Abstract

We study soliton reflection/transmission at the interface between uniform medium and the optical lattice with focusing Kerr nonlinearity. We reveal that such interfaces afford rich new opportunities for controlling the reflection and transmission coefficients and nonlinear Snell law, the key control parameters being the spatial frequency and depth of the lattice.

© 2006 Optical Society of America

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  1. A. E. Kaplan, "Hysteresis reflection and refraction at the nonlinear interface - a new class of effects in nonlinear optics," JETP Lett. 24, 114 (1976).
  2. P. W. Smith, J. P. Hermann, W. J. Tomlinson, and P. J. Maloney, "Optical bistability at a nonlinear interface," Appl. Phys. Lett. 35, 846 (1979).
    [CrossRef]
  3. A. B. Aceves, J. V. Moloney, and A. C. Newell, "Theory of light-beam propagation at nonlinear interfaces. I. Equivalent-particle theory for a single interface," Phys. Rev. A 39, 1809 (1989).
    [CrossRef] [PubMed]
  4. A. B. Aceves, J. V. Moloney, and A. C. Newell, "Theory of light-beam propagation at nonlinear interfaces. II. Multiple-particle and multiple-interface extensions," Phys. Rev. A 39, 1828 (1989).
    [CrossRef] [PubMed]
  5. V. A. Aleshkevich, Y. V. Kartashov, A. S. Zelenina, V. A. Vysloukh, J. P. Torres, and L. Torner, "Eigenvalue control and switching by fission of multisoliton bound states in planar waveguides," Opt. Lett. 29, 483 (2004).
    [CrossRef]
  6. E. Alvarado Mendez, R. Rojas Laguna, J. G. Aviña Cervantes, M. Torres Cisneros, J. A. Andrade Lucio, R. Ramos-Garcia, E. A. Kuzin, J. J. Sánchez Mondragón, and V. Vysloukh, "Total internal reflection of spatial solitons at interface formed by a nonlinear saturable and a linear medium," Opt. Commun. 193, 267 (2001).
    [CrossRef] [PubMed]
  7. M. Cronin Golomb, "Photorefractive surface waves," Opt. Lett. 20, 2075 (1995).
    [CrossRef] [PubMed]
  8. P. Yeh, A, Yariv, and A. Y. Cho, "Optical surface waves in periodic layered media," Appl. Phys. Lett. 32, 104 (1978).
    [CrossRef]
  9. J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of discrete solitons in optically induced real time waveguide arrays" Phys. Rev. Lett. 90, 023902 (2003).
    [CrossRef] [PubMed]
  10. 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 (2003).
    [CrossRef] [PubMed]
  11. D. Neshev, E. Ostrovskaya, Y. Kivshar, and W. Krolikowski, "Spatial solitons in optically induced gratings," Opt. Lett. 28, 710 (2003).
    [CrossRef] [PubMed]
  12. Z. Chen, H. Martin, E. D. Eugenieva, J. Xu, and A. Bezryadina, "Anisotropic enhancement of discrete diffraction and formation of two-dimensional discrete-soliton trains," Phys. Rev. Lett. 92, 143902 (2004).
    [CrossRef]
  13. D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Band-gap structure of waveguide arrays and excitation of Floquet-Bloch solitons," Phys. Rev. Lett. 90, 053902 (2003).
    [CrossRef] [PubMed]
  14. H. S. Eisenberg, Y. Silberberg, Y. Morandotti, R. Boyd, and J. S. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383 (1998).
    [CrossRef] [PubMed]
  15. J. Meier, J. Hudock, D. N. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Discrete vector solitons in Kerr nonlinear waveguide arrays," Phys. Rev. Lett. 91, 143907 (2003).
    [CrossRef] [PubMed]
  16. D. N. Christodoulides, F. Lederer, and Y. Silberberg, "Discretizing light behaviour in linear and nonlinear waveguide lattices," Nature 424, 817 (2003).
    [CrossRef] [PubMed]
  17. Y. V. Kartashov, A. S. Zelenina, L. Torner, and V. A. Vysloukh, "Spatial soliton switching in quasi-continuous optical arrays," Opt. Lett. 29, 766 (2004).
    [CrossRef] [PubMed]
  18. Y. V. Kartashov, L. Torner, and V. A. Vysloukh, "Parametric amplification of soliton steering in optical lattices," Opt. Lett. 29, 1102 (2004).
    [CrossRef]
  19. C. R. Rosberg, D. N. Neshev, A. A. Sukhorukov, Y. S. Kivshar, and W. Krolikowski, "Tunable positive and negative refraction in optically-induced photonic lattices," Opt. Lett. 30, 2293 (2005).
    [CrossRef] [PubMed]

