Abstract

We study the space–time dynamical behavior of broad-area semiconductor lasers, using an extended phenomenological laser model to include transverse diffraction of the counterpropagating optical fields and transverse diffusion of carriers. Numerical results show that the profile of the output intensity exhibits spatiotemporal chaos by way of changing random filaments. A small confinement factor and/or linewidth enhancement factor can prevent instabilities. Simulations also confirm experimental results showing that a half-symmetric unstable resonator with a suitable mirror curvature restores stability.

© 1993 Optical Society of America

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  1. G. H. B. Thompson, “A theory for filamentation in semiconductor lasers including the dependence of dielectric constant on injected carrier density,” Optoelectronics 4, 257–310 (1972).
  2. L. Goldberg and M. K. Chun, “Injection locking characteristics of a 1 W. broad stripe laser diode,” Appl. Phys. Lett. 53, 1900–1902 (1988).
    [CrossRef]
  3. W. T. Tsang, “Low-current threshold and high lasing uniformity GaAs-AlxGa1−xAs double-heterostructure lasers grown by molecular beam epitaxy,” Appl. Phys. Lett. 34, 473–475 (1979).
    [CrossRef]
  4. M. Sakamoto and Y. Kato, “High power (710 mW cw) single-lobe operation of broad-area AlGaAs double-heterostructure lasers grown by metalorganic chemical vapor deposition,” Appl. Phys. Lett. 50, 869–870 (1987).
    [CrossRef]
  5. A. Larsson, M. Mittelstein, Y. Arakawa, and A. Yariv, “High-efficiency broad-area single-quantum-well lasers with narrow single-lobed far-field patterns prepared by molecular beam epitaxy,” Electron. Lett. 22, 79–81 (1986).
    [CrossRef]
  6. D. Mehuys, R. J. Lang, M. Mittelstein, J. Salzman, and A. Yariv, “Self-stabilized nonlinear lateral modes of broad-area lasers,” IEEE J. Quantum Electron. QE-23, 1909–1920 (1987).
    [CrossRef]
  7. R. J. Lang, A. G. Larsson, and J. G. Cody, “Lateral modes of broad-area semiconductor lasers: theory and experiment,” IEEE J. Quantum Electron. 27, 312–320 (1991).
    [CrossRef]
  8. W. W. Chow and D. Depatie, “Filamentation in conventional double heterostructure and quantum well semiconductor lasers,” IEEE J. Quantum Electron. 24, 1297–1301 (1988).
    [CrossRef]
  9. E. Abraham, H. Adachihara, O. Hess, R. A. Indik, P. Jacobsen, J. V. Moloney, and P. Ru, “Optical turbulence in semiconductor lasers,” in Nonlinear Processes in Physics, D. Kaup and A. Fokas, eds. (Springer-Verlag, Berlin, 1993).
    [CrossRef]
  10. H. Adachihara, R. Indik, J. V. Moloney, and O. Hess, “Semiconductor laser array dynamics: numerical simulations on multistripe index-guided lasers,” J. Opt. Soc. Am. B 10, 496–506 (1993).
    [CrossRef]
  11. H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors (World Scientific, Singapore, 1990).
  12. P. Jakobsen, J. V. Moloney, A. C. Newell, and R. A. Indik, “Space–time dynamics of wide gain section lasers,” Phys. Rev. A 45, 8129–8137 (1992).
    [CrossRef] [PubMed]
  13. S. S. Wang and H. G. Winful, “Dynamics of phase-locked semiconductor laser arrays,” Appl. Phys. Lett. 52, 1774–1776 (1988).
    [CrossRef]
  14. H. G. Winful and S. S. Wang, “Stability of phase locking in coupled semiconductor laser arrays,” Appl. Phys. Lett. 52, 1894–1896 (1988).
    [CrossRef]
  15. E. Abraham and S. D. Smith, “Optical bistability and related devices,” Rep. Prog. Phys. 45, 815–885 (1982).
    [CrossRef]
  16. K. Tai, T. R. Hayes, S. L. McCall, and W. T. Tsang, “Optical measurement of surface recombination in InGaAs quantum-well mesostructures,” Appl. Phys. Lett. 53, 302–303 (1988).
    [CrossRef]
  17. M. L. Tilton, G. C. Dente, A. H. Paxton, J. Cser, R. K. DeFreez, C. E. Moeller, and D. Depatie, “High power, nearly diffraction-limited output from a semiconductor laser with an unstable resonator,” IEEE J. Quantum Electron. 27, 2098–2108 (1991).
    [CrossRef]

