Abstract

We consider a broad-area vertical microresonator with an active layer constituted by bulk GaAs driven by an external coherent homogeneous electromagnetic field, and we adopt a microscopic model that describes the field and carrier dynamics in the quasi-equilibrium regime. The theory is developed within the free-carrier approximation, with some relevant effects, such as the Urbach tail and the bandgap renormalization, which are taken into account in a phenomenological way. We include in the model the description of paraxial diffraction and carrier diffusion. A detailed study of the instabilities, both modulational and plane wave, affecting the homogeneous stationary state of the output field is performed. In this way we address the numerical research of cavity solitons, which appear as self-organized light peaks embedded in a homogeneous background, as discussed in a companion paper [J. Opt. Soc. Am. B 16, 2095 (1999)]. Optimal conditions for cavity solitons’ existence are found in extended regions of the parameter space.

© 1999 Optical Society of America

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1999 (5)

L. A. Lugiato, L. Spinelli, G. Tissoni, and M. Brambilla, “Modulational instabilities and cavity solitons in semiconductor microcavities,” J. Opt. B 1, 43–51 (1999).
[CrossRef]

M. Le Berre, D. Leduc, S. Patrascu, E. Ressayre, and A. Tallet, “Beyond the mean-field model of the ring cavity,” Chaos Solitons Fractals 10, 627–649 (1999).
[CrossRef]

G. L. Oppo, A. J. Scroggie, and W. J. Firth, “From domain walls to localized structures in degenerate optical parametric oscillators,” J. Opt. B 1, 133–138 (1999).
[CrossRef]

M. Le Berre, D. Leduc, E. Ressayre, and A. Tallet, “Striped and circular domain walls in the degenerate optical parametric oscillator,” J. Opt. B 1, 153–160 (1999).
[CrossRef]

G. Tissoni, L. Spinelli, M. Brambilla, T. Maggipinto, I. M. Perrini, and L. A. Lugiato, “Cavity solitons in passive bulk semiconductor microcavities. II. Dynamical properties and control,” J. Opt. Soc. Am. B 16, 2095–2105 (1999).
[CrossRef]

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 (5)

M. Brambilla, L. A. Lugiato, F. Prati, L. Spinelli, and W. J. Firth, “Spatial soliton pixels in semiconductor devices,” Phys. Rev. Lett. 79, 2042–2045 (1997).
[CrossRef]

K. Staliunas and V. J. Sanchez-Morcillo, “Localized structures in degenerate optical parametric oscillator,” Opt. Commun. 139, 306–312 (1997).
[CrossRef]

C. Etrich, V. Peschel, and F. Lederer, “Solitary waves in quadratically nonlinear resonators,” Phys. Rev. Lett. 79, 2454–2457 (1997).
[CrossRef]

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

V. B. Taranenko, K. Staliunas, and C. O. Weiss, “Spatial soliton laser: localized structures in a laser with a saturable absorber in a self-imaging resonator,” Phys. Rev. A 56, 1582–1591 (1997).
[CrossRef]

1996 (1)

W. J. Firth and A. J. Scroggie, “Optical bullet holes: robust controllable localized states of a nonlinear cavity,” Phys. Rev. Lett. 76, 1623–1626 (1996).
[CrossRef] [PubMed]

1994 (5)

W. J. Firth and A. J. Scroggie, “Spontaneous pattern formation in an absorptive system,” Europhys. Lett. 26, 521–526 (1994).
[CrossRef]

M. Tlidi, P. Mandel, and R. Lefever, “Localized structures and localized patterns in optical bistability,” Phys. Rev. Lett. 73, 640–643 (1994).
[CrossRef] [PubMed]

M. Tlidi and P. Mandel, “Spatial patterns in nascent optical bistability,” Chaos Solitons Fractals 4, 1475–1486 (1994).
[CrossRef]

F. Prati, A. Tesei, L. A. Lugiato, and R. J. Horowicz, “Stable states in surface-emitting semiconductor lasers,” Chaos Solitons Fractals 4, 1637–1654 (1994).
[CrossRef]

M. Saffman, D. Montgomery, and D. Z. Anderson, “Collapse of a transverse-mode continuum in a self-imaging photorefractively pumped ring resonator,” Opt. Lett. 19, 518–520 (1994).
[CrossRef] [PubMed]

1992 (2)

P. K. Jakobsen, J. V. Moloney, A. C. Newell, and R. Indik, “Space–time dynamics of wide-gain-section lasers,” Phys. Rev. A 45, 8129–8137 (1992).
[CrossRef] [PubMed]

V. Yu. Bazhenov, V. B. Taranenko, and M. V. Vasnetsov, “WTA dynamics in large aperture active cavity with saturable absorber,” in Topical Meeting on Optical Computing, A. M. Goncharenko, F. V. Karpushko, G. V. Sinitsyn, and S. P. Apanasevich, eds., Proc. SPIE 1806, 14–21 (1992).