2005 (1)

2004 (4)

2003 (6)

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Band-gap structure of waveguide arrays and excitation of Floquet-Bloch solitons," Phys. Rev. Lett. 90, 053902 (2003).
[CrossRef] [PubMed]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of discrete solitons in optically induced real time waveguide arrays" Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

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

D. Neshev, E. Ostrovskaya, Y. Kivshar, and W. Krolikowski, "Spatial solitons in optically induced gratings," Opt. Lett. 28, 710 (2003).
[CrossRef] [PubMed]

J. Meier, J. Hudock, D. N. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Discrete vector solitons in Kerr nonlinear waveguide arrays," Phys. Rev. Lett. 91, 143907 (2003).
[CrossRef] [PubMed]

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

2001 (1)

E. Alvarado Mendez, R. Rojas Laguna, J. G. Aviña Cervantes, M. Torres Cisneros, J. A. Andrade Lucio, R. Ramos-Garcia, E. A. Kuzin, J. J. Sánchez Mondragón, and V. Vysloukh, "Total internal reflection of spatial solitons at interface formed by a nonlinear saturable and a linear medium," Opt. Commun. 193, 267 (2001).
[CrossRef] [PubMed]

1998 (1)

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

1995 (1)

1989 (2)

A. B. Aceves, J. V. Moloney, and A. C. Newell, "Theory of light-beam propagation at nonlinear interfaces. I. Equivalent-particle theory for a single interface," Phys. Rev. A 39, 1809 (1989).
[CrossRef] [PubMed]

A. B. Aceves, J. V. Moloney, and A. C. Newell, "Theory of light-beam propagation at nonlinear interfaces. II. Multiple-particle and multiple-interface extensions," Phys. Rev. A 39, 1828 (1989).
[CrossRef] [PubMed]

1979 (1)

P. W. Smith, J. P. Hermann, W. J. Tomlinson, and P. J. Maloney, "Optical bistability at a nonlinear interface," Appl. Phys. Lett. 35, 846 (1979).
[CrossRef]

1978 (1)

P. Yeh, A, Yariv, and A. Y. Cho, "Optical surface waves in periodic layered media," Appl. Phys. Lett. 32, 104 (1978).
[CrossRef]

1976 (1)

A. E. Kaplan, "Hysteresis reflection and refraction at the nonlinear interface - a new class of effects in nonlinear optics," JETP Lett. 24, 114 (1976).

Aceves, A. B.

A. B. Aceves, J. V. Moloney, and A. C. Newell, "Theory of light-beam propagation at nonlinear interfaces. I. Equivalent-particle theory for a single interface," Phys. Rev. A 39, 1809 (1989).
[CrossRef] [PubMed]

A. B. Aceves, J. V. Moloney, and A. C. Newell, "Theory of light-beam propagation at nonlinear interfaces. II. Multiple-particle and multiple-interface extensions," Phys. Rev. A 39, 1828 (1989).
[CrossRef] [PubMed]

Aitchison, J. S.

J. Meier, J. Hudock, D. N. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Discrete vector solitons in Kerr nonlinear waveguide arrays," Phys. Rev. Lett. 91, 143907 (2003).
[CrossRef] [PubMed]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Band-gap structure of waveguide arrays and excitation of Floquet-Bloch solitons," Phys. Rev. Lett. 90, 053902 (2003).
[CrossRef] [PubMed]

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

Aleshkevich, V. A.

Alvarado Mendez, E.

E. Alvarado Mendez, R. Rojas Laguna, J. G. Aviña Cervantes, M. Torres Cisneros, J. A. Andrade Lucio, R. Ramos-Garcia, E. A. Kuzin, J. J. Sánchez Mondragón, and V. Vysloukh, "Total internal reflection of spatial solitons at interface formed by a nonlinear saturable and a linear medium," Opt. Commun. 193, 267 (2001).
[CrossRef] [PubMed]

Andrade Lucio, J. A.

