Abstract

We demonstrate that the group velocity dispersion (GVD) of the supermodes in a small array of silicon photonic wires can differ dramatically from the single wire GVD. This enables soliton propagation and modulational instability to be seen at wavelengths where single wires have strongly normal GVD.

© 2009 Optical Society of America

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  1. M. A. Foster, A. C. Turner, M. Lipson, and A. L. Gaeta, "Nonlinear optics in photonic nanowires," Opt. Express 16, 1300-1320 (2008).
    [CrossRef] [PubMed]
  2. Q. Lin, O. J. Painter, and G. P. Agrawal, "Nonlinear optical phenomena in silicon waveguides: modeling and applications," Opt. Express 15, 16604-16644 (2007).
    [CrossRef] [PubMed]
  3. M. Hochberg, T. Baehr-Jones, G. Wang, and M. Shearn, "Terahertz all-optical modulation in a silicon-polymer hybrid system," Nat. Maters. 5, 703-709 (2006).
    [CrossRef]
  4. M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, "Broad-band optical parametric gain on a silicon photonic chip," Nature 441, 960-963 (2006).
    [CrossRef] [PubMed]
  5. V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, "All-optical control of light on a silicon chip," Nature 431, 1081-1084 (2004).
    [CrossRef] [PubMed]
  6. Y. Vlasov, W. M. J. Green, and F. Xia, "High-throughput silicon nanophotonic wavelength-insensitive switch for on-chip optical networks," Nat. Photonics 2, 242-246 (2008).
    [CrossRef]
  7. Q. Lin, J. Zhang, G. Piredda, R. W. Boyd, P. M. Fauchet, and G. P. Agrawal. "Dispersion of silicon nonlinearities in the near infrared region," Appl. Phys. Lett. 91, 021111 (2007).
    [CrossRef]
  8. A. C. Turner, C. Manolatou, B. S. Schmidt, M. Lipson, M. A. Foster, J. E. Sharping, and A. L. Gaeta, "Tailored anomalous group-velocity dispersion in silicon channel waveguides," Opt. Express 14, 4357-4362 (2006).
    [CrossRef] [PubMed]
  9. E. Dulkeith, F. Xia, L. Schares, W. M. J. Green, and Y. A. Vlasov, "Group index and group velocity dispersion in silicon-on-insulator photonic wires," Opt. Express 14, 3853-3863 (2006).
    [CrossRef] [PubMed]
  10. E. Dulkeith, Y. A. Vlasov, X. Chen, N. C. Panoiu, and R. M. Osgood, "Self-phase-modulation in submicron silicon-on-insulator photonic wires," Opt. Express 14, 5524-5534 (2006).
    [CrossRef] [PubMed]
  11. W. Ding, C. Benton, A. V. Gorbach, W. J. Wadsworth, J. C. Knight, D. V. Skryabin, M. Gnan, M. Sorrel, and R. M. De-La-Rue, "Solitons and spectral broadening in long silicon-on- insulator photonic wires," Opt. Express 16, 3310-3319 (2008).
    [CrossRef] [PubMed]
  12. J. Zhang, Q. Lin, G. Piredda, R. W. Boyd, G. P. Agrawal, and P. M. Fauchet, "Optical solitons in a silicon waveguide," Opt. Express 15, 7682-7688 (2007).
    [CrossRef] [PubMed]
  13. J. I. Dadap, N. C. Panoiu, X. Chen, I. W. Hsieh, X. Liu, C. Y. Chou, E. Dulkeith, S. J. McNab, F. Xia, W. M. J. Green, L. Sekaric, Y. A. Vlasov, and R. M. Osgood Jr., "Nonlinear-optical phase modification in dispersionengineered si photonic wires," Opt. Express 16, 1280-1299 (2008).
    [CrossRef] [PubMed]
  14. T. Pertsch, T. Zentgraf, U. Peschel1, A. Bruer, and F. Lederer, "Anomalous refraction and diffraction in discrete optical systems," Phys. Rev. Lett. 88, 093901 (2002).
    [CrossRef] [PubMed]
  15. F. Lederer, G.I. Stegeman, D.N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, "Discrete solitons in optics," Phys. Rep. 463, 1-126 (2008).
    [CrossRef]
  16. A. V. Yulin, D. V. Skryabin, and A. G. Vladimirov, "Modulational instability of discrete solitons in coupled waveguides with group velocity dispersion," Opt. Express 14, 12347-12352 (2006).
    [CrossRef] [PubMed]
  17. P. D. Rasmussen, A. A. Sukhorukov, D. N. Neshev, W. Krolikowski, O. Bang, J. Lagsgaard, and Y. S. Kivshar, "Spatiotemporal control of light by bloch-mode dispersion in multi-core fibers," Opt. Express 16, 5878-5891 (2008).
    [CrossRef] [PubMed]
  18. 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, 033818 (2008).
    [CrossRef]
  19. K. S. Chiang, Y. T. Chow, D. J. Richardson, D. Taverner, L. Dong, L. Reekie, and K. M. Lo, "Experimental demonstration of intermodal dispersion in a two-core optical fibre," Opt. Commun. 143, 189-192 (1997).
    [CrossRef]
  20. M. Yu, C. J. Mckinstrie, and G. P. Agrawal, "Modulational instabilities in dispersion-flattened fibers," Phys. Rev. E 52, 1072-1080 (1995).
    [CrossRef]
  21. F. Biancalana, D. V. Skryabin, and P. S. Russell, "Four-wave mixing instabilities in photonic-crystal and tapered fibers," Phys. Rev. E 68, 046603 (2003).
    [CrossRef]
  22. N. Akhmediev and A. Ankiewicz, "Novel soliton states and bifurcation phenomena in nonlinear fiber couplers," Phys. Rev. Lett. 70, 2395-2398 (1993).
    [CrossRef] [PubMed]

