Abstract

We study experimentally an electrically pumped GaAs-based bandgap structure based on a vertical cavity surface emitting laser (VCSEL). We demonstrate that a microcavity embedded into this bandgap VCSEL structure supports localized optical modes without any holding beam. We propose a model of surface-structured VCSELs based on a reduced dissipative wave equation for describing electromagnetic modes in such semiconductor cavities and anal yze a crossover between linear and nonlinear solitonlike cavity modes.

© 2010 Optical Society of America

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  1. Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: from Fibers to Photonic Crystals (Academic, 2003).
  2. A. Scott, Nonlinear Science (Oxford U. Press, 2003).
  3. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 1995).
  4. S. F. Mingaleev and Yu. S. Kivshar, Phys. Rev. Lett. 86, 5474(2001).
    [CrossRef] [PubMed]
  5. K. Staliunas, Phys. Rev. Lett. 91, 053901 (2003).
    [CrossRef] [PubMed]
  6. D. Gomila, R. Zambrini, and G.-L. Oppo, Phys. Rev. Lett. 92, 253904 (2004).
    [CrossRef] [PubMed]
  7. K. Staliunas, O. Egorov, Yu. S. Kivshar, and F. Lederer, Phys. Rev. Lett. 101, 153903 (2008).
    [CrossRef] [PubMed]
  8. B. Terhalle, N. Radwell, P. Rose, C. Denz, and T. Ackemann, Appl. Phys. Lett. 93, 151114 (2008).
    [CrossRef]
  9. T. D. Lee, C.-Y. Chen, Y. Y. Lin, M.-C. Chou, T.-H. Wu, and R.-K. Lee, Phys. Rev. Lett. 101, 084101 (2008).
    [CrossRef] [PubMed]
  10. Y. Y. Lin, C.-Y. Chen, W. Chein, J. S. Pan, T. D. Lee, and R.-K. Lee, Appl. Phys. Lett. 94, 221112 (2009).
    [CrossRef]
  11. T. Maggipinto, M. Brambilla, G. K. Harkness, and W. J. Firth, Phys. Rev. E 62, 8726 (2000).
    [CrossRef]
  12. Y. Tanguy, T. Ackemann, W. J. Firth, and R. Jäger, Phys. Rev. Lett. 100, 013907 (2008).
    [CrossRef] [PubMed]
  13. P. Genevet, S. Barland, M. Giudici, and J. R. Tredicce, Phys. Rev. Lett. 101, 123905 (2008).
    [CrossRef] [PubMed]
  14. A. J. Scroggie, W. J. Firth, and G.-L. Oppo, Phys. Rev. A 80, 013829 (2009).
    [CrossRef]
  15. M. Tlidi, A. G. Vladimirov, D. Pieroux, and D. Turaev, Phys. Rev. Lett. 103, 103904 (2009).
    [CrossRef] [PubMed]
  16. C.-J. Cheng, Y. Y. Lin, C.-Y. Chen, T.-D. Lee, and R.-K. Lee, Appl. Phys. B 97, 619 (2009).
    [CrossRef]
  17. I. Fischer, O. Hess, W. Elsässer, and E. Gäobel, Europhys. Lett. 35, 579 (1996).
    [CrossRef]
  18. S.Trillo and W.Torruella, eds., Spatial Solitons(Springer, 2001).
  19. C. Denz, M. Schwab, and C. Weilnau, Transverse-Pattern Formation in Photorefractive Optics (Springer, 2003).
  20. C.-C. Jeng, Y. Y. Lin, R.-C. Hong, and R.-K. Lee, Phys. Rev. Lett. 102, 153905 (2009).
    [CrossRef] [PubMed]
  21. D. F. Siriani, M. P. Tan, A. M. Kasten, A. C. L. Harren, P. O. Leisher, J. D. Sulkin, J. J. Raftery, A. J. Danner, A. V. Giannopoulos, and K. D. Choquette, IEEE J. Sel. Top. Quantum Electron. 15, 909 (2009).
    [CrossRef]