1993 (1)

1992 (1)

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

1991 (2)

M. L. Tilton, G. C. Dente, A. H. Paxton, J. Cser, R. K. DeFreez, C. E. Moeller, and D. Depatie, “High power, nearly diffraction-limited output from a semiconductor laser with an unstable resonator,” IEEE J. Quantum Electron. 27, 2098–2108 (1991).
[CrossRef]

R. J. Lang, A. G. Larsson, and J. G. Cody, “Lateral modes of broad-area semiconductor lasers: theory and experiment,” IEEE J. Quantum Electron. 27, 312–320 (1991).
[CrossRef]

1988 (5)

W. W. Chow and D. Depatie, “Filamentation in conventional double heterostructure and quantum well semiconductor lasers,” IEEE J. Quantum Electron. 24, 1297–1301 (1988).
[CrossRef]

L. Goldberg and M. K. Chun, “Injection locking characteristics of a 1 W. broad stripe laser diode,” Appl. Phys. Lett. 53, 1900–1902 (1988).
[CrossRef]

K. Tai, T. R. Hayes, S. L. McCall, and W. T. Tsang, “Optical measurement of surface recombination in InGaAs quantum-well mesostructures,” Appl. Phys. Lett. 53, 302–303 (1988).
[CrossRef]

S. S. Wang and H. G. Winful, “Dynamics of phase-locked semiconductor laser arrays,” Appl. Phys. Lett. 52, 1774–1776 (1988).
[CrossRef]

H. G. Winful and S. S. Wang, “Stability of phase locking in coupled semiconductor laser arrays,” Appl. Phys. Lett. 52, 1894–1896 (1988).
[CrossRef]

1987 (2)

M. Sakamoto and Y. Kato, “High power (710 mW cw) single-lobe operation of broad-area AlGaAs double-heterostructure lasers grown by metalorganic chemical vapor deposition,” Appl. Phys. Lett. 50, 869–870 (1987).
[CrossRef]

D. Mehuys, R. J. Lang, M. Mittelstein, J. Salzman, and A. Yariv, “Self-stabilized nonlinear lateral modes of broad-area lasers,” IEEE J. Quantum Electron. QE-23, 1909–1920 (1987).
[CrossRef]

1986 (1)

A. Larsson, M. Mittelstein, Y. Arakawa, and A. Yariv, “High-efficiency broad-area single-quantum-well lasers with narrow single-lobed far-field patterns prepared by molecular beam epitaxy,” Electron. Lett. 22, 79–81 (1986).
[CrossRef]

1982 (1)

E. Abraham and S. D. Smith, “Optical bistability and related devices,” Rep. Prog. Phys. 45, 815–885 (1982).
[CrossRef]

1979 (1)

W. T. Tsang, “Low-current threshold and high lasing uniformity GaAs-AlxGa1−xAs double-heterostructure lasers grown by molecular beam epitaxy,” Appl. Phys. Lett. 34, 473–475 (1979).
[CrossRef]

1972 (1)

G. H. B. Thompson, “A theory for filamentation in semiconductor lasers including the dependence of dielectric constant on injected carrier density,” Optoelectronics 4, 257–310 (1972).

Abraham, E.

