Abstract

Bright and dark spatial solitons are observed in an optically pumped semiconductor resonator. The pumping allows us to reduce considerably the light intensity necessary for the existence of the solitons and alleviates thermal load problems. Experiments are found to agree qualitatively with calculations based on a simple large-aperture semiconductor resonator model. The role of the signs of the absorptive and reactive nonlinearities in soliton existence is discussed in relation to the nonlinear resonance effect, the tilted-wave mechanism of pattern formation, and the sign of the population inversion.

© 2001 Optical Society of America

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  1. See, e.g., W. J. Firth and G. K. Harkness, Asian J. Phys. 7, 665 (1998).
  2. V. B. Taranenko, I. Ganne, R. Kuszelewicz, and C. O. Weiss, Appl. Phys. B 72, 377 (2001).
    [CrossRef]
  3. V. B. Taranenko and C. O. Weiss, Appl. Phys. B 72, 893 (2001).
    [CrossRef]
  4. B. G. Sfez, J. L. Oudar, J. C. Michel, R. Kuszelewicz, and R. Azoulay, Appl. Phys. Lett. 57, 1849 (1990).
    [CrossRef]
  5. P. K. Jakobsen, J. V. Moloney, A. C. Newell, and R. Indik, Phys. Rev. A 45, 8129 (1992).
    [CrossRef] [PubMed]
  6. L. Spinelli, G. Tissoni, M. Brambilla, F. Prati, and L. A. Lugiato, Phys. Rev. A 58, 2542 (1998).
    [CrossRef]
  7. L. A. Lugiato, Department of Sciences, University of Insubria, Como, Italy ( personal communication, March2, 2001).
  8. C. O. Weiss, H. R. Telle, K. Staliunas, and M. Brambilla, Phys. Rev. A 47, R1616 (1993).
    [CrossRef]
  9. G. J. de Valcarcel, K. Staliunas, V. J. Sanchez-Morcillo, and E. Roldan, Phys. Rev. A 54, 1609 (1996).
    [CrossRef]

2001 (2)

V. B. Taranenko, I. Ganne, R. Kuszelewicz, and C. O. Weiss, Appl. Phys. B 72, 377 (2001).
[CrossRef]

V. B. Taranenko and C. O. Weiss, Appl. Phys. B 72, 893 (2001).
[CrossRef]

1998 (2)

See, e.g., W. J. Firth and G. K. Harkness, Asian J. Phys. 7, 665 (1998).

L. Spinelli, G. Tissoni, M. Brambilla, F. Prati, and L. A. Lugiato, Phys. Rev. A 58, 2542 (1998).
[CrossRef]

1996 (1)

G. J. de Valcarcel, K. Staliunas, V. J. Sanchez-Morcillo, and E. Roldan, Phys. Rev. A 54, 1609 (1996).
[CrossRef]

1993 (1)

C. O. Weiss, H. R. Telle, K. Staliunas, and M. Brambilla, Phys. Rev. A 47, R1616 (1993).
[CrossRef]

1992 (1)

P. K. Jakobsen, J. V. Moloney, A. C. Newell, and R. Indik, Phys. Rev. A 45, 8129 (1992).
[CrossRef] [PubMed]

1990 (1)

B. G. Sfez, J. L. Oudar, J. C. Michel, R. Kuszelewicz, and R. Azoulay, Appl. Phys. Lett. 57, 1849 (1990).
[CrossRef]

Azoulay, R.

B. G. Sfez, J. L. Oudar, J. C. Michel, R. Kuszelewicz, and R. Azoulay, Appl. Phys. Lett. 57, 1849 (1990).
[CrossRef]

Brambilla, M.

L. Spinelli, G. Tissoni, M. Brambilla, F. Prati, and L. A. Lugiato, Phys. Rev. A 58, 2542 (1998).
[CrossRef]

C. O. Weiss, H. R. Telle, K. Staliunas, and M. Brambilla, Phys. Rev. A 47, R1616 (1993).
[CrossRef]

de Valcarcel, G. J.

G. J. de Valcarcel, K. Staliunas, V. J. Sanchez-Morcillo, and E. Roldan, Phys. Rev. A 54, 1609 (1996).
[CrossRef]

Firth, W. J.