2008

Y. Vlasov, W. M. J. Green, and F. Xia, "High-throughput silicon nanophotonic wavelength-insensitive switch for on-chip optical networks," Nat. Photonics 2, 242-246 (2008).
[CrossRef]

F. Lederer, G.I. Stegeman, D.N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, "Discrete solitons in optics," Phys. Rep. 463, 1-126 (2008).
[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, 033818 (2008).
[CrossRef]

J. I. Dadap, N. C. Panoiu, X. Chen, I. W. Hsieh, X. Liu, C. Y. Chou, E. Dulkeith, S. J. McNab, F. Xia, W. M. J. Green, L. Sekaric, Y. A. Vlasov, and R. M. Osgood Jr., "Nonlinear-optical phase modification in dispersionengineered si photonic wires," Opt. Express 16, 1280-1299 (2008).
[CrossRef] [PubMed]

M. A. Foster, A. C. Turner, M. Lipson, and A. L. Gaeta, "Nonlinear optics in photonic nanowires," Opt. Express 16, 1300-1320 (2008).
[CrossRef] [PubMed]

W. Ding, C. Benton, A. V. Gorbach, W. J. Wadsworth, J. C. Knight, D. V. Skryabin, M. Gnan, M. Sorrel, and R. M. De-La-Rue, "Solitons and spectral broadening in long silicon-on- insulator photonic wires," Opt. Express 16, 3310-3319 (2008).
[CrossRef] [PubMed]

P. D. Rasmussen, A. A. Sukhorukov, D. N. Neshev, W. Krolikowski, O. Bang, J. Lagsgaard, and Y. S. Kivshar, "Spatiotemporal control of light by bloch-mode dispersion in multi-core fibers," Opt. Express 16, 5878-5891 (2008).
[CrossRef] [PubMed]

2007

2006

2004

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, "All-optical control of light on a silicon chip," Nature 431, 1081-1084 (2004).
[CrossRef] [PubMed]

