Abstract

We theoretically investigate the spatial modulation instability (MI) properties of an electrically pumped, periodically patterned semiconductor optical amplifier. The MI spatial period is found to be related to the widths of the stable solitons supported by this device. Specific conditions for the observation of MI in such dissipative structures are given in terms of relevant examples.

© 2006 Optical Society of America

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  1. G. I. Stegeman and M. Segev, "Optical spatial solitons and their interactions: universality and diversity," Science 286, 1518-1523 (1999).
    [CrossRef] [PubMed]
  2. E. A. Ultanir, G. I. Stegeman, D. Michaelis, C. H. Lange, and F. Lederer, "Stable dissipative solitons in semiconductor optical amplifiers," Phys. Rev. Lett. 90, 253903 (2003).
    [CrossRef] [PubMed]
  3. E. A. Ultanir, D. Michaelis, F. Lederer, and G. I. Stegeman, "Stable spatial solitons in semiconductor optical amplifiers," Opt. Lett. 28, 251-253 (2003).
    [CrossRef] [PubMed]
  4. D. Michaelis, U. Peschel, and F. Lederer, "Multistable localized structures and superlattices in semiconductor optical resonators," Phys. Rev. A 56, R3366-R3369 (1997).
    [CrossRef]
  5. L. Spinelli, G. Tissoni, M. Brambilla, F. Prati, and L. A. Lugiato, "Spatial solitons in semiconductor microcavities," Phys. Rev. A 58, 2542-2559 (1998).
    [CrossRef]
  6. E. A. Ultanir, G. I. Stegeman, C. H. Lange, and F. Lederer, "Coherent interactions of dissipative spatial solitons," Opt. Lett. 29, 283-285 (2004).
    [CrossRef] [PubMed]
  7. S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Guidici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, "Cavity solitons as pixels in semiconductor microcavities," Nature 419, 699-702 (2002).
    [CrossRef] [PubMed]
  8. Z. Chen and K. McCarthy, "Spatial soliton pixels from partially incoherent light," Opt. Lett. 27, 2019-2021 (2002).
    [CrossRef]
  9. J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature 422, 147-150 (2003).
    [CrossRef] [PubMed]
  10. G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, 1995), pp. 133-142.
  11. M. Soljacic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, "Modulation instability of incoherent beams in noninstantaneous nonlinear media," Phys. Rev. Lett. 84, 467-470 (2000).
    [CrossRef] [PubMed]
  12. A. Hasegawa and W. F. Brinkman, "Tunable coherent IR and FIR sources utilizing modulational instability," IEEE J. Quantum Electron. 16694-697 (1980).
    [CrossRef]
  13. J. R. Tredicce, E. J. Quel, A. M. Ghazzawi, C. Green, M. A. Pernigo, L. M. Narducci, and L. A. Lugiato, "Spatial and temporal instabilities in a CO2 laser," Phys. Rev. Lett. 62, 1274-1277 (1989).
    [CrossRef] [PubMed]
  14. M. Nakazawa, K. Suzukki, and H. A. Haus, "Modulational instability oscillation in nonlinear dispersive ring cavity," Phys. Rev. A 38, 5193-5196 (1988).
    [CrossRef] [PubMed]
  15. M. Haelterman, S. Trillo, and S. Wabnitz, "Additive-modulation instability ring laser in the normal dispersion regime of a fiber," Opt. Lett. 17, 745-747 (1992).
    [CrossRef] [PubMed]
  16. L. Goldberg, M. R. Surette, and D. Mehuys, "Filament formation in a tapered GaAlAs optical amplifier," Appl. Phys. Lett. 62, 2304-2306 (1993).
    [CrossRef]
  17. A. H. Paxton and G. C. Dente, "Filament formation in semiconductor laser gain regions," J. Appl. Phys. 70, 2921-2925 (1991).
    [CrossRef]
  18. 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, 167-174 (1996).
    [CrossRef]
  19. S. Trillo and P. Ferro, "Modulational instability in second-harmonic generation," Opt. Lett. 20, 438-440 (1995).
    [CrossRef] [PubMed]
  20. P. Ferro and S. Trillo, "Periodical waves, domain walls, and modulational instability in dispersive quadratic nonlinear media," Phys. Rev. E 51, 4994-4998 (1995).
    [CrossRef]