2009

Y. Y. Lin, C.-Y. Chen, W. Chein, J. S. Pan, T. D. Lee, and R.-K. Lee, Appl. Phys. Lett. 94, 221112 (2009).
[CrossRef]

A. J. Scroggie, W. J. Firth, and G.-L. Oppo, Phys. Rev. A 80, 013829 (2009).
[CrossRef]

M. Tlidi, A. G. Vladimirov, D. Pieroux, and D. Turaev, Phys. Rev. Lett. 103, 103904 (2009).
[CrossRef] [PubMed]

C.-J. Cheng, Y. Y. Lin, C.-Y. Chen, T.-D. Lee, and R.-K. Lee, Appl. Phys. B 97, 619 (2009).
[CrossRef]

C.-C. Jeng, Y. Y. Lin, R.-C. Hong, and R.-K. Lee, Phys. Rev. Lett. 102, 153905 (2009).
[CrossRef] [PubMed]

D. F. Siriani, M. P. Tan, A. M. Kasten, A. C. L. Harren, P. O. Leisher, J. D. Sulkin, J. J. Raftery, A. J. Danner, A. V. Giannopoulos, and K. D. Choquette, IEEE J. Sel. Top. Quantum Electron. 15, 909 (2009).
[CrossRef]

2008

Y. Tanguy, T. Ackemann, W. J. Firth, and R. Jäger, Phys. Rev. Lett. 100, 013907 (2008).
[CrossRef] [PubMed]

P. Genevet, S. Barland, M. Giudici, and J. R. Tredicce, Phys. Rev. Lett. 101, 123905 (2008).
[CrossRef] [PubMed]

K. Staliunas, O. Egorov, Yu. S. Kivshar, and F. Lederer, Phys. Rev. Lett. 101, 153903 (2008).
[CrossRef] [PubMed]

B. Terhalle, N. Radwell, P. Rose, C. Denz, and T. Ackemann, Appl. Phys. Lett. 93, 151114 (2008).
[CrossRef]

T. D. Lee, C.-Y. Chen, Y. Y. Lin, M.-C. Chou, T.-H. Wu, and R.-K. Lee, Phys. Rev. Lett. 101, 084101 (2008).
[CrossRef] [PubMed]

2004

D. Gomila, R. Zambrini, and G.-L. Oppo, Phys. Rev. Lett. 92, 253904 (2004).
[CrossRef] [PubMed]

2003

K. Staliunas, Phys. Rev. Lett. 91, 053901 (2003).
[CrossRef] [PubMed]

2001

S. F. Mingaleev and Yu. S. Kivshar, Phys. Rev. Lett. 86, 5474(2001).
[CrossRef] [PubMed]

2000

T. Maggipinto, M. Brambilla, G. K. Harkness, and W. J. Firth, Phys. Rev. E 62, 8726 (2000).
[CrossRef]

1996

I. Fischer, O. Hess, W. Elsässer, and E. Gäobel, Europhys. Lett. 35, 579 (1996).
[CrossRef]

Ackemann, T.

Y. Tanguy, T. Ackemann, W. J. Firth, and R. Jäger, Phys. Rev. Lett. 100, 013907 (2008).
[CrossRef] [PubMed]

B. Terhalle, N. Radwell, P. Rose, C. Denz, and T. Ackemann, Appl. Phys. Lett. 93, 151114 (2008).
[CrossRef]

Agrawal, G. P.

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

Barland, S.

P. Genevet, S. Barland, M. Giudici, and J. R. Tredicce, Phys. Rev. Lett. 101, 123905 (2008).
[CrossRef] [PubMed]

Brambilla, M.

T. Maggipinto, M. Brambilla, G. K. Harkness, and W. J. Firth, Phys. Rev. E 62, 8726 (2000).
[CrossRef]

Chein, W.

Y. Y. Lin, C.-Y. Chen, W. Chein, J. S. Pan, T. D. Lee, and R.-K. Lee, Appl. Phys. Lett. 94, 221112 (2009).
[CrossRef]

Chen, C.-Y.