2003

F. Biancalana, D. V. Skryabin, and P. S. Russell, "Four-wave mixing instabilities in photonic-crystal and tapered fibers," Phys. Rev. E 68, 046603 (2003).
[CrossRef]

2002

T. Pertsch, T. Zentgraf, U. Peschel1, A. Bruer, and F. Lederer, "Anomalous refraction and diffraction in discrete optical systems," Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

1997

K. S. Chiang, Y. T. Chow, D. J. Richardson, D. Taverner, L. Dong, L. Reekie, and K. M. Lo, "Experimental demonstration of intermodal dispersion in a two-core optical fibre," Opt. Commun. 143, 189-192 (1997).
[CrossRef]

1995

M. Yu, C. J. Mckinstrie, and G. P. Agrawal, "Modulational instabilities in dispersion-flattened fibers," Phys. Rev. E 52, 1072-1080 (1995).
[CrossRef]

1993

N. Akhmediev and A. Ankiewicz, "Novel soliton states and bifurcation phenomena in nonlinear fiber couplers," Phys. Rev. Lett. 70, 2395-2398 (1993).
[CrossRef] [PubMed]

Agrawal, G. P.

Q. Lin, O. J. Painter, and G. P. Agrawal, "Nonlinear optical phenomena in silicon waveguides: modeling and applications," Opt. Express 15, 16604-16644 (2007).
[CrossRef] [PubMed]

J. Zhang, Q. Lin, G. Piredda, R. W. Boyd, G. P. Agrawal, and P. M. Fauchet, "Optical solitons in a silicon waveguide," Opt. Express 15, 7682-7688 (2007).
[CrossRef] [PubMed]

Q. Lin, J. Zhang, G. Piredda, R. W. Boyd, P. M. Fauchet, and G. P. Agrawal. "Dispersion of silicon nonlinearities in the near infrared region," Appl. Phys. Lett. 91, 021111 (2007).
[CrossRef]

M. Yu, C. J. Mckinstrie, and G. P. Agrawal, "Modulational instabilities in dispersion-flattened fibers," Phys. Rev. E 52, 1072-1080 (1995).
[CrossRef]

Akhmediev, N.

N. Akhmediev and A. Ankiewicz, "Novel soliton states and bifurcation phenomena in nonlinear fiber couplers," Phys. Rev. Lett. 70, 2395-2398 (1993).
[CrossRef] [PubMed]

Almeida, V. R.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, "All-optical control of light on a silicon chip," Nature 431, 1081-1084 (2004).
[CrossRef] [PubMed]

Ankiewicz, A.

N. Akhmediev and A. Ankiewicz, "Novel soliton states and bifurcation phenomena in nonlinear fiber couplers," Phys. Rev. Lett. 70, 2395-2398 (1993).
[CrossRef] [PubMed]

Assanto, G.

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

Baehr-Jones, T.

M. Hochberg, T. Baehr-Jones, G. Wang, and M. Shearn, "Terahertz all-optical modulation in a silicon-polymer hybrid system," Nat. Maters. 5, 703-709 (2006).
[CrossRef]

Bang, O.

Barrios, C. A.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, "All-optical control of light on a silicon chip," Nature 431, 1081-1084 (2004).
[CrossRef] [PubMed]

Benton, C.

Benton, C. J.

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, 033818 (2008).
[CrossRef]

Biancalana, F.

F. Biancalana, D. V. Skryabin, and P. S. Russell, "Four-wave mixing instabilities in photonic-crystal and tapered fibers," Phys. Rev. E 68, 046603 (2003).
[CrossRef]

Boyd, R. W.