E. Abraham and S. D. Smith, “Optical bistability and related devices,” Rep. Prog. Phys. 45, 815–885 (1982).
[CrossRef]

E. Abraham, H. Adachihara, O. Hess, R. A. Indik, P. Jacobsen, J. V. Moloney, and P. Ru, “Optical turbulence in semiconductor lasers,” in Nonlinear Processes in Physics, D. Kaup and A. Fokas, eds. (Springer-Verlag, Berlin, 1993).
[CrossRef]

Adachihara, H.

H. Adachihara, R. Indik, J. V. Moloney, and O. Hess, “Semiconductor laser array dynamics: numerical simulations on multistripe index-guided lasers,” J. Opt. Soc. Am. B 10, 496–506 (1993).
[CrossRef]

E. Abraham, H. Adachihara, O. Hess, R. A. Indik, P. Jacobsen, J. V. Moloney, and P. Ru, “Optical turbulence in semiconductor lasers,” in Nonlinear Processes in Physics, D. Kaup and A. Fokas, eds. (Springer-Verlag, Berlin, 1993).
[CrossRef]

Arakawa, Y.

A. Larsson, M. Mittelstein, Y. Arakawa, and A. Yariv, “High-efficiency broad-area single-quantum-well lasers with narrow single-lobed far-field patterns prepared by molecular beam epitaxy,” Electron. Lett. 22, 79–81 (1986).
[CrossRef]

Chow, W. W.

W. W. Chow and D. Depatie, “Filamentation in conventional double heterostructure and quantum well semiconductor lasers,” IEEE J. Quantum Electron. 24, 1297–1301 (1988).
[CrossRef]

Chun, M. K.

L. Goldberg and M. K. Chun, “Injection locking characteristics of a 1 W. broad stripe laser diode,” Appl. Phys. Lett. 53, 1900–1902 (1988).
[CrossRef]

Cody, J. G.

R. J. Lang, A. G. Larsson, and J. G. Cody, “Lateral modes of broad-area semiconductor lasers: theory and experiment,” IEEE J. Quantum Electron. 27, 312–320 (1991).
[CrossRef]

Cser, J.

M. L. Tilton, G. C. Dente, A. H. Paxton, J. Cser, R. K. DeFreez, C. E. Moeller, and D. Depatie, “High power, nearly diffraction-limited output from a semiconductor laser with an unstable resonator,” IEEE J. Quantum Electron. 27, 2098–2108 (1991).
[CrossRef]

DeFreez, R. K.

M. L. Tilton, G. C. Dente, A. H. Paxton, J. Cser, R. K. DeFreez, C. E. Moeller, and D. Depatie, “High power, nearly diffraction-limited output from a semiconductor laser with an unstable resonator,” IEEE J. Quantum Electron. 27, 2098–2108 (1991).
[CrossRef]

Dente, G. C.

M. L. Tilton, G. C. Dente, A. H. Paxton, J. Cser, R. K. DeFreez, C. E. Moeller, and D. Depatie, “High power, nearly diffraction-limited output from a semiconductor laser with an unstable resonator,” IEEE J. Quantum Electron. 27, 2098–2108 (1991).
[CrossRef]

Depatie, D.

M. L. Tilton, G. C. Dente, A. H. Paxton, J. Cser, R. K. DeFreez, C. E. Moeller, and D. Depatie, “High power, nearly diffraction-limited output from a semiconductor laser with an unstable resonator,” IEEE J. Quantum Electron. 27, 2098–2108 (1991).
[CrossRef]

W. W. Chow and D. Depatie, “Filamentation in conventional double heterostructure and quantum well semiconductor lasers,” IEEE J. Quantum Electron. 24, 1297–1301 (1988).
[CrossRef]

Goldberg, L.

L. Goldberg and M. K. Chun, “Injection locking characteristics of a 1 W. broad stripe laser diode,” Appl. Phys. Lett. 53, 1900–1902 (1988).
[CrossRef]

Haug, H.

H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors (World Scientific, Singapore, 1990).

