Abstract

We study spatiotemporal dynamics of soliton-induced two-octave-broad supercontinuum generated by fs pulses in an array of coupled nonlinear waveguides. We show that after fission of the input pulse into several fundamental solitons, red and blue-shifted nonsolitonic radiation, as well as solitons with lower intensity, spread away in transverse direction, while the most intense spikes self-trap into spatiotemporal discrete solitons.

© 2007 Optical Society of America

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  1. D. N. Christodoulides and R. I. Joseph, "Discrete self-focusing in nonlinear arrays of coupled waveguides," Opt. Lett. 13, 794-796 (1988).
    [CrossRef] [PubMed]
  2. 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]
  3. Yu. S. Kivshar, G. P. Agrawal, Optical Solitons: from Fibers to Photonic Crystals (Academic Press, San Diego, 2003).
  4. D. N. Christodoulides, F. Lederer, and Y. Silberberg, "Discretizing light behaviour in linear and nonlinear waveguide lattices," Nature 424, 817-823 (2003).
    [CrossRef] [PubMed]
  5. A. B. Aceves, C. De Angelis, A. M. Rubenchik, and S. K. Turitsyn, "Multidimensional solitons in fiber arrays," Opt. Lett. 19, 329-331 (1994).
    [CrossRef] [PubMed]
  6. A. B. Aceves, G. G. Luther, C. De Angelis, A. M. Rubenchik, and S. K. Turitsyn, "Energy localization in nonlinear fiber arrays: Collapse-effect compresor," Phys. Rev. Lett. 75, 73-76 (1995).
    [CrossRef] [PubMed]
  7. D. Cheskis, S. Bar-Ad, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, and D. Ross, "Strong spatiotemporal localization in a silica nonlinear waveguide array," Phys. Rev. Lett. 91, 223901 (2003).
    [CrossRef] [PubMed]
  8. A. Yulin, D. V. Skryabin, and A. Vladimirov, "Modulational instability of discrete solitons in coupled waveguides with group velocity dispersion," Opt. Express 14, 12347-12352 (2006),
    [CrossRef] [PubMed]
  9. K. Motzek, A. A. Sukhorukov, and Yu. S. Kivshar, "Self-trapping of polychromatic light in nonlinear periodic photonic structures," Opt. Express 14, 9873-9878 (2006),
    [CrossRef] [PubMed]
  10. A. A. Sukhorukov, D. N. Neshev, A. Dreischuh, R. Fischer, S. Ha, W. Krolikowski, J. Bolger, A. Mitchell, B. J. Eggleton, and Yu. S. Kivshar, "Polychromatic nonlinear surface modes generated by supercontinuum light," Opt. Express 14, 11265-11270 (2006).
    [CrossRef] [PubMed]
  11. J. K. Ranka, R. S. Windeler, and A. J. Steinz, "Visible continuum generation in air silica microstructure optical fibers with anomalous dispersion at 800 nm," Opt. Lett. 25, 25-27 (2000).
    [CrossRef]
  12. A. Husakou and J. Herrmann, "Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers," Phys. Rev. Lett. 87, 203901 (2001).
    [CrossRef] [PubMed]
  13. J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, "Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers," Phys. Rev. Lett. 88, 173901 (2002).
    [CrossRef] [PubMed]
  14. W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. J. Omenetto, A. Efimov, A. J. Taylor, "Tanformation and control of ultra-short pulses in dispersion-engineered photonic crystal fibers," Nature 424, 511-515 (2003).
    [CrossRef] [PubMed]
  15. G. Genty, M. Lehtonen, and H. Ludvigsen, "Effect of cross-phase modulation on supercontinuum generated in microstructured fibers with sub-30 fs pulses," Opt. Express 12, 4614-4624 (2004).
    [CrossRef] [PubMed]
  16. A. V. Gorbach, D. V. Skryabin, J. M. Stone, and J. C. Knight, "Four-wave mixing of solitons with radiation and quasi-nondispersive wave packets at the short-wavelength edge of a supercontinuum," Opt. Express 14, 9854- 9863 (2006).
    [CrossRef] [PubMed]
  17. J. M. Dudley, G. Genty, and S. Coen, "Supercontinuum generation in photonic crystal fiber," Rev. Mod. Phys. 78, 1135-1184 (2006).
    [CrossRef]
  18. O. Fedotova, A. Husakou, and J. Herrmann, "Supercontinuum generation in planar rib waveguides enabled by anomalous dispersion," Opt. Express 14, 1512-1517 (2006).
    [CrossRef] [PubMed]
  19. M. J. Adams, An Introduction to Optical Waveguides (John Wiley & Sons, 1981).
  20. A. Husakou and J. Herrmann, "Supercontinuum generation in photonic crystal fibers made from highly nonlinear glasses," Appl. Phys. B 77, 227-234 (2003).
    [CrossRef]
  21. M. Frosz, P. Falk, and O. Bang, "The role of the second zero-dispersion wavelength in generation of supercontinua and bright-bright soliton-pairs across the zero-dispersion wavelength," Opt. Express 13, 6181-6192 (2005).
    [CrossRef] [PubMed]