1990 (1)

1988 (2)

S. W. Koch, N. Peyghambarian, and H. M. Gibbs, “Band-edge nonlinearities in direct-gap semiconductors and their application to optical bistability and optical computing,” J. Appl. Phys. 63, R1–R11 (1988).
[CrossRef]

N. N. Rosanov and G. V. Khodova, “Autosolitons in bistable interferometers,” Opt. Spectrosc. 65, 449–450 (1988).

1987 (1)

H. Haug and S. W. Koch, “Semiconductor laser theory with many-body effects,” Phys. Rev. A 39, 1887–1898 (1987).
[CrossRef]

1986 (1)

Y. H. Lee, A. Chavez-Pirson, H. M. Gibbs, S. H. Park, J. Morhange, A. Jeffery, N. Peyghambarian, L. Banyai, A. C. Gossard, and W. Wiegmann, “Room-temperature optical nonlinearities in GaAs,” Phys. Rev. Lett. 57, 2446–2449 (1986).
[CrossRef] [PubMed]

1985 (1)

1984 (1)

D. S. Chemla, D. A. B. Miller, P. W. Smith, A. C. Gossard, and W. Wiegmann, “Room temperature excitonic nonlinear absorption and refraction in GaAs/AlGaAs multiple quantum well structures,” IEEE J. Quantum Electron. QE-20, 265–275 (1984).
[CrossRef]

1983 (1)

D. W. McLaughlin, J. V. Moloney, and A. C. Newell, “Solitary waves as fixed points of infinite-dimensional maps in an optical bistable ring cavity,” Phys. Rev. Lett. 51, 75–78 (1983).
[CrossRef]

1982 (1)

J. V. Moloney and H. M. Gibbs, “Role of diffractive coupling and self-focusing or defocusing in the dynamical switching of a bistable optical cavity,” Phys. Rev. Lett. 48, 1607–1610 (1982).
[CrossRef]

1978 (2)

R. Bonifacio and L. A. Lugiato, “Optical bistability and cooperative effects in resonance fluorescence,” Phys. Rev. A 18, 1129–1144 (1978).
[CrossRef]

R. Bonifacio and L. A. Lugiato, “Bistable absorption in a ring cavity,” Lett. Nuovo Cimento 21, 505–509 (1978).
[CrossRef]

Anderson, D. Z.

Banyai, L.

Y. H. Lee, A. Chavez-Pirson, H. M. Gibbs, S. H. Park, J. Morhange, A. Jeffery, N. Peyghambarian, L. Banyai, A. C. Gossard, and W. Wiegmann, “Room-temperature optical nonlinearities in GaAs,” Phys. Rev. Lett. 57, 2446–2449 (1986).
[CrossRef] [PubMed]

Bazhenov, V. Yu.

V. Yu. Bazhenov, V. B. Taranenko, and M. V. Vasnetsov, “WTA dynamics in large aperture active cavity with saturable absorber,” in Topical Meeting on Optical Computing, A. M. Goncharenko, F. V. Karpushko, G. V. Sinitsyn, and S. P. Apanasevich, eds., Proc. SPIE 1806, 14–21 (1992).

Bonifacio, R.

R. Bonifacio and L. A. Lugiato, “Optical bistability and cooperative effects in resonance fluorescence,” Phys. Rev. A 18, 1129–1144 (1978).
[CrossRef]

R. Bonifacio and L. A. Lugiato, “Bistable absorption in a ring cavity,” Lett. Nuovo Cimento 21, 505–509 (1978).
[CrossRef]

Brambilla, M.

L. A. Lugiato, L. Spinelli, G. Tissoni, and M. Brambilla, “Modulational instabilities and cavity solitons in semiconductor microcavities,” J. Opt. B 1, 43–51 (1999).
[CrossRef]

G. Tissoni, L. Spinelli, M. Brambilla, T. Maggipinto, I. M. Perrini, and L. A. Lugiato, “Cavity solitons in passive bulk semiconductor microcavities. II. Dynamical properties and control,” J. Opt. Soc. Am. B 16, 2095–2105 (1999).
[CrossRef]

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]

M. Brambilla, L. A. Lugiato, F. Prati, L. Spinelli, and W. J. Firth, “Spatial soliton pixels in semiconductor devices,” Phys. Rev. Lett. 79, 2042–2045 (1997).
[CrossRef]

Chavez-Pirson, A.

Y. H. Lee, A. Chavez-Pirson, H. M. Gibbs, S. H. Park, J. Morhange, A. Jeffery, N. Peyghambarian, L. Banyai, A. C. Gossard, and W. Wiegmann, “Room-temperature optical nonlinearities in GaAs,” Phys. Rev. Lett. 57, 2446–2449 (1986).
[CrossRef] [PubMed]

Chemla, D. S.

D. S. Chemla, D. A. B. Miller, P. W. Smith, A. C. Gossard, and W. Wiegmann, “Room temperature excitonic nonlinear absorption and refraction in GaAs/AlGaAs multiple quantum well structures,” IEEE J. Quantum Electron. QE-20, 265–275 (1984).
[CrossRef]

Etrich, C.

C. Etrich, V. Peschel, and F. Lederer, “Solitary waves in quadratically nonlinear resonators,” Phys. Rev. Lett. 79, 2454–2457 (1997).
[CrossRef]

Firth, W. J.

G. L. Oppo, A. J. Scroggie, and W. J. Firth, “From domain walls to localized structures in degenerate optical parametric oscillators,” J. Opt. B 1, 133–138 (1999).
[CrossRef]

M. Brambilla, L. A. Lugiato, F. Prati, L. Spinelli, and W. J. Firth, “Spatial soliton pixels in semiconductor devices,” Phys. Rev. Lett. 79, 2042–2045 (1997).
[CrossRef]

W. J. Firth and A. J. Scroggie, “Optical bullet holes: robust controllable localized states of a nonlinear cavity,” Phys. Rev. Lett. 76, 1623–1626 (1996).
[CrossRef] [PubMed]

W. J. Firth and A. J. Scroggie, “Spontaneous pattern formation in an absorptive system,” Europhys. Lett. 26, 521–526 (1994).
[CrossRef]

Gibbs, H. M.