E. Alvarado Mendez, R. Rojas Laguna, J. G. Aviña Cervantes, M. Torres Cisneros, J. A. Andrade Lucio, R. Ramos-Garcia, E. A. Kuzin, J. J. Sánchez Mondragón, and V. Vysloukh, "Total internal reflection of spatial solitons at interface formed by a nonlinear saturable and a linear medium," Opt. Commun. 193, 267 (2001).
[CrossRef] [PubMed]

Aviña Cervantes, J. G.

E. Alvarado Mendez, R. Rojas Laguna, J. G. Aviña Cervantes, M. Torres Cisneros, J. A. Andrade Lucio, R. Ramos-Garcia, E. A. Kuzin, J. J. Sánchez Mondragón, and V. Vysloukh, "Total internal reflection of spatial solitons at interface formed by a nonlinear saturable and a linear medium," Opt. Commun. 193, 267 (2001).
[CrossRef] [PubMed]

Bezryadina, A.

Z. Chen, H. Martin, E. D. Eugenieva, J. Xu, and A. Bezryadina, "Anisotropic enhancement of discrete diffraction and formation of two-dimensional discrete-soliton trains," Phys. Rev. Lett. 92, 143902 (2004).
[CrossRef]

Boyd, R.

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

Carmon, T.

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of discrete solitons in optically induced real time waveguide arrays" Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

Chen, Z.

Z. Chen, H. Martin, E. D. Eugenieva, J. Xu, and A. Bezryadina, "Anisotropic enhancement of discrete diffraction and formation of two-dimensional discrete-soliton trains," Phys. Rev. Lett. 92, 143902 (2004).
[CrossRef]

Christodoulides, D. N.

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 (2003).
[CrossRef] [PubMed]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of discrete solitons in optically induced real time waveguide arrays" Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

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

J. Meier, J. Hudock, D. N. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Discrete vector solitons in Kerr nonlinear waveguide arrays," Phys. Rev. Lett. 91, 143907 (2003).
[CrossRef] [PubMed]

Cronin Golomb, M.

Efremidis, N. K.

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of discrete solitons in optically induced real time waveguide arrays" Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

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

Eisenberg, H. S.

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Band-gap structure of waveguide arrays and excitation of Floquet-Bloch solitons," Phys. Rev. Lett. 90, 053902 (2003).
[CrossRef] [PubMed]

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

Eugenieva, E. D.

Z. Chen, H. Martin, E. D. Eugenieva, J. Xu, and A. Bezryadina, "Anisotropic enhancement of discrete diffraction and formation of two-dimensional discrete-soliton trains," Phys. Rev. Lett. 92, 143902 (2004).
[CrossRef]

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 (2003).
[CrossRef] [PubMed]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of discrete solitons in optically induced real time waveguide arrays" Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

Hermann, J. P.

P. W. Smith, J. P. Hermann, W. J. Tomlinson, and P. J. Maloney, "Optical bistability at a nonlinear interface," Appl. Phys. Lett. 35, 846 (1979).
[CrossRef]

Hudock, J.

J. Meier, J. Hudock, D. N. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Discrete vector solitons in Kerr nonlinear waveguide arrays," Phys. Rev. Lett. 91, 143907 (2003).
[CrossRef] [PubMed]

Kaplan, A. E.

A. E. Kaplan, "Hysteresis reflection and refraction at the nonlinear interface - a new class of effects in nonlinear optics," JETP Lett. 24, 114 (1976).

Kartashov, Y. V.

Kivshar, Y.

Kivshar, Y. S.

Krolikowski, W.

Kuzin, E. A.

E. Alvarado Mendez, R. Rojas Laguna, J. G. Aviña Cervantes, M. Torres Cisneros, J. A. Andrade Lucio, R. Ramos-Garcia, E. A. Kuzin, J. J. Sánchez Mondragón, and V. Vysloukh, "Total internal reflection of spatial solitons at interface formed by a nonlinear saturable and a linear medium," Opt. Commun. 193, 267 (2001).
[CrossRef] [PubMed]

Lederer, F.

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

Maloney, P. J.

P. W. Smith, J. P. Hermann, W. J. Tomlinson, and P. J. Maloney, "Optical bistability at a nonlinear interface," Appl. Phys. Lett. 35, 846 (1979).
[CrossRef]

Mandelik, D.

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Band-gap structure of waveguide arrays and excitation of Floquet-Bloch solitons," Phys. Rev. Lett. 90, 053902 (2003).
[CrossRef] [PubMed]

Martin, H.

