Abstract

We address the properties of two-color localized nonlinear modes supported by one-dimensional chirped photonic lattices imprinted in quadratic media. The impacts of chirp rate and phase mismatch on the two-color solitons are investigated. Various families of two-color soliton solutions are found. In contrast to the unchirped lattices, chirped lattices can enhance the stability of two-color solitons. Odd solitons can be completely stable provided that the chirp rate exceeds a critical value, even for varying phase mismatches. We also study the excitation, unpacking, and oscillation of two-color solitons in chirped lattices. Our results may enrich the potential applications of two-color solitons in all-optical communications.

© 2010 Optical Society of America

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  1. Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, 2003).
  2. A. V. Buryak, P. D. Trapani, D. V. Skryabin, and S. Trillo, “Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications,” Phys. Rep. 370, 63–235 (2002).
    [CrossRef]
  3. G. I. Stegeman, D. J. Hagan, and L. Torner, “χ2 cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996).
    [CrossRef]
  4. 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]
  5. J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature 422, 147–150 (2003).
    [CrossRef] [PubMed]
  6. A. V. Buryak and Y. S. Kivshar, “Spatial optical solitons governed by quadratic nonlinearity,” Opt. Lett. 19, 1612–1614 (1994).
    [CrossRef] [PubMed]
  7. L. Torner and G. I. Stegeman, “Multicolor solitons,” Opt. Photonics News 12, 36–39 (2001).
    [CrossRef]
  8. W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
    [CrossRef] [PubMed]
  9. R. Schiek, Y. Baek, and G. I. Stegeman, “One-dimensional spatial solitary waves due to cascaded second-order nonlinearities in planar waveguides,” Phys. Rev. E 53, 1138–1141 (1996).
    [CrossRef]
  10. B. A. Malomed, P. G. Kevrekidis, D. J. Frantzeskakis, H. E. Nistazakis, and A. N. Yannacopoulos, “One-and two-dimensional solitons in second-harmonic-generating lattices,” Phys. Rev. E 65, 056606 (2002).
    [CrossRef]
  11. Y. V. Kartashov, G. Molina-Terriza, and L. Torner, “Multicolor soliton clusters,” J. Opt. Soc. Am. B 19, 2682–2691 (2002).
    [CrossRef]
  12. Y. V. Kartashov, A. A. Egorov, A. S. Zelenina, V. A. Vysloukh, and L. Torner, “Stable multicolor periodic-wave arrays,” Phys. Rev. Lett. 92, 033901 (2004).
    [CrossRef] [PubMed]
  13. Y. V. Kartashov, L. Torner, and V. A. Vysloukh, “Multicolor lattice solitons,” Opt. Lett. 29, 1117–1119 (2004).
    [CrossRef] [PubMed]
  14. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Packing, unpacking, and steering of multicolor solitons in optical lattices,” Opt. Lett. 29, 1399–1401 (2004).
    [CrossRef] [PubMed]
  15. G. A. Siviloglou, K. G. Makris, R. Iwanow, R. Schiek, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, “Observation of discrete quadratic surface solitons,” Opt. Express 14, 5508–5516 (2006).
    [CrossRef] [PubMed]
  16. Z. Xu, Y. V. Kartashov, L.-C. Crasovan, D. Mihalache, and L. Torner, “Multicolor vortex solitons in two-dimensional photonic lattices,” Phys. Rev. E 71, 016616 (2005).
    [CrossRef]
  17. H. Susanto, P. G. Kevrekidis, R. Carretero-González, B. A. Malomed, and D. J. Frantzeskakis, “Mobility of discrete solitons in quadratically nonlinear media,” Phys. Rev. Lett. 99, 214103 (2007).
    [CrossRef]
  18. Z. Xu and Y. S. Kivshar, “Two-color surface lattice solitons,” Opt. Lett. 33, 2551–2553 (2008).
    [CrossRef] [PubMed]
  19. M. I. Molina and Y. S. Kivshar, “Two-color surface solitons in two-dimensional quadratic photonic lattices,” J. Opt. Soc. Am. B 26, 1545–1548 (2009).
    [CrossRef]
  20. Z. Xu, M. I. Molina, and Y. S. Kivshar, “Interface solitons in quadratic nonlinear photonic lattices,” Phys. Rev. A 80, 013817 (2009).
    [CrossRef]
  21. Z. Xu, “Multipole-mode interface solitons in quadratic nonlinear photonic lattices,” Phys. Rev. A 80, 053827 (2009).
    [CrossRef]
  22. Z. Xu, “Two-color interface vortex solitons,” Phys. Rev. A 81, 023828 (2010).
    [CrossRef]
  23. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton control in chirped photonic lattices,” J. Opt. Soc. Am. B 22, 1356–1359 (2005).
    [CrossRef]
  24. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Dynamics of surface solitons at the edge of chirped optical lattices,” Phys. Rev. A 76, 013831 (2007).
    [CrossRef]
  25. M. I. Molina, Y. V. Kartashov, L. Torner, and Y. S. Kivshar, “Surface solitons in chirped photonic lattices,” Opt. Lett. 32, 2668–2670 (2007).
    [CrossRef] [PubMed]
  26. J. Xie, Y. He, and H. Wang, “Surface defect gap solitons in one-dimensional chirped optical lattices,” J. Opt. Soc. Am. B 27, 484–487 (2010).
    [CrossRef]
  27. G. Yin, J. Zheng, and L. Dong, “Spatial solitons in linearly and nonlinearly amplitude-modulated optical lattices,” Opt. Commun. 283, 583–590 (2010).
    [CrossRef]
  28. Z. Xu, Y. V. Kartashov, and L. Torner, “Soliton mobility in nonlocal optical lattices,” Phys. Rev. Lett. 95, 113901 (2005).
    [CrossRef] [PubMed]
  29. L. W. Dong and H. Wang, “Oscillatory behavior of spatial soliton in a gradient refractive index waveguide with nonlocal nonlinearity,” Appl. Phys. B 84, 465–469 (2006).
    [CrossRef]