S. W. Koch, N. Peyghambarian, and H. M. Gibbs, “Band-edge nonlinearities in direct-gap semiconductors and their application to optical bistability and optical computing,” J. Appl. Phys. 63, R1–R11 (1988).
[CrossRef]

Y. H. Lee, A. Chavez-Pirson, H. M. Gibbs, S. H. Park, J. Morhange, A. Jeffery, N. Peyghambarian, L. Banyai, A. C. Gossard, and W. Wiegmann, “Room-temperature optical nonlinearities in GaAs,” Phys. Rev. Lett. 57, 2446–2449 (1986).
[CrossRef] [PubMed]

J. V. Moloney and H. M. Gibbs, “Role of diffractive coupling and self-focusing or defocusing in the dynamical switching of a bistable optical cavity,” Phys. Rev. Lett. 48, 1607–1610 (1982).
[CrossRef]

Gossard, A. C.

Y. H. Lee, A. Chavez-Pirson, H. M. Gibbs, S. H. Park, J. Morhange, A. Jeffery, N. Peyghambarian, L. Banyai, A. C. Gossard, and W. Wiegmann, “Room-temperature optical nonlinearities in GaAs,” Phys. Rev. Lett. 57, 2446–2449 (1986).
[CrossRef] [PubMed]

D. S. Chemla, D. A. B. Miller, P. W. Smith, A. C. Gossard, and W. Wiegmann, “Room temperature excitonic nonlinear absorption and refraction in GaAs/AlGaAs multiple quantum well structures,” IEEE J. Quantum Electron. QE-20, 265–275 (1984).
[CrossRef]

Haug, H.

Horowicz, R. J.

F. Prati, A. Tesei, L. A. Lugiato, and R. J. Horowicz, “Stable states in surface-emitting semiconductor lasers,” Chaos Solitons Fractals 4, 1637–1654 (1994).
[CrossRef]

Indik, R.

P. K. Jakobsen, J. V. Moloney, A. C. Newell, and R. Indik, “Space–time dynamics of wide-gain-section lasers,” Phys. Rev. A 45, 8129–8137 (1992).
[CrossRef] [PubMed]

Jakobsen, P. K.

P. K. Jakobsen, J. V. Moloney, A. C. Newell, and R. Indik, “Space–time dynamics of wide-gain-section lasers,” Phys. Rev. A 45, 8129–8137 (1992).
[CrossRef] [PubMed]

Jeffery, A.

Y. H. Lee, A. Chavez-Pirson, H. M. Gibbs, S. H. Park, J. Morhange, A. Jeffery, N. Peyghambarian, L. Banyai, A. C. Gossard, and W. Wiegmann, “Room-temperature optical nonlinearities in GaAs,” Phys. Rev. Lett. 57, 2446–2449 (1986).
[CrossRef] [PubMed]

Khodova, G. V.

N. N. Rosanov and G. V. Khodova, “Autosolitons in bistable interferometers,” Opt. Spectrosc. 65, 449–450 (1988).

Koch, S. W.

S. W. Koch, N. Peyghambarian, and H. M. Gibbs, “Band-edge nonlinearities in direct-gap semiconductors and their application to optical bistability and optical computing,” J. Appl. Phys. 63, R1–R11 (1988).
[CrossRef]

H. Haug and S. W. Koch, “Semiconductor laser theory with many-body effects,” Phys. Rev. A 39, 1887–1898 (1987).
[CrossRef]

Le Berre, M.

M. Le Berre, D. Leduc, S. Patrascu, E. Ressayre, and A. Tallet, “Beyond the mean-field model of the ring cavity,” Chaos Solitons Fractals 10, 627–649 (1999).
[CrossRef]

M. Le Berre, D. Leduc, E. Ressayre, and A. Tallet, “Striped and circular domain walls in the degenerate optical parametric oscillator,” J. Opt. B 1, 153–160 (1999).
[CrossRef]

Lederer, F.

C. Etrich, V. Peschel, and F. Lederer, “Solitary waves in quadratically nonlinear resonators,” Phys. Rev. Lett. 79, 2454–2457 (1997).
[CrossRef]

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

Leduc, D.

M. Le Berre, D. Leduc, S. Patrascu, E. Ressayre, and A. Tallet, “Beyond the mean-field model of the ring cavity,” Chaos Solitons Fractals 10, 627–649 (1999).
[CrossRef]

M. Le Berre, D. Leduc, E. Ressayre, and A. Tallet, “Striped and circular domain walls in the degenerate optical parametric oscillator,” J. Opt. B 1, 153–160 (1999).
[CrossRef]

Lee, Y. H.

Y. H. Lee, A. Chavez-Pirson, H. M. Gibbs, S. H. Park, J. Morhange, A. Jeffery, N. Peyghambarian, L. Banyai, A. C. Gossard, and W. Wiegmann, “Room-temperature optical nonlinearities in GaAs,” Phys. Rev. Lett. 57, 2446–2449 (1986).
[CrossRef] [PubMed]

Lefever, R.

M. Tlidi, P. Mandel, and R. Lefever, “Localized structures and localized patterns in optical bistability,” Phys. Rev. Lett. 73, 640–643 (1994).
[CrossRef] [PubMed]

Lugiato, L. A.

L. A. Lugiato, L. Spinelli, G. Tissoni, and M. Brambilla, “Modulational instabilities and cavity solitons in semiconductor microcavities,” J. Opt. B 1, 43–51 (1999).
[CrossRef]

G. Tissoni, L. Spinelli, M. Brambilla, T. Maggipinto, I. M. Perrini, and L. A. Lugiato, “Cavity solitons in passive bulk semiconductor microcavities. II. Dynamical properties and control,” J. Opt. Soc. Am. B 16, 2095–2105 (1999).
[CrossRef]

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]

M. Brambilla, L. A. Lugiato, F. Prati, L. Spinelli, and W. J. Firth, “Spatial soliton pixels in semiconductor devices,” Phys. Rev. Lett. 79, 2042–2045 (1997).
[CrossRef]

F. Prati, A. Tesei, L. A. Lugiato, and R. J. Horowicz, “Stable states in surface-emitting semiconductor lasers,” Chaos Solitons Fractals 4, 1637–1654 (1994).
[CrossRef]

R. Bonifacio and L. A. Lugiato, “Bistable absorption in a ring cavity,” Lett. Nuovo Cimento 21, 505–509 (1978).
[CrossRef]

R. Bonifacio and L. A. Lugiato, “Optical bistability and cooperative effects in resonance fluorescence,” Phys. Rev. A 18, 1129–1144 (1978).
[CrossRef]

Maggipinto, T.