Y. Y. Lin, C.-Y. Chen, W. Chein, J. S. Pan, T. D. Lee, and R.-K. Lee, Appl. Phys. Lett. 94, 221112 (2009).
[CrossRef]

C.-J. Cheng, Y. Y. Lin, C.-Y. Chen, T.-D. Lee, and R.-K. Lee, Appl. Phys. B 97, 619 (2009).
[CrossRef]

T. D. Lee, C.-Y. Chen, Y. Y. Lin, M.-C. Chou, T.-H. Wu, and R.-K. Lee, Phys. Rev. Lett. 101, 084101 (2008).
[CrossRef] [PubMed]

Cheng, C.-J.

C.-J. Cheng, Y. Y. Lin, C.-Y. Chen, T.-D. Lee, and R.-K. Lee, Appl. Phys. B 97, 619 (2009).
[CrossRef]

Choquette, K. D.

D. F. Siriani, M. P. Tan, A. M. Kasten, A. C. L. Harren, P. O. Leisher, J. D. Sulkin, J. J. Raftery, A. J. Danner, A. V. Giannopoulos, and K. D. Choquette, IEEE J. Sel. Top. Quantum Electron. 15, 909 (2009).
[CrossRef]

Chou, M.-C.

T. D. Lee, C.-Y. Chen, Y. Y. Lin, M.-C. Chou, T.-H. Wu, and R.-K. Lee, Phys. Rev. Lett. 101, 084101 (2008).
[CrossRef] [PubMed]

Danner, A. J.

D. F. Siriani, M. P. Tan, A. M. Kasten, A. C. L. Harren, P. O. Leisher, J. D. Sulkin, J. J. Raftery, A. J. Danner, A. V. Giannopoulos, and K. D. Choquette, IEEE J. Sel. Top. Quantum Electron. 15, 909 (2009).
[CrossRef]

Denz, C.

B. Terhalle, N. Radwell, P. Rose, C. Denz, and T. Ackemann, Appl. Phys. Lett. 93, 151114 (2008).
[CrossRef]

C. Denz, M. Schwab, and C. Weilnau, Transverse-Pattern Formation in Photorefractive Optics (Springer, 2003).

Egorov, O.

K. Staliunas, O. Egorov, Yu. S. Kivshar, and F. Lederer, Phys. Rev. Lett. 101, 153903 (2008).
[CrossRef] [PubMed]

Elsässer, W.

I. Fischer, O. Hess, W. Elsässer, and E. Gäobel, Europhys. Lett. 35, 579 (1996).
[CrossRef]

Firth, W. J.

A. J. Scroggie, W. J. Firth, and G.-L. Oppo, Phys. Rev. A 80, 013829 (2009).
[CrossRef]

Y. Tanguy, T. Ackemann, W. J. Firth, and R. Jäger, Phys. Rev. Lett. 100, 013907 (2008).
[CrossRef] [PubMed]

T. Maggipinto, M. Brambilla, G. K. Harkness, and W. J. Firth, Phys. Rev. E 62, 8726 (2000).
[CrossRef]

Fischer, I.

I. Fischer, O. Hess, W. Elsässer, and E. Gäobel, Europhys. Lett. 35, 579 (1996).
[CrossRef]

Gäobel, E.

I. Fischer, O. Hess, W. Elsässer, and E. Gäobel, Europhys. Lett. 35, 579 (1996).
[CrossRef]

Genevet, P.

P. Genevet, S. Barland, M. Giudici, and J. R. Tredicce, Phys. Rev. Lett. 101, 123905 (2008).
[CrossRef] [PubMed]

Giannopoulos, A. V.

D. F. Siriani, M. P. Tan, A. M. Kasten, A. C. L. Harren, P. O. Leisher, J. D. Sulkin, J. J. Raftery, A. J. Danner, A. V. Giannopoulos, and K. D. Choquette, IEEE J. Sel. Top. Quantum Electron. 15, 909 (2009).
[CrossRef]

Giudici, M.