2010 (3)

Z. Xu, “Two-color interface vortex solitons,” Phys. Rev. A 81, 023828 (2010).
[CrossRef]

J. Xie, Y. He, and H. Wang, “Surface defect gap solitons in one-dimensional chirped optical lattices,” J. Opt. Soc. Am. B 27, 484–487 (2010).
[CrossRef]

G. Yin, J. Zheng, and L. Dong, “Spatial solitons in linearly and nonlinearly amplitude-modulated optical lattices,” Opt. Commun. 283, 583–590 (2010).
[CrossRef]

2009 (3)

M. I. Molina and Y. S. Kivshar, “Two-color surface solitons in two-dimensional quadratic photonic lattices,” J. Opt. Soc. Am. B 26, 1545–1548 (2009).
[CrossRef]

Z. Xu, M. I. Molina, and Y. S. Kivshar, “Interface solitons in quadratic nonlinear photonic lattices,” Phys. Rev. A 80, 013817 (2009).
[CrossRef]

Z. Xu, “Multipole-mode interface solitons in quadratic nonlinear photonic lattices,” Phys. Rev. A 80, 053827 (2009).
[CrossRef]

2008 (2)

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]

Z. Xu and Y. S. Kivshar, “Two-color surface lattice solitons,” Opt. Lett. 33, 2551–2553 (2008).
[CrossRef] [PubMed]

2007 (3)

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Dynamics of surface solitons at the edge of chirped optical lattices,” Phys. Rev. A 76, 013831 (2007).
[CrossRef]

M. I. Molina, Y. V. Kartashov, L. Torner, and Y. S. Kivshar, “Surface solitons in chirped photonic lattices,” Opt. Lett. 32, 2668–2670 (2007).
[CrossRef] [PubMed]

H. Susanto, P. G. Kevrekidis, R. Carretero-González, B. A. Malomed, and D. J. Frantzeskakis, “Mobility of discrete solitons in quadratically nonlinear media,” Phys. Rev. Lett. 99, 214103 (2007).
[CrossRef]