Mandel, P.

M. Tlidi, P. Mandel, and R. Lefever, “Localized structures and localized patterns in optical bistability,” Phys. Rev. Lett. 73, 640–643 (1994).
[CrossRef] [PubMed]

M. Tlidi and P. Mandel, “Spatial patterns in nascent optical bistability,” Chaos Solitons Fractals 4, 1475–1486 (1994).
[CrossRef]

McLaughlin, D. W.

D. W. McLaughlin, J. V. Moloney, and A. C. Newell, “Solitary waves as fixed points of infinite-dimensional maps in an optical bistable ring cavity,” Phys. Rev. Lett. 51, 75–78 (1983).
[CrossRef]

Michaelis, D.

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, D. A. B.

D. S. Chemla, D. A. B. Miller, P. W. Smith, A. C. Gossard, and W. Wiegmann, “Room temperature excitonic nonlinear absorption and refraction in GaAs/AlGaAs multiple quantum well structures,” IEEE J. Quantum Electron. QE-20, 265–275 (1984).
[CrossRef]

Moloney, J. V.

P. K. Jakobsen, J. V. Moloney, A. C. Newell, and R. Indik, “Space–time dynamics of wide-gain-section lasers,” Phys. Rev. A 45, 8129–8137 (1992).
[CrossRef] [PubMed]

D. W. McLaughlin, J. V. Moloney, and A. C. Newell, “Solitary waves as fixed points of infinite-dimensional maps in an optical bistable ring cavity,” Phys. Rev. Lett. 51, 75–78 (1983).
[CrossRef]

J. V. Moloney and H. M. Gibbs, “Role of diffractive coupling and self-focusing or defocusing in the dynamical switching of a bistable optical cavity,” Phys. Rev. Lett. 48, 1607–1610 (1982).
[CrossRef]

Montgomery, D.

Morhange, J.

Y. H. Lee, A. Chavez-Pirson, H. M. Gibbs, S. H. Park, J. Morhange, A. Jeffery, N. Peyghambarian, L. Banyai, A. C. Gossard, and W. Wiegmann, “Room-temperature optical nonlinearities in GaAs,” Phys. Rev. Lett. 57, 2446–2449 (1986).
[CrossRef] [PubMed]

Newell, A. C.

P. K. Jakobsen, J. V. Moloney, A. C. Newell, and R. Indik, “Space–time dynamics of wide-gain-section lasers,” Phys. Rev. A 45, 8129–8137 (1992).
[CrossRef] [PubMed]

D. W. McLaughlin, J. V. Moloney, and A. C. Newell, “Solitary waves as fixed points of infinite-dimensional maps in an optical bistable ring cavity,” Phys. Rev. Lett. 51, 75–78 (1983).
[CrossRef]

Oppo, G. L.

G. L. Oppo, A. J. Scroggie, and W. J. Firth, “From domain walls to localized structures in degenerate optical parametric oscillators,” J. Opt. B 1, 133–138 (1999).
[CrossRef]

Park, S. H.

Y. H. Lee, A. Chavez-Pirson, H. M. Gibbs, S. H. Park, J. Morhange, A. Jeffery, N. Peyghambarian, L. Banyai, A. C. Gossard, and W. Wiegmann, “Room-temperature optical nonlinearities in GaAs,” Phys. Rev. Lett. 57, 2446–2449 (1986).
[CrossRef] [PubMed]

Patrascu, S.

M. Le Berre, D. Leduc, S. Patrascu, E. Ressayre, and A. Tallet, “Beyond the mean-field model of the ring cavity,” Chaos Solitons Fractals 10, 627–649 (1999).
[CrossRef]

Perrini, I. M.

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]

Peschel, V.

C. Etrich, V. Peschel, and F. Lederer, “Solitary waves in quadratically nonlinear resonators,” Phys. Rev. Lett. 79, 2454–2457 (1997).
[CrossRef]

Peyghambarian, N.

S. W. Koch, N. Peyghambarian, and H. M. Gibbs, “Band-edge nonlinearities in direct-gap semiconductors and their application to optical bistability and optical computing,” J. Appl. Phys. 63, R1–R11 (1988).
[CrossRef]

Y. H. Lee, A. Chavez-Pirson, H. M. Gibbs, S. H. Park, J. Morhange, A. Jeffery, N. Peyghambarian, L. Banyai, A. C. Gossard, and W. Wiegmann, “Room-temperature optical nonlinearities in GaAs,” Phys. Rev. Lett. 57, 2446–2449 (1986).
[CrossRef] [PubMed]

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]

M. Brambilla, L. A. Lugiato, F. Prati, L. Spinelli, and W. J. Firth, “Spatial soliton pixels in semiconductor devices,” Phys. Rev. Lett. 79, 2042–2045 (1997).
[CrossRef]

F. Prati, A. Tesei, L. A. Lugiato, and R. J. Horowicz, “Stable states in surface-emitting semiconductor lasers,” Chaos Solitons Fractals 4, 1637–1654 (1994).
[CrossRef]

Ressayre, E.

