Abstract

We consider a degenerate optical parametric oscillator containing a left-handed material. We show that the inclusion of a left-handed material layer allows for controlling the strength and sign of the diffraction coefficient at either the pump or the signal frequency. Subsequently, we demonstrate the existence of stable dissipative structures without diffraction matching, i.e., without the usual relationship between the diffraction coefficients of the signal and pump fields. Finally, we investigate the size scaling of these light structures with decreasing diffraction strength.

©2009 Optical Society of America

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References

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  1. C. L. Tang and L. K. Cheng, “Fundamentals of Optical Parametric Processes and Oscillators,” vol. 20 of Laser Science and Technology Series (Harwood Academic Publishers GmbH, Amsterdam, 1995).
  2. M. Ebrahim-Zadeh and I. T. Sorokina, “Mid-Infrared Coherent Sources and Applications,” (Springer, Dordrecht, 2008).
  3. G.-L. Oppo, M. Brambilla, and L. A. Lugiato, “Formation and evolution of roll patterns in optical parametric oscillators,” Phys. Rev. A 49, 2028–2032 (1994).
    [Crossref] [PubMed]
  4. M. Tlidi, P. Mandel, and M. Haelterman, “Spatiotemporal patterns and localized structures in nonlinear optics,” Phys. Rev. E 22, 970–972 (1997).
  5. D. V. Skryabin and W. J. Firth, “Interaction of cavity solitons in degenerate optical parametric oscillators,” Opt. Lett. 24, 1056–1058 (1999).
    [Crossref]
  6. M. Tlidi, P. Mandel, and R. Lefever, “Kinetics of Localized Pattern Formation in Optical Systems,” Phys. Rev. Lett. 81, 979–982 (1998).
    [Crossref]
  7. S. Trillo, M. Haelterman, and A. Sheppard, “Stable topological spatial solitons in optical parametric oscillators,” Opt. Lett. 22, 970–972 (1997).
    [Crossref] [PubMed]
  8. K. Staliunas and V. J. Sanchez-Morcillo, “Dynamics of Domains in Swift-Hohenberg Equation,” Phys. Lett. A 241, 28 (1998).
    [Crossref]
  9. M. Le Berre, D. Leduc, E. Ressayre, and A. Tallet, “Striped and circular domain walls in the DOPO,” Quantum Semiclassic. Opt. 1, 107 (1999).
  10. G. L. Oppo, A. J. Scroggie, and W. J. Firth, “From domain walls to localized structures in degenerate optical parametric oscillators,” Quantum Semiclass. Opt. 1, 133 (1999).
    [Crossref]
  11. M. Tlidi, M. Le Berre, E. Ressayre, A. Tallet, and L. Di Menza, “High-intensity localized structures in the degenerate optical parametric oscillator,” Phys. Rev. A 61, 043806 (2000).
    [Crossref]
  12. D. Gomila, P. Colet, G. L. Oppo, and M. San Miguel, “Stable Droplets and Growth Laws Close to the Modulational Instability of a Domain Wall,” Phys. Rev. Lett. 87, 194101 (2001).
    [Crossref] [PubMed]
  13. A. V. Buryak, P. Di Trapani, D. V. Skryabin, and S. Trillo, “Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications,” Phys. Rep. 370, 63 (2002).
    [Crossref]
  14. K. Staliunas and V. J. Sanchez-Morcillo, Transverse Patterns in Nonlinear Optical Resonators, vol. 183 of Springer Tracts in Modern Physics (Springer-Verlag, Berlin, 2003).
  15. P. Mandel and M. Tlidi, “Transverse dynamics in cavity nonlinear optics (2000 2003),” J. Opt. Soc. Am. B 6, R60 (2004).
  16. M. Tlidi, T. Kolokolnikov, and M. Taki, Focus Issue “Dissipative Localized Structures in Extended Systems,” Chaos,  17, Issue 3 (2007).
    [Crossref] [PubMed]
  17. N. Akhmediev and A. Ankiewicz, “Dissipative Solitons: From Optics to Biology and Medicine” (Springer-Verlag, Berlin, Heidelberg, 2008).
  18. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509–514 (1968).
    [Crossref]
  19. J. B. Pendry, “Negative Refraction Makes a Perfect Lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
    [Crossref] [PubMed]
  20. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental Verification of a Negative Index of Refraction,” Science 292, 77–79 (2001).
    [Crossref] [PubMed]
  21. K. Aydin, K. Guven, M. Kafesaki, L. Zhang, C. M. Soukoulis, and E. Ozbay, “Experimental observation of true left-handed transmission peaks in metamaterials,” Opt. Lett. 29, 2623–2625 (2004).
    [Crossref] [PubMed]
  22. C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic Metamaterials at Telecommunication and Visible Frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
    [Crossref] [PubMed]
  23. T. F. Gundogdu, I. Tsiapa, A. Kostopoulos, G. Konstantinidis, N. Katsarakis, R. S. Penciu, M. Kafesaki, E. N. Economou, T. Koschny, and C. M. Soukoulis, “Experimental demonstration of negative magnetic permeability in the far-infrared frequency regime,” Appl. Phys. Lett. 89, 084103 (2006).
    [Crossref]
  24. D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and Negative Refractive Index,” Science 305, 788–792 (2004).
    [Crossref] [PubMed]
  25. M. W. Feise, I. V. Shadrivov, and Y. S. Kivshar, “Bistable diode action in left-handed periodic structures,” Phys. Rev. E 71, 037602 (2005).
    [Crossref]
  26. A. A. Zharov, N. A. Zharova, I. V. Shadrivov, and Y. S. Kivshar, “Subwavelength imaging with opaque nonlinear left-handed lenses,” Appl. Phys. Lett. 87, 091104 (2005).
    [Crossref]
  27. N. Lazarides and G. P. Tsironis, “Coupled nonlinear Schrödinger field equations for electromagnetic wave propagation in nonlinear left-handed materials,” Phys. Rev. E 71, 036614 (2005).
    [Crossref]
  28. G. D’Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, “Bright and Dark Gap Solitons in a Negative Index Fabry-Pérot Etalon,” Phys. Rev. Lett. 93, 213902 (2004).
    [Crossref] [PubMed]
  29. M. Scalora, M. S. Syrchin, N. Akozbek, E. Y. Poliakov, G. D’Aguanno, N. Mattiucci, M. J. Bloemer, and A. M. Zheltikov, “Generalized Nonlinear Schrödinger Equation for Dispersive Susceptibility and Permeability: Application to Negative Index Materials,” Phys. Rev. Lett. 95, 013902 (2005).
    [Crossref] [PubMed]
  30. P. Kockaert, P. Tassin, G. Van der Sande, I. Veretennicoff, and M. Tlidi, “Negative diffraction pattern dynamics in nonlinear cavities with left-handed materials,” Phys. Rev. A 74, 033822 (2006).
    [Crossref]
  31. P. Tassin, G. Van der Sande, N. Veretenov, P. Kockaert, I. Veretennicoff, and M. Tlidi, “Three-dimensional structures in nonlinear cavities containing left-handed materials,” Opt. Express 14, 9338–9343 (2006).
    [Crossref] [PubMed]
  32. P. Tassin, L. Gelens, J. Danckaert, I. Veretennicoff, G. Van der Sande, P. Kockaert, and M. Tlidi, “Dissipative structures in left-handed material cavity optics,” Chaos 17, 037116 (2007).
    [Crossref] [PubMed]
  33. L. Gelens, G. Van der Sande, P. Tassin, M. Tlidi, P. Kockaert, D. Gomila, I. Veretennicoff, and J. Danckaert, “Impact of nonlocal interactions in dissipative systems,” Phys. Rev. A 75, 063812 (2007).
    [Crossref]
  34. A. D. Boardman, N. King, R. C. Mitchell-Thomas, V. N. Malnev, and Y. G Rapoport, “Gain control and diffraction-managed solitons in metamaterials,” Metamaterials 2, 145–154 (2008).
    [Crossref]