2004 (1)

2003 (3)

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

E. A. Ultanir, G. I. Stegeman, D. Michaelis, C. H. Lange, and F. Lederer, "Stable dissipative solitons in semiconductor optical amplifiers," Phys. Rev. Lett. 90, 253903 (2003).
[CrossRef] [PubMed]

E. A. Ultanir, D. Michaelis, F. Lederer, and G. I. Stegeman, "Stable spatial solitons in semiconductor optical amplifiers," Opt. Lett. 28, 251-253 (2003).
[CrossRef] [PubMed]

2002 (2)

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Guidici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, "Cavity solitons as pixels in semiconductor microcavities," Nature 419, 699-702 (2002).
[CrossRef] [PubMed]

Z. Chen and K. McCarthy, "Spatial soliton pixels from partially incoherent light," Opt. Lett. 27, 2019-2021 (2002).
[CrossRef]

2000 (1)

M. Soljacic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, "Modulation instability of incoherent beams in noninstantaneous nonlinear media," Phys. Rev. Lett. 84, 467-470 (2000).
[CrossRef] [PubMed]

1999 (1)

G. I. Stegeman and M. Segev, "Optical spatial solitons and their interactions: universality and diversity," Science 286, 1518-1523 (1999).
[CrossRef] [PubMed]

1998 (1)

L. Spinelli, G. Tissoni, M. Brambilla, F. Prati, and L. A. Lugiato, "Spatial solitons in semiconductor microcavities," Phys. Rev. A 58, 2542-2559 (1998).
[CrossRef]

1997 (1)

D. Michaelis, U. Peschel, and F. Lederer, "Multistable localized structures and superlattices in semiconductor optical resonators," Phys. Rev. A 56, R3366-R3369 (1997).
[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, 167-174 (1996).
[CrossRef]

1995 (2)

S. Trillo and P. Ferro, "Modulational instability in second-harmonic generation," Opt. Lett. 20, 438-440 (1995).
[CrossRef] [PubMed]

P. Ferro and S. Trillo, "Periodical waves, domain walls, and modulational instability in dispersive quadratic nonlinear media," Phys. Rev. E 51, 4994-4998 (1995).
[CrossRef]

1993 (1)

L. Goldberg, M. R. Surette, and D. Mehuys, "Filament formation in a tapered GaAlAs optical amplifier," Appl. Phys. Lett. 62, 2304-2306 (1993).
[CrossRef]

1992 (1)

1991 (1)

A. H. Paxton and G. C. Dente, "Filament formation in semiconductor laser gain regions," J. Appl. Phys. 70, 2921-2925 (1991).
[CrossRef]

1989 (1)

J. R. Tredicce, E. J. Quel, A. M. Ghazzawi, C. Green, M. A. Pernigo, L. M. Narducci, and L. A. Lugiato, "Spatial and temporal instabilities in a CO2 laser," Phys. Rev. Lett. 62, 1274-1277 (1989).
[CrossRef] [PubMed]

1988 (1)

M. Nakazawa, K. Suzukki, and H. A. Haus, "Modulational instability oscillation in nonlinear dispersive ring cavity," Phys. Rev. A 38, 5193-5196 (1988).
[CrossRef] [PubMed]

1980 (1)

A. Hasegawa and W. F. Brinkman, "Tunable coherent IR and FIR sources utilizing modulational instability," IEEE J. Quantum Electron. 16694-697 (1980).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, 1995), pp. 133-142.