Hayes, T. R.

K. Tai, T. R. Hayes, S. L. McCall, and W. T. Tsang, “Optical measurement of surface recombination in InGaAs quantum-well mesostructures,” Appl. Phys. Lett. 53, 302–303 (1988).
[CrossRef]

Hess, O.

H. Adachihara, R. Indik, J. V. Moloney, and O. Hess, “Semiconductor laser array dynamics: numerical simulations on multistripe index-guided lasers,” J. Opt. Soc. Am. B 10, 496–506 (1993).
[CrossRef]

E. Abraham, H. Adachihara, O. Hess, R. A. Indik, P. Jacobsen, J. V. Moloney, and P. Ru, “Optical turbulence in semiconductor lasers,” in Nonlinear Processes in Physics, D. Kaup and A. Fokas, eds. (Springer-Verlag, Berlin, 1993).
[CrossRef]

Indik, R.

Indik, R. A.

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

E. Abraham, H. Adachihara, O. Hess, R. A. Indik, P. Jacobsen, J. V. Moloney, and P. Ru, “Optical turbulence in semiconductor lasers,” in Nonlinear Processes in Physics, D. Kaup and A. Fokas, eds. (Springer-Verlag, Berlin, 1993).
[CrossRef]

Jacobsen, P.

E. Abraham, H. Adachihara, O. Hess, R. A. Indik, P. Jacobsen, J. V. Moloney, and P. Ru, “Optical turbulence in semiconductor lasers,” in Nonlinear Processes in Physics, D. Kaup and A. Fokas, eds. (Springer-Verlag, Berlin, 1993).
[CrossRef]

Jakobsen, P.

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

Kato, Y.

M. Sakamoto and Y. Kato, “High power (710 mW cw) single-lobe operation of broad-area AlGaAs double-heterostructure lasers grown by metalorganic chemical vapor deposition,” Appl. Phys. Lett. 50, 869–870 (1987).
[CrossRef]

Koch, S. W.

H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors (World Scientific, Singapore, 1990).

Lang, R. J.

R. J. Lang, A. G. Larsson, and J. G. Cody, “Lateral modes of broad-area semiconductor lasers: theory and experiment,” IEEE J. Quantum Electron. 27, 312–320 (1991).
[CrossRef]

D. Mehuys, R. J. Lang, M. Mittelstein, J. Salzman, and A. Yariv, “Self-stabilized nonlinear lateral modes of broad-area lasers,” IEEE J. Quantum Electron. QE-23, 1909–1920 (1987).
[CrossRef]

Larsson, A.

A. Larsson, M. Mittelstein, Y. Arakawa, and A. Yariv, “High-efficiency broad-area single-quantum-well lasers with narrow single-lobed far-field patterns prepared by molecular beam epitaxy,” Electron. Lett. 22, 79–81 (1986).
[CrossRef]

Larsson, A. G.

R. J. Lang, A. G. Larsson, and J. G. Cody, “Lateral modes of broad-area semiconductor lasers: theory and experiment,” IEEE J. Quantum Electron. 27, 312–320 (1991).
[CrossRef]

McCall, S. L.

K. Tai, T. R. Hayes, S. L. McCall, and W. T. Tsang, “Optical measurement of surface recombination in InGaAs quantum-well mesostructures,” Appl. Phys. Lett. 53, 302–303 (1988).
[CrossRef]

Mehuys, D.

D. Mehuys, R. J. Lang, M. Mittelstein, J. Salzman, and A. Yariv, “Self-stabilized nonlinear lateral modes of broad-area lasers,” IEEE J. Quantum Electron. QE-23, 1909–1920 (1987).
[CrossRef]

Mittelstein, M.