2008 (1)

A. D. Boardman, N. King, R. C. Mitchell-Thomas, V. N. Malnev, and Y. G Rapoport, “Gain control and diffraction-managed solitons in metamaterials,” Metamaterials 2, 145–154 (2008).
[Crossref]

2007 (3)

P. Tassin, L. Gelens, J. Danckaert, I. Veretennicoff, G. Van der Sande, P. Kockaert, and M. Tlidi, “Dissipative structures in left-handed material cavity optics,” Chaos 17, 037116 (2007).
[Crossref] [PubMed]

L. Gelens, G. Van der Sande, P. Tassin, M. Tlidi, P. Kockaert, D. Gomila, I. Veretennicoff, and J. Danckaert, “Impact of nonlocal interactions in dissipative systems,” Phys. Rev. A 75, 063812 (2007).
[Crossref]

M. Tlidi, T. Kolokolnikov, and M. Taki, Focus Issue “Dissipative Localized Structures in Extended Systems,” Chaos,  17, Issue 3 (2007).
[Crossref] [PubMed]

2006 (3)

T. F. Gundogdu, I. Tsiapa, A. Kostopoulos, G. Konstantinidis, N. Katsarakis, R. S. Penciu, M. Kafesaki, E. N. Economou, T. Koschny, and C. M. Soukoulis, “Experimental demonstration of negative magnetic permeability in the far-infrared frequency regime,” Appl. Phys. Lett. 89, 084103 (2006).
[Crossref]

P. Kockaert, P. Tassin, G. Van der Sande, I. Veretennicoff, and M. Tlidi, “Negative diffraction pattern dynamics in nonlinear cavities with left-handed materials,” Phys. Rev. A 74, 033822 (2006).
[Crossref]

P. Tassin, G. Van der Sande, N. Veretenov, P. Kockaert, I. Veretennicoff, and M. Tlidi, “Three-dimensional structures in nonlinear cavities containing left-handed materials,” Opt. Express 14, 9338–9343 (2006).
[Crossref] [PubMed]

2005 (5)

M. Scalora, M. S. Syrchin, N. Akozbek, E. Y. Poliakov, G. D’Aguanno, N. Mattiucci, M. J. Bloemer, and A. M. Zheltikov, “Generalized Nonlinear Schrödinger Equation for Dispersive Susceptibility and Permeability: Application to Negative Index Materials,” Phys. Rev. Lett. 95, 013902 (2005).
[Crossref] [PubMed]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic Metamaterials at Telecommunication and Visible Frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[Crossref] [PubMed]

M. W. Feise, I. V. Shadrivov, and Y. S. Kivshar, “Bistable diode action in left-handed periodic structures,” Phys. Rev. E 71, 037602 (2005).
[Crossref]

A. A. Zharov, N. A. Zharova, I. V. Shadrivov, and Y. S. Kivshar, “Subwavelength imaging with opaque nonlinear left-handed lenses,” Appl. Phys. Lett. 87, 091104 (2005).
[Crossref]

N. Lazarides and G. P. Tsironis, “Coupled nonlinear Schrödinger field equations for electromagnetic wave propagation in nonlinear left-handed materials,” Phys. Rev. E 71, 036614 (2005).
[Crossref]

2004 (4)

G. D’Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, “Bright and Dark Gap Solitons in a Negative Index Fabry-Pérot Etalon,” Phys. Rev. Lett. 93, 213902 (2004).
[Crossref] [PubMed]

P. Mandel and M. Tlidi, “Transverse dynamics in cavity nonlinear optics (2000 2003),” J. Opt. Soc. Am. B 6, R60 (2004).

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and Negative Refractive Index,” Science 305, 788–792 (2004).
[Crossref] [PubMed]

K. Aydin, K. Guven, M. Kafesaki, L. Zhang, C. M. Soukoulis, and E. Ozbay, “Experimental observation of true left-handed transmission peaks in metamaterials,” Opt. Lett. 29, 2623–2625 (2004).
[Crossref] [PubMed]

2002 (1)

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

2001 (2)

D. Gomila, P. Colet, G. L. Oppo, and M. San Miguel, “Stable Droplets and Growth Laws Close to the Modulational Instability of a Domain Wall,” Phys. Rev. Lett. 87, 194101 (2001).
[Crossref] [PubMed]

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental Verification of a Negative Index of Refraction,” Science 292, 77–79 (2001).
[Crossref] [PubMed]

2000 (2)

J. B. Pendry, “Negative Refraction Makes a Perfect Lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[Crossref] [PubMed]

M. Tlidi, M. Le Berre, E. Ressayre, A. Tallet, and L. Di Menza, “High-intensity localized structures in the degenerate optical parametric oscillator,” Phys. Rev. A 61, 043806 (2000).
[Crossref]

1999 (3)

M. Le Berre, D. Leduc, E. Ressayre, and A. Tallet, “Striped and circular domain walls in the DOPO,” Quantum Semiclassic. Opt. 1, 107 (1999).