See, e.g., W. J. Firth and G. K. Harkness, Asian J. Phys. 7, 665 (1998).

Ganne, I.

V. B. Taranenko, I. Ganne, R. Kuszelewicz, and C. O. Weiss, Appl. Phys. B 72, 377 (2001).
[CrossRef]

Harkness, G. K.

See, e.g., W. J. Firth and G. K. Harkness, Asian J. Phys. 7, 665 (1998).

Indik, R.

P. K. Jakobsen, J. V. Moloney, A. C. Newell, and R. Indik, Phys. Rev. A 45, 8129 (1992).
[CrossRef] [PubMed]

Jakobsen, P. K.

P. K. Jakobsen, J. V. Moloney, A. C. Newell, and R. Indik, Phys. Rev. A 45, 8129 (1992).
[CrossRef] [PubMed]

Kuszelewicz, R.

V. B. Taranenko, I. Ganne, R. Kuszelewicz, and C. O. Weiss, Appl. Phys. B 72, 377 (2001).
[CrossRef]

B. G. Sfez, J. L. Oudar, J. C. Michel, R. Kuszelewicz, and R. Azoulay, Appl. Phys. Lett. 57, 1849 (1990).
[CrossRef]

Lugiato, L. A.

L. Spinelli, G. Tissoni, M. Brambilla, F. Prati, and L. A. Lugiato, Phys. Rev. A 58, 2542 (1998).
[CrossRef]

L. A. Lugiato, Department of Sciences, University of Insubria, Como, Italy ( personal communication, March2, 2001).

Michel, J. C.

B. G. Sfez, J. L. Oudar, J. C. Michel, R. Kuszelewicz, and R. Azoulay, Appl. Phys. Lett. 57, 1849 (1990).
[CrossRef]

Moloney, J. V.

P. K. Jakobsen, J. V. Moloney, A. C. Newell, and R. Indik, Phys. Rev. A 45, 8129 (1992).
[CrossRef] [PubMed]

Newell, A. C.

P. K. Jakobsen, J. V. Moloney, A. C. Newell, and R. Indik, Phys. Rev. A 45, 8129 (1992).
[CrossRef] [PubMed]

Oudar, J. L.

B. G. Sfez, J. L. Oudar, J. C. Michel, R. Kuszelewicz, and R. Azoulay, Appl. Phys. Lett. 57, 1849 (1990).
[CrossRef]

Prati, F.

L. Spinelli, G. Tissoni, M. Brambilla, F. Prati, and L. A. Lugiato, Phys. Rev. A 58, 2542 (1998).
[CrossRef]

Roldan, E.

G. J. de Valcarcel, K. Staliunas, V. J. Sanchez-Morcillo, and E. Roldan, Phys. Rev. A 54, 1609 (1996).
[CrossRef]

Sanchez-Morcillo, V. J.

G. J. de Valcarcel, K. Staliunas, V. J. Sanchez-Morcillo, and E. Roldan, Phys. Rev. A 54, 1609 (1996).
[CrossRef]

Sfez, B. G.

B. G. Sfez, J. L. Oudar, J. C. Michel, R. Kuszelewicz, and R. Azoulay, Appl. Phys. Lett. 57, 1849 (1990).
[CrossRef]

Spinelli, L.

L. Spinelli, G. Tissoni, M. Brambilla, F. Prati, and L. A. Lugiato, Phys. Rev. A 58, 2542 (1998).
[CrossRef]

Staliunas, K.

G. J. de Valcarcel, K. Staliunas, V. J. Sanchez-Morcillo, and E. Roldan, Phys. Rev. A 54, 1609 (1996).
[CrossRef]

C. O. Weiss, H. R. Telle, K. Staliunas, and M. Brambilla, Phys. Rev. A 47, R1616 (1993).
[CrossRef]

Taranenko, V. B.

V. B. Taranenko, I. Ganne, R. Kuszelewicz, and C. O. Weiss, Appl. Phys. B 72, 377 (2001).
[CrossRef]

V. B. Taranenko and C. O. Weiss, Appl. Phys. B 72, 893 (2001).
[CrossRef]

Telle, H. R.

C. O. Weiss, H. R. Telle, K. Staliunas, and M. Brambilla, Phys. Rev. A 47, R1616 (1993).
[CrossRef]

Tissoni, G.