D. Mehuys, R. J. Lang, M. Mittelstein, J. Salzman, and A. Yariv, “Self-stabilized nonlinear lateral modes of broad-area lasers,” IEEE J. Quantum Electron. QE-23, 1909–1920 (1987).
[CrossRef]

A. Larsson, M. Mittelstein, Y. Arakawa, and A. Yariv, “High-efficiency broad-area single-quantum-well lasers with narrow single-lobed far-field patterns prepared by molecular beam epitaxy,” Electron. Lett. 22, 79–81 (1986).
[CrossRef]

Moeller, C. E.

M. L. Tilton, G. C. Dente, A. H. Paxton, J. Cser, R. K. DeFreez, C. E. Moeller, and D. Depatie, “High power, nearly diffraction-limited output from a semiconductor laser with an unstable resonator,” IEEE J. Quantum Electron. 27, 2098–2108 (1991).
[CrossRef]

Moloney, J. V.

H. Adachihara, R. Indik, J. V. Moloney, and O. Hess, “Semiconductor laser array dynamics: numerical simulations on multistripe index-guided lasers,” J. Opt. Soc. Am. B 10, 496–506 (1993).
[CrossRef]

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

E. Abraham, H. Adachihara, O. Hess, R. A. Indik, P. Jacobsen, J. V. Moloney, and P. Ru, “Optical turbulence in semiconductor lasers,” in Nonlinear Processes in Physics, D. Kaup and A. Fokas, eds. (Springer-Verlag, Berlin, 1993).
[CrossRef]

Newell, A. C.

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

Paxton, A. H.

M. L. Tilton, G. C. Dente, A. H. Paxton, J. Cser, R. K. DeFreez, C. E. Moeller, and D. Depatie, “High power, nearly diffraction-limited output from a semiconductor laser with an unstable resonator,” IEEE J. Quantum Electron. 27, 2098–2108 (1991).
[CrossRef]

Ru, P.

E. Abraham, H. Adachihara, O. Hess, R. A. Indik, P. Jacobsen, J. V. Moloney, and P. Ru, “Optical turbulence in semiconductor lasers,” in Nonlinear Processes in Physics, D. Kaup and A. Fokas, eds. (Springer-Verlag, Berlin, 1993).
[CrossRef]

Sakamoto, M.

M. Sakamoto and Y. Kato, “High power (710 mW cw) single-lobe operation of broad-area AlGaAs double-heterostructure lasers grown by metalorganic chemical vapor deposition,” Appl. Phys. Lett. 50, 869–870 (1987).
[CrossRef]

Salzman, J.

D. Mehuys, R. J. Lang, M. Mittelstein, J. Salzman, and A. Yariv, “Self-stabilized nonlinear lateral modes of broad-area lasers,” IEEE J. Quantum Electron. QE-23, 1909–1920 (1987).
[CrossRef]

Smith, S. D.

E. Abraham and S. D. Smith, “Optical bistability and related devices,” Rep. Prog. Phys. 45, 815–885 (1982).
[CrossRef]

Tai, K.

K. Tai, T. R. Hayes, S. L. McCall, and W. T. Tsang, “Optical measurement of surface recombination in InGaAs quantum-well mesostructures,” Appl. Phys. Lett. 53, 302–303 (1988).
[CrossRef]

Thompson, G. H. B.

G. H. B. Thompson, “A theory for filamentation in semiconductor lasers including the dependence of dielectric constant on injected carrier density,” Optoelectronics 4, 257–310 (1972).

Tilton, M. L.

M. L. Tilton, G. C. Dente, A. H. Paxton, J. Cser, R. K. DeFreez, C. E. Moeller, and D. Depatie, “High power, nearly diffraction-limited output from a semiconductor laser with an unstable resonator,” IEEE J. Quantum Electron. 27, 2098–2108 (1991).
[CrossRef]

Tsang, W. T.

K. Tai, T. R. Hayes, S. L. McCall, and W. T. Tsang, “Optical measurement of surface recombination in InGaAs quantum-well mesostructures,” Appl. Phys. Lett. 53, 302–303 (1988).
[CrossRef]

W. T. Tsang, “Low-current threshold and high lasing uniformity GaAs-AlxGa1−xAs double-heterostructure lasers grown by molecular beam epitaxy,” Appl. Phys. Lett. 34, 473–475 (1979).
[CrossRef]

Wang, S. S.