Q. Lin, J. Zhang, G. Piredda, R. W. Boyd, P. M. Fauchet, and G. P. Agrawal. "Dispersion of silicon nonlinearities in the near infrared region," Appl. Phys. Lett. 91, 021111 (2007).
[CrossRef]

J. Zhang, Q. Lin, G. Piredda, R. W. Boyd, G. P. Agrawal, and P. M. Fauchet, "Optical solitons in a silicon waveguide," Opt. Express 15, 7682-7688 (2007).
[CrossRef] [PubMed]

Bruer, A.

T. Pertsch, T. Zentgraf, U. Peschel1, A. Bruer, and F. Lederer, "Anomalous refraction and diffraction in discrete optical systems," Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

Chen, X.

Chiang, K. S.

K. S. Chiang, Y. T. Chow, D. J. Richardson, D. Taverner, L. Dong, L. Reekie, and K. M. Lo, "Experimental demonstration of intermodal dispersion in a two-core optical fibre," Opt. Commun. 143, 189-192 (1997).
[CrossRef]

Chou, C. Y.

Chow, Y. T.

K. S. Chiang, Y. T. Chow, D. J. Richardson, D. Taverner, L. Dong, L. Reekie, and K. M. Lo, "Experimental demonstration of intermodal dispersion in a two-core optical fibre," Opt. Commun. 143, 189-192 (1997).
[CrossRef]

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, 1-126 (2008).
[CrossRef]

Dadap, J. I.

De-La-Rue,, R. M.

Ding, W.

Dong, L.

K. S. Chiang, Y. T. Chow, D. J. Richardson, D. Taverner, L. Dong, L. Reekie, and K. M. Lo, "Experimental demonstration of intermodal dispersion in a two-core optical fibre," Opt. Commun. 143, 189-192 (1997).
[CrossRef]

Dulkeith, E.

Fauchet, P. M.

Q. Lin, J. Zhang, G. Piredda, R. W. Boyd, P. M. Fauchet, and G. P. Agrawal. "Dispersion of silicon nonlinearities in the near infrared region," Appl. Phys. Lett. 91, 021111 (2007).
[CrossRef]

Fauchet,, P. M.

Foster, M. A.

Gaeta, A. L.

M. A. Foster, A. C. Turner, M. Lipson, and A. L. Gaeta, "Nonlinear optics in photonic nanowires," Opt. Express 16, 1300-1320 (2008).
[CrossRef] [PubMed]

M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, "Broad-band optical parametric gain on a silicon photonic chip," Nature 441, 960-963 (2006).
[CrossRef] [PubMed]

Gaeta,, A. L.

Gnan, M.

Gorbach, A. V.

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, 033818 (2008).
[CrossRef]

W. Ding, C. Benton, A. V. Gorbach, W. J. Wadsworth, J. C. Knight, D. V. Skryabin, M. Gnan, M. Sorrel, and R. M. De-La-Rue, "Solitons and spectral broadening in long silicon-on- insulator photonic wires," Opt. Express 16, 3310-3319 (2008).
[CrossRef] [PubMed]

Green, W. M. J.

Hochberg, M.

M. Hochberg, T. Baehr-Jones, G. Wang, and M. Shearn, "Terahertz all-optical modulation in a silicon-polymer hybrid system," Nat. Maters. 5, 703-709 (2006).
[CrossRef]

Hsieh, I. W.

Kivshar, Y. S.

Knight, J. C.

Krolikowski, W.

Lagsgaard, J.

Lederer, F.

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

Lederer,, F.

T. Pertsch, T. Zentgraf, U. Peschel1, A. Bruer, and F. Lederer, "Anomalous refraction and diffraction in discrete optical systems," Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

Lin, Q.

Lipson, M.

M. A. Foster, A. C. Turner, M. Lipson, and A. L. Gaeta, "Nonlinear optics in photonic nanowires," Opt. Express 16, 1300-1320 (2008).
[CrossRef] [PubMed]

A. C. Turner, C. Manolatou, B. S. Schmidt, M. Lipson, M. A. Foster, J. E. Sharping, and A. L. Gaeta, "Tailored anomalous group-velocity dispersion in silicon channel waveguides," Opt. Express 14, 4357-4362 (2006).
[CrossRef] [PubMed]

M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, "Broad-band optical parametric gain on a silicon photonic chip," Nature 441, 960-963 (2006).
[CrossRef] [PubMed]

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, "All-optical control of light on a silicon chip," Nature 431, 1081-1084 (2004).
[CrossRef] [PubMed]

Liu, X.