G. L. Oppo, A. J. Scroggie, and W. J. Firth, “From domain walls to localized structures in degenerate optical parametric oscillators,” Quantum Semiclass. Opt. 1, 133 (1999).
[Crossref]

D. V. Skryabin and W. J. Firth, “Interaction of cavity solitons in degenerate optical parametric oscillators,” Opt. Lett. 24, 1056–1058 (1999).
[Crossref]

1998 (2)

M. Tlidi, P. Mandel, and R. Lefever, “Kinetics of Localized Pattern Formation in Optical Systems,” Phys. Rev. Lett. 81, 979–982 (1998).
[Crossref]

K. Staliunas and V. J. Sanchez-Morcillo, “Dynamics of Domains in Swift-Hohenberg Equation,” Phys. Lett. A 241, 28 (1998).
[Crossref]

1997 (2)

S. Trillo, M. Haelterman, and A. Sheppard, “Stable topological spatial solitons in optical parametric oscillators,” Opt. Lett. 22, 970–972 (1997).
[Crossref] [PubMed]

M. Tlidi, P. Mandel, and M. Haelterman, “Spatiotemporal patterns and localized structures in nonlinear optics,” Phys. Rev. E 22, 970–972 (1997).

1994 (1)

G.-L. Oppo, M. Brambilla, and L. A. Lugiato, “Formation and evolution of roll patterns in optical parametric oscillators,” Phys. Rev. A 49, 2028–2032 (1994).
[Crossref] [PubMed]

1968 (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509–514 (1968).
[Crossref]

Akhmediev, N.

N. Akhmediev and A. Ankiewicz, “Dissipative Solitons: From Optics to Biology and Medicine” (Springer-Verlag, Berlin, Heidelberg, 2008).

Akozbek, N.

M. Scalora, M. S. Syrchin, N. Akozbek, E. Y. Poliakov, G. D’Aguanno, N. Mattiucci, M. J. Bloemer, and A. M. Zheltikov, “Generalized Nonlinear Schrödinger Equation for Dispersive Susceptibility and Permeability: Application to Negative Index Materials,” Phys. Rev. Lett. 95, 013902 (2005).
[Crossref] [PubMed]

Ankiewicz, A.

N. Akhmediev and A. Ankiewicz, “Dissipative Solitons: From Optics to Biology and Medicine” (Springer-Verlag, Berlin, Heidelberg, 2008).

Aydin, K.

Bloemer, M. J.

M. Scalora, M. S. Syrchin, N. Akozbek, E. Y. Poliakov, G. D’Aguanno, N. Mattiucci, M. J. Bloemer, and A. M. Zheltikov, “Generalized Nonlinear Schrödinger Equation for Dispersive Susceptibility and Permeability: Application to Negative Index Materials,” Phys. Rev. Lett. 95, 013902 (2005).
[Crossref] [PubMed]

G. D’Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, “Bright and Dark Gap Solitons in a Negative Index Fabry-Pérot Etalon,” Phys. Rev. Lett. 93, 213902 (2004).
[Crossref] [PubMed]

Boardman, A. D.

A. D. Boardman, N. King, R. C. Mitchell-Thomas, V. N. Malnev, and Y. G Rapoport, “Gain control and diffraction-managed solitons in metamaterials,” Metamaterials 2, 145–154 (2008).
[Crossref]

Brambilla, M.

G.-L. Oppo, M. Brambilla, and L. A. Lugiato, “Formation and evolution of roll patterns in optical parametric oscillators,” Phys. Rev. A 49, 2028–2032 (1994).
[Crossref] [PubMed]

Burger, S.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic Metamaterials at Telecommunication and Visible Frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[Crossref] [PubMed]

Buryak, A. V.

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

Cheng, L. K.

C. L. Tang and L. K. Cheng, “Fundamentals of Optical Parametric Processes and Oscillators,” vol. 20 of Laser Science and Technology Series (Harwood Academic Publishers GmbH, Amsterdam, 1995).

Colet, P.

D. Gomila, P. Colet, G. L. Oppo, and M. San Miguel, “Stable Droplets and Growth Laws Close to the Modulational Instability of a Domain Wall,” Phys. Rev. Lett. 87, 194101 (2001).
[Crossref] [PubMed]

D’Aguanno, G.

M. Scalora, M. S. Syrchin, N. Akozbek, E. Y. Poliakov, G. D’Aguanno, N. Mattiucci, M. J. Bloemer, and A. M. Zheltikov, “Generalized Nonlinear Schrödinger Equation for Dispersive Susceptibility and Permeability: Application to Negative Index Materials,” Phys. Rev. Lett. 95, 013902 (2005).
[Crossref] [PubMed]

G. D’Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, “Bright and Dark Gap Solitons in a Negative Index Fabry-Pérot Etalon,” Phys. Rev. Lett. 93, 213902 (2004).
[Crossref] [PubMed]

Danckaert, J.

P. Tassin, L. Gelens, J. Danckaert, I. Veretennicoff, G. Van der Sande, P. Kockaert, and M. Tlidi, “Dissipative structures in left-handed material cavity optics,” Chaos 17, 037116 (2007).
[Crossref] [PubMed]

L. Gelens, G. Van der Sande, P. Tassin, M. Tlidi, P. Kockaert, D. Gomila, I. Veretennicoff, and J. Danckaert, “Impact of nonlocal interactions in dissipative systems,” Phys. Rev. A 75, 063812 (2007).
[Crossref]

Ebrahim-Zadeh, M.

M. Ebrahim-Zadeh and I. T. Sorokina, “Mid-Infrared Coherent Sources and Applications,” (Springer, Dordrecht, 2008).

Economou, E. N.

T. F. Gundogdu, I. Tsiapa, A. Kostopoulos, G. Konstantinidis, N. Katsarakis, R. S. Penciu, M. Kafesaki, E. N. Economou, T. Koschny, and C. M. Soukoulis, “Experimental demonstration of negative magnetic permeability in the far-infrared frequency regime,” Appl. Phys. Lett. 89, 084103 (2006).
[Crossref]

Enkrich, C.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic Metamaterials at Telecommunication and Visible Frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[Crossref] [PubMed]

Feise, M. W.

M. W. Feise, I. V. Shadrivov, and Y. S. Kivshar, “Bistable diode action in left-handed periodic structures,” Phys. Rev. E 71, 037602 (2005).
[Crossref]

Firth, W. J.