Balle, S.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Guidici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, "Cavity solitons as pixels in semiconductor microcavities," Nature 419, 699-702 (2002).
[CrossRef] [PubMed]

Barland, S.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Guidici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, "Cavity solitons as pixels in semiconductor microcavities," Nature 419, 699-702 (2002).
[CrossRef] [PubMed]

Brambilla, M.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Guidici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, "Cavity solitons as pixels in semiconductor microcavities," Nature 419, 699-702 (2002).
[CrossRef] [PubMed]

L. Spinelli, G. Tissoni, M. Brambilla, F. Prati, and L. A. Lugiato, "Spatial solitons in semiconductor microcavities," Phys. Rev. A 58, 2542-2559 (1998).
[CrossRef]

Brinkman, W. F.

A. Hasegawa and W. F. Brinkman, "Tunable coherent IR and FIR sources utilizing modulational instability," IEEE J. Quantum Electron. 16694-697 (1980).
[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, 167-174 (1996).
[CrossRef]

Chen, Z.

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, 147-150 (2003).
[CrossRef] [PubMed]

M. Soljacic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, "Modulation instability of incoherent beams in noninstantaneous nonlinear media," Phys. Rev. Lett. 84, 467-470 (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, 167-174 (1996).
[CrossRef]

Coskun, T.

M. Soljacic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, "Modulation instability of incoherent beams in noninstantaneous nonlinear media," Phys. Rev. Lett. 84, 467-470 (2000).
[CrossRef] [PubMed]

Dente, G. C.

A. H. Paxton and G. C. Dente, "Filament formation in semiconductor laser gain regions," J. Appl. Phys. 70, 2921-2925 (1991).
[CrossRef]

Efremidis, N. K.

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

Ferro, P.

S. Trillo and P. Ferro, "Modulational instability in second-harmonic generation," Opt. Lett. 20, 438-440 (1995).
[CrossRef] [PubMed]

P. Ferro and S. Trillo, "Periodical waves, domain walls, and modulational instability in dispersive quadratic nonlinear media," Phys. Rev. E 51, 4994-4998 (1995).
[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, 147-150 (2003).
[CrossRef] [PubMed]

Ghazzawi, A. M.

J. R. Tredicce, E. J. Quel, A. M. Ghazzawi, C. Green, M. A. Pernigo, L. M. Narducci, and L. A. Lugiato, "Spatial and temporal instabilities in a CO2 laser," Phys. Rev. Lett. 62, 1274-1277 (1989).
[CrossRef] [PubMed]

Goldberg, L.

L. Goldberg, M. R. Surette, and D. Mehuys, "Filament formation in a tapered GaAlAs optical amplifier," Appl. Phys. Lett. 62, 2304-2306 (1993).
[CrossRef]

Green, C.

J. R. Tredicce, E. J. Quel, A. M. Ghazzawi, C. Green, M. A. Pernigo, L. M. Narducci, and L. A. Lugiato, "Spatial and temporal instabilities in a CO2 laser," Phys. Rev. Lett. 62, 1274-1277 (1989).
[CrossRef] [PubMed]

Guidici, M.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Guidici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, "Cavity solitons as pixels in semiconductor microcavities," Nature 419, 699-702 (2002).
[CrossRef] [PubMed]

Haelterman, M.

Hasegawa, A.

A. Hasegawa and W. F. Brinkman, "Tunable coherent IR and FIR sources utilizing modulational instability," IEEE J. Quantum Electron. 16694-697 (1980).
[CrossRef]

Haus, H. A.

M. Nakazawa, K. Suzukki, and H. A. Haus, "Modulational instability oscillation in nonlinear dispersive ring cavity," Phys. Rev. A 38, 5193-5196 (1988).
[CrossRef] [PubMed]

Jager, R.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Guidici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, "Cavity solitons as pixels in semiconductor microcavities," Nature 419, 699-702 (2002).
[CrossRef] [PubMed]

Knodl, T.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Guidici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, "Cavity solitons as pixels in semiconductor microcavities," Nature 419, 699-702 (2002).
[CrossRef] [PubMed]

Lange, C. H.