Lo, K. M.

K. S. Chiang, Y. T. Chow, D. J. Richardson, D. Taverner, L. Dong, L. Reekie, and K. M. Lo, "Experimental demonstration of intermodal dispersion in a two-core optical fibre," Opt. Commun. 143, 189-192 (1997).
[CrossRef]

Manolatou, C.

Mckinstrie, C. J.

M. Yu, C. J. Mckinstrie, and G. P. Agrawal, "Modulational instabilities in dispersion-flattened fibers," Phys. Rev. E 52, 1072-1080 (1995).
[CrossRef]

McNab, S. J.

Neshev, D. N.

Osgood,, R. M.

Osgood, Jr., R. M.

Painter, O. J.

Panepucci, R. R.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, "All-optical control of light on a silicon chip," Nature 431, 1081-1084 (2004).
[CrossRef] [PubMed]

Panoiu, N. C.

Pertsch, T.

T. Pertsch, T. Zentgraf, U. Peschel1, A. Bruer, and F. Lederer, "Anomalous refraction and diffraction in discrete optical systems," Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

Peschel1, U.

T. Pertsch, T. Zentgraf, U. Peschel1, A. Bruer, and F. Lederer, "Anomalous refraction and diffraction in discrete optical systems," Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

Piredda, G.

J. Zhang, Q. Lin, G. Piredda, R. W. Boyd, G. P. Agrawal, and P. M. Fauchet, "Optical solitons in a silicon waveguide," Opt. Express 15, 7682-7688 (2007).
[CrossRef] [PubMed]

Q. Lin, J. Zhang, G. Piredda, R. W. Boyd, P. M. Fauchet, and G. P. Agrawal. "Dispersion of silicon nonlinearities in the near infrared region," Appl. Phys. Lett. 91, 021111 (2007).
[CrossRef]

Rasmussen, P. D.

Reekie, L.

K. S. Chiang, Y. T. Chow, D. J. Richardson, D. Taverner, L. Dong, L. Reekie, and K. M. Lo, "Experimental demonstration of intermodal dispersion in a two-core optical fibre," Opt. Commun. 143, 189-192 (1997).
[CrossRef]

Richardson, D. J.

K. S. Chiang, Y. T. Chow, D. J. Richardson, D. Taverner, L. Dong, L. Reekie, and K. M. Lo, "Experimental demonstration of intermodal dispersion in a two-core optical fibre," Opt. Commun. 143, 189-192 (1997).
[CrossRef]

Russell, P. S.

F. Biancalana, D. V. Skryabin, and P. S. Russell, "Four-wave mixing instabilities in photonic-crystal and tapered fibers," Phys. Rev. E 68, 046603 (2003).
[CrossRef]

Schares, L.

Schmidt, B. S.

A. C. Turner, C. Manolatou, B. S. Schmidt, M. Lipson, M. A. Foster, J. E. Sharping, and A. L. Gaeta, "Tailored anomalous group-velocity dispersion in silicon channel waveguides," Opt. Express 14, 4357-4362 (2006).
[CrossRef] [PubMed]

M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, "Broad-band optical parametric gain on a silicon photonic chip," Nature 441, 960-963 (2006).
[CrossRef] [PubMed]

Segev, M.

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

Sekaric, L.

Sharping, J. E.