2006 (2)

G. A. Siviloglou, K. G. Makris, R. Iwanow, R. Schiek, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, “Observation of discrete quadratic surface solitons,” Opt. Express 14, 5508–5516 (2006).
[CrossRef] [PubMed]

L. W. Dong and H. Wang, “Oscillatory behavior of spatial soliton in a gradient refractive index waveguide with nonlocal nonlinearity,” Appl. Phys. B 84, 465–469 (2006).
[CrossRef]

2005 (3)

Z. Xu, Y. V. Kartashov, and L. Torner, “Soliton mobility in nonlocal optical lattices,” Phys. Rev. Lett. 95, 113901 (2005).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton control in chirped photonic lattices,” J. Opt. Soc. Am. B 22, 1356–1359 (2005).
[CrossRef]

Z. Xu, Y. V. Kartashov, L.-C. Crasovan, D. Mihalache, and L. Torner, “Multicolor vortex solitons in two-dimensional photonic lattices,” Phys. Rev. E 71, 016616 (2005).
[CrossRef]

2004 (3)

2003 (1)

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

2002 (3)

A. V. Buryak, P. D. Trapani, D. V. Skryabin, and S. Trillo, “Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications,” Phys. Rep. 370, 63–235 (2002).
[CrossRef]

B. A. Malomed, P. G. Kevrekidis, D. J. Frantzeskakis, H. E. Nistazakis, and A. N. Yannacopoulos, “One-and two-dimensional solitons in second-harmonic-generating lattices,” Phys. Rev. E 65, 056606 (2002).
[CrossRef]

Y. V. Kartashov, G. Molina-Terriza, and L. Torner, “Multicolor soliton clusters,” J. Opt. Soc. Am. B 19, 2682–2691 (2002).
[CrossRef]

2001 (1)

L. Torner and G. I. Stegeman, “Multicolor solitons,” Opt. Photonics News 12, 36–39 (2001).
[CrossRef]

1996 (2)

G. I. Stegeman, D. J. Hagan, and L. Torner, “χ2 cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996).
[CrossRef]

R. Schiek, Y. Baek, and G. I. Stegeman, “One-dimensional spatial solitary waves due to cascaded second-order nonlinearities in planar waveguides,” Phys. Rev. E 53, 1138–1141 (1996).
[CrossRef]

1995 (1)

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[CrossRef] [PubMed]

1994 (1)

Agrawal, G. P.

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

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]

Baek, Y.

R. Schiek, Y. Baek, and G. I. Stegeman, “One-dimensional spatial solitary waves due to cascaded second-order nonlinearities in planar waveguides,” Phys. Rev. E 53, 1138–1141 (1996).
[CrossRef]

Buryak, A. V.

A. V. Buryak, P. D. Trapani, D. V. Skryabin, and S. Trillo, “Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications,” Phys. Rep. 370, 63–235 (2002).
[CrossRef]

A. V. Buryak and Y. S. Kivshar, “Spatial optical solitons governed by quadratic nonlinearity,” Opt. Lett. 19, 1612–1614 (1994).
[CrossRef] [PubMed]

Carretero-González, R.

H. Susanto, P. G. Kevrekidis, R. Carretero-González, B. A. Malomed, and D. J. Frantzeskakis, “Mobility of discrete solitons in quadratically nonlinear media,” Phys. Rev. Lett. 99, 214103 (2007).
[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]

G. A. Siviloglou, K. G. Makris, R. Iwanow, R. Schiek, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, “Observation of discrete quadratic surface solitons,” Opt. Express 14, 5508–5516 (2006).
[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, 147–150 (2003).
[CrossRef] [PubMed]

Crasovan, L. -C.

Z. Xu, Y. V. Kartashov, L.-C. Crasovan, D. Mihalache, and L. Torner, “Multicolor vortex solitons in two-dimensional photonic lattices,” Phys. Rev. E 71, 016616 (2005).
[CrossRef]

Dong, L.