E. A. Ultanir, G. I. Stegeman, C. H. Lange, and F. Lederer, "Coherent interactions of dissipative spatial solitons," Opt. Lett. 29, 283-285 (2004).
[CrossRef] [PubMed]

E. A. Ultanir, G. I. Stegeman, D. Michaelis, C. H. Lange, and F. Lederer, "Stable dissipative solitons in semiconductor optical amplifiers," Phys. Rev. Lett. 90, 253903 (2003).
[CrossRef] [PubMed]

Lederer, F.

E. A. Ultanir, G. I. Stegeman, C. H. Lange, and F. Lederer, "Coherent interactions of dissipative spatial solitons," Opt. Lett. 29, 283-285 (2004).
[CrossRef] [PubMed]

E. A. Ultanir, G. I. Stegeman, D. Michaelis, C. H. Lange, and F. Lederer, "Stable dissipative solitons in semiconductor optical amplifiers," Phys. Rev. Lett. 90, 253903 (2003).
[CrossRef] [PubMed]

E. A. Ultanir, D. Michaelis, F. Lederer, and G. I. Stegeman, "Stable spatial solitons in semiconductor optical amplifiers," Opt. Lett. 28, 251-253 (2003).
[CrossRef] [PubMed]

D. Michaelis, U. Peschel, and F. Lederer, "Multistable localized structures and superlattices in semiconductor optical resonators," Phys. Rev. A 56, R3366-R3369 (1997).
[CrossRef]

Lugiato, L. A.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Guidici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, "Cavity solitons as pixels in semiconductor microcavities," Nature 419, 699-702 (2002).
[CrossRef] [PubMed]

L. Spinelli, G. Tissoni, M. Brambilla, F. Prati, and L. A. Lugiato, "Spatial solitons in semiconductor microcavities," Phys. Rev. A 58, 2542-2559 (1998).
[CrossRef]

J. R. Tredicce, E. J. Quel, A. M. Ghazzawi, C. Green, M. A. Pernigo, L. M. Narducci, and L. A. Lugiato, "Spatial and temporal instabilities in a CO2 laser," Phys. Rev. Lett. 62, 1274-1277 (1989).
[CrossRef] [PubMed]

Maggipinto, T.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Guidici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, "Cavity solitons as pixels in semiconductor microcavities," Nature 419, 699-702 (2002).
[CrossRef] [PubMed]

McCarthy, K.

Mehuys, D.

L. Goldberg, M. R. Surette, and D. Mehuys, "Filament formation in a tapered GaAlAs optical amplifier," Appl. Phys. Lett. 62, 2304-2306 (1993).
[CrossRef]

Michaelis, D.

E. A. Ultanir, G. I. Stegeman, D. Michaelis, C. H. Lange, and F. Lederer, "Stable dissipative solitons in semiconductor optical amplifiers," Phys. Rev. Lett. 90, 253903 (2003).
[CrossRef] [PubMed]

E. A. Ultanir, D. Michaelis, F. Lederer, and G. I. Stegeman, "Stable spatial solitons in semiconductor optical amplifiers," Opt. Lett. 28, 251-253 (2003).
[CrossRef] [PubMed]

D. Michaelis, U. Peschel, and F. Lederer, "Multistable localized structures and superlattices in semiconductor optical resonators," Phys. Rev. A 56, R3366-R3369 (1997).
[CrossRef]

Miller, M.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Guidici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, "Cavity solitons as pixels in semiconductor microcavities," Nature 419, 699-702 (2002).
[CrossRef] [PubMed]

Nakazawa, M.

M. Nakazawa, K. Suzukki, and H. A. Haus, "Modulational instability oscillation in nonlinear dispersive ring cavity," Phys. Rev. A 38, 5193-5196 (1988).
[CrossRef] [PubMed]

Narducci, L. M.