M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, "Broad-band optical parametric gain on a silicon photonic chip," Nature 441, 960-963 (2006).
[CrossRef] [PubMed]

A. C. Turner, C. Manolatou, B. S. Schmidt, M. Lipson, M. A. Foster, J. E. Sharping, and A. L. Gaeta, "Tailored anomalous group-velocity dispersion in silicon channel waveguides," Opt. Express 14, 4357-4362 (2006).
[CrossRef] [PubMed]

Shearn, M.

M. Hochberg, T. Baehr-Jones, G. Wang, and M. Shearn, "Terahertz all-optical modulation in a silicon-polymer hybrid system," Nat. Maters. 5, 703-709 (2006).
[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, 1-126 (2008).
[CrossRef]

Skryabin, D. V.

W. Ding, C. Benton, A. V. Gorbach, W. J. Wadsworth, J. C. Knight, D. V. Skryabin, M. Gnan, M. Sorrel, and R. M. De-La-Rue, "Solitons and spectral broadening in long silicon-on- insulator photonic wires," Opt. Express 16, 3310-3319 (2008).
[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, 033818 (2008).
[CrossRef]

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

F. Biancalana, D. V. Skryabin, and P. S. Russell, "Four-wave mixing instabilities in photonic-crystal and tapered fibers," Phys. Rev. E 68, 046603 (2003).
[CrossRef]

Sorrel, M.

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, 1-126 (2008).
[CrossRef]

Sukhorukov, A. A.

Taverner, D.

K. S. Chiang, Y. T. Chow, D. J. Richardson, D. Taverner, L. Dong, L. Reekie, and K. M. Lo, "Experimental demonstration of intermodal dispersion in a two-core optical fibre," Opt. Commun. 143, 189-192 (1997).
[CrossRef]

Turner, A. C.

Vladimirov, A. G.

Vlasov, Y.

Y. Vlasov, W. M. J. Green, and F. Xia, "High-throughput silicon nanophotonic wavelength-insensitive switch for on-chip optical networks," Nat. Photonics 2, 242-246 (2008).
[CrossRef]

Vlasov, Y. A.

Vlasov,, Y. A.

Wadsworth, W. J.

Wang, G.

M. Hochberg, T. Baehr-Jones, G. Wang, and M. Shearn, "Terahertz all-optical modulation in a silicon-polymer hybrid system," Nat. Maters. 5, 703-709 (2006).
[CrossRef]

Xia, F.

Xia,, F.

Y. Vlasov, W. M. J. Green, and F. Xia, "High-throughput silicon nanophotonic wavelength-insensitive switch for on-chip optical networks," Nat. Photonics 2, 242-246 (2008).
[CrossRef]

Yu, M.

M. Yu, C. J. Mckinstrie, and G. P. Agrawal, "Modulational instabilities in dispersion-flattened fibers," Phys. Rev. E 52, 1072-1080 (1995).
[CrossRef]

Yulin, A. V.

Zentgraf, T.

T. Pertsch, T. Zentgraf, U. Peschel1, A. Bruer, and F. Lederer, "Anomalous refraction and diffraction in discrete optical systems," Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

Zhang, J.

J. Zhang, Q. Lin, G. Piredda, R. W. Boyd, G. P. Agrawal, and P. M. Fauchet, "Optical solitons in a silicon waveguide," Opt. Express 15, 7682-7688 (2007).
[CrossRef] [PubMed]

Q. Lin, J. Zhang, G. Piredda, R. W. Boyd, P. M. Fauchet, and G. P. Agrawal. "Dispersion of silicon nonlinearities in the near infrared region," Appl. Phys. Lett. 91, 021111 (2007).
[CrossRef]

Appl. Phys. Lett.

Q. Lin, J. Zhang, G. Piredda, R. W. Boyd, P. M. Fauchet, and G. P. Agrawal. "Dispersion of silicon nonlinearities in the near infrared region," Appl. Phys. Lett. 91, 021111 (2007).
[CrossRef]

Nat. Maters.

