Abstract

Propagation of extended Floquet-Bloch modes in the first three bands of a one-dimensional photonic lattice possessing a self-defocusing saturable nonlinearity is studied experimentally and numerically on the example of waveguide arrays in lithium niobate. Discrete modulation instability is observed in all bands in the region of anomalous diffraction, whereas modes propagate stable in the normal diffraction regime.

© 2007 Optical Society of America

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  1. A. Hasegawa, "Theory and computer experiment on self-trapping instability of plasma cyclotron," Phys. Fluids 15, 870 (1972).
    [CrossRef]
  2. T. B. Benjamin and J. E. Feir, "Disintegration of wave trains on deep water," J. Fluid Mech. 27, 417 (1967).
    [CrossRef]
  3. P. Marquie, J. M. Bilbaut, and M. Remoissenet, "Generation of envelope and hole solitons in an experimental transmission line," Phys. Rev. E 49, 828 (1994).
    [CrossRef]
  4. K. E. Strecker, G. B. Partridge, A. G. Truscott, and R. G. Hulet, "Formation and propagation of matter-wave soliton trains," Nature 417, 150 (2002).
    [CrossRef] [PubMed]
  5. K. Tai, A. Hasegawa, and A. Tomita, "Observation of modulational instability in optical fibers," Phys. Rev. Lett. 56, 135 (1986).
    [CrossRef] [PubMed]
  6. M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, "Modulational instability of quasi-plane-wave optical beams biased in photorefractive crystals," Opt. Commun. 126, 167 (1996).
    [CrossRef]
  7. D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, "Modulation instability and pattern formation in spatially incoherent light beams," Science 290, 495 (2000).
    [CrossRef] [PubMed]
  8. D. N. Christodoulides, F. Lederer, and Y. Silberberg, "Discretizing light behavior in linear and nonlinear waveguide lattices," Nature 424, 817 (2003).
    [CrossRef] [PubMed]
  9. Yu. S. Kivshar and M. Peyrard, "Modulation instabilities in discrete lattices," Phys. Rev. A 46, 3198 (1992).
    [CrossRef] [PubMed]
  10. D. N. Christodoulides and R. I. Joseph, "Discrete self-focusing in nonlinear arrays of coupled waveguides," Opt. Lett. 19, 794 (1988).
    [CrossRef]
  11. H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383 (1998).
    [CrossRef]
  12. F. Chen, M. Stepić, C. E. Rüter, D. Runde, D. Kip, V. Shandarov, O. Manela, and M. Segev, "Discrete diffraction and spatial gap solitons in photovoltaic LiNbO3 waveguide arrays," Opt. Express 13, 4314 (2005).
    [CrossRef] [PubMed]
  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. J.  Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, J. S. Aitchison, "Observation of discrete modulational instability," Phys. Rev. Lett. 92, 163902 (2004).
    [CrossRef] [PubMed]
  15. M. Stepić, C. Wirth, C. E. Rüter, and D. Kip, "Observation of modulation instability in discrete media with self-defocusing nonlinearity," Opt. Lett. 31, 247 (2006).
    [CrossRef] [PubMed]
  16. C. E. Rüter, J. Wisniewski, and D. Kip, "Prism coupling method to excite and analyze Floquet-Bloch modes in linear and nonlinear waveguide arrays," Opt. Lett. 31, 2768 (2006).
    [CrossRef] [PubMed]
  17. J. Vollmer, J. P. Nisius, P. Hertel, and E. Krätzig, "Refractive index profiles of LiNbO3:Ti waveguides," Appl. Phys. A 32, 125 (1983).
    [CrossRef]
  18. M. Stepić, C. E. Rüter, D. Kip, A. Maluckov, and Lj. Hadžievski, "Modulational instability in one-dimen-sional saturable waveguide arrays: comparison with Kerr nonlinearity," Opt. Commun. 267, 229 (2006).
    [CrossRef]

2006 (3)

2005 (1)

2004 (1)

J.  Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, J. S. Aitchison, "Observation of discrete modulational instability," Phys. Rev. Lett. 92, 163902 (2004).
[CrossRef] [PubMed]

2003 (2)

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]

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

2002 (1)

K. E. Strecker, G. B. Partridge, A. G. Truscott, and R. G. Hulet, "Formation and propagation of matter-wave soliton trains," Nature 417, 150 (2002).
[CrossRef] [PubMed]

2000 (1)

D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, "Modulation instability and pattern formation in spatially incoherent light beams," Science 290, 495 (2000).
[CrossRef] [PubMed]

1998 (1)

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

1996 (1)

M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, "Modulational instability of quasi-plane-wave optical beams biased in photorefractive crystals," Opt. Commun. 126, 167 (1996).
[CrossRef]