G. L. Oppo, A. J. Scroggie, and W. J. Firth, “From domain walls to localized structures in degenerate optical parametric oscillators,” Quantum Semiclass. Opt. 1, 133 (1999).
[Crossref]

D. V. Skryabin and W. J. Firth, “Interaction of cavity solitons in degenerate optical parametric oscillators,” Opt. Lett. 24, 1056–1058 (1999).
[Crossref]

Gelens, L.

L. Gelens, G. Van der Sande, P. Tassin, M. Tlidi, P. Kockaert, D. Gomila, I. Veretennicoff, and J. Danckaert, “Impact of nonlocal interactions in dissipative systems,” Phys. Rev. A 75, 063812 (2007).
[Crossref]

P. Tassin, L. Gelens, J. Danckaert, I. Veretennicoff, G. Van der Sande, P. Kockaert, and M. Tlidi, “Dissipative structures in left-handed material cavity optics,” Chaos 17, 037116 (2007).
[Crossref] [PubMed]

Gomila, D.

L. Gelens, G. Van der Sande, P. Tassin, M. Tlidi, P. Kockaert, D. Gomila, I. Veretennicoff, and J. Danckaert, “Impact of nonlocal interactions in dissipative systems,” Phys. Rev. A 75, 063812 (2007).
[Crossref]

D. Gomila, P. Colet, G. L. Oppo, and M. San Miguel, “Stable Droplets and Growth Laws Close to the Modulational Instability of a Domain Wall,” Phys. Rev. Lett. 87, 194101 (2001).
[Crossref] [PubMed]

Gundogdu, T. F.

T. F. Gundogdu, I. Tsiapa, A. Kostopoulos, G. Konstantinidis, N. Katsarakis, R. S. Penciu, M. Kafesaki, E. N. Economou, T. Koschny, and C. M. Soukoulis, “Experimental demonstration of negative magnetic permeability in the far-infrared frequency regime,” Appl. Phys. Lett. 89, 084103 (2006).
[Crossref]

Guven, K.

Haelterman, M.

S. Trillo, M. Haelterman, and A. Sheppard, “Stable topological spatial solitons in optical parametric oscillators,” Opt. Lett. 22, 970–972 (1997).
[Crossref] [PubMed]

M. Tlidi, P. Mandel, and M. Haelterman, “Spatiotemporal patterns and localized structures in nonlinear optics,” Phys. Rev. E 22, 970–972 (1997).

Kafesaki, M.

T. F. Gundogdu, I. Tsiapa, A. Kostopoulos, G. Konstantinidis, N. Katsarakis, R. S. Penciu, M. Kafesaki, E. N. Economou, T. Koschny, and C. M. Soukoulis, “Experimental demonstration of negative magnetic permeability in the far-infrared frequency regime,” Appl. Phys. Lett. 89, 084103 (2006).
[Crossref]

K. Aydin, K. Guven, M. Kafesaki, L. Zhang, C. M. Soukoulis, and E. Ozbay, “Experimental observation of true left-handed transmission peaks in metamaterials,” Opt. Lett. 29, 2623–2625 (2004).
[Crossref] [PubMed]

Katsarakis, N.

T. F. Gundogdu, I. Tsiapa, A. Kostopoulos, G. Konstantinidis, N. Katsarakis, R. S. Penciu, M. Kafesaki, E. N. Economou, T. Koschny, and C. M. Soukoulis, “Experimental demonstration of negative magnetic permeability in the far-infrared frequency regime,” Appl. Phys. Lett. 89, 084103 (2006).
[Crossref]

King, N.

A. D. Boardman, N. King, R. C. Mitchell-Thomas, V. N. Malnev, and Y. G Rapoport, “Gain control and diffraction-managed solitons in metamaterials,” Metamaterials 2, 145–154 (2008).
[Crossref]

Kivshar, Y. S.

M. W. Feise, I. V. Shadrivov, and Y. S. Kivshar, “Bistable diode action in left-handed periodic structures,” Phys. Rev. E 71, 037602 (2005).
[Crossref]

A. A. Zharov, N. A. Zharova, I. V. Shadrivov, and Y. S. Kivshar, “Subwavelength imaging with opaque nonlinear left-handed lenses,” Appl. Phys. Lett. 87, 091104 (2005).
[Crossref]

Kockaert, P.

P. Tassin, L. Gelens, J. Danckaert, I. Veretennicoff, G. Van der Sande, P. Kockaert, and M. Tlidi, “Dissipative structures in left-handed material cavity optics,” Chaos 17, 037116 (2007).
[Crossref] [PubMed]

L. Gelens, G. Van der Sande, P. Tassin, M. Tlidi, P. Kockaert, D. Gomila, I. Veretennicoff, and J. Danckaert, “Impact of nonlocal interactions in dissipative systems,” Phys. Rev. A 75, 063812 (2007).
[Crossref]

P. Kockaert, P. Tassin, G. Van der Sande, I. Veretennicoff, and M. Tlidi, “Negative diffraction pattern dynamics in nonlinear cavities with left-handed materials,” Phys. Rev. A 74, 033822 (2006).
[Crossref]

P. Tassin, G. Van der Sande, N. Veretenov, P. Kockaert, I. Veretennicoff, and M. Tlidi, “Three-dimensional structures in nonlinear cavities containing left-handed materials,” Opt. Express 14, 9338–9343 (2006).
[Crossref] [PubMed]

Kolokolnikov, T.

M. Tlidi, T. Kolokolnikov, and M. Taki, Focus Issue “Dissipative Localized Structures in Extended Systems,” Chaos,  17, Issue 3 (2007).
[Crossref] [PubMed]

Konstantinidis, G.

T. F. Gundogdu, I. Tsiapa, A. Kostopoulos, G. Konstantinidis, N. Katsarakis, R. S. Penciu, M. Kafesaki, E. N. Economou, T. Koschny, and C. M. Soukoulis, “Experimental demonstration of negative magnetic permeability in the far-infrared frequency regime,” Appl. Phys. Lett. 89, 084103 (2006).
[Crossref]

Koschny, T.

T. F. Gundogdu, I. Tsiapa, A. Kostopoulos, G. Konstantinidis, N. Katsarakis, R. S. Penciu, M. Kafesaki, E. N. Economou, T. Koschny, and C. M. Soukoulis, “Experimental demonstration of negative magnetic permeability in the far-infrared frequency regime,” Appl. Phys. Lett. 89, 084103 (2006).
[Crossref]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic Metamaterials at Telecommunication and Visible Frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[Crossref] [PubMed]

Kostopoulos, A.