G. Yin, J. Zheng, and L. Dong, “Spatial solitons in linearly and nonlinearly amplitude-modulated optical lattices,” Opt. Commun. 283, 583–590 (2010).
[CrossRef]

Dong, L. W.

L. W. Dong and H. Wang, “Oscillatory behavior of spatial soliton in a gradient refractive index waveguide with nonlocal nonlinearity,” Appl. Phys. B 84, 465–469 (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, 147–150 (2003).
[CrossRef] [PubMed]

Egorov, A. A.

Y. V. Kartashov, A. A. Egorov, A. S. Zelenina, V. A. Vysloukh, and L. Torner, “Stable multicolor periodic-wave arrays,” Phys. Rev. Lett. 92, 033901 (2004).
[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, 147–150 (2003).
[CrossRef] [PubMed]

Frantzeskakis, D. J.

H. Susanto, P. G. Kevrekidis, R. Carretero-González, B. A. Malomed, and D. J. Frantzeskakis, “Mobility of discrete solitons in quadratically nonlinear media,” Phys. Rev. Lett. 99, 214103 (2007).
[CrossRef]

B. A. Malomed, P. G. Kevrekidis, D. J. Frantzeskakis, H. E. Nistazakis, and A. N. Yannacopoulos, “One-and two-dimensional solitons in second-harmonic-generating lattices,” Phys. Rev. E 65, 056606 (2002).
[CrossRef]

Hagan, D. J.

G. I. Stegeman, D. J. Hagan, and L. Torner, “χ2 cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996).
[CrossRef]

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[CrossRef] [PubMed]

He, Y.

Iwanow, R.

Kartashov, Y. V.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Dynamics of surface solitons at the edge of chirped optical lattices,” Phys. Rev. A 76, 013831 (2007).
[CrossRef]

M. I. Molina, Y. V. Kartashov, L. Torner, and Y. S. Kivshar, “Surface solitons in chirped photonic lattices,” Opt. Lett. 32, 2668–2670 (2007).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton control in chirped photonic lattices,” J. Opt. Soc. Am. B 22, 1356–1359 (2005).
[CrossRef]

Z. Xu, Y. V. Kartashov, and L. Torner, “Soliton mobility in nonlocal optical lattices,” Phys. Rev. Lett. 95, 113901 (2005).
[CrossRef] [PubMed]

Z. Xu, Y. V. Kartashov, L.-C. Crasovan, D. Mihalache, and L. Torner, “Multicolor vortex solitons in two-dimensional photonic lattices,” Phys. Rev. E 71, 016616 (2005).
[CrossRef]

Y. V. Kartashov, L. Torner, and V. A. Vysloukh, “Multicolor lattice solitons,” Opt. Lett. 29, 1117–1119 (2004).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Packing, unpacking, and steering of multicolor solitons in optical lattices,” Opt. Lett. 29, 1399–1401 (2004).
[CrossRef] [PubMed]

Y. V. Kartashov, A. A. Egorov, A. S. Zelenina, V. A. Vysloukh, and L. Torner, “Stable multicolor periodic-wave arrays,” Phys. Rev. Lett. 92, 033901 (2004).
[CrossRef] [PubMed]

Y. V. Kartashov, G. Molina-Terriza, and L. Torner, “Multicolor soliton clusters,” J. Opt. Soc. Am. B 19, 2682–2691 (2002).
[CrossRef]

Kevrekidis, P. G.

H. Susanto, P. G. Kevrekidis, R. Carretero-González, B. A. Malomed, and D. J. Frantzeskakis, “Mobility of discrete solitons in quadratically nonlinear media,” Phys. Rev. Lett. 99, 214103 (2007).
[CrossRef]

B. A. Malomed, P. G. Kevrekidis, D. J. Frantzeskakis, H. E. Nistazakis, and A. N. Yannacopoulos, “One-and two-dimensional solitons in second-harmonic-generating lattices,” Phys. Rev. E 65, 056606 (2002).
[CrossRef]

Kivshar, Y. S.

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]

Makris, K. G.

Malomed, B. A.