1994 (1)

P. Marquie, J. M. Bilbaut, and M. Remoissenet, "Generation of envelope and hole solitons in an experimental transmission line," Phys. Rev. E 49, 828 (1994).
[CrossRef]

1992 (1)

Yu. S. Kivshar and M. Peyrard, "Modulation instabilities in discrete lattices," Phys. Rev. A 46, 3198 (1992).
[CrossRef] [PubMed]

1988 (1)

D. N. Christodoulides and R. I. Joseph, "Discrete self-focusing in nonlinear arrays of coupled waveguides," Opt. Lett. 19, 794 (1988).
[CrossRef]

1986 (1)

K. Tai, A. Hasegawa, and A. Tomita, "Observation of modulational instability in optical fibers," Phys. Rev. Lett. 56, 135 (1986).
[CrossRef] [PubMed]

1983 (1)

J. Vollmer, J. P. Nisius, P. Hertel, and E. Krätzig, "Refractive index profiles of LiNbO3:Ti waveguides," Appl. Phys. A 32, 125 (1983).
[CrossRef]

1972 (1)

A. Hasegawa, "Theory and computer experiment on self-trapping instability of plasma cyclotron," Phys. Fluids 15, 870 (1972).
[CrossRef]

1967 (1)

T. B. Benjamin and J. E. Feir, "Disintegration of wave trains on deep water," J. Fluid Mech. 27, 417 (1967).
[CrossRef]

Aitchison, J. S.

J.  Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, J. S. Aitchison, "Observation of discrete modulational instability," Phys. Rev. Lett. 92, 163902 (2004).
[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, R. Morandotti, A. R. Boyd, and J. S. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Benjamin, T. B.

T. B. Benjamin and J. E. Feir, "Disintegration of wave trains on deep water," J. Fluid Mech. 27, 417 (1967).
[CrossRef]

Bilbaut, J. M.

P. Marquie, J. M. Bilbaut, and M. Remoissenet, "Generation of envelope and hole solitons in an experimental transmission line," Phys. Rev. E 49, 828 (1994).
[CrossRef]

Boyd, A. R.

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

Carvalho, M. I.

M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, "Modulational instability of quasi-plane-wave optical beams biased in photorefractive crystals," Opt. Commun. 126, 167 (1996).
[CrossRef]

Chen, F.

Christodoulides, D. N.

J.  Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, J. S. Aitchison, "Observation of discrete modulational instability," Phys. Rev. Lett. 92, 163902 (2004).
[CrossRef] [PubMed]

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

D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, "Modulation instability and pattern formation in spatially incoherent light beams," Science 290, 495 (2000).
[CrossRef] [PubMed]

M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, "Modulational instability of quasi-plane-wave optical beams biased in photorefractive crystals," Opt. Commun. 126, 167 (1996).
[CrossRef]

D. N. Christodoulides and R. I. Joseph, "Discrete self-focusing in nonlinear arrays of coupled waveguides," Opt. Lett. 19, 794 (1988).
[CrossRef]

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

Eugenieva, E.

D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, "Modulation instability and pattern formation in spatially incoherent light beams," Science 290, 495 (2000).
[CrossRef] [PubMed]

Feir, J. E.

T. B. Benjamin and J. E. Feir, "Disintegration of wave trains on deep water," J. Fluid Mech. 27, 417 (1967).
[CrossRef]

Hadžievski, Lj.

M. Stepić, C. E. Rüter, D. Kip, A. Maluckov, and Lj. Hadžievski, "Modulational instability in one-dimen-sional saturable waveguide arrays: comparison with Kerr nonlinearity," Opt. Commun. 267, 229 (2006).
[CrossRef]

Hasegawa, A.

K. Tai, A. Hasegawa, and A. Tomita, "Observation of modulational instability in optical fibers," Phys. Rev. Lett. 56, 135 (1986).
[CrossRef] [PubMed]

A. Hasegawa, "Theory and computer experiment on self-trapping instability of plasma cyclotron," Phys. Fluids 15, 870 (1972).
[CrossRef]

Hertel, P.

J. Vollmer, J. P. Nisius, P. Hertel, and E. Krätzig, "Refractive index profiles of LiNbO3:Ti waveguides," Appl. Phys. A 32, 125 (1983).
[CrossRef]

Hulet, R. G.

K. E. Strecker, G. B. Partridge, A. G. Truscott, and R. G. Hulet, "Formation and propagation of matter-wave soliton trains," Nature 417, 150 (2002).
[CrossRef] [PubMed]

Joseph, R. I.