T. F. Gundogdu, I. Tsiapa, A. Kostopoulos, G. Konstantinidis, N. Katsarakis, R. S. Penciu, M. Kafesaki, E. N. Economou, T. Koschny, and C. M. Soukoulis, “Experimental demonstration of negative magnetic permeability in the far-infrared frequency regime,” Appl. Phys. Lett. 89, 084103 (2006).
[Crossref]

Lazarides, N.

N. Lazarides and G. P. Tsironis, “Coupled nonlinear Schrödinger field equations for electromagnetic wave propagation in nonlinear left-handed materials,” Phys. Rev. E 71, 036614 (2005).
[Crossref]

Le Berre, M.

M. Tlidi, M. Le Berre, E. Ressayre, A. Tallet, and L. Di Menza, “High-intensity localized structures in the degenerate optical parametric oscillator,” Phys. Rev. A 61, 043806 (2000).
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M. Le Berre, D. Leduc, E. Ressayre, and A. Tallet, “Striped and circular domain walls in the DOPO,” Quantum Semiclassic. Opt. 1, 107 (1999).

Leduc, D.

M. Le Berre, D. Leduc, E. Ressayre, and A. Tallet, “Striped and circular domain walls in the DOPO,” Quantum Semiclassic. Opt. 1, 107 (1999).

Lefever, R.

M. Tlidi, P. Mandel, and R. Lefever, “Kinetics of Localized Pattern Formation in Optical Systems,” Phys. Rev. Lett. 81, 979–982 (1998).
[Crossref]

Linden, S.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic Metamaterials at Telecommunication and Visible Frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[Crossref] [PubMed]

Lugiato, L. A.

G.-L. Oppo, M. Brambilla, and L. A. Lugiato, “Formation and evolution of roll patterns in optical parametric oscillators,” Phys. Rev. A 49, 2028–2032 (1994).
[Crossref] [PubMed]

Malnev, V. N.

A. D. Boardman, N. King, R. C. Mitchell-Thomas, V. N. Malnev, and Y. G Rapoport, “Gain control and diffraction-managed solitons in metamaterials,” Metamaterials 2, 145–154 (2008).
[Crossref]

Mandel, P.

P. Mandel and M. Tlidi, “Transverse dynamics in cavity nonlinear optics (2000 2003),” J. Opt. Soc. Am. B 6, R60 (2004).

M. Tlidi, P. Mandel, and R. Lefever, “Kinetics of Localized Pattern Formation in Optical Systems,” Phys. Rev. Lett. 81, 979–982 (1998).
[Crossref]

M. Tlidi, P. Mandel, and M. Haelterman, “Spatiotemporal patterns and localized structures in nonlinear optics,” Phys. Rev. E 22, 970–972 (1997).

Mattiucci, N.

M. Scalora, M. S. Syrchin, N. Akozbek, E. Y. Poliakov, G. D’Aguanno, N. Mattiucci, M. J. Bloemer, and A. M. Zheltikov, “Generalized Nonlinear Schrödinger Equation for Dispersive Susceptibility and Permeability: Application to Negative Index Materials,” Phys. Rev. Lett. 95, 013902 (2005).
[Crossref] [PubMed]

G. D’Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, “Bright and Dark Gap Solitons in a Negative Index Fabry-Pérot Etalon,” Phys. Rev. Lett. 93, 213902 (2004).
[Crossref] [PubMed]

Menza, L. Di

M. Tlidi, M. Le Berre, E. Ressayre, A. Tallet, and L. Di Menza, “High-intensity localized structures in the degenerate optical parametric oscillator,” Phys. Rev. A 61, 043806 (2000).
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Miguel, M. San

D. Gomila, P. Colet, G. L. Oppo, and M. San Miguel, “Stable Droplets and Growth Laws Close to the Modulational Instability of a Domain Wall,” Phys. Rev. Lett. 87, 194101 (2001).
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Mitchell-Thomas, R. C.

A. D. Boardman, N. King, R. C. Mitchell-Thomas, V. N. Malnev, and Y. G Rapoport, “Gain control and diffraction-managed solitons in metamaterials,” Metamaterials 2, 145–154 (2008).
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Oppo, G. L.

D. Gomila, P. Colet, G. L. Oppo, and M. San Miguel, “Stable Droplets and Growth Laws Close to the Modulational Instability of a Domain Wall,” Phys. Rev. Lett. 87, 194101 (2001).
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G. L. Oppo, A. J. Scroggie, and W. J. Firth, “From domain walls to localized structures in degenerate optical parametric oscillators,” Quantum Semiclass. Opt. 1, 133 (1999).
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Oppo, G.-L.

G.-L. Oppo, M. Brambilla, and L. A. Lugiato, “Formation and evolution of roll patterns in optical parametric oscillators,” Phys. Rev. A 49, 2028–2032 (1994).
[Crossref] [PubMed]

Ozbay, E.

Penciu, R. S.

T. F. Gundogdu, I. Tsiapa, A. Kostopoulos, G. Konstantinidis, N. Katsarakis, R. S. Penciu, M. Kafesaki, E. N. Economou, T. Koschny, and C. M. Soukoulis, “Experimental demonstration of negative magnetic permeability in the far-infrared frequency regime,” Appl. Phys. Lett. 89, 084103 (2006).
[Crossref]

Pendry, J. B.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and Negative Refractive Index,” Science 305, 788–792 (2004).
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J. B. Pendry, “Negative Refraction Makes a Perfect Lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
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Poliakov, E. Y.

M. Scalora, M. S. Syrchin, N. Akozbek, E. Y. Poliakov, G. D’Aguanno, N. Mattiucci, M. J. Bloemer, and A. M. Zheltikov, “Generalized Nonlinear Schrödinger Equation for Dispersive Susceptibility and Permeability: Application to Negative Index Materials,” Phys. Rev. Lett. 95, 013902 (2005).
[Crossref] [PubMed]

Rapoport, Y. G

A. D. Boardman, N. King, R. C. Mitchell-Thomas, V. N. Malnev, and Y. G Rapoport, “Gain control and diffraction-managed solitons in metamaterials,” Metamaterials 2, 145–154 (2008).
[Crossref]

Ressayre, E.