M. Hochberg, T. Baehr-Jones, G. Wang, and M. Shearn, "Terahertz all-optical modulation in a silicon-polymer hybrid system," Nat. Maters. 5, 703-709 (2006).
[CrossRef]

Nat. Photonics

Y. Vlasov, W. M. J. Green, and F. Xia, "High-throughput silicon nanophotonic wavelength-insensitive switch for on-chip optical networks," Nat. Photonics 2, 242-246 (2008).
[CrossRef]

Nature

M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, "Broad-band optical parametric gain on a silicon photonic chip," Nature 441, 960-963 (2006).
[CrossRef] [PubMed]

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, "All-optical control of light on a silicon chip," Nature 431, 1081-1084 (2004).
[CrossRef] [PubMed]

Opt. Commun.

K. S. Chiang, Y. T. Chow, D. J. Richardson, D. Taverner, L. Dong, L. Reekie, and K. M. Lo, "Experimental demonstration of intermodal dispersion in a two-core optical fibre," Opt. Commun. 143, 189-192 (1997).
[CrossRef]

Opt. Express

E. Dulkeith, F. Xia, L. Schares, W. M. J. Green, and Y. A. Vlasov, "Group index and group velocity dispersion in silicon-on-insulator photonic wires," Opt. Express 14, 3853-3863 (2006).
[CrossRef] [PubMed]

A. C. Turner, C. Manolatou, B. S. Schmidt, M. Lipson, M. A. Foster, J. E. Sharping, and A. L. Gaeta, "Tailored anomalous group-velocity dispersion in silicon channel waveguides," Opt. Express 14, 4357-4362 (2006).
[CrossRef] [PubMed]

E. Dulkeith, Y. A. Vlasov, X. Chen, N. C. Panoiu, and R. M. Osgood, "Self-phase-modulation in submicron silicon-on-insulator photonic wires," Opt. Express 14, 5524-5534 (2006).
[CrossRef] [PubMed]

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

J. Zhang, Q. Lin, G. Piredda, R. W. Boyd, G. P. Agrawal, and P. M. Fauchet, "Optical solitons in a silicon waveguide," Opt. Express 15, 7682-7688 (2007).
[CrossRef] [PubMed]

Q. Lin, O. J. Painter, and G. P. Agrawal, "Nonlinear optical phenomena in silicon waveguides: modeling and applications," Opt. Express 15, 16604-16644 (2007).
[CrossRef] [PubMed]

J. I. Dadap, N. C. Panoiu, X. Chen, I. W. Hsieh, X. Liu, C. Y. Chou, E. Dulkeith, S. J. McNab, F. Xia, W. M. J. Green, L. Sekaric, Y. A. Vlasov, and R. M. Osgood Jr., "Nonlinear-optical phase modification in dispersionengineered si photonic wires," Opt. Express 16, 1280-1299 (2008).
[CrossRef] [PubMed]

M. A. Foster, A. C. Turner, M. Lipson, and A. L. Gaeta, "Nonlinear optics in photonic nanowires," Opt. Express 16, 1300-1320 (2008).
[CrossRef] [PubMed]

W. Ding, C. Benton, A. V. Gorbach, W. J. Wadsworth, J. C. Knight, D. V. Skryabin, M. Gnan, M. Sorrel, and R. M. De-La-Rue, "Solitons and spectral broadening in long silicon-on- insulator photonic wires," Opt. Express 16, 3310-3319 (2008).
[CrossRef] [PubMed]

P. D. Rasmussen, A. A. Sukhorukov, D. N. Neshev, W. Krolikowski, O. Bang, J. Lagsgaard, and Y. S. Kivshar, "Spatiotemporal control of light by bloch-mode dispersion in multi-core fibers," Opt. Express 16, 5878-5891 (2008).
[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, 1-126 (2008).
[CrossRef]

Phys. Rev. A

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, 033818 (2008).
[CrossRef]

Phys. Rev. E

M. Yu, C. J. Mckinstrie, and G. P. Agrawal, "Modulational instabilities in dispersion-flattened fibers," Phys. Rev. E 52, 1072-1080 (1995).
[CrossRef]

F. Biancalana, D. V. Skryabin, and P. S. Russell, "Four-wave mixing instabilities in photonic-crystal and tapered fibers," Phys. Rev. E 68, 046603 (2003).
[CrossRef]

Phys. Rev. Lett.