P. Genevet, S. Barland, M. Giudici, and J. R. Tredicce, Phys. Rev. Lett. 101, 123905 (2008).
[CrossRef] [PubMed]

Gomila, D.

D. Gomila, R. Zambrini, and G.-L. Oppo, Phys. Rev. Lett. 92, 253904 (2004).
[CrossRef] [PubMed]

Harkness, G. K.

T. Maggipinto, M. Brambilla, G. K. Harkness, and W. J. Firth, Phys. Rev. E 62, 8726 (2000).
[CrossRef]

Harren, A. C. L.

D. F. Siriani, M. P. Tan, A. M. Kasten, A. C. L. Harren, P. O. Leisher, J. D. Sulkin, J. J. Raftery, A. J. Danner, A. V. Giannopoulos, and K. D. Choquette, IEEE J. Sel. Top. Quantum Electron. 15, 909 (2009).
[CrossRef]

Hess, O.

I. Fischer, O. Hess, W. Elsässer, and E. Gäobel, Europhys. Lett. 35, 579 (1996).
[CrossRef]

Hong, R.-C.

C.-C. Jeng, Y. Y. Lin, R.-C. Hong, and R.-K. Lee, Phys. Rev. Lett. 102, 153905 (2009).
[CrossRef] [PubMed]

Jäger, R.

Y. Tanguy, T. Ackemann, W. J. Firth, and R. Jäger, Phys. Rev. Lett. 100, 013907 (2008).
[CrossRef] [PubMed]

Jeng, C.-C.

C.-C. Jeng, Y. Y. Lin, R.-C. Hong, and R.-K. Lee, Phys. Rev. Lett. 102, 153905 (2009).
[CrossRef] [PubMed]

Joannopoulos, J. D.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 1995).

Kasten, A. M.

D. F. Siriani, M. P. Tan, A. M. Kasten, A. C. L. Harren, P. O. Leisher, J. D. Sulkin, J. J. Raftery, A. J. Danner, A. V. Giannopoulos, and K. D. Choquette, IEEE J. Sel. Top. Quantum Electron. 15, 909 (2009).
[CrossRef]

Kivshar, Yu. S.

K. Staliunas, O. Egorov, Yu. S. Kivshar, and F. Lederer, Phys. Rev. Lett. 101, 153903 (2008).
[CrossRef] [PubMed]

S. F. Mingaleev and Yu. S. Kivshar, Phys. Rev. Lett. 86, 5474(2001).
[CrossRef] [PubMed]

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

Lederer, F.

K. Staliunas, O. Egorov, Yu. S. Kivshar, and F. Lederer, Phys. Rev. Lett. 101, 153903 (2008).
[CrossRef] [PubMed]

Lee, R.-K.

Y. Y. Lin, C.-Y. Chen, W. Chein, J. S. Pan, T. D. Lee, and R.-K. Lee, Appl. Phys. Lett. 94, 221112 (2009).
[CrossRef]

C.-J. Cheng, Y. Y. Lin, C.-Y. Chen, T.-D. Lee, and R.-K. Lee, Appl. Phys. B 97, 619 (2009).
[CrossRef]

C.-C. Jeng, Y. Y. Lin, R.-C. Hong, and R.-K. Lee, Phys. Rev. Lett. 102, 153905 (2009).
[CrossRef] [PubMed]

T. D. Lee, C.-Y. Chen, Y. Y. Lin, M.-C. Chou, T.-H. Wu, and R.-K. Lee, Phys. Rev. Lett. 101, 084101 (2008).
[CrossRef] [PubMed]

Lee, T. D.

Y. Y. Lin, C.-Y. Chen, W. Chein, J. S. Pan, T. D. Lee, and R.-K. Lee, Appl. Phys. Lett. 94, 221112 (2009).
[CrossRef]

T. D. Lee, C.-Y. Chen, Y. Y. Lin, M.-C. Chou, T.-H. Wu, and R.-K. Lee, Phys. Rev. Lett. 101, 084101 (2008).
[CrossRef] [PubMed]

Lee, T.-D.

