Abstract

The gain and carrier temperature response of semiconductor laser media to picosecond optical pulses with various pulse energies is obtained by means of a model that is based on rate equations extended to include the carrier energy density equation. The temperature dynamics are obtained from the carrier energy density by use of a quasi-equilibrium Fermi–Dirac distribution. We study the cases of media whose prepulse states are strongly absorbing, transparent, and strongly amplifying at the frequency of the pulse. The results show that the various physical processes that influence the gain and carrier temperature contribute differently, depending on both the initial state of the medium and the pulse energy. In particular, the influence of free-carrier absorption and two-photon absorption on the dynamics of the carrier temperature and the gain coefficient is discussed in detail.

© 2000 Optical Society of America

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    [CrossRef]
  34. A. Villeneuve, M. Sundheimer, N. Finalayson, G. I. Stegeman, S. Morasca, C. Rigo, R. Calvani, and C. DeBernardi, “Two-photon absorption in In1−x−yGaxAlyAs/InP waveguides at communications wavelengths,” Appl. Phys. Lett. 56, 1865–1867 (1990).
    [CrossRef]
  35. J. R. Karin, A. V. Uskov, R. Nagarajan, J. E. Bowers, and J. Mørk, “Carrier heating dynamics in semiconductor waveguide saturable absorbers,” Appl. Phys. Lett. 65, 2708–2711 (1994).
    [CrossRef]
  36. A. V. Uskov, J. R. Karin, R. Nagarajan, and J. E. Bowers, “Dynamics of carrier heating and sweepout in waveguide saturable absorbers,” IEEE J. Sel. Top. Quantum Electron. 1, 552–561 (1995).
    [CrossRef]
  37. A. V. Uskov, J. R. Karin, J. E. Bowers, J. G. McInerney, and J. Le Bihan, “Effects of carrier cooling and carrier heating in saturation dynamics and pulse propagation through bulk semiconductor absorbers,” IEEE J. Quantum Electron. 34, 2162–2171 (1998).
    [CrossRef]
  38. D. Bimberg and J. Mycielski, “Recombination-induced heating of free carriers in a semiconductor,” Phys. Rev. B 31, 5490–5493 (1985).
    [CrossRef]
  39. D. Bimberg and J. Mycielski, “The recombination-induced temperature change of no-equilibrium charge carriers,” J. Phys. C 19, 2363–2373 (1986).
    [CrossRef]
  40. A. N. Oraevsky, T. Sarkisyan, and D. K. Bandy, “Dynamics of the temperature of a recombining ensemble of fermions,” JETP Lett. 62, 673–676 (1995).
  41. P. Borri, S. Scaffetti, J. Mørk, W. Langbein, J. M. Hvam, A. Mecozzi, and F. Martelli, “Measurement and calculation of the critical pulsewidth for gain saturation in semiconductor optical amplifiers,” Opt. Commun. 164, 51–55 (1999).
    [CrossRef]

1999

P. Borri, S. Scaffetti, J. Mørk, W. Langbein, J. M. Hvam, A. Mecozzi, and F. Martelli, “Measurement and calculation of the critical pulsewidth for gain saturation in semiconductor optical amplifiers,” Opt. Commun. 164, 51–55 (1999).
[CrossRef]

1998

A. V. Uskov, J. R. Karin, J. E. Bowers, J. G. McInerney, and J. Le Bihan, “Effects of carrier cooling and carrier heating in saturation dynamics and pulse propagation through bulk semiconductor absorbers,” IEEE J. Quantum Electron. 34, 2162–2171 (1998).
[CrossRef]

T. V. Sarkisyan, A. N. Oraevsky, A. T. Rosenberger, R. L. Rolleigh, and D. K. Bandy, “Nonlinear gain and carrier temperature dynamics in semiconductor laser media,” J. Opt. Soc. Am. B 15, 1107–1119 (1998).
[CrossRef]

1997

A. N. Oraevsky, T. V. Sarkisyan, and D. K. Bandy, “Nonlinear gain and bistable regime of free-running oscillation in a semiconductor laser,” Laser Phys. 7, 920–927 (1997).