D. N. Christodoulides and R. I. Joseph, "Discrete self-focusing in nonlinear arrays of coupled waveguides," Opt. Lett. 19, 794 (1988).
[CrossRef]

Kip, D.

Kivshar, Yu. S.

Yu. S. Kivshar and M. Peyrard, "Modulation instabilities in discrete lattices," Phys. Rev. A 46, 3198 (1992).
[CrossRef] [PubMed]

Krätzig, E.

J. Vollmer, J. P. Nisius, P. Hertel, and E. Krätzig, "Refractive index profiles of LiNbO3:Ti waveguides," Appl. Phys. A 32, 125 (1983).
[CrossRef]

Lederer, F.

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

Maluckov, A.

M. Stepić, C. E. Rüter, D. Kip, A. Maluckov, and Lj. Hadžievski, "Modulational instability in one-dimen-sional saturable waveguide arrays: comparison with Kerr nonlinearity," Opt. Commun. 267, 229 (2006).
[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]

Manela, O.

Marquie, P.

P. Marquie, J. M. Bilbaut, and M. Remoissenet, "Generation of envelope and hole solitons in an experimental transmission line," Phys. Rev. E 49, 828 (1994).
[CrossRef]

Meier, J.

J.  Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, J. S. Aitchison, "Observation of discrete modulational instability," Phys. Rev. Lett. 92, 163902 (2004).
[CrossRef] [PubMed]

Morandotti, R.

J.  Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, J. S. Aitchison, "Observation of discrete modulational instability," Phys. Rev. Lett. 92, 163902 (2004).
[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, R. Morandotti, A. R. Boyd, and J. S. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Nisius, J. P.

J. Vollmer, J. P. Nisius, P. Hertel, and E. Krätzig, "Refractive index profiles of LiNbO3:Ti waveguides," Appl. Phys. A 32, 125 (1983).
[CrossRef]

Partridge, G. B.

K. E. Strecker, G. B. Partridge, A. G. Truscott, and R. G. Hulet, "Formation and propagation of matter-wave soliton trains," Nature 417, 150 (2002).
[CrossRef] [PubMed]

Peyrard, M.

Yu. S. Kivshar and M. Peyrard, "Modulation instabilities in discrete lattices," Phys. Rev. A 46, 3198 (1992).
[CrossRef] [PubMed]

Remoissenet, M.

P. Marquie, J. M. Bilbaut, and M. Remoissenet, "Generation of envelope and hole solitons in an experimental transmission line," Phys. Rev. E 49, 828 (1994).
[CrossRef]

Runde, D.

Rüter, C. E.

Salamo, G.

J.  Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, J. S. Aitchison, "Observation of discrete modulational instability," Phys. Rev. Lett. 92, 163902 (2004).
[CrossRef] [PubMed]

Segev, M.

F. Chen, M. Stepić, C. E. Rüter, D. Runde, D. Kip, V. Shandarov, O. Manela, and M. Segev, "Discrete diffraction and spatial gap solitons in photovoltaic LiNbO3 waveguide arrays," Opt. Express 13, 4314 (2005).
[CrossRef] [PubMed]

D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, "Modulation instability and pattern formation in spatially incoherent light beams," Science 290, 495 (2000).
[CrossRef] [PubMed]

Shandarov, V.

Silberberg, Y.

J.  Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, J. S. Aitchison, "Observation of discrete modulational instability," Phys. Rev. Lett. 92, 163902 (2004).
[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]

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

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

Singh, S. R.

M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, "Modulational instability of quasi-plane-wave optical beams biased in photorefractive crystals," Opt. Commun. 126, 167 (1996).
[CrossRef]

Soljacic, M.

D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, "Modulation instability and pattern formation in spatially incoherent light beams," Science 290, 495 (2000).
[CrossRef] [PubMed]

Sorel, M.

J.  Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, J. S. Aitchison, "Observation of discrete modulational instability," Phys. Rev. Lett. 92, 163902 (2004).
[CrossRef] [PubMed]

Stegeman, G. I.

J.  Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, J. S. Aitchison, "Observation of discrete modulational instability," Phys. Rev. Lett. 92, 163902 (2004).
[CrossRef] [PubMed]

Stepic, M.

Strecker, K. E.

K. E. Strecker, G. B. Partridge, A. G. Truscott, and R. G. Hulet, "Formation and propagation of matter-wave soliton trains," Nature 417, 150 (2002).
[CrossRef] [PubMed]

Tai, K.

K. Tai, A. Hasegawa, and A. Tomita, "Observation of modulational instability in optical fibers," Phys. Rev. Lett. 56, 135 (1986).
[CrossRef] [PubMed]

Tomita, A.