J. R. Tredicce, E. J. Quel, A. M. Ghazzawi, C. Green, M. A. Pernigo, L. M. Narducci, and L. A. Lugiato, "Spatial and temporal instabilities in a CO2 laser," Phys. Rev. Lett. 62, 1274-1277 (1989).
[CrossRef] [PubMed]

Paxton, A. H.

A. H. Paxton and G. C. Dente, "Filament formation in semiconductor laser gain regions," J. Appl. Phys. 70, 2921-2925 (1991).
[CrossRef]

Pernigo, M. A.

J. R. Tredicce, E. J. Quel, A. M. Ghazzawi, C. Green, M. A. Pernigo, L. M. Narducci, and L. A. Lugiato, "Spatial and temporal instabilities in a CO2 laser," Phys. Rev. Lett. 62, 1274-1277 (1989).
[CrossRef] [PubMed]

Peschel, U.

D. Michaelis, U. Peschel, and F. Lederer, "Multistable localized structures and superlattices in semiconductor optical resonators," Phys. Rev. A 56, R3366-R3369 (1997).
[CrossRef]

Prati, F.

L. Spinelli, G. Tissoni, M. Brambilla, F. Prati, and L. A. Lugiato, "Spatial solitons in semiconductor microcavities," Phys. Rev. A 58, 2542-2559 (1998).
[CrossRef]

Quel, E. J.

J. R. Tredicce, E. J. Quel, A. M. Ghazzawi, C. Green, M. A. Pernigo, L. M. Narducci, and L. A. Lugiato, "Spatial and temporal instabilities in a CO2 laser," Phys. Rev. Lett. 62, 1274-1277 (1989).
[CrossRef] [PubMed]

Segev, M.

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

M. Soljacic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, "Modulation instability of incoherent beams in noninstantaneous nonlinear media," Phys. Rev. Lett. 84, 467-470 (2000).
[CrossRef] [PubMed]

G. I. Stegeman and M. Segev, "Optical spatial solitons and their interactions: universality and diversity," Science 286, 1518-1523 (1999).
[CrossRef] [PubMed]

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, 167-174 (1996).
[CrossRef]

Soljacic, M.

M. Soljacic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, "Modulation instability of incoherent beams in noninstantaneous nonlinear media," Phys. Rev. Lett. 84, 467-470 (2000).
[CrossRef] [PubMed]

Spinelli, L.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Guidici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, "Cavity solitons as pixels in semiconductor microcavities," Nature 419, 699-702 (2002).
[CrossRef] [PubMed]

L. Spinelli, G. Tissoni, M. Brambilla, F. Prati, and L. A. Lugiato, "Spatial solitons in semiconductor microcavities," Phys. Rev. A 58, 2542-2559 (1998).
[CrossRef]

Stegeman, G. I.

E. A. Ultanir, G. I. Stegeman, C. H. Lange, and F. Lederer, "Coherent interactions of dissipative spatial solitons," Opt. Lett. 29, 283-285 (2004).
[CrossRef] [PubMed]

E. A. Ultanir, D. Michaelis, F. Lederer, and G. I. Stegeman, "Stable spatial solitons in semiconductor optical amplifiers," Opt. Lett. 28, 251-253 (2003).
[CrossRef] [PubMed]

E. A. Ultanir, G. I. Stegeman, D. Michaelis, C. H. Lange, and F. Lederer, "Stable dissipative solitons in semiconductor optical amplifiers," Phys. Rev. Lett. 90, 253903 (2003).
[CrossRef] [PubMed]

G. I. Stegeman and M. Segev, "Optical spatial solitons and their interactions: universality and diversity," Science 286, 1518-1523 (1999).
[CrossRef] [PubMed]

Surette, M. R.

L. Goldberg, M. R. Surette, and D. Mehuys, "Filament formation in a tapered GaAlAs optical amplifier," Appl. Phys. Lett. 62, 2304-2306 (1993).
[CrossRef]

Suzukki, K.