M. Tlidi, M. Le Berre, E. Ressayre, A. Tallet, and L. Di Menza, “High-intensity localized structures in the degenerate optical parametric oscillator,” Phys. Rev. A 61, 043806 (2000).
[Crossref]

M. Le Berre, D. Leduc, E. Ressayre, and A. Tallet, “Striped and circular domain walls in the DOPO,” Quantum Semiclassic. Opt. 1, 107 (1999).

Sanchez-Morcillo, V. J.

K. Staliunas and V. J. Sanchez-Morcillo, “Dynamics of Domains in Swift-Hohenberg Equation,” Phys. Lett. A 241, 28 (1998).
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K. Staliunas and V. J. Sanchez-Morcillo, Transverse Patterns in Nonlinear Optical Resonators, vol. 183 of Springer Tracts in Modern Physics (Springer-Verlag, Berlin, 2003).

Sande, G. Van der

P. Tassin, L. Gelens, J. Danckaert, I. Veretennicoff, G. Van der Sande, P. Kockaert, and M. Tlidi, “Dissipative structures in left-handed material cavity optics,” Chaos 17, 037116 (2007).
[Crossref] [PubMed]

L. Gelens, G. Van der Sande, P. Tassin, M. Tlidi, P. Kockaert, D. Gomila, I. Veretennicoff, and J. Danckaert, “Impact of nonlocal interactions in dissipative systems,” Phys. Rev. A 75, 063812 (2007).
[Crossref]

P. Kockaert, P. Tassin, G. Van der Sande, I. Veretennicoff, and M. Tlidi, “Negative diffraction pattern dynamics in nonlinear cavities with left-handed materials,” Phys. Rev. A 74, 033822 (2006).
[Crossref]

P. Tassin, G. Van der Sande, N. Veretenov, P. Kockaert, I. Veretennicoff, and M. Tlidi, “Three-dimensional structures in nonlinear cavities containing left-handed materials,” Opt. Express 14, 9338–9343 (2006).
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Scalora, M.

M. Scalora, M. S. Syrchin, N. Akozbek, E. Y. Poliakov, G. D’Aguanno, N. Mattiucci, M. J. Bloemer, and A. M. Zheltikov, “Generalized Nonlinear Schrödinger Equation for Dispersive Susceptibility and Permeability: Application to Negative Index Materials,” Phys. Rev. Lett. 95, 013902 (2005).
[Crossref] [PubMed]

G. D’Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, “Bright and Dark Gap Solitons in a Negative Index Fabry-Pérot Etalon,” Phys. Rev. Lett. 93, 213902 (2004).
[Crossref] [PubMed]

Schmidt, F.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic Metamaterials at Telecommunication and Visible Frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
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Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental Verification of a Negative Index of Refraction,” Science 292, 77–79 (2001).
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Scroggie, A. J.

G. L. Oppo, A. J. Scroggie, and W. J. Firth, “From domain walls to localized structures in degenerate optical parametric oscillators,” Quantum Semiclass. Opt. 1, 133 (1999).
[Crossref]

Shadrivov, I. V.

M. W. Feise, I. V. Shadrivov, and Y. S. Kivshar, “Bistable diode action in left-handed periodic structures,” Phys. Rev. E 71, 037602 (2005).
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A. A. Zharov, N. A. Zharova, I. V. Shadrivov, and Y. S. Kivshar, “Subwavelength imaging with opaque nonlinear left-handed lenses,” Appl. Phys. Lett. 87, 091104 (2005).
[Crossref]

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental Verification of a Negative Index of Refraction,” Science 292, 77–79 (2001).
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Sheppard, A.

Skryabin, D. V.

A. V. Buryak, P. Di Trapani, D. V. Skryabin, and S. Trillo, “Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications,” Phys. Rep. 370, 63 (2002).
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D. V. Skryabin and W. J. Firth, “Interaction of cavity solitons in degenerate optical parametric oscillators,” Opt. Lett. 24, 1056–1058 (1999).
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Smith, D. R.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and Negative Refractive Index,” Science 305, 788–792 (2004).
[Crossref] [PubMed]

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental Verification of a Negative Index of Refraction,” Science 292, 77–79 (2001).
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Sorokina, I. T.

M. Ebrahim-Zadeh and I. T. Sorokina, “Mid-Infrared Coherent Sources and Applications,” (Springer, Dordrecht, 2008).

Soukoulis, C. M.

T. F. Gundogdu, I. Tsiapa, A. Kostopoulos, G. Konstantinidis, N. Katsarakis, R. S. Penciu, M. Kafesaki, E. N. Economou, T. Koschny, and C. M. Soukoulis, “Experimental demonstration of negative magnetic permeability in the far-infrared frequency regime,” Appl. Phys. Lett. 89, 084103 (2006).
[Crossref]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic Metamaterials at Telecommunication and Visible Frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
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K. Aydin, K. Guven, M. Kafesaki, L. Zhang, C. M. Soukoulis, and E. Ozbay, “Experimental observation of true left-handed transmission peaks in metamaterials,” Opt. Lett. 29, 2623–2625 (2004).
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Staliunas, K.

K. Staliunas and V. J. Sanchez-Morcillo, “Dynamics of Domains in Swift-Hohenberg Equation,” Phys. Lett. A 241, 28 (1998).
[Crossref]

K. Staliunas and V. J. Sanchez-Morcillo, Transverse Patterns in Nonlinear Optical Resonators, vol. 183 of Springer Tracts in Modern Physics (Springer-Verlag, Berlin, 2003).

Syrchin, M. S.

M. Scalora, M. S. Syrchin, N. Akozbek, E. Y. Poliakov, G. D’Aguanno, N. Mattiucci, M. J. Bloemer, and A. M. Zheltikov, “Generalized Nonlinear Schrödinger Equation for Dispersive Susceptibility and Permeability: Application to Negative Index Materials,” Phys. Rev. Lett. 95, 013902 (2005).
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Taki, M.

M. Tlidi, T. Kolokolnikov, and M. Taki, Focus Issue “Dissipative Localized Structures in Extended Systems,” Chaos,  17, Issue 3 (2007).
[Crossref] [PubMed]

Tallet, A.

M. Tlidi, M. Le Berre, E. Ressayre, A. Tallet, and L. Di Menza, “High-intensity localized structures in the degenerate optical parametric oscillator,” Phys. Rev. A 61, 043806 (2000).
[Crossref]

M. Le Berre, D. Leduc, E. Ressayre, and A. Tallet, “Striped and circular domain walls in the DOPO,” Quantum Semiclassic. Opt. 1, 107 (1999).

Tang, C. L.