C.-J. Cheng, Y. Y. Lin, C.-Y. Chen, T.-D. Lee, and R.-K. Lee, Appl. Phys. B 97, 619 (2009).
[CrossRef]

Leisher, P. O.

D. F. Siriani, M. P. Tan, A. M. Kasten, A. C. L. Harren, P. O. Leisher, J. D. Sulkin, J. J. Raftery, A. J. Danner, A. V. Giannopoulos, and K. D. Choquette, IEEE J. Sel. Top. Quantum Electron. 15, 909 (2009).
[CrossRef]

Lin, Y. Y.

Y. Y. Lin, C.-Y. Chen, W. Chein, J. S. Pan, T. D. Lee, and R.-K. Lee, Appl. Phys. Lett. 94, 221112 (2009).
[CrossRef]

C.-J. Cheng, Y. Y. Lin, C.-Y. Chen, T.-D. Lee, and R.-K. Lee, Appl. Phys. B 97, 619 (2009).
[CrossRef]

C.-C. Jeng, Y. Y. Lin, R.-C. Hong, and R.-K. Lee, Phys. Rev. Lett. 102, 153905 (2009).
[CrossRef] [PubMed]

T. D. Lee, C.-Y. Chen, Y. Y. Lin, M.-C. Chou, T.-H. Wu, and R.-K. Lee, Phys. Rev. Lett. 101, 084101 (2008).
[CrossRef] [PubMed]

Maggipinto, T.

T. Maggipinto, M. Brambilla, G. K. Harkness, and W. J. Firth, Phys. Rev. E 62, 8726 (2000).
[CrossRef]

Meade, R. D.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 1995).

Mingaleev, S. F.

S. F. Mingaleev and Yu. S. Kivshar, Phys. Rev. Lett. 86, 5474(2001).
[CrossRef] [PubMed]

Oppo, G.-L.

A. J. Scroggie, W. J. Firth, and G.-L. Oppo, Phys. Rev. A 80, 013829 (2009).
[CrossRef]

D. Gomila, R. Zambrini, and G.-L. Oppo, Phys. Rev. Lett. 92, 253904 (2004).
[CrossRef] [PubMed]

Pan, J. S.

Y. Y. Lin, C.-Y. Chen, W. Chein, J. S. Pan, T. D. Lee, and R.-K. Lee, Appl. Phys. Lett. 94, 221112 (2009).
[CrossRef]

Pieroux, D.

M. Tlidi, A. G. Vladimirov, D. Pieroux, and D. Turaev, Phys. Rev. Lett. 103, 103904 (2009).
[CrossRef] [PubMed]

Radwell, N.

B. Terhalle, N. Radwell, P. Rose, C. Denz, and T. Ackemann, Appl. Phys. Lett. 93, 151114 (2008).
[CrossRef]

Raftery, J. J.

D. F. Siriani, M. P. Tan, A. M. Kasten, A. C. L. Harren, P. O. Leisher, J. D. Sulkin, J. J. Raftery, A. J. Danner, A. V. Giannopoulos, and K. D. Choquette, IEEE J. Sel. Top. Quantum Electron. 15, 909 (2009).
[CrossRef]

Rose, P.

B. Terhalle, N. Radwell, P. Rose, C. Denz, and T. Ackemann, Appl. Phys. Lett. 93, 151114 (2008).
[CrossRef]

Schwab, M.

C. Denz, M. Schwab, and C. Weilnau, Transverse-Pattern Formation in Photorefractive Optics (Springer, 2003).

Scott, A.

A. Scott, Nonlinear Science (Oxford U. Press, 2003).

Scroggie, A. J.

A. J. Scroggie, W. J. Firth, and G.-L. Oppo, Phys. Rev. A 80, 013829 (2009).
[CrossRef]

Siriani, D. F.