S. S. Wang and H. G. Winful, “Dynamics of phase-locked semiconductor laser arrays,” Appl. Phys. Lett. 52, 1774–1776 (1988).
[CrossRef]

H. G. Winful and S. S. Wang, “Stability of phase locking in coupled semiconductor laser arrays,” Appl. Phys. Lett. 52, 1894–1896 (1988).
[CrossRef]

Winful, H. G.

S. S. Wang and H. G. Winful, “Dynamics of phase-locked semiconductor laser arrays,” Appl. Phys. Lett. 52, 1774–1776 (1988).
[CrossRef]

H. G. Winful and S. S. Wang, “Stability of phase locking in coupled semiconductor laser arrays,” Appl. Phys. Lett. 52, 1894–1896 (1988).
[CrossRef]

Yariv, A.

D. Mehuys, R. J. Lang, M. Mittelstein, J. Salzman, and A. Yariv, “Self-stabilized nonlinear lateral modes of broad-area lasers,” IEEE J. Quantum Electron. QE-23, 1909–1920 (1987).
[CrossRef]

A. Larsson, M. Mittelstein, Y. Arakawa, and A. Yariv, “High-efficiency broad-area single-quantum-well lasers with narrow single-lobed far-field patterns prepared by molecular beam epitaxy,” Electron. Lett. 22, 79–81 (1986).
[CrossRef]

Appl. Phys. Lett. (6)

L. Goldberg and M. K. Chun, “Injection locking characteristics of a 1 W. broad stripe laser diode,” Appl. Phys. Lett. 53, 1900–1902 (1988).
[CrossRef]

W. T. Tsang, “Low-current threshold and high lasing uniformity GaAs-AlxGa1−xAs double-heterostructure lasers grown by molecular beam epitaxy,” Appl. Phys. Lett. 34, 473–475 (1979).
[CrossRef]

M. Sakamoto and Y. Kato, “High power (710 mW cw) single-lobe operation of broad-area AlGaAs double-heterostructure lasers grown by metalorganic chemical vapor deposition,” Appl. Phys. Lett. 50, 869–870 (1987).
[CrossRef]

S. S. Wang and H. G. Winful, “Dynamics of phase-locked semiconductor laser arrays,” Appl. Phys. Lett. 52, 1774–1776 (1988).
[CrossRef]

H. G. Winful and S. S. Wang, “Stability of phase locking in coupled semiconductor laser arrays,” Appl. Phys. Lett. 52, 1894–1896 (1988).
[CrossRef]

K. Tai, T. R. Hayes, S. L. McCall, and W. T. Tsang, “Optical measurement of surface recombination in InGaAs quantum-well mesostructures,” Appl. Phys. Lett. 53, 302–303 (1988).
[CrossRef]

Electron. Lett. (1)

A. Larsson, M. Mittelstein, Y. Arakawa, and A. Yariv, “High-efficiency broad-area single-quantum-well lasers with narrow single-lobed far-field patterns prepared by molecular beam epitaxy,” Electron. Lett. 22, 79–81 (1986).
[CrossRef]

IEEE J. Quantum Electron. (4)

D. Mehuys, R. J. Lang, M. Mittelstein, J. Salzman, and A. Yariv, “Self-stabilized nonlinear lateral modes of broad-area lasers,” IEEE J. Quantum Electron. QE-23, 1909–1920 (1987).
[CrossRef]

R. J. Lang, A. G. Larsson, and J. G. Cody, “Lateral modes of broad-area semiconductor lasers: theory and experiment,” IEEE J. Quantum Electron. 27, 312–320 (1991).
[CrossRef]