M. Le Berre, D. Leduc, S. Patrascu, E. Ressayre, and A. Tallet, “Beyond the mean-field model of the ring cavity,” Chaos Solitons Fractals 10, 627–649 (1999).
[CrossRef]

M. Le Berre, D. Leduc, E. Ressayre, and A. Tallet, “Striped and circular domain walls in the degenerate optical parametric oscillator,” J. Opt. B 1, 153–160 (1999).
[CrossRef]

Rosanov, N. N.

N. N. Rosanov, “Diffractive autosolitons in nonlinear interferometers,” J. Opt. Soc. Am. B 7, 1057–1065 (1990).
[CrossRef]

N. N. Rosanov and G. V. Khodova, “Autosolitons in bistable interferometers,” Opt. Spectrosc. 65, 449–450 (1988).

Saffman, M.

Sanchez-Morcillo, V. J.

K. Staliunas and V. J. Sanchez-Morcillo, “Localized structures in degenerate optical parametric oscillator,” Opt. Commun. 139, 306–312 (1997).
[CrossRef]

Schmitt-Rink, S.

Scroggie, A. J.

G. L. Oppo, A. J. Scroggie, and W. J. Firth, “From domain walls to localized structures in degenerate optical parametric oscillators,” J. Opt. B 1, 133–138 (1999).
[CrossRef]

W. J. Firth and A. J. Scroggie, “Optical bullet holes: robust controllable localized states of a nonlinear cavity,” Phys. Rev. Lett. 76, 1623–1626 (1996).
[CrossRef] [PubMed]

W. J. Firth and A. J. Scroggie, “Spontaneous pattern formation in an absorptive system,” Europhys. Lett. 26, 521–526 (1994).
[CrossRef]

Smith, P. W.

D. S. Chemla, D. A. B. Miller, P. W. Smith, A. C. Gossard, and W. Wiegmann, “Room temperature excitonic nonlinear absorption and refraction in GaAs/AlGaAs multiple quantum well structures,” IEEE J. Quantum Electron. QE-20, 265–275 (1984).
[CrossRef]

Spinelli, L.

L. A. Lugiato, L. Spinelli, G. Tissoni, and M. Brambilla, “Modulational instabilities and cavity solitons in semiconductor microcavities,” J. Opt. B 1, 43–51 (1999).
[CrossRef]

G. Tissoni, L. Spinelli, M. Brambilla, T. Maggipinto, I. M. Perrini, and L. A. Lugiato, “Cavity solitons in passive bulk semiconductor microcavities. II. Dynamical properties and control,” J. Opt. Soc. Am. B 16, 2095–2105 (1999).
[CrossRef]

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]

M. Brambilla, L. A. Lugiato, F. Prati, L. Spinelli, and W. J. Firth, “Spatial soliton pixels in semiconductor devices,” Phys. Rev. Lett. 79, 2042–2045 (1997).
[CrossRef]

Staliunas, K.

K. Staliunas and V. J. Sanchez-Morcillo, “Localized structures in degenerate optical parametric oscillator,” Opt. Commun. 139, 306–312 (1997).
[CrossRef]

V. B. Taranenko, K. Staliunas, and C. O. Weiss, “Spatial soliton laser: localized structures in a laser with a saturable absorber in a self-imaging resonator,” Phys. Rev. A 56, 1582–1591 (1997).
[CrossRef]

Tallet, A.

M. Le Berre, D. Leduc, E. Ressayre, and A. Tallet, “Striped and circular domain walls in the degenerate optical parametric oscillator,” J. Opt. B 1, 153–160 (1999).
[CrossRef]

M. Le Berre, D. Leduc, S. Patrascu, E. Ressayre, and A. Tallet, “Beyond the mean-field model of the ring cavity,” Chaos Solitons Fractals 10, 627–649 (1999).
[CrossRef]

Taranenko, V. B.

V. B. Taranenko, K. Staliunas, and C. O. Weiss, “Spatial soliton laser: localized structures in a laser with a saturable absorber in a self-imaging resonator,” Phys. Rev. A 56, 1582–1591 (1997).
[CrossRef]

V. Yu. Bazhenov, V. B. Taranenko, and M. V. Vasnetsov, “WTA dynamics in large aperture active cavity with saturable absorber,” in Topical Meeting on Optical Computing, A. M. Goncharenko, F. V. Karpushko, G. V. Sinitsyn, and S. P. Apanasevich, eds., Proc. SPIE 1806, 14–21 (1992).

Tesei, A.

F. Prati, A. Tesei, L. A. Lugiato, and R. J. Horowicz, “Stable states in surface-emitting semiconductor lasers,” Chaos Solitons Fractals 4, 1637–1654 (1994).
[CrossRef]

Tissoni, G.

G. Tissoni, L. Spinelli, M. Brambilla, T. Maggipinto, I. M. Perrini, and L. A. Lugiato, “Cavity solitons in passive bulk semiconductor microcavities. II. Dynamical properties and control,” J. Opt. Soc. Am. B 16, 2095–2105 (1999).
[CrossRef]

L. A. Lugiato, L. Spinelli, G. Tissoni, and M. Brambilla, “Modulational instabilities and cavity solitons in semiconductor microcavities,” J. Opt. B 1, 43–51 (1999).
[CrossRef]

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]

Tlidi, M.

M. Tlidi, P. Mandel, and R. Lefever, “Localized structures and localized patterns in optical bistability,” Phys. Rev. Lett. 73, 640–643 (1994).
[CrossRef] [PubMed]

M. Tlidi and P. Mandel, “Spatial patterns in nascent optical bistability,” Chaos Solitons Fractals 4, 1475–1486 (1994).
[CrossRef]

Vasnetsov, M. V.