D. F. Siriani, M. P. Tan, A. M. Kasten, A. C. L. Harren, P. O. Leisher, J. D. Sulkin, J. J. Raftery, A. J. Danner, A. V. Giannopoulos, and K. D. Choquette, IEEE J. Sel. Top. Quantum Electron. 15, 909 (2009).
[CrossRef]

Staliunas, K.

K. Staliunas, O. Egorov, Yu. S. Kivshar, and F. Lederer, Phys. Rev. Lett. 101, 153903 (2008).
[CrossRef] [PubMed]

K. Staliunas, Phys. Rev. Lett. 91, 053901 (2003).
[CrossRef] [PubMed]

Sulkin, J. D.

D. F. Siriani, M. P. Tan, A. M. Kasten, A. C. L. Harren, P. O. Leisher, J. D. Sulkin, J. J. Raftery, A. J. Danner, A. V. Giannopoulos, and K. D. Choquette, IEEE J. Sel. Top. Quantum Electron. 15, 909 (2009).
[CrossRef]

Tan, M. P.

D. F. Siriani, M. P. Tan, A. M. Kasten, A. C. L. Harren, P. O. Leisher, J. D. Sulkin, J. J. Raftery, A. J. Danner, A. V. Giannopoulos, and K. D. Choquette, IEEE J. Sel. Top. Quantum Electron. 15, 909 (2009).
[CrossRef]

Tanguy, Y.

Y. Tanguy, T. Ackemann, W. J. Firth, and R. Jäger, Phys. Rev. Lett. 100, 013907 (2008).
[CrossRef] [PubMed]

Terhalle, B.

B. Terhalle, N. Radwell, P. Rose, C. Denz, and T. Ackemann, Appl. Phys. Lett. 93, 151114 (2008).
[CrossRef]

Tlidi, M.

M. Tlidi, A. G. Vladimirov, D. Pieroux, and D. Turaev, Phys. Rev. Lett. 103, 103904 (2009).
[CrossRef] [PubMed]

Tredicce, J. R.

P. Genevet, S. Barland, M. Giudici, and J. R. Tredicce, Phys. Rev. Lett. 101, 123905 (2008).
[CrossRef] [PubMed]

Turaev, D.

M. Tlidi, A. G. Vladimirov, D. Pieroux, and D. Turaev, Phys. Rev. Lett. 103, 103904 (2009).
[CrossRef] [PubMed]

Vladimirov, A. G.

M. Tlidi, A. G. Vladimirov, D. Pieroux, and D. Turaev, Phys. Rev. Lett. 103, 103904 (2009).
[CrossRef] [PubMed]

Weilnau, C.

C. Denz, M. Schwab, and C. Weilnau, Transverse-Pattern Formation in Photorefractive Optics (Springer, 2003).

Winn, J. N.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 1995).

Wu, T.-H.

T. D. Lee, C.-Y. Chen, Y. Y. Lin, M.-C. Chou, T.-H. Wu, and R.-K. Lee, Phys. Rev. Lett. 101, 084101 (2008).
[CrossRef] [PubMed]

Zambrini, R.

D. Gomila, R. Zambrini, and G.-L. Oppo, Phys. Rev. Lett. 92, 253904 (2004).
[CrossRef] [PubMed]

Appl. Phys. B

C.-J. Cheng, Y. Y. Lin, C.-Y. Chen, T.-D. Lee, and R.-K. Lee, Appl. Phys. B 97, 619 (2009).
[CrossRef]

Appl. Phys. Lett.

Y. Y. Lin, C.-Y. Chen, W. Chein, J. S. Pan, T. D. Lee, and R.-K. Lee, Appl. Phys. Lett. 94, 221112 (2009).
[CrossRef]

B. Terhalle, N. Radwell, P. Rose, C. Denz, and T. Ackemann, Appl. Phys. Lett. 93, 151114 (2008).
[CrossRef]

Europhys. Lett.