N. Akhmediev and A. Ankiewicz, "Novel soliton states and bifurcation phenomena in nonlinear fiber couplers," Phys. Rev. Lett. 70, 2395-2398 (1993).
[CrossRef] [PubMed]

T. Pertsch, T. Zentgraf, U. Peschel1, A. Bruer, and F. Lederer, "Anomalous refraction and diffraction in discrete optical systems," Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1.
Fig. 1.

(a) Supermodes of the directional coupler, shown as transmitted power as function of transverse distance. The red (blue) line shows the symmetric (antisymmetric) supermode. The wire dimensions are shown overlaid. The dots show linear superpositions of the single-wire modes, confirming the validity of our use of this approximation. (b) Coupling length Lc as a function of λ for the structures shown in (a).

Fig. 2.
Fig. 2.

(a) The full line shows the coupling dispersion (- (ω 2/2πc) ω 2 K for 220nm × 330nm wires with a 330nm gap. The dashed line shows the same, but for 220nm × 420nm wires with a 700nm gap. (b) The full line is the dispersion (- (ω 2/2πc) ω 2 D) of an isolated 220 × 330nm wire. The dashed lines are the dispersions of the in-phase (below the full line) and anti-phase (above the full line) modes of the coupler. The dotted lines are the dispersions of supermodes in the 6-wire array. The shaded area spans the region between the dispersions of the in-phase and out-of-phase modes of an infinite array. The wire size for (b) is 230 × 330nm. (c) The linear supermodes for a six wire array. The index j in (b) and (c) corresponds to that in Eq. 2

Fig. 3.
Fig. 3.

(a) Predicted wavelengths of MI sidebands versus pump wavelength. Anomalous GVD of a single wire is in the region between the vertical dashed-grey lines. The dashed loops correspond to uncoupled wires, showing that no MI occurs at the 1.5μm pump. The solid loops correspond to antisymmetric supermode, showing that MI does occur. (b) Spectral output after a distance of 1.93 mm, of a rectangular pulse with power 10P 0 and duration 10ps. The overlaid prediction for gain (dotted grey line) is for 5P 0, to allow for the effect of damping. (c) As for (b), but with free-carrier effects included. The predicted gain overlay is for 3.5P 0.

Fig. 4.
Fig. 4.

a) Evolution of a pulse with peak power 15P 0 fired into the 1st wire of a 2 wire system. The pulses in the symmetric and antisymmetric modes separate to to group-velocity mismatch, with the latter becoming a soliton. b) Evolution of a pulse with peak power 150P 0 fired into the 3rd wire of a 6 wire system. Six supermodal pulses are formed (with index j corresponding to that in Eq. 2 and figure 2(c)) The amplitude plotted is derived as n E n 2 . )

Equations (4)

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z E n i D ̂ ( i t ) E n = i C ̂ ( i t ) ( E n 1 + E n + 1 ) + i ( 1 + i ε tpa ) E n 2 E n ( ε + ε f c Q n ) E n ,
z E ̃ j i D ̂ j ( i t ) E ̃ j = i Γ N j E ̃ j 2 E ̃ j + f N j ( E ̃ 1 , E ̃ 2 , , E ̃ N ) ,
D j ( ω ) = D ( ω ) + χ j C ( ω ) , χ j 2 cos ( π j N + 1 ) .
E ̃ j = e iqz 2 ( q χ j c 0 ) Γ Nj sech ( q χ j c 0 ( d 2 + χ j c 2 ) ( t z χ j c 1 ) ) .

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