V. Yu. Bazhenov, V. B. Taranenko, and M. V. Vasnetsov, “WTA dynamics in large aperture active cavity with saturable absorber,” in Topical Meeting on Optical Computing, A. M. Goncharenko, F. V. Karpushko, G. V. Sinitsyn, and S. P. Apanasevich, eds., Proc. SPIE 1806, 14–21 (1992).

Weiss, C. O.

V. B. Taranenko, K. Staliunas, and C. O. Weiss, “Spatial soliton laser: localized structures in a laser with a saturable absorber in a self-imaging resonator,” Phys. Rev. A 56, 1582–1591 (1997).
[CrossRef]

Wiegmann, W.

Y. H. Lee, A. Chavez-Pirson, H. M. Gibbs, S. H. Park, J. Morhange, A. Jeffery, N. Peyghambarian, L. Banyai, A. C. Gossard, and W. Wiegmann, “Room-temperature optical nonlinearities in GaAs,” Phys. Rev. Lett. 57, 2446–2449 (1986).
[CrossRef] [PubMed]

D. S. Chemla, D. A. B. Miller, P. W. Smith, A. C. Gossard, and W. Wiegmann, “Room temperature excitonic nonlinear absorption and refraction in GaAs/AlGaAs multiple quantum well structures,” IEEE J. Quantum Electron. QE-20, 265–275 (1984).
[CrossRef]

Chaos Solitons Fractals (3)

M. Tlidi and P. Mandel, “Spatial patterns in nascent optical bistability,” Chaos Solitons Fractals 4, 1475–1486 (1994).
[CrossRef]

M. Le Berre, D. Leduc, S. Patrascu, E. Ressayre, and A. Tallet, “Beyond the mean-field model of the ring cavity,” Chaos Solitons Fractals 10, 627–649 (1999).
[CrossRef]

F. Prati, A. Tesei, L. A. Lugiato, and R. J. Horowicz, “Stable states in surface-emitting semiconductor lasers,” Chaos Solitons Fractals 4, 1637–1654 (1994).
[CrossRef]

Europhys. Lett. (1)

W. J. Firth and A. J. Scroggie, “Spontaneous pattern formation in an absorptive system,” Europhys. Lett. 26, 521–526 (1994).
[CrossRef]

IEEE J. Quantum Electron. (1)

D. S. Chemla, D. A. B. Miller, P. W. Smith, A. C. Gossard, and W. Wiegmann, “Room temperature excitonic nonlinear absorption and refraction in GaAs/AlGaAs multiple quantum well structures,” IEEE J. Quantum Electron. QE-20, 265–275 (1984).
[CrossRef]

J. Appl. Phys. (1)

S. W. Koch, N. Peyghambarian, and H. M. Gibbs, “Band-edge nonlinearities in direct-gap semiconductors and their application to optical bistability and optical computing,” J. Appl. Phys. 63, R1–R11 (1988).
[CrossRef]

J. Opt. B (3)

G. L. Oppo, A. J. Scroggie, and W. J. Firth, “From domain walls to localized structures in degenerate optical parametric oscillators,” J. Opt. B 1, 133–138 (1999).
[CrossRef]

M. Le Berre, D. Leduc, E. Ressayre, and A. Tallet, “Striped and circular domain walls in the degenerate optical parametric oscillator,” J. Opt. B 1, 153–160 (1999).
[CrossRef]

L. A. Lugiato, L. Spinelli, G. Tissoni, and M. Brambilla, “Modulational instabilities and cavity solitons in semiconductor microcavities,” J. Opt. B 1, 43–51 (1999).
[CrossRef]

J. Opt. Soc. Am. B (3)

Lett. Nuovo Cimento (1)

R. Bonifacio and L. A. Lugiato, “Bistable absorption in a ring cavity,” Lett. Nuovo Cimento 21, 505–509 (1978).
[CrossRef]

Opt. Commun. (1)

K. Staliunas and V. J. Sanchez-Morcillo, “Localized structures in degenerate optical parametric oscillator,” Opt. Commun. 139, 306–312 (1997).
[CrossRef]

Opt. Lett. (1)

Opt. Spectrosc. (1)

N. N. Rosanov and G. V. Khodova, “Autosolitons in bistable interferometers,” Opt. Spectrosc. 65, 449–450 (1988).

Phys. Rev. A (6)

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

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]

P. K. Jakobsen, J. V. Moloney, A. C. Newell, and R. Indik, “Space–time dynamics of wide-gain-section lasers,” Phys. Rev. A 45, 8129–8137 (1992).
[CrossRef] [PubMed]

R. Bonifacio and L. A. Lugiato, “Optical bistability and cooperative effects in resonance fluorescence,” Phys. Rev. A 18, 1129–1144 (1978).
[CrossRef]

H. Haug and S. W. Koch, “Semiconductor laser theory with many-body effects,” Phys. Rev. A 39, 1887–1898 (1987).
[CrossRef]

V. B. Taranenko, K. Staliunas, and C. O. Weiss, “Spatial soliton laser: localized structures in a laser with a saturable absorber in a self-imaging resonator,” Phys. Rev. A 56, 1582–1591 (1997).
[CrossRef]

Phys. Rev. Lett. (7)

Y. H. Lee, A. Chavez-Pirson, H. M. Gibbs, S. H. Park, J. Morhange, A. Jeffery, N. Peyghambarian, L. Banyai, A. C. Gossard, and W. Wiegmann, “Room-temperature optical nonlinearities in GaAs,” Phys. Rev. Lett. 57, 2446–2449 (1986).
[CrossRef] [PubMed]