M. Nakazawa, K. Suzukki, and H. A. Haus, "Modulational instability oscillation in nonlinear dispersive ring cavity," Phys. Rev. A 38, 5193-5196 (1988).
[CrossRef] [PubMed]

Tissoni, G.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Guidici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, "Cavity solitons as pixels in semiconductor microcavities," Nature 419, 699-702 (2002).
[CrossRef] [PubMed]

L. Spinelli, G. Tissoni, M. Brambilla, F. Prati, and L. A. Lugiato, "Spatial solitons in semiconductor microcavities," Phys. Rev. A 58, 2542-2559 (1998).
[CrossRef]

Tredicce, J. R.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Guidici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, "Cavity solitons as pixels in semiconductor microcavities," Nature 419, 699-702 (2002).
[CrossRef] [PubMed]

J. R. Tredicce, E. J. Quel, A. M. Ghazzawi, C. Green, M. A. Pernigo, L. M. Narducci, and L. A. Lugiato, "Spatial and temporal instabilities in a CO2 laser," Phys. Rev. Lett. 62, 1274-1277 (1989).
[CrossRef] [PubMed]

Trillo, S.

Ultanir, E. A.

Vishwanath, A.

M. Soljacic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, "Modulation instability of incoherent beams in noninstantaneous nonlinear media," Phys. Rev. Lett. 84, 467-470 (2000).
[CrossRef] [PubMed]

Wabnitz, S.

Appl. Phys. Lett. (1)

L. Goldberg, M. R. Surette, and D. Mehuys, "Filament formation in a tapered GaAlAs optical amplifier," Appl. Phys. Lett. 62, 2304-2306 (1993).
[CrossRef]

IEEE J. Quantum Electron. (1)

A. Hasegawa and W. F. Brinkman, "Tunable coherent IR and FIR sources utilizing modulational instability," IEEE J. Quantum Electron. 16694-697 (1980).
[CrossRef]

J. Appl. Phys. (1)

A. H. Paxton and G. C. Dente, "Filament formation in semiconductor laser gain regions," J. Appl. Phys. 70, 2921-2925 (1991).
[CrossRef]

Nature (2)

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Guidici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, "Cavity solitons as pixels in semiconductor microcavities," Nature 419, 699-702 (2002).
[CrossRef] [PubMed]

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

Opt. Commun. (1)

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Figures (8)

Fig. 1
Fig. 1

Solutions for the MI gain, k z R , versus spatial frequency p of the perturbations: The top plot is for the case k z R = g { g 2 [ ( p 4 4 ) + p 2 h g ] } 1 2 , the middle is for k z R = g + { g 2 [ ( p 4 4 ) + p 2 h g ] } 1 2 , and the bottom is for k z R = g . (Calculations are done for π = 9.4 , where stable solitons start to appear at a pumping current density around 266 A cm 2 . As the current density is increased above this value, the gain curve on the top shifts more toward higher values, and the curves in the middle and on the bottom shifts toward smaller values).

Fig. 2
Fig. 2

(left) Growth of the transverse sinusoidal perturbations at a current pumping level of π = 50 or current density around 1415 A cm 2 ( h = 3 ) , with increases in the propagation distance of 1 cm between the curves. (right) The gain coefficient at two different spatial modulation frequencies. The dashed line shows the gain from Eq. (15), and the solid curve is the result from beam propagation simulations.

Fig. 3
Fig. 3

(a) Modulation gain versus spatial modulation frequency at h = 3 , for different current pumping levels. (b) For a pumping level of π = 9.4 , the change in the gain curves with linewidth enhancement factor h.

Fig. 4
Fig. 4

Top figure shows the intensity spectrum of the simulations at input (left) and after 1 cm propagation (right). The bottom figure gives the intensity profile at the input (left), which is generated by two-beam interference as described in the text, and the intensity profile after 1 cm propagation (right) ( π = 9.4 , h = 3 , and a seeding spatial frequency of 35 mm 1 ).

