22 mm as a function of the launched pulse energy for (dashed) L = 20 mm just after the excitation of the 1st LB and (solid) L = 60 mm after both LBs have decayed. Speedup due to decay visible for L = 60 mm, if energy is sufficient to excite LB. (1st LB at 80 nJ, and 2nd LB at 160 nJ)

Fig. 9
Fig. 9

(a) Simulated delay of arrival <ΔT> of pulse in central waveguide and nearest neighbour as a function of the launched pulse energy for (dashed) L = 20 mm just after the excitation of the 1st LB and (solid) L = 60 mm after both LBs have decayed. All simulations for an array geometry with LDiff = 22 mm and (black) realistic level of STC (see Fig. 1) and (red) no STC, i.e. LDiff = const. Speedup due to decay visible for L = 60 mm and realistic STC, if energy is sufficient to excite LB. (1st LB at 120 nJ, and 2nd LB at 240 nJ). (b) Difference in delay of arrival for both models. A signification difference is visible for z > 50 mm, where decay of the LBs starts to set in.

Equations (15)

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D nm = 2 β ξ n ξ m , ξ 1 =ω, ξ 2 =μ, ξ 3 =ν.
[ 2 + k 2 (ω) ]U( x,y,z,ω )=0,
β=k( ω ) k x 2 + k y 2 2 k 0 [ 1 ω ω 0 k 0 V g 0 ],
τ 0 ω 0 1 1.2fs,
β= β 0 ( ω )+2c( ω )[ cos( ν )+cos( μ )+cos( ν+μ ) ],
D 13 = D 31 =2 c ( ω )[ sin( ν )+sin( ν+μ ) ]0,
τ 0 c ( ω 0 ) c( ω 0 ) 100fs,
i A nm ( Z,T ) Z = 1 2 2 A nm T 2 + | A nm | 2 A nm + ( 1+i α 1 T )( A n+1m + A nm+1 + A n1m + A nm1 + A n+1m+1 + A n1m1 ),
Ω ( ν )= dΩΩ | A 0ν ( Ω ) | 2 dΩ | A 0ν ( Ω ) | 2 Δ= Ω ( 0 ) Ω ( π ).
Δ SF [ nm ]=45 α 1 ( 9.6mm L Diff ) 1/2 ,
( v g ) 1 ( v g 0 ) 1 = d dZ T = d dZ nm dTT| a nm | 2 = nm dT{ m( a nm,T * a nm )+2 α 1 e( [ a n+1m +... ] a nm * ) } =A+2 α 1 B { A= nm dTm( a nm,T * a nm ) B= nm dTe( [ a n+1m +... ] a nm * ) ,
( v g ) 1 = β 0 ( 1 ) +12 c 1 ( v g 0 ) 1 = β 0 ( 1 ) ,
( v g 0 ) 1 ( v g ) 1 =12 c 1 = d dZ T MAX
δ v g = v g v g 0 = [ β 0 ( 1 ) +12 c 1 ] 1 1/ β 0 ( 1 ) ( v g 0 ) 2 d dZ T MAX =12 c 1 ( v g 0 ) 2 ,
ΔT= T C T O ,

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