M. Brambilla, L. A. Lugiato, F. Prati, L. Spinelli, and W. J. Firth, “Spatial soliton pixels in semiconductor devices,” Phys. Rev. Lett. 79, 2042–2045 (1997).
[CrossRef]

C. Etrich, V. Peschel, and F. Lederer, “Solitary waves in quadratically nonlinear resonators,” Phys. Rev. Lett. 79, 2454–2457 (1997).
[CrossRef]

W. J. Firth and A. J. Scroggie, “Optical bullet holes: robust controllable localized states of a nonlinear cavity,” Phys. Rev. Lett. 76, 1623–1626 (1996).
[CrossRef] [PubMed]

M. Tlidi, P. Mandel, and R. Lefever, “Localized structures and localized patterns in optical bistability,” Phys. Rev. Lett. 73, 640–643 (1994).
[CrossRef] [PubMed]

J. V. Moloney and H. M. Gibbs, “Role of diffractive coupling and self-focusing or defocusing in the dynamical switching of a bistable optical cavity,” Phys. Rev. Lett. 48, 1607–1610 (1982).
[CrossRef]

D. W. McLaughlin, J. V. Moloney, and A. C. Newell, “Solitary waves as fixed points of infinite-dimensional maps in an optical bistable ring cavity,” Phys. Rev. Lett. 51, 75–78 (1983).
[CrossRef]

Proc. SPIE (1)

V. Yu. Bazhenov, V. B. Taranenko, and M. V. Vasnetsov, “WTA dynamics in large aperture active cavity with saturable absorber,” in Topical Meeting on Optical Computing, A. M. Goncharenko, F. V. Karpushko, G. V. Sinitsyn, and S. P. Apanasevich, eds., Proc. SPIE 1806, 14–21 (1992).

Other (14)

G. P. Bava, P. Debernardi, and A. Pisoni, “QW optical response including valence band mixing and many body effects,” Internal Rep. DE/GE 91–002 (Politecnico di Torino, Turin, Italy, 1993).

K. W. Boer, Survey of Semiconductor Physics (Van Nostrand Reinhold, New York, 1990).

H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors, 2nd ed. (World Scientific, Singapore, 1993).

W. W. Chow, S. W. Koch, and M. Sargent III, Semiconductor Laser Physics (Springer-Verlag, Berlin, 1994).

R. Kuszelewicz, CNET, Laboratoire de Bagneux, 92225 Bagneux Cedex, France (personal communication, 1999).

H. Haken, Synergetics. An Introduction, 2nd ed., Vol. 1. of Springer Series in Synergetics (Springer-Verlag, Berlin, 1977), p. 123.

F. T. Arecchi, “Space–time complexity in nonlinear optics,” Physica D 51, 450–464 (1991); L. A. Lugiato, “Spatio–temporal structures. Part I,” Phys. Rep. 219, 293–310 (1992); C. O. Weiss, “Spatio–temporal structures. Part II,” Phys. Rep. PRPLCM 219, 311–328 (1992); L. A. Lugiato, “Transverse nonlinear optics: introduction and review,” Chaos Solitons Fractals CSFOEH 4, 1251–1258 (1994); W. J. Firth, “Pattern formation in passive nonlinear optical systems,” in Self-Organization in Optical Systems and Applications in Information Technology, M. A. Vorontsov and W. B. Miller, eds. (Springer-Verlag, Berlin, 1995), pp. 69–96; L. A. Lugiato, M. Brambilla, and A. Gatti, Optical Pattern Formation, Vol. 40 of Advances in Atomic, Molecular and Optical Physics, B. Bederson and H. Walther, eds. (Academic, New York, 1998), pp. 229–306.
[CrossRef]

C. Z. Ning, R. A. Indik, and J. V. Moloney, “Self-consistent approach to thermal effects in vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 12, 1993–2004 (1995); T. Rossler, R. A. Indik, G. K. Harkness, J. V. Moloney, and C. Z. Ning, “Modeling the interplay of thermal effects and transverse mode behavior in native-oxide-confined vertical-cavity surface-emitting lasers,” Phys. Rev. A 58, 3279–3292 (1998).
[CrossRef]

H. M. Gibbs, Optical Bistability: Controlling Light with Light (Academic, New York, 1985).

N. N. Rosanov, “Transverse patterns in wide-aperture nonlinear optical systems,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1996), Vol. XXXV, pp. 1–60.

M. Brambilla, L. A. Lugiato, and M. Stefani, “Interaction and control of optical localized structures,” Europhys. Lett. 34, 109–114 (1996); “Formation and control of localized structures in nonlinear optical systems,” Chaos 6, 368–372 (1996).
[CrossRef] [PubMed]

A. Schreiber, B. Thüring, M. Kreuzer, and T. Tschudi, “Experimental investigation of solitary structures in a nonlinear optical feedback system,” Opt. Commun. 136, 415–418 (1997); R. Neubecker, B. Thuring, M. Kreuzer, and T. Tschudi, “Transition from spatio-temporal order to disorder in a single-feedback experiment,” Chaos Solitons Fractals 10, 681–692 (1999).
[CrossRef]

C. O. Weiss, “Processing by arrays of spatial solitons,” Basic Research Project Final Rep. (European Strategic Programme for R & D in Information Technology, Braunschweig, Germany, 1998).

J. V. Moloney, H. Adachihara, D. W. McLaughlin, and A. C. Newell, “Fixed points and chaotic dynamics of an infinite-dimensional map,” in Chaos, Noise and Fractals, R. Pike and L. A. Lugiato, eds. (Hilger, Bristol, UK, 1987), pp. 137–186.