W. W. Chow and D. Depatie, “Filamentation in conventional double heterostructure and quantum well semiconductor lasers,” IEEE J. Quantum Electron. 24, 1297–1301 (1988).
[CrossRef]

M. L. Tilton, G. C. Dente, A. H. Paxton, J. Cser, R. K. DeFreez, C. E. Moeller, and D. Depatie, “High power, nearly diffraction-limited output from a semiconductor laser with an unstable resonator,” IEEE J. Quantum Electron. 27, 2098–2108 (1991).
[CrossRef]

J. Opt. Soc. Am. B (1)

Optoelectronics (1)

G. H. B. Thompson, “A theory for filamentation in semiconductor lasers including the dependence of dielectric constant on injected carrier density,” Optoelectronics 4, 257–310 (1972).

Phys. Rev. A (1)

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

Rep. Prog. Phys. (1)

E. Abraham and S. D. Smith, “Optical bistability and related devices,” Rep. Prog. Phys. 45, 815–885 (1982).
[CrossRef]

Other (2)

H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors (World Scientific, Singapore, 1990).

E. Abraham, H. Adachihara, O. Hess, R. A. Indik, P. Jacobsen, J. V. Moloney, and P. Ru, “Optical turbulence in semiconductor lasers,” in Nonlinear Processes in Physics, D. Kaup and A. Fokas, eds. (Springer-Verlag, Berlin, 1993).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Schematic of a broad-area semiconductor laser. A current stripe is laid upon the cladding, and carriers injected into the active layer can diffuse transversely in x and recombine with holes to generate the light field propagating in the z direction. Laser output occurs through the low-reflectivity facet.

Fig. 2
Fig. 2

Growth rates σ1 and σ2 versus transverse wave number k as obtained from the linear stability analysis. Parameters: κ0 = 0.36, Γ = 0.5, Dp = 0.2, Df = 3.6 × 10−4, γ = 6 × 10−4, γc = 0.65, R1 = 1, Δ J = 2 J th. (a) Plot of σ1 versus k showing the dependence on the linewidth enhancement factor R. Note the shrinkage of the unstable window of modes as R is decreased. (b) Effect of a small imaginary component in the diffraction coefficient, i.e., Dp′ = Dp(1 − i∊), is to dampen high-k modes, as shown in the plot of σ2 versus k; here = 0.01. The finite transverse laser width of 80 μm allows the discrete modes with the k values indicated by the dots on the σ1 curve to become unstable: k = π/8, 2π/8, 3π/8, 4π/8, 5π/8. In both plots, R = 2 was chosen.

Fig. 3
Fig. 3

Contour plot of the near-field emission from an 80-μm-wide broad-area laser over a period of 12 ns for zero index guiding. Light shading corresponds to high-intensity excursions. The bars at the bottom and top of each picture indicate the emitter’s transverse dimension. After the initial relaxation oscillation the output never settles down but pulsates randomly in chaotic fashion. As Δ = 0, the fields diffract away at the edges.

Fig. 4
Fig. 4

As in fig. 3 but with passive index guiding (Δ ≠ 0): (a) near field, (b) far field. Note that diffraction from the edges is markedly suppressed.

Fig. 5
Fig. 5

Transverse profile of the intensity (solid curves) and carrier density (dotted curves) showing filamentation at different time frames. The simulation corresponds to that of Fig. 4. Note the anticorrelation between intensity peaks and carrier concentration profiles. (a) 1.73 ns, (b) 3.73 ns, (c) 4.15 ns.

Fig. 6
Fig. 6

Half-symmetric unstable resonator design. The output mirror has a radius of curvature RM, and the aperture radius is b. F and B stand for forward and backward field envelopes, respectively.

Fig. 7
Fig. 7

As in Fig. 4(a) but with the stable resonator replaced by the half-symmetric unstable design of Fig. 6. (a) RM = 5000 μm. High-k transverse modes are damped, but instability remains. (b) RM = 2500 μm. After initial relaxation oscillations the emission becomes stable. The far field (not shown) is single lobed. (c) RM = 500 μm. Excessive curvature of the mirror restores instability.