H. Susanto, P. G. Kevrekidis, R. Carretero-González, B. A. Malomed, and D. J. Frantzeskakis, “Mobility of discrete solitons in quadratically nonlinear media,” Phys. Rev. Lett. 99, 214103 (2007).
[CrossRef]

B. A. Malomed, P. G. Kevrekidis, D. J. Frantzeskakis, H. E. Nistazakis, and A. N. Yannacopoulos, “One-and two-dimensional solitons in second-harmonic-generating lattices,” Phys. Rev. E 65, 056606 (2002).
[CrossRef]

Menyuk, C. R.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[CrossRef] [PubMed]

Mihalache, D.

Z. Xu, Y. V. Kartashov, L.-C. Crasovan, D. Mihalache, and L. Torner, “Multicolor vortex solitons in two-dimensional photonic lattices,” Phys. Rev. E 71, 016616 (2005).
[CrossRef]

Min, Y.

Molina, M. I.

Molina-Terriza, G.

Nistazakis, H. E.

B. A. Malomed, P. G. Kevrekidis, D. J. Frantzeskakis, H. E. Nistazakis, and A. N. Yannacopoulos, “One-and two-dimensional solitons in second-harmonic-generating lattices,” Phys. Rev. E 65, 056606 (2002).
[CrossRef]

Schiek, R.

G. A. Siviloglou, K. G. Makris, R. Iwanow, R. Schiek, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, “Observation of discrete quadratic surface solitons,” Opt. Express 14, 5508–5516 (2006).
[CrossRef] [PubMed]

R. Schiek, Y. Baek, and G. I. Stegeman, “One-dimensional spatial solitary waves due to cascaded second-order nonlinearities in planar waveguides,” Phys. Rev. E 53, 1138–1141 (1996).
[CrossRef]

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]

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

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]

Siviloglou, G. A.

Skryabin, D. V.

A. V. Buryak, P. D. Trapani, D. V. Skryabin, and S. Trillo, “Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications,” Phys. Rep. 370, 63–235 (2002).
[CrossRef]

Sohler, W.

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]

G. A. Siviloglou, K. G. Makris, R. Iwanow, R. Schiek, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, “Observation of discrete quadratic surface solitons,” Opt. Express 14, 5508–5516 (2006).
[CrossRef] [PubMed]

L. Torner and G. I. Stegeman, “Multicolor solitons,” Opt. Photonics News 12, 36–39 (2001).
[CrossRef]

R. Schiek, Y. Baek, and G. I. Stegeman, “One-dimensional spatial solitary waves due to cascaded second-order nonlinearities in planar waveguides,” Phys. Rev. E 53, 1138–1141 (1996).
[CrossRef]

G. I. Stegeman, D. J. Hagan, and L. Torner, “χ2 cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996).
[CrossRef]

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[CrossRef] [PubMed]

Susanto, H.

H. Susanto, P. G. Kevrekidis, R. Carretero-González, B. A. Malomed, and D. J. Frantzeskakis, “Mobility of discrete solitons in quadratically nonlinear media,” Phys. Rev. Lett. 99, 214103 (2007).
[CrossRef]

Torner, L.

M. I. Molina, Y. V. Kartashov, L. Torner, and Y. S. Kivshar, “Surface solitons in chirped photonic lattices,” Opt. Lett. 32, 2668–2670 (2007).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Dynamics of surface solitons at the edge of chirped optical lattices,” Phys. Rev. A 76, 013831 (2007).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton control in chirped photonic lattices,” J. Opt. Soc. Am. B 22, 1356–1359 (2005).
[CrossRef]

Z. Xu, Y. V. Kartashov, and L. Torner, “Soliton mobility in nonlocal optical lattices,” Phys. Rev. Lett. 95, 113901 (2005).
[CrossRef] [PubMed]

Z. Xu, Y. V. Kartashov, L.-C. Crasovan, D. Mihalache, and L. Torner, “Multicolor vortex solitons in two-dimensional photonic lattices,” Phys. Rev. E 71, 016616 (2005).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Packing, unpacking, and steering of multicolor solitons in optical lattices,” Opt. Lett. 29, 1399–1401 (2004).
[CrossRef] [PubMed]