L. Spinelli, G. Tissoni, M. Brambilla, F. Prati, and L. A. Lugiato, Phys. Rev. A 58, 2542 (1998).
[CrossRef]

Weiss, C. O.

V. B. Taranenko and C. O. Weiss, Appl. Phys. B 72, 893 (2001).
[CrossRef]

V. B. Taranenko, I. Ganne, R. Kuszelewicz, and C. O. Weiss, Appl. Phys. B 72, 377 (2001).
[CrossRef]

C. O. Weiss, H. R. Telle, K. Staliunas, and M. Brambilla, Phys. Rev. A 47, R1616 (1993).
[CrossRef]

Appl. Phys. B (2)

V. B. Taranenko, I. Ganne, R. Kuszelewicz, and C. O. Weiss, Appl. Phys. B 72, 377 (2001).
[CrossRef]

V. B. Taranenko and C. O. Weiss, Appl. Phys. B 72, 893 (2001).
[CrossRef]

Appl. Phys. Lett. (1)

B. G. Sfez, J. L. Oudar, J. C. Michel, R. Kuszelewicz, and R. Azoulay, Appl. Phys. Lett. 57, 1849 (1990).
[CrossRef]

Asian J. Phys. (1)

See, e.g., W. J. Firth and G. K. Harkness, Asian J. Phys. 7, 665 (1998).

Phys. Rev. A (4)

C. O. Weiss, H. R. Telle, K. Staliunas, and M. Brambilla, Phys. Rev. A 47, R1616 (1993).
[CrossRef]

G. J. de Valcarcel, K. Staliunas, V. J. Sanchez-Morcillo, and E. Roldan, Phys. Rev. A 54, 1609 (1996).
[CrossRef]

P. K. Jakobsen, J. V. Moloney, A. C. Newell, and R. Indik, Phys. Rev. A 45, 8129 (1992).
[CrossRef] [PubMed]

L. Spinelli, G. Tissoni, M. Brambilla, F. Prati, and L. A. Lugiato, Phys. Rev. A 58, 2542 (1998).
[CrossRef]

Other (1)

L. A. Lugiato, Department of Sciences, University of Insubria, Como, Italy ( personal communication, March2, 2001).

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Figures (4)

Fig. 1
Fig. 1

Spatial resonator solitons in the pumped semiconductor quantum-well resonator, observed in reflection: (a) bright soliton (view from the bottom), (b) dark soliton (normal, or top, view). The vertical coordinate is the sample reflectivity. The pump strength is near the crossing point of the switching thresholds in Fig.  2, below.

Fig. 2
Fig. 2

(a) Measured switch-on and switch-off intensities of the bistable resonator as a function of pump strength. The solid and dashed curves are guides for the eye. (b) Calculated plane-wave switching intensities obtained from the rate-equation model (1). The parameters are η=0.5, C=36, Imα=1, Reα=-0.02, θ=-2, and γ=0.1. Transparency corresponds to P=0.1.

Fig. 3
Fig. 3

Plane-wave resonator characteristics calculated from model (1). The bright and dark soliton solutions shown at the top exist close to the bistability range. The parameters are η=0.5, C=36, Imα=1, Reα=-0.02, θ=-2, P=0.055, γ=0.1, and d=0.1. Refl., reflected.

Fig. 4
Fig. 4

Dynamic features of (a) a bright soliton and (b) a dark soliton. (a) Dotted curve, reflected intensity without pumping. The switch-on intensity is not reached; thus the incident intensity equals the reflected intensity. For the solid curve, with pumping, a soliton switches on directly (without delay from thermal effects) at 0.5 μs and off at a slightly smaller intensity. The pump strength is near the threshold crossing point of Fig.  2 (as in Fig.  1). (b) Dashed curve, incident intensity; dotted curve, reflected intensity without pumping. A certain area in the illumination beam is switched on at 0.5 μs, but no soliton is formed. Solid curve, reflected intensity with pumping. A dark soliton is switched on at 0.5 μs. Slow changes of the reflected intensity are due to motion of the soliton (see text). The intensity scales of (a) and (b) are normalized to the same value.

Equations (1)

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E/t=Ein-1+η+C Imα1-N+iθ-C ReαN-2E,N/t=P-γN-E21-N-d2N,

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