1996

O. Hess and T. Kuhn, “Maxwell–Bloch equations for spatially inhomogeneous semiconductor lasers. I. Theoretical formulation,” Phys. Rev. A 54, 3347–3359 (1996).
[CrossRef] [PubMed]

J. Mørk and A. Mecozzi, “Theory of the ultrafast optical response of active semiconductor waveguides,” J. Opt. Soc. Am. B 13, 1803–1816 (1996).
[CrossRef]

C.-Y. Tsai, R. M. Spencer, Y.-H. Lo, and L. F. Eastman, “Nonlinear gain coefficients in semiconductor lasers: effects of carrier heating,” IEEE J. Quantum Electron. 32, 201–212 (1996).
[CrossRef]

R. A. Indik, R. Binder, M. Mlejnek, J. V. Moloney, S. Hughes, A. Knorr, and S. W. Koch, “Role of plasma cooling, heating, and memory effects in subpicosecond pulse propagation in semiconductor amplifiers,” Phys. Rev. A 53, 3614–3620 (1996).
[CrossRef] [PubMed]

1995

V. I. Tolstikhin and M. Willander, “Carrier heating effects in dynamic-single-frequency GaInAsP–InP laser diodes,” IEEE J. Quantum Electron. 31, 814–833 (1995).
[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).
[CrossRef]

C. M. Bowden and G. P. Agrawal, “Bloch–Maxwell formulation for semiconductors: effects of coherent Coulomb exchange,” Phys. Rev. A 51, 4132–4139 (1995).
[CrossRef] [PubMed]

A. N. Oraevsky, T. Sarkisyan, and D. K. Bandy, “Dynamics of the temperature of a recombining ensemble of fermions,” JETP Lett. 62, 673–676 (1995).

A. V. Uskov, J. R. Karin, R. Nagarajan, and J. E. Bowers, “Dynamics of carrier heating and sweepout in waveguide saturable absorbers,” IEEE J. Sel. Top. Quantum Electron. 1, 552–561 (1995).
[CrossRef]

1994

J. R. Karin, A. V. Uskov, R. Nagarajan, J. E. Bowers, and J. Mørk, “Carrier heating dynamics in semiconductor waveguide saturable absorbers,” Appl. Phys. Lett. 65, 2708–2711 (1994).
[CrossRef]

1992

A. Knorr, R. Binder, M. Lindberg, and S. W. Koch, “Theoretical study of resonant ultrashort-pulse propagation in semiconductors,” Phys. Rev. A 46, 7179–7186 (1992).
[CrossRef] [PubMed]

M. Willatzen, T. Takahashi, and Y. Arakawa, “Nonlinear gain effects due to carrier heating and spectral hole burning in strained-quantum well lasers,” IEEE Photon. Technol. Lett. 4, 682–685 (1992).
[CrossRef]

A. V. Uskov, J. Mørk, and J. Mark, “Theory of short-pulse gain saturation in semiconductor laser amplifiers,” IEEE Photon. Technol. Lett. 4, 443–446 (1992).
[CrossRef]

J. Mark and J. Mørk, “Subpicosecond gain dynamics in InGaAsP optical amplifiers: experiment and theory,” Appl. Phys. Lett. 61, 2281–2283 (1992).
[CrossRef]

1991

M. Willatzen, A. Uskov, J. Mørk, H. Olesen, B. Tromborg, and A.-P. Jauho, “Nonlinear gain suppression in semiconductor lasers due to carrier heating,” IEEE Photon. Technol. Lett. 3, 606–609 (1991).
[CrossRef]

A. N. Oraevsky, M. M. Clark, and D. K. Bandy, “Many-temperature model of laser with dynamics,” Opt. Commun. 85, 360–364 (1991).
[CrossRef]

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electronic nonlinear refraction in solids,” IEEE J. Quantum Electron. 27, 1296–1309 (1991).
[CrossRef]

1990

A. Villeneuve, M. Sundheimer, N. Finalayson, G. I. Stegeman, S. Morasca, C. Rigo, R. Calvani, and C. DeBernardi, “Two-photon absorption in In1−x−yGaxAlyAs/InP waveguides at communications wavelengths,” Appl. Phys. Lett. 56, 1865–1867 (1990).
[CrossRef]

B. N. Gomatam and A. P. DeFonzo, “Theory of hot carrier effects on non-linear gain in GaAs–GaAlAs lasers and amplifiers,” IEEE J. Quantum Electron. 26, 1689–1704 (1990).
[CrossRef]

K. L. Hall, J. Mark, E. P. Ippen, and G. Eisenstein, “Femtosecond gain dynamics in InGaAsP optical amplifiers,” Appl. Phys. Lett. 56, 1740–1742 (1990).
[CrossRef]

W. Schäfer and K. Henneberger, “Pulse propagation and carrier kinetics in laser excited semiconductors,” Phys. Status Solidi B 159, 59–69 (1990).
[CrossRef]