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Figures (9)

Fig. 1
Fig. 1

(a) Real part and (b) imaginary part of the nonlinear susceptibility χnl as functions of the carrier density N, for various values of the input frequency (parameter Δ). Note that the transparency value N0 of the carrier density corresponds to the point at which Im(χnl)=0.

Fig. 2
Fig. 2

(a) Refractive-index variation and (b) absorption coefficient as functions of the bandgap detuning Δ and of the input photon energy, for various values of the carrier density N.

Fig. 3
Fig. 3

Examples of Turing domains for various values of (a) diffusion d and of (b) the S-shaped homogeneous steady state corresponding to d=0.2. The other parameters are Δ=-3, Σ=210, θ=-20, β=0.

Fig. 4
Fig. 4

Case below the bandgap. MI and PWI boundaries as functions of the cavity detuning θ: (a) Δ=3; (b) Δ=1. The other parameters are Σ=210, d=0.2, β=0.

Fig. 5
Fig. 5

Case above the bandgap. MI and PWI boundaries as functions of the cavity detuning θ: (a) Δ=-3; (b) Δ=-5. The other parameters are Σ=210, d=0.2, β=0.

Fig. 6
Fig. 6

Case above the bandgap. MI and PWI boundaries as functions of the cavity detuning θ. The other parameters are Δ=-3, Σ=80, d=0.2, β=0.

Fig. 7
Fig. 7

Case below the bandgap. MI and PWI boundaries as functions of the parameter Σ. The other parameters are Δ=1, θ=-9, d=0.2, β=0.

Fig. 8
Fig. 8

Case below the bandgap. MI and PWI boundaries in the plane (θ, |EI|). The circle in (a) is expanded in (b). The other parameters are Δ=1, Σ=80, d=0.2, β=0.

Fig. 9
Fig. 9

Scheme of the optical cavity. The slowly varying envelopes of the intracavity fields (EF, EB) and of the injected, reflected, and transmitted fields (EI, ER, and ET, respectively) are shown.

Equations (52)

Equations on this page are rendered with MathJax. Learn more.

E=½ [EF(x, y, z; t)exp(ikzz)+EB(x, y, z; t)×exp(-ikzz)]exp(-iω0t)+c.c.,
12i kz2EF+EFz+1vEFt=i ω0Γ2ncχnlEF,
12i kz2EB-EBz+1vEBt=i ω0Γ2ncχnlEB,
Nt=-Nτr-BN2+02Im(χnl)(|EF|2+|EB|2)+D˜2N,
2=2x2+2y2,
α=kz2Im(χnl)
αLAT=n22Σ Im(χnl),
Σ=LAω0ncT.
E=0τrN0 F,
Et=-(1+iθ)E+EI+iΣχnlE+i2E,
N˜t=-γ[N˜+βN˜2-Im(χnl)|E|2-d2N˜],
λ0895 nm,n3.5,LA200 nm,
τr10 ns,T2÷6×10-3,
L2÷3 µm,
χ(N, ω0)=-i0VAk|μk|2 fek(N)+fhk(N)-1i(ωk-ω0)+γp,
fαk(N)=1exp {β¯[α(k)-μα(N)]}+1,
δn=n2Re(χnl),
Re(χnl)=Re[χ(N)]-Re[χ(Nth)],
γk=2γpexpωk-ω0E0+1,
Δ=(ωgap-ω0)/γp,
n=n0+nnl=n0+n2|E|2,
Re(χnl)|E|2S=Re(χnl)NN|E|2S.
|EI|2=|ES|2{[1+Σ Im(χnl)]2+[θ-Σ Re(χnl)]2},
|ES|2=NS+βNS2Im(χnl).
ES=EI1+Σ Im(χnl)+i[θ-Σ Re(χnl)].
E(x, y, t)E*(x, y, t)N(x, y, t)
=ESES*NS+exp[λt+i(Kxx+Kyy)]δE0δE0*δN0,
λ3+a2λ2+a1λ+a0=0,
a2=2A1+γ(A4+dK2),
a1=A12(A2+K2)2+γ2A1(A4+dK2)+A3 Im(χnl)N,
a0=γ[A12+(A2+K2)2](A4+dK2)-A3(A2+K2) Re(χnl)N-A1 Im(χnl)N,
A1=1+Σ Im(χnl),
A2=θ-Σ Re(χnl),
A3=2Σ|ES|2 Im(χnl),
A4=1+2βNS-|ES|2 Im(χnl)N.
d(K2)3+b2(K2)2+b1(K2)+b0=0,
b2=A4+2dA2,
b1=d(A12+A22)+2A2A4-Re(χnl)NA3,
b0=A4(A12+A22)-A3A2 Re(χnl)N-A1 Im(χnl)N.
|ES-|<|ES|and/or|ES+|>|ES|.
|EI-|<|EI|and/or|EI+|>|EI|.
EF(x, y, 0; t)=iTEI+REB(x, y, 0; t),
EB(x, y, L; t)=R exp(-iδ0)EF(x, y, L; t),
δ0=ωC-ω02nL/c,
ET=iTEF(x, y, L; t),
ER=iTEB(x, y, 0; t)+REI.
|ES|2=NS+βNS2Im(χnl),
|ES|2NS=Im(χnl)(1+2βNS)-(NS+βNS2) Im(χnl)NSIm(χnl)2=A4Im(χnl).
|EI|2|ES|2=A12+A22+2Σ|ES|2×A1 Im(χnl)|ES|2-A2 Re(χnl)|ES|2,
χnl|ES|2=χnlNSNS|ES|2,
NS|ES|2=Im(χnl)1+2βNS-|ES|2 Im(χnl)NS=Im(χnl)A4.
|EI|2|ES|2=A12+A22-A3A4×A2 Re(χnl)NS-A1 Im(χnl)NS=b0A4.

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