Tables (1)

Tables Icon

Table 1 Scaling of Conventional Variables (Primed) and Constants to Dimensionless Forma

Equations (30)

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

F z + F t = i D p 2 F x 2 - i Δ F + κ 0 Γ [ g ( N ) - i R N ] F ,
- B z + B t = i D p 2 B x 2 - i Δ B + κ 0 Γ [ g ( N ) - i R N ] B ,
N t = D f 2 N x 2 + J - γ N - Γ g ( N ) ( F 2 + B 2 ) .
F ( x , z = 0 , t ) = - ( R 1 ) 1 / 2 B ( x , z = 0 , t ) ,
B ( x , z = 1 , t ) = - ( R 2 ) 1 / 2 F ( x , z = 1 , t ) ,
F x = - c 1 F ,             N x = - c 2 N             at x = + 1 / 2 ,
F x = + c 1 F ,             N x = + c 2 N             at x = - 1 / 2 ,
F ¯ t = - γ c F ¯ + i D p 2 F ¯ x 2 - i Δ F ¯ + κ 0 Γ [ g ( N ¯ ) - i R N ¯ ] F ¯ ,
N ¯ t = D f 2 N ¯ x 2 + J - γ N ¯ - 2 Γ g ( N ¯ ) F ¯ 2 ,
N 0 = γ c κ 0 Γ + 1 ,
F 0 ( t ) = [ ( κ 0 2 γ c ) ( J - J th ) ] 1 / 2 exp ( - i κ 0 Γ R N 0 t + i Θ 0 ) ,
F ¯ = F 0 ( 1 + f ) ,
N ¯ = N 0 ( 1 + n ) .
f t = i D p 2 f x 2 + κ 0 Γ N 0 ( 1 - i R ) n ,
n t = D f 2 n x 2 - n ( γ + 2 Γ F 0 2 ) - 2 Γ F 0 2 g ( N 0 ) ( f + f * ) N 0 ,
( λ + p ) ( λ 2 + 1 ) - q ( R - λ ) = 0 ,
λ λ / k 2 D p , p κ 0 Γ ( J - J th ) + γ γ c + γ c k 2 D f γ c k 2 D p , q 2 κ 0 Γ ( J - J th ) ( k 2 D p ) 2 .
q R / p > 1
k 2 < - ( γ γ c + Δ J 2 γ c D f ) + [ ( γ γ c + Δ J 2 γ c D f ) 2 + 2 Γ R Δ J κ 0 γ c D p D f ] 1 / 2 ,
k 2 < Γ R Δ J κ 0 γ c D p D f ;
ξ 3 + p ξ + q = 0 ,
p = 1 + q - p 2 3 , q = 2 p 3 27 + p 3 ( 2 - q ) - q R ,
ξ 1 = [ - q 2 + ( q 2 4 + p 3 27 ) 1 / 2 ] 1 / 3 - [ q 2 + ( q 2 4 + p 3 27 ) 1 / 2 ] 1 / 3 , α - α ξ 2 , 3 = - ξ 1 2 ± i α + α 2 3 .
σ 1 Re λ 1 = k 2 D p ( ξ 1 - p 3 ) ,
σ 2 Re λ 2 , 3 = - k 2 D p ( ξ 1 2 + p 3 ) .
p = D f D p + O ( k - 2 )             k 1.
ξ 1 - 2 3 p + O ( k - 4 ) ;
lim k σ 1 = - , lim k σ 2 = 0.
σ 1 = k 2 D p ( ξ 1 - p 3 ) - k 2 D p , σ 2 = - k 2 D p ( ξ 1 2 + p 3 ) - k 2 D p .
B ( x , z , t ) = - ( R 2 ) 1 / 2 F ( x , z , t ) exp [ - 2 π i ( x 2 - b 2 ) λ R M ] ,

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