I. Fischer, O. Hess, W. Elsässer, and E. Gäobel, Europhys. Lett. 35, 579 (1996).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

D. F. Siriani, M. P. Tan, A. M. Kasten, A. C. L. Harren, P. O. Leisher, J. D. Sulkin, J. J. Raftery, A. J. Danner, A. V. Giannopoulos, and K. D. Choquette, IEEE J. Sel. Top. Quantum Electron. 15, 909 (2009).
[CrossRef]

Phys. Rev. A

A. J. Scroggie, W. J. Firth, and G.-L. Oppo, Phys. Rev. A 80, 013829 (2009).
[CrossRef]

Phys. Rev. E

T. Maggipinto, M. Brambilla, G. K. Harkness, and W. J. Firth, Phys. Rev. E 62, 8726 (2000).
[CrossRef]

Phys. Rev. Lett.

Y. Tanguy, T. Ackemann, W. J. Firth, and R. Jäger, Phys. Rev. Lett. 100, 013907 (2008).
[CrossRef] [PubMed]

P. Genevet, S. Barland, M. Giudici, and J. R. Tredicce, Phys. Rev. Lett. 101, 123905 (2008).
[CrossRef] [PubMed]

T. D. Lee, C.-Y. Chen, Y. Y. Lin, M.-C. Chou, T.-H. Wu, and R.-K. Lee, Phys. Rev. Lett. 101, 084101 (2008).
[CrossRef] [PubMed]

S. F. Mingaleev and Yu. S. Kivshar, Phys. Rev. Lett. 86, 5474(2001).
[CrossRef] [PubMed]

K. Staliunas, Phys. Rev. Lett. 91, 053901 (2003).
[CrossRef] [PubMed]

D. Gomila, R. Zambrini, and G.-L. Oppo, Phys. Rev. Lett. 92, 253904 (2004).
[CrossRef] [PubMed]

K. Staliunas, O. Egorov, Yu. S. Kivshar, and F. Lederer, Phys. Rev. Lett. 101, 153903 (2008).
[CrossRef] [PubMed]

M. Tlidi, A. G. Vladimirov, D. Pieroux, and D. Turaev, Phys. Rev. Lett. 103, 103904 (2009).
[CrossRef] [PubMed]

C.-C. Jeng, Y. Y. Lin, R.-C. Hong, and R.-K. Lee, Phys. Rev. Lett. 102, 153905 (2009).
[CrossRef] [PubMed]

Other

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

A. Scott, Nonlinear Science (Oxford U. Press, 2003).

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 1995).

S.Trillo and W.Torruella, eds., Spatial Solitons(Springer, 2001).

C. Denz, M. Schwab, and C. Weilnau, Transverse-Pattern Formation in Photorefractive Optics (Springer, 2003).

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Figures (3)

Fig. 1
Fig. 1

(a) Structure of VCSEL with a surface PhCl cavity; (b) top-view SEM image.

Fig. 2
Fig. 2

(a) Dependence of the output lasing power on the injection current, measured experimentally (marked as •) and calculated from a theoretical model (solid curve). (b) Four low-order linear eigenmodes (solid curves) in a lossy cavity with periodic modulations of V ( ξ ) (shaded areas) and the corresponding nonlinear cavity modes (dashed curves) calculated at the injection current I = 36 mA . The modes are normalized, and a constant level is added to the real part of their eigenvalues.

Fig. 3
Fig. 3

Experimental demonstration of soliton lattices with 3D and 2D NSOM images (first and second columns). The injection currents are 33, 35, 36, and 37 mA , respectively. The third column shows the mode profile along the horizontal direction, i.e., along the dashed line in (e). The shaded areas mark a periodic lattice. The corresponding theoretical results are presented in the fourth column, for the parameters η = 5 , C = 2 , α = 5 , and d = 0.0001 .

Equations (1)

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i τ E + 1 α θ ¯ E ( 1 + i 1 α ) [ ( 1 + η ) + 2 C ( I 1 ) 1 + | E | 2 ] E + ( 1 i 1 α d ) ξ 2 E = 0 ,

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