Y. V. Kartashov, L. Torner, and V. A. Vysloukh, “Multicolor lattice solitons,” Opt. Lett. 29, 1117–1119 (2004).
[CrossRef] [PubMed]

Y. V. Kartashov, A. A. Egorov, A. S. Zelenina, V. A. Vysloukh, and L. Torner, “Stable multicolor periodic-wave arrays,” Phys. Rev. Lett. 92, 033901 (2004).
[CrossRef] [PubMed]

Y. V. Kartashov, G. Molina-Terriza, and L. Torner, “Multicolor soliton clusters,” J. Opt. Soc. Am. B 19, 2682–2691 (2002).
[CrossRef]

L. Torner and G. I. Stegeman, “Multicolor solitons,” Opt. Photonics News 12, 36–39 (2001).
[CrossRef]

G. I. Stegeman, D. J. Hagan, and L. Torner, “χ2 cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996).
[CrossRef]

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[CrossRef] [PubMed]

Torruellas, W. E.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[CrossRef] [PubMed]

Trapani, P. D.

A. V. Buryak, P. D. Trapani, D. V. Skryabin, and S. Trillo, “Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications,” Phys. Rep. 370, 63–235 (2002).
[CrossRef]

Trillo, S.

A. V. Buryak, P. D. Trapani, D. V. Skryabin, and S. Trillo, “Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications,” Phys. Rep. 370, 63–235 (2002).
[CrossRef]

VanStryland, E. W.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[CrossRef] [PubMed]

Vysloukh, V. A.

Wang, H.

J. Xie, Y. He, and H. Wang, “Surface defect gap solitons in one-dimensional chirped optical lattices,” J. Opt. Soc. Am. B 27, 484–487 (2010).
[CrossRef]

L. W. Dong and H. Wang, “Oscillatory behavior of spatial soliton in a gradient refractive index waveguide with nonlocal nonlinearity,” Appl. Phys. B 84, 465–469 (2006).
[CrossRef]

Wang, Z.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[CrossRef] [PubMed]

Xie, J.

Xu, Z.

Z. Xu, “Two-color interface vortex solitons,” Phys. Rev. A 81, 023828 (2010).
[CrossRef]

Z. Xu, “Multipole-mode interface solitons in quadratic nonlinear photonic lattices,” Phys. Rev. A 80, 053827 (2009).
[CrossRef]

Z. Xu, M. I. Molina, and Y. S. Kivshar, “Interface solitons in quadratic nonlinear photonic lattices,” Phys. Rev. A 80, 013817 (2009).
[CrossRef]

Z. Xu and Y. S. Kivshar, “Two-color surface lattice solitons,” Opt. Lett. 33, 2551–2553 (2008).
[CrossRef] [PubMed]

Z. Xu, Y. V. Kartashov, L.-C. Crasovan, D. Mihalache, and L. Torner, “Multicolor vortex solitons in two-dimensional photonic lattices,” Phys. Rev. E 71, 016616 (2005).
[CrossRef]

Z. Xu, Y. V. Kartashov, and L. Torner, “Soliton mobility in nonlocal optical lattices,” Phys. Rev. Lett. 95, 113901 (2005).
[CrossRef] [PubMed]

Yannacopoulos, A. N.

B. A. Malomed, P. G. Kevrekidis, D. J. Frantzeskakis, H. E. Nistazakis, and A. N. Yannacopoulos, “One-and two-dimensional solitons in second-harmonic-generating lattices,” Phys. Rev. E 65, 056606 (2002).
[CrossRef]

Yin, G.

G. Yin, J. Zheng, and L. Dong, “Spatial solitons in linearly and nonlinearly amplitude-modulated optical lattices,” Opt. Commun. 283, 583–590 (2010).
[CrossRef]

Zelenina, A. S.

Y. V. Kartashov, A. A. Egorov, A. S. Zelenina, V. A. Vysloukh, and L. Torner, “Stable multicolor periodic-wave arrays,” Phys. Rev. Lett. 92, 033901 (2004).
[CrossRef] [PubMed]

Zheng, J.