2006 (6)

A. Yulin, D. V. Skryabin, and A. Vladimirov, "Modulational instability of discrete solitons in coupled waveguides with group velocity dispersion," Opt. Express 14, 12347-12352 (2006),
[CrossRef] [PubMed]

K. Motzek, A. A. Sukhorukov, and Yu. S. Kivshar, "Self-trapping of polychromatic light in nonlinear periodic photonic structures," Opt. Express 14, 9873-9878 (2006),
[CrossRef] [PubMed]

A. A. Sukhorukov, D. N. Neshev, A. Dreischuh, R. Fischer, S. Ha, W. Krolikowski, J. Bolger, A. Mitchell, B. J. Eggleton, and Yu. S. Kivshar, "Polychromatic nonlinear surface modes generated by supercontinuum light," Opt. Express 14, 11265-11270 (2006).
[CrossRef] [PubMed]

A. V. Gorbach, D. V. Skryabin, J. M. Stone, and J. C. Knight, "Four-wave mixing of solitons with radiation and quasi-nondispersive wave packets at the short-wavelength edge of a supercontinuum," Opt. Express 14, 9854- 9863 (2006).
[CrossRef] [PubMed]

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

O. Fedotova, A. Husakou, and J. Herrmann, "Supercontinuum generation in planar rib waveguides enabled by anomalous dispersion," Opt. Express 14, 1512-1517 (2006).
[CrossRef] [PubMed]

2005 (1)

2004 (1)

2003 (4)

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. J. Omenetto, A. Efimov, A. J. Taylor, "Tanformation and control of ultra-short pulses in dispersion-engineered photonic crystal fibers," Nature 424, 511-515 (2003).
[CrossRef] [PubMed]

A. Husakou and J. Herrmann, "Supercontinuum generation in photonic crystal fibers made from highly nonlinear glasses," Appl. Phys. B 77, 227-234 (2003).
[CrossRef]

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

2002 (1)

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, "Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers," Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef] [PubMed]

2001 (1)

A. Husakou and J. Herrmann, "Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers," Phys. Rev. Lett. 87, 203901 (2001).
[CrossRef] [PubMed]

2000 (1)

1998 (1)

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

1995 (1)

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

1994 (1)

1988 (1)

Appl. Phys. B (1)

A. Husakou and J. Herrmann, "Supercontinuum generation in photonic crystal fibers made from highly nonlinear glasses," Appl. Phys. B 77, 227-234 (2003).
[CrossRef]

Nature (2)

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

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. J. Omenetto, A. Efimov, A. J. Taylor, "Tanformation and control of ultra-short pulses in dispersion-engineered photonic crystal fibers," Nature 424, 511-515 (2003).
[CrossRef] [PubMed]

Opt. Express (7)

G. Genty, M. Lehtonen, and H. Ludvigsen, "Effect of cross-phase modulation on supercontinuum generated in microstructured fibers with sub-30 fs pulses," Opt. Express 12, 4614-4624 (2004).
[CrossRef] [PubMed]