K. Tai, A. Hasegawa, and A. Tomita, "Observation of modulational instability in optical fibers," Phys. Rev. Lett. 56, 135 (1986).
[CrossRef] [PubMed]

Truscott, A. G.

K. E. Strecker, G. B. Partridge, A. G. Truscott, and R. G. Hulet, "Formation and propagation of matter-wave soliton trains," Nature 417, 150 (2002).
[CrossRef] [PubMed]

Vollmer, J.

J. Vollmer, J. P. Nisius, P. Hertel, and E. Krätzig, "Refractive index profiles of LiNbO3:Ti waveguides," Appl. Phys. A 32, 125 (1983).
[CrossRef]

Wirth, C.

Wisniewski, J.

Yang, H.

J.  Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, J. S. Aitchison, "Observation of discrete modulational instability," Phys. Rev. Lett. 92, 163902 (2004).
[CrossRef] [PubMed]

Appl. Phys. A (1)

J. Vollmer, J. P. Nisius, P. Hertel, and E. Krätzig, "Refractive index profiles of LiNbO3:Ti waveguides," Appl. Phys. A 32, 125 (1983).
[CrossRef]

J. Fluid Mech. (1)

T. B. Benjamin and J. E. Feir, "Disintegration of wave trains on deep water," J. Fluid Mech. 27, 417 (1967).
[CrossRef]

Nature (2)

K. E. Strecker, G. B. Partridge, A. G. Truscott, and R. G. Hulet, "Formation and propagation of matter-wave soliton trains," Nature 417, 150 (2002).
[CrossRef] [PubMed]

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

Opt. Commun. (2)

M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, "Modulational instability of quasi-plane-wave optical beams biased in photorefractive crystals," Opt. Commun. 126, 167 (1996).
[CrossRef]

M. Stepić, C. E. Rüter, D. Kip, A. Maluckov, and Lj. Hadžievski, "Modulational instability in one-dimen-sional saturable waveguide arrays: comparison with Kerr nonlinearity," Opt. Commun. 267, 229 (2006).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Phys. Fluids (1)

A. Hasegawa, "Theory and computer experiment on self-trapping instability of plasma cyclotron," Phys. Fluids 15, 870 (1972).
[CrossRef]

Phys. Rev. A (1)

Yu. S. Kivshar and M. Peyrard, "Modulation instabilities in discrete lattices," Phys. Rev. A 46, 3198 (1992).
[CrossRef] [PubMed]

Phys. Rev. E (1)

P. Marquie, J. M. Bilbaut, and M. Remoissenet, "Generation of envelope and hole solitons in an experimental transmission line," Phys. Rev. E 49, 828 (1994).
[CrossRef]

Phys. Rev. Lett. (4)

K. Tai, A. Hasegawa, and A. Tomita, "Observation of modulational instability in optical fibers," Phys. Rev. Lett. 56, 135 (1986).
[CrossRef] [PubMed]

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

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, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, J. S. Aitchison, "Observation of discrete modulational instability," Phys. Rev. Lett. 92, 163902 (2004).
[CrossRef] [PubMed]

Science (1)

D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, "Modulation instability and pattern formation in spatially incoherent light beams," Science 290, 495 (2000).
[CrossRef] [PubMed]

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Figures (6)

Fig. 1.
Fig. 1.

Measured (symbols) and calculated (lines) band structure of the two arrays used with grating periods 8 μm [left hand side (lhs)] and 9 μm [right hand side (rhs)]

Fig. 2.
Fig. 2.

Time dependent output intensity at the rear facet of a WA with period Λ = 8 μm in the 1st band at the edge of the BZ for input powers (a) 2 μW, (b) 10μW, and (c) 26 μW. Corresponding simulations with intensity ratios I/Id = 0.5 (d), I/Id = 3 (e), and I/Id = 9 (f).

Fig. 3.
Fig. 3.

(a). Absence of MI in 2nd band at kz = π/Λ for Pin = 6 μW. (b) Simulation with I/Id = 1.

Fig. 4.
Fig. 4.

Discrete MI in the 2nd band of a WA with Λ = 8 μm at kz = 2π/Λ for Pin = 7 μW (a) and Pin = 21 μW. (b) Simulations with I/Id = 1 (c) and I/Id = 3 (d).

Fig. 5.
Fig. 5.

(a). Discrete MI in the 3rd band of a WA with Λ = 8 μm at kz = π/Λ and Pin = 20 μW. (b) Corresponding simulation with I/Id = 1.

Fig. 7.
Fig. 7.

Discrete MI in a WA with Λ = 9 μm: (a) 2nd band at kz = 2π/Λ and Pin = 20 μW. (b) 3rd band at kz = π/Λ and Pin = 7 μW. (c,d) Corresponding simulations with I/Id = 3.

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