G. Yin, J. Zheng, and L. Dong, “Spatial solitons in linearly and nonlinearly amplitude-modulated optical lattices,” Opt. Commun. 283, 583–590 (2010).
[CrossRef]

Appl. Phys. B (1)

L. W. Dong and H. Wang, “Oscillatory behavior of spatial soliton in a gradient refractive index waveguide with nonlocal nonlinearity,” Appl. Phys. B 84, 465–469 (2006).
[CrossRef]

J. Opt. Soc. Am. B (4)

Nature (1)

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

Opt. Commun. (1)

G. Yin, J. Zheng, and L. Dong, “Spatial solitons in linearly and nonlinearly amplitude-modulated optical lattices,” Opt. Commun. 283, 583–590 (2010).
[CrossRef]

Opt. Express (1)

Opt. Lett. (5)

Opt. Photonics News (1)

L. Torner and G. I. Stegeman, “Multicolor solitons,” Opt. Photonics News 12, 36–39 (2001).
[CrossRef]

Opt. Quantum Electron. (1)

G. I. Stegeman, D. J. Hagan, and L. Torner, “χ2 cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996).
[CrossRef]

Phys. Rep. (2)

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]

A. V. Buryak, P. D. Trapani, D. V. Skryabin, and S. Trillo, “Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications,” Phys. Rep. 370, 63–235 (2002).
[CrossRef]

Phys. Rev. A (4)

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Dynamics of surface solitons at the edge of chirped optical lattices,” Phys. Rev. A 76, 013831 (2007).
[CrossRef]

Z. Xu, M. I. Molina, and Y. S. Kivshar, “Interface solitons in quadratic nonlinear photonic lattices,” Phys. Rev. A 80, 013817 (2009).
[CrossRef]

Z. Xu, “Multipole-mode interface solitons in quadratic nonlinear photonic lattices,” Phys. Rev. A 80, 053827 (2009).
[CrossRef]

Z. Xu, “Two-color interface vortex solitons,” Phys. Rev. A 81, 023828 (2010).
[CrossRef]

Phys. Rev. E (3)

Z. Xu, Y. V. Kartashov, L.-C. Crasovan, D. Mihalache, and L. Torner, “Multicolor vortex solitons in two-dimensional photonic lattices,” Phys. Rev. E 71, 016616 (2005).
[CrossRef]

R. Schiek, Y. Baek, and G. I. Stegeman, “One-dimensional spatial solitary waves due to cascaded second-order nonlinearities in planar waveguides,” Phys. Rev. E 53, 1138–1141 (1996).
[CrossRef]

B. A. Malomed, P. G. Kevrekidis, D. J. Frantzeskakis, H. E. Nistazakis, and A. N. Yannacopoulos, “One-and two-dimensional solitons in second-harmonic-generating lattices,” Phys. Rev. E 65, 056606 (2002).
[CrossRef]

Phys. Rev. Lett. (4)

Y. V. Kartashov, A. A. Egorov, A. S. Zelenina, V. A. Vysloukh, and L. Torner, “Stable multicolor periodic-wave arrays,” Phys. Rev. Lett. 92, 033901 (2004).
[CrossRef] [PubMed]

H. Susanto, P. G. Kevrekidis, R. Carretero-González, B. A. Malomed, and D. J. Frantzeskakis, “Mobility of discrete solitons in quadratically nonlinear media,” Phys. Rev. Lett. 99, 214103 (2007).
[CrossRef]

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[CrossRef] [PubMed]

Z. Xu, Y. V. Kartashov, and L. Torner, “Soliton mobility in nonlocal optical lattices,” Phys. Rev. Lett. 95, 113901 (2005).
[CrossRef] [PubMed]

Other (1)

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

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Figures (6)

Fig. 1
Fig. 1

Profiles of (a) odd and (b) even solitons at b 1 = 1.3 , α = 0.1 . (c) Profiles of odd solitons at different chirp rates α, b 1 = 0.9 , and only the SH wave is shown. (d) Chirped three-peak solitons at b 1 = 1.4 , α = 0.1 . (e) Energy flow versus propagation constant for chirped odd and even solitons at α = 0.08 . (f) Lower propagation constant cutoffs of chirped odd and even solitons versus α. In all cases p = 2 , β = 0 .