Z. Chen, H. Martin, E. D. Eugenieva, J. Xu, and A. Bezryadina, "Anisotropic enhancement of discrete diffraction and formation of two-dimensional discrete-soliton trains," Phys. Rev. Lett. 92, 143902 (2004).
[CrossRef]

Meier, J.

J. Meier, J. Hudock, D. N. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Discrete vector solitons in Kerr nonlinear waveguide arrays," Phys. Rev. Lett. 91, 143907 (2003).
[CrossRef] [PubMed]

Moloney, J. V.

A. B. Aceves, J. V. Moloney, and A. C. Newell, "Theory of light-beam propagation at nonlinear interfaces. II. Multiple-particle and multiple-interface extensions," Phys. Rev. A 39, 1828 (1989).
[CrossRef] [PubMed]

A. B. Aceves, J. V. Moloney, and A. C. Newell, "Theory of light-beam propagation at nonlinear interfaces. I. Equivalent-particle theory for a single interface," Phys. Rev. A 39, 1809 (1989).
[CrossRef] [PubMed]

Morandotti, R.

J. Meier, J. Hudock, D. N. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Discrete vector solitons in Kerr nonlinear waveguide arrays," Phys. Rev. Lett. 91, 143907 (2003).
[CrossRef] [PubMed]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Band-gap structure of waveguide arrays and excitation of Floquet-Bloch solitons," Phys. Rev. Lett. 90, 053902 (2003).
[CrossRef] [PubMed]

Morandotti, Y.

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

Neshev, D.

Neshev, D. N.

Newell, A. C.

A. B. Aceves, J. V. Moloney, and A. C. Newell, "Theory of light-beam propagation at nonlinear interfaces. I. Equivalent-particle theory for a single interface," Phys. Rev. A 39, 1809 (1989).
[CrossRef] [PubMed]

A. B. Aceves, J. V. Moloney, and A. C. Newell, "Theory of light-beam propagation at nonlinear interfaces. II. Multiple-particle and multiple-interface extensions," Phys. Rev. A 39, 1828 (1989).
[CrossRef] [PubMed]

Ostrovskaya, E.

Ramos-Garcia, R.

E. Alvarado Mendez, R. Rojas Laguna, J. G. Aviña Cervantes, M. Torres Cisneros, J. A. Andrade Lucio, R. Ramos-Garcia, E. A. Kuzin, J. J. Sánchez Mondragón, and V. Vysloukh, "Total internal reflection of spatial solitons at interface formed by a nonlinear saturable and a linear medium," Opt. Commun. 193, 267 (2001).
[CrossRef] [PubMed]

Rojas Laguna, R.

E. Alvarado Mendez, R. Rojas Laguna, J. G. Aviña Cervantes, M. Torres Cisneros, J. A. Andrade Lucio, R. Ramos-Garcia, E. A. Kuzin, J. J. Sánchez Mondragón, and V. Vysloukh, "Total internal reflection of spatial solitons at interface formed by a nonlinear saturable and a linear medium," Opt. Commun. 193, 267 (2001).
[CrossRef] [PubMed]

Rosberg, C. R.

Sánchez Mondragón, J. J.

E. Alvarado Mendez, R. Rojas Laguna, J. G. Aviña Cervantes, M. Torres Cisneros, J. A. Andrade Lucio, R. Ramos-Garcia, E. A. Kuzin, J. J. Sánchez Mondragón, and V. Vysloukh, "Total internal reflection of spatial solitons at interface formed by a nonlinear saturable and a linear medium," Opt. Commun. 193, 267 (2001).
[CrossRef] [PubMed]

Segev, M.

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of discrete solitons in optically induced real time waveguide arrays" Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

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

Silberberg, Y.

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

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Band-gap structure of waveguide arrays and excitation of Floquet-Bloch solitons," Phys. Rev. Lett. 90, 053902 (2003).
[CrossRef] [PubMed]

J. Meier, J. Hudock, D. N. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Discrete vector solitons in Kerr nonlinear waveguide arrays," Phys. Rev. Lett. 91, 143907 (2003).
[CrossRef] [PubMed]

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

Smith, P. W.

P. W. Smith, J. P. Hermann, W. J. Tomlinson, and P. J. Maloney, "Optical bistability at a nonlinear interface," Appl. Phys. Lett. 35, 846 (1979).
[CrossRef]

Stegeman, G.