A. V. Gorbach, D. V. Skryabin, J. M. Stone, and J. C. Knight, "Four-wave mixing of solitons with radiation and quasi-nondispersive wave packets at the short-wavelength edge of a supercontinuum," Opt. Express 14, 9854- 9863 (2006).
[CrossRef] [PubMed]

O. Fedotova, A. Husakou, and J. Herrmann, "Supercontinuum generation in planar rib waveguides enabled by anomalous dispersion," Opt. Express 14, 1512-1517 (2006).
[CrossRef] [PubMed]

A. Yulin, D. V. Skryabin, and A. Vladimirov, "Modulational instability of discrete solitons in coupled waveguides with group velocity dispersion," Opt. Express 14, 12347-12352 (2006),
[CrossRef] [PubMed]

K. Motzek, A. A. Sukhorukov, and Yu. S. Kivshar, "Self-trapping of polychromatic light in nonlinear periodic photonic structures," Opt. Express 14, 9873-9878 (2006),
[CrossRef] [PubMed]

A. A. Sukhorukov, D. N. Neshev, A. Dreischuh, R. Fischer, S. Ha, W. Krolikowski, J. Bolger, A. Mitchell, B. J. Eggleton, and Yu. S. Kivshar, "Polychromatic nonlinear surface modes generated by supercontinuum light," Opt. Express 14, 11265-11270 (2006).
[CrossRef] [PubMed]

M. Frosz, P. Falk, and O. Bang, "The role of the second zero-dispersion wavelength in generation of supercontinua and bright-bright soliton-pairs across the zero-dispersion wavelength," Opt. Express 13, 6181-6192 (2005).
[CrossRef] [PubMed]

Opt. Lett. (3)

Phys. Rev. Lett. (5)

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]

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

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

A. Husakou and J. Herrmann, "Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers," Phys. Rev. Lett. 87, 203901 (2001).
[CrossRef] [PubMed]

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, "Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers," Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

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

Other (2)

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

M. J. Adams, An Introduction to Optical Waveguides (John Wiley & Sons, 1981).

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Figures (5)

Fig. 1.
Fig. 1.

(a) Schematic of a waveguide array created by planar rib waveguides. (b) Group-velocity dispersion for an Air-TaFD5-SiO2 rib waveguide (black line) and bulk TaFD5 (red line). Waveguide dimensions are a=4:0 µm, d=1:0 µm, and f=0:5 µm.

Fig. 2.
Fig. 2.

Evolution of an input 32-fs pulse with peak intensity of 0.5 TW/cm2 and central wavelength λ=1600 nm in an isolated waveguide (a) and the central waveguide of an array (b). Soliton fission appears both in (a) and (b), which leads to formation of three stable solitons in an isolated waveguide (marked by arrows), whereas only one most intense soliton resists diffractive spreading in the array.

Fig. 3.
Fig. 3.

(a,b) Temporal profile and (c) spectrum of pulse in the central [black curve in (a,c)] and neighboring [red curve in (b,c)] waveguide. Parameters of the input pulse are the same as in Fig. 2(b), propagation length is 5 cm. (d) Quadratic mean of the mode diameter W RMS(ω) characterizing the field localization. Nonsolitonic radiation (NSR) and soliton are separated both in (a,b) temporal and (c) spectral domains.

Fig. 4.
Fig. 4.

(a,c,e) Spectrum and (b,d,f) temporal shape calculated for a 200 fs input pulse with peak intensity 0.5 TW/cm2 and central wavelength 1600 nm in (a,b) an isolated waveguide and (c-f) waveguide array. Propagation length is (a–d) 5 cm and (e,f) 20 cm, respectively.

Fig. 5.
Fig. 5.

(a) Spectrum and (b) temporal shape calculated for a 200-fs input pulse with peak intensity 0.5 TW/cm2 and central wavelength 800 nm propagating for z=5 cm.

Equations (1)

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i E j z + { β ( ω ) ω ν } E j + κ ( E j 1 + E j + 1 ) + μ 0 α ( ω ) ω 2 2 β ( ω ) P nl ( j ) ( z , ω ) = 0 .

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