Fig. 2
Fig. 2

Instability growth rate of the (a) odd solitons and (b) multi-peak solitons at α = 0.08 . (c) Lower cutoff of odd and even solitons versus lattice depth at α = 0.1 . (d) Unstable propagation of an even soliton at α = 0.08 , b 1 = 1.4 . Here, β = 0 , p = 2 .

Fig. 3
Fig. 3

(a) Power versus propagation constant of odd solitons at different phase mismatches, α = 0.08 . (b) Lower cutoff versus phase mismatch at α = 0.1 . (c) Lower cutoff of even solitons versus chirp rate at different phase mismatches. Perturbation growth rate of (d) even and (e) odd solitons. α = 0.08 in (d) and β = 1.2 in (e). (f) Critical chirp rate α c r for odd solitons versus phase mismatch. p = 2 in (a)–(f).

Fig. 4
Fig. 4

(a) Power versus propagation constant for different order twisted solitons; dashed lines denote the unstable branches. Profiles of the (b) first, (c) second, and (d) third twisted solitons marked by circles in (a). Stable propagation of the (e) first and (f) third twisted solitons shown in (b) and (d); white noises were added into the initial inputs, and only the SH waves are displayed. p = 2 , α = 0.08 . β = 0 in (a)–(f).

Fig. 5
Fig. 5

(a) Power versus propagation constant of the first twisted solitons at different phase mismatches. (b) Lower cutoff of the first twisted solitons versus phase mismatch. (c) Perturbation growth rate of different order twisted solitons at β = 1.2 . (d) Instability area (shaded) of the first twisted solitons on the ( b 1 , p ) plane at β = 0 , α = 0.1 . (e) Stable and (f) unstable propagation of the first twisted solitons marked by circles in (c). p = 2 , α = 0.08 in (a)–(c) and β = 1.2 , α = 0.08 in (e) and (f).

Fig. 6
Fig. 6

(a) Excitation of the second twisted soliton. (b) Real and imaginary parts of the FF wave field at z = 256 . Unpacking of the third twisted solitons at U = 56 in (c) unchirped lattice and (d) chirped lattice with α = 0.3 . Periodic oscillations of an odd soliton at α = 0.05 (e) and 0.2 (f), only FF waves are illustrated. α = 0.1 in (a) and (b), and T = π / 7 , b 1 = 2 , ϕ = 0.3 , U = 26 in (e) and (f). p = 4 , β = 0 in (a)–(f).

Equations (8)

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i q 1 z = d 1 2 2 q 1 x 2 q 1 q 2   exp ( i β z ) p R ( x ) q 1 ,
i q 2 z = d 2 2 2 q 2 x 2 q 1 2   exp ( i β z ) 2 p R ( x ) q 2 ,
d 1 2 d 2 w 1 d x 2 w 1 w 2 + b 1 w 1 p R ( x ) w 1 = 0 ,
d 2 2 d 2 w 2 d x 2 w 1 2 + b 2 w 2 2 p R ( x ) w 2 = 0.
λ u 1 = d 1 2 d 2 v 1 d x 2 ( w 1 v 2 w 2 v 1 ) p R ( x ) v 1 + b 1 v 1 ,
λ v 1 = d 1 2 d 2 u 1 d x 2 + ( w 1 u 2 + w 2 u 1 ) + p R ( x ) u 1 b 1 u 1 ,
λ u 2 = d 2 2 d 2 v 2 d x 2 2 w 1 v 1 2 p R ( x ) v 2 + b 2 v 2 ,
λ v 2 = d 2 2 d 2 u 2 d x 2 + 2 w 1 u 1 + 2 p R ( x ) u 2 b 2 u 2 ,

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