J. Meier, J. Hudock, D. N. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Discrete vector solitons in Kerr nonlinear waveguide arrays," Phys. Rev. Lett. 91, 143907 (2003).
[CrossRef] [PubMed]

Sukhorukov, A. A.

Tomlinson, W. J.

P. W. Smith, J. P. Hermann, W. J. Tomlinson, and P. J. Maloney, "Optical bistability at a nonlinear interface," Appl. Phys. Lett. 35, 846 (1979).
[CrossRef]

Torner, L.

Torres, J. P.

Torres Cisneros, M.

E. Alvarado Mendez, R. Rojas Laguna, J. G. Aviña Cervantes, M. Torres Cisneros, J. A. Andrade Lucio, R. Ramos-Garcia, E. A. Kuzin, J. J. Sánchez Mondragón, and V. Vysloukh, "Total internal reflection of spatial solitons at interface formed by a nonlinear saturable and a linear medium," Opt. Commun. 193, 267 (2001).
[CrossRef] [PubMed]

Vysloukh, V.

E. Alvarado Mendez, R. Rojas Laguna, J. G. Aviña Cervantes, M. Torres Cisneros, J. A. Andrade Lucio, R. Ramos-Garcia, E. A. Kuzin, J. J. Sánchez Mondragón, and V. Vysloukh, "Total internal reflection of spatial solitons at interface formed by a nonlinear saturable and a linear medium," Opt. Commun. 193, 267 (2001).
[CrossRef] [PubMed]

Vysloukh, V. A.

Xu, J.

Z. Chen, H. Martin, E. D. Eugenieva, J. Xu, and A. Bezryadina, "Anisotropic enhancement of discrete diffraction and formation of two-dimensional discrete-soliton trains," Phys. Rev. Lett. 92, 143902 (2004).
[CrossRef]

Yeh, P.

P. Yeh, A, Yariv, and A. Y. Cho, "Optical surface waves in periodic layered media," Appl. Phys. Lett. 32, 104 (1978).
[CrossRef]

Zelenina, A. S.

Appl. Phys. Lett. (2)

P. W. Smith, J. P. Hermann, W. J. Tomlinson, and P. J. Maloney, "Optical bistability at a nonlinear interface," Appl. Phys. Lett. 35, 846 (1979).
[CrossRef]

P. Yeh, A, Yariv, and A. Y. Cho, "Optical surface waves in periodic layered media," Appl. Phys. Lett. 32, 104 (1978).
[CrossRef]

JETP Lett. (1)

A. E. Kaplan, "Hysteresis reflection and refraction at the nonlinear interface - a new class of effects in nonlinear optics," JETP Lett. 24, 114 (1976).

Nature (2)

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 (2003).
[CrossRef] [PubMed]

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Figures (2)

Fig. 1.
Fig. 1.

(a) Schematic representation of the geometry of soliton refraction at the boundary between the lattice and uniform medium. Soliton propagation dynamics in illustrative cases, at Ω = 8 (b), 3.5 (c), and 2 (d). In all cases α in = 1, p = 1, χ = 1 .

Fig. 2.
Fig. 2.

(a) Reflected energy vs lattice frequency at α in = 1. (b) Propagation angle of transmitted soliton vs lattice frequency at α in = 1, p = 1. (c) Reflected energy vs lattice depth at α in = 1, Ω = 4.2. (d) Propagation angle of transmitted soliton vs lattice depth at α in = 1, Ω = 4.2. Curve 1 - numerical results, curve 2 - analytical effective index approximation. (e) Energy of transmitted soliton vs incident angle at p = 1 , Ω = 3. Curve 1 - numerical results, curve 2 - analytical effective index approximation. (f) Ratio of propagation angles of transmitted and incident solitons versus incident angle at p = 1, Ω = 3 . In all cases χ = 1.

Equations (6)

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i q ξ = 1 2 2 q η 2 q q 2 p R ( η ) q .
U = q 2 d η
η c ( ξ ) = U 1 q 2 η d η ,
d 2 η c d ξ 2 = p U d R d η q 2 d η .
d 2 η c d ξ 2 = p χ 2 coash 2 ( χ η c ) ,
U ref = 0 q 2 d η and U tr = 0 q 2 d η .

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