C. L. Tang and L. K. Cheng, “Fundamentals of Optical Parametric Processes and Oscillators,” vol. 20 of Laser Science and Technology Series (Harwood Academic Publishers GmbH, Amsterdam, 1995).

Tassin, P.

L. Gelens, G. Van der Sande, P. Tassin, M. Tlidi, P. Kockaert, D. Gomila, I. Veretennicoff, and J. Danckaert, “Impact of nonlocal interactions in dissipative systems,” Phys. Rev. A 75, 063812 (2007).
[Crossref]

P. Tassin, L. Gelens, J. Danckaert, I. Veretennicoff, G. Van der Sande, P. Kockaert, and M. Tlidi, “Dissipative structures in left-handed material cavity optics,” Chaos 17, 037116 (2007).
[Crossref] [PubMed]

P. Kockaert, P. Tassin, G. Van der Sande, I. Veretennicoff, and M. Tlidi, “Negative diffraction pattern dynamics in nonlinear cavities with left-handed materials,” Phys. Rev. A 74, 033822 (2006).
[Crossref]

P. Tassin, G. Van der Sande, N. Veretenov, P. Kockaert, I. Veretennicoff, and M. Tlidi, “Three-dimensional structures in nonlinear cavities containing left-handed materials,” Opt. Express 14, 9338–9343 (2006).
[Crossref] [PubMed]

Tlidi, M.

L. Gelens, G. Van der Sande, P. Tassin, M. Tlidi, P. Kockaert, D. Gomila, I. Veretennicoff, and J. Danckaert, “Impact of nonlocal interactions in dissipative systems,” Phys. Rev. A 75, 063812 (2007).
[Crossref]

P. Tassin, L. Gelens, J. Danckaert, I. Veretennicoff, G. Van der Sande, P. Kockaert, and M. Tlidi, “Dissipative structures in left-handed material cavity optics,” Chaos 17, 037116 (2007).
[Crossref] [PubMed]

M. Tlidi, T. Kolokolnikov, and M. Taki, Focus Issue “Dissipative Localized Structures in Extended Systems,” Chaos,  17, Issue 3 (2007).
[Crossref] [PubMed]

P. Kockaert, P. Tassin, G. Van der Sande, I. Veretennicoff, and M. Tlidi, “Negative diffraction pattern dynamics in nonlinear cavities with left-handed materials,” Phys. Rev. A 74, 033822 (2006).
[Crossref]

P. Tassin, G. Van der Sande, N. Veretenov, P. Kockaert, I. Veretennicoff, and M. Tlidi, “Three-dimensional structures in nonlinear cavities containing left-handed materials,” Opt. Express 14, 9338–9343 (2006).
[Crossref] [PubMed]

P. Mandel and M. Tlidi, “Transverse dynamics in cavity nonlinear optics (2000 2003),” J. Opt. Soc. Am. B 6, R60 (2004).

M. Tlidi, M. Le Berre, E. Ressayre, A. Tallet, and L. Di Menza, “High-intensity localized structures in the degenerate optical parametric oscillator,” Phys. Rev. A 61, 043806 (2000).
[Crossref]

M. Tlidi, P. Mandel, and R. Lefever, “Kinetics of Localized Pattern Formation in Optical Systems,” Phys. Rev. Lett. 81, 979–982 (1998).
[Crossref]

M. Tlidi, P. Mandel, and M. Haelterman, “Spatiotemporal patterns and localized structures in nonlinear optics,” Phys. Rev. E 22, 970–972 (1997).

Trapani, P. Di

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

Trillo, S.

A. V. Buryak, P. Di Trapani, D. V. Skryabin, and S. Trillo, “Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications,” Phys. Rep. 370, 63 (2002).
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S. Trillo, M. Haelterman, and A. Sheppard, “Stable topological spatial solitons in optical parametric oscillators,” Opt. Lett. 22, 970–972 (1997).
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Tsiapa, I.

T. F. Gundogdu, I. Tsiapa, A. Kostopoulos, G. Konstantinidis, N. Katsarakis, R. S. Penciu, M. Kafesaki, E. N. Economou, T. Koschny, and C. M. Soukoulis, “Experimental demonstration of negative magnetic permeability in the far-infrared frequency regime,” Appl. Phys. Lett. 89, 084103 (2006).
[Crossref]

Tsironis, G. P.

N. Lazarides and G. P. Tsironis, “Coupled nonlinear Schrödinger field equations for electromagnetic wave propagation in nonlinear left-handed materials,” Phys. Rev. E 71, 036614 (2005).
[Crossref]

Veretennicoff, I.

P. Tassin, L. Gelens, J. Danckaert, I. Veretennicoff, G. Van der Sande, P. Kockaert, and M. Tlidi, “Dissipative structures in left-handed material cavity optics,” Chaos 17, 037116 (2007).
[Crossref] [PubMed]

L. Gelens, G. Van der Sande, P. Tassin, M. Tlidi, P. Kockaert, D. Gomila, I. Veretennicoff, and J. Danckaert, “Impact of nonlocal interactions in dissipative systems,” Phys. Rev. A 75, 063812 (2007).
[Crossref]

P. Kockaert, P. Tassin, G. Van der Sande, I. Veretennicoff, and M. Tlidi, “Negative diffraction pattern dynamics in nonlinear cavities with left-handed materials,” Phys. Rev. A 74, 033822 (2006).
[Crossref]

P. Tassin, G. Van der Sande, N. Veretenov, P. Kockaert, I. Veretennicoff, and M. Tlidi, “Three-dimensional structures in nonlinear cavities containing left-handed materials,” Opt. Express 14, 9338–9343 (2006).
[Crossref] [PubMed]

Veretenov, N.

Veselago, V. G.

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509–514 (1968).
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Wegener, M.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic Metamaterials at Telecommunication and Visible Frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[Crossref] [PubMed]

Wiltshire, M. C. K.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and Negative Refractive Index,” Science 305, 788–792 (2004).
[Crossref] [PubMed]

Zhang, L.

Zharov, A. A.

A. A. Zharov, N. A. Zharova, I. V. Shadrivov, and Y. S. Kivshar, “Subwavelength imaging with opaque nonlinear left-handed lenses,” Appl. Phys. Lett. 87, 091104 (2005).
[Crossref]

Zharova, N. A.

A. A. Zharov, N. A. Zharova, I. V. Shadrivov, and Y. S. Kivshar, “Subwavelength imaging with opaque nonlinear left-handed lenses,” Appl. Phys. Lett. 87, 091104 (2005).
[Crossref]

Zheltikov, A. M.