Fig. 5
Fig. 5

Contour plot of the modulation gain with propagation distance for a 8 mW probe beam (bright regions have higher gain).

Fig. 6
Fig. 6

Contour plot of the modulation gain with propagation distance for a 0.4 mW probe beam.

Fig. 7
Fig. 7

Beam breakup into three identical filaments with 17 μ m beam waists of a 950 nm Gaussian-shaped beam of width 22.75 μ m input into a PPSOA. Under the same pumping conditions but with narrower input beam waists, single solitons with 17 μ m beam waists were observed.

Fig. 8
Fig. 8

Simulated output profile after 1.5 cm propagation while the current is increased (a) at the input power of 66 mW and the waist of 17.5 μ m at FWHM and (b) at the same input power but with a waist of 24.8 μ m at FWHM. (c) The formation of multiple peaks through propagation at 4.9 A current with the same input conditions in (b).

Equations (25)

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ψ z = i 2 ψ x x + ψ [ f ¯ ( N 1 , N 2 ) ( 1 i h ) α ] ,
D N 1 x x + π B N 1 2 C N 1 3 f ( N 1 ) ψ 2 = 0 ,
D N 2 x x B N 2 2 C N 2 3 f ( N 2 ) ψ 2 = 0 ,
ψ = [ ψ 0 + ϵ ( x , z ) ] exp ( i β z ) ,
N 1 ( 2 ) = N 10 ( 20 ) + n 1 ( 2 ) ( x , z ) ,
i β ψ 0 = ψ 0 [ f ¯ ( 1 i h ) α ] ,
β = α h ,
f ¯ = f ¯ ( N 10 , N 20 ) = α .
ϵ z = i 2 ϵ x x + r 0 ( N ¯ 1 w ¯ 1 n 1 + N ¯ 2 w ¯ 2 n 2 ) ( 1 i h ) ,
D n 1 ( 2 ) x x + γ 1 ( 2 ) n 1 ( 2 ) f 1 ( 2 ) r 0 ( ϵ * + ϵ ) = 0 .
n ̂ 1 ( 2 ) = 2 π f 1 ( 2 ) r 0 [ ( a * + b ) δ ( ω + p ) + ( a + b * ) δ ( ω p ) ] D ω 2 + γ 1 ( 2 ) .
n 1 ( 2 ) = f 1 ( 2 ) r 0 [ ( a * + b ) exp ( i p x ) + ( a + b * ) exp ( i p x ) ] D p 2 + γ 1 ( 2 ) .
d a d z exp ( i p x ) + d b d z exp ( i p x ) = i 2 ( p 2 ) [ a exp ( i p x ) + b exp ( i p x ) ] + G ( p ) [ ( a * + b ) exp ( i p x ) + ( a + b * ) exp ( i p x ) ] .
d a d z = i p 2 2 a + G ( p ) ( b * + a ) ,
d b d z = i p 2 2 b + G ( p ) ( a * + b ) ,
G ( p ) = r 0 2 ( 1 i h ) ( f 1 N ¯ 1 w ¯ 1 D p 2 + γ 1 + f 2 N ¯ 2 w ¯ 2 D p 2 + γ 2 ) .
g ( p ) = r 0 2 ( f 1 N ¯ 1 w ¯ 1 D p 2 + γ 1 + f 2 N ¯ 2 w ¯ 2 D p 2 + γ 2 ) ,
d a d z = Δ a + G b * ,
d b d z = Δ b + G a * .
( k z R + i k z l Δ ) ( k z R + i k z l Δ * ) = G 2 .
k z R 2 k z I 2 2 Re { Δ } k z R + Δ 2 = G 2
k z R 2 k z I 2 2 g k z R + p 4 4 + p 2 h g = 0 ,
k z I ( k z R g ) = 0 .
k z R = g ± [ g 2 ( p 4 4 + p 2 h g ) ] 1 2 .
k z I = ± g 2 + p 2 h g + p 4 4 .

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