M. Scalora, M. S. Syrchin, N. Akozbek, E. Y. Poliakov, G. D’Aguanno, N. Mattiucci, M. J. Bloemer, and A. M. Zheltikov, “Generalized Nonlinear Schrödinger Equation for Dispersive Susceptibility and Permeability: Application to Negative Index Materials,” Phys. Rev. Lett. 95, 013902 (2005).
[Crossref] [PubMed]

Zhou, J. F.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic Metamaterials at Telecommunication and Visible Frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[Crossref] [PubMed]

Zschiedrich, L.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic Metamaterials at Telecommunication and Visible Frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[Crossref] [PubMed]

Appl. Phys. Lett. (2)

T. F. Gundogdu, I. Tsiapa, A. Kostopoulos, G. Konstantinidis, N. Katsarakis, R. S. Penciu, M. Kafesaki, E. N. Economou, T. Koschny, and C. M. Soukoulis, “Experimental demonstration of negative magnetic permeability in the far-infrared frequency regime,” Appl. Phys. Lett. 89, 084103 (2006).
[Crossref]

A. A. Zharov, N. A. Zharova, I. V. Shadrivov, and Y. S. Kivshar, “Subwavelength imaging with opaque nonlinear left-handed lenses,” Appl. Phys. Lett. 87, 091104 (2005).
[Crossref]

Chaos (2)

P. Tassin, L. Gelens, J. Danckaert, I. Veretennicoff, G. Van der Sande, P. Kockaert, and M. Tlidi, “Dissipative structures in left-handed material cavity optics,” Chaos 17, 037116 (2007).
[Crossref] [PubMed]

M. Tlidi, T. Kolokolnikov, and M. Taki, Focus Issue “Dissipative Localized Structures in Extended Systems,” Chaos,  17, Issue 3 (2007).
[Crossref] [PubMed]

J. Opt. Soc. Am. B (1)

P. Mandel and M. Tlidi, “Transverse dynamics in cavity nonlinear optics (2000 2003),” J. Opt. Soc. Am. B 6, R60 (2004).

Metamaterials (1)

A. D. Boardman, N. King, R. C. Mitchell-Thomas, V. N. Malnev, and Y. G Rapoport, “Gain control and diffraction-managed solitons in metamaterials,” Metamaterials 2, 145–154 (2008).
[Crossref]

Opt. Express (1)

Opt. Lett. (3)

Phys. Lett. A (1)

K. Staliunas and V. J. Sanchez-Morcillo, “Dynamics of Domains in Swift-Hohenberg Equation,” Phys. Lett. A 241, 28 (1998).
[Crossref]

Phys. Rep. (1)

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

Phys. Rev. A (4)

M. Tlidi, M. Le Berre, E. Ressayre, A. Tallet, and L. Di Menza, “High-intensity localized structures in the degenerate optical parametric oscillator,” Phys. Rev. A 61, 043806 (2000).
[Crossref]

L. Gelens, G. Van der Sande, P. Tassin, M. Tlidi, P. Kockaert, D. Gomila, I. Veretennicoff, and J. Danckaert, “Impact of nonlocal interactions in dissipative systems,” Phys. Rev. A 75, 063812 (2007).
[Crossref]

P. Kockaert, P. Tassin, G. Van der Sande, I. Veretennicoff, and M. Tlidi, “Negative diffraction pattern dynamics in nonlinear cavities with left-handed materials,” Phys. Rev. A 74, 033822 (2006).
[Crossref]

G.-L. Oppo, M. Brambilla, and L. A. Lugiato, “Formation and evolution of roll patterns in optical parametric oscillators,” Phys. Rev. A 49, 2028–2032 (1994).
[Crossref] [PubMed]

Phys. Rev. E (3)

M. Tlidi, P. Mandel, and M. Haelterman, “Spatiotemporal patterns and localized structures in nonlinear optics,” Phys. Rev. E 22, 970–972 (1997).

N. Lazarides and G. P. Tsironis, “Coupled nonlinear Schrödinger field equations for electromagnetic wave propagation in nonlinear left-handed materials,” Phys. Rev. E 71, 036614 (2005).
[Crossref]

M. W. Feise, I. V. Shadrivov, and Y. S. Kivshar, “Bistable diode action in left-handed periodic structures,” Phys. Rev. E 71, 037602 (2005).
[Crossref]

Phys. Rev. Lett. (6)

G. D’Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, “Bright and Dark Gap Solitons in a Negative Index Fabry-Pérot Etalon,” Phys. Rev. Lett. 93, 213902 (2004).
[Crossref] [PubMed]

M. Scalora, M. S. Syrchin, N. Akozbek, E. Y. Poliakov, G. D’Aguanno, N. Mattiucci, M. J. Bloemer, and A. M. Zheltikov, “Generalized Nonlinear Schrödinger Equation for Dispersive Susceptibility and Permeability: Application to Negative Index Materials,” Phys. Rev. Lett. 95, 013902 (2005).
[Crossref] [PubMed]

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Figures (3)

Fig. 1.
Fig. 1. Schematic setup of the degenerate optical parametric oscillator with a LHM.
Fig. 2.
Fig. 2. Dissipative structures due to modulational instability below threshold. Signal diffraction strength is decreased from left to right: D s = −2.0, D s = −1.0, D s = −0.5, and D s = −0.3. Maxima are plain white and the mesh integration is 128×128.
Fig. 3.
Fig. 3. Phase domains and solitons above the lasing threshold for decreasing signal diffraction strength (from left to right: D s = −3.0, D s = −1.5, D s = −1.0, D s = −0.8, and D s = −0.5). Maxima are plain white and the mesh integration is 128 × 128.

Equations (8)

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Asz+nscAst=iωχ(2)cηs Ap As* +ic2ωns 2 As ,
Apz+npcApt=iiωχ(2)2cηp As2 +icωnp 2 Ap .
Ast=(1+iΔs)As+ApAs*+iDs2As,
Apt=E(1+iΔp)ApAs2+iDp2Ap,
Ds=c2πω(lQCnQC+lLHMnLHM(ω/2)),Dp=c4πω(lQCnQC+lLHMnLHM(ω)),
As=±eiϕ1+ΔsΔp+E2(Δs+Δp)2,
4As2[As2+Qs(1Qp)+Qp]+Qp(QsAp2)=0,
ΛM=2πDs/Δs.

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