1987

W. Z. Lin, L. G. Fujimoto, E. P. Ippen, and R. A. Logan, “Femtosecond carrier dynamics in GaAs,” Appl. Phys. Lett. 50, 124–126 (1987).
[CrossRef]

M. P. Kesler and E. P. Ippen, “Subpicosecond gain dynamics in GaAlAs laser diodes,” Appl. Phys. Lett. 51, 1765–1767 (1987).
[CrossRef]

1986

M. S. Stix, M. P. Kesler, and E. P. Ippen, “Observations of subpicosecond dynamics in GaAlAs laser diodes,” Appl. Phys. Lett. 48, 1722–1725 (1986).
[CrossRef]

L. A. Rivlin, “Dynamics and emission spectra of semiconductor lasers,” J. Sov. Laser Res. 7, 57–206 (1986).
[CrossRef]

D. Bimberg and J. Mycielski, “The recombination-induced temperature change of no-equilibrium charge carriers,” J. Phys. C 19, 2363–2373 (1986).
[CrossRef]

1985

D. Bimberg and J. Mycielski, “Recombination-induced heating of free carriers in a semiconductor,” Phys. Rev. B 31, 5490–5493 (1985).
[CrossRef]

1976

H. C. Casey, Jr., and F. Stern, “Concentration-dependent absorption and spontaneous emission in heavily doped GaAs,” J. Appl. Phys. 47, 631–643 (1976).
[CrossRef]

Agrawal, G. P.

C. M. Bowden and G. P. Agrawal, “Bloch–Maxwell formulation for semiconductors: effects of coherent Coulomb exchange,” Phys. Rev. A 51, 4132–4139 (1995).
[CrossRef] [PubMed]

Arakawa, Y.

M. Willatzen, T. Takahashi, and Y. Arakawa, “Nonlinear gain effects due to carrier heating and spectral hole burning in strained-quantum well lasers,” IEEE Photon. Technol. Lett. 4, 682–685 (1992).
[CrossRef]

Bandy, D. K.

T. V. Sarkisyan, A. N. Oraevsky, A. T. Rosenberger, R. L. Rolleigh, and D. K. Bandy, “Nonlinear gain and carrier temperature dynamics in semiconductor laser media,” J. Opt. Soc. Am. B 15, 1107–1119 (1998).
[CrossRef]

A. N. Oraevsky, T. V. Sarkisyan, and D. K. Bandy, “Nonlinear gain and bistable regime of free-running oscillation in a semiconductor laser,” Laser Phys. 7, 920–927 (1997).

A. N. Oraevsky, T. Sarkisyan, and D. K. Bandy, “Dynamics of the temperature of a recombining ensemble of fermions,” JETP Lett. 62, 673–676 (1995).

A. N. Oraevsky, M. M. Clark, and D. K. Bandy, “Many-temperature model of laser with dynamics,” Opt. Commun. 85, 360–364 (1991).
[CrossRef]

Bimberg, D.

D. Bimberg and J. Mycielski, “The recombination-induced temperature change of no-equilibrium charge carriers,” J. Phys. C 19, 2363–2373 (1986).
[CrossRef]

D. Bimberg and J. Mycielski, “Recombination-induced heating of free carriers in a semiconductor,” Phys. Rev. B 31, 5490–5493 (1985).
[CrossRef]

Binder, R.

R. A. Indik, R. Binder, M. Mlejnek, J. V. Moloney, S. Hughes, A. Knorr, and S. W. Koch, “Role of plasma cooling, heating, and memory effects in subpicosecond pulse propagation in semiconductor amplifiers,” Phys. Rev. A 53, 3614–3620 (1996).
[CrossRef] [PubMed]

A. Knorr, R. Binder, M. Lindberg, and S. W. Koch, “Theoretical study of resonant ultrashort-pulse propagation in semiconductors,” Phys. Rev. A 46, 7179–7186 (1992).
[CrossRef] [PubMed]

Borri, P.

P. Borri, S. Scaffetti, J. Mørk, W. Langbein, J. M. Hvam, A. Mecozzi, and F. Martelli, “Measurement and calculation of the critical pulsewidth for gain saturation in semiconductor optical amplifiers,” Opt. Commun. 164, 51–55 (1999).
[CrossRef]

Bowden, C. M.

C. M. Bowden and G. P. Agrawal, “Bloch–Maxwell formulation for semiconductors: effects of coherent Coulomb exchange,” Phys. Rev. A 51, 4132–4139 (1995).
[CrossRef] [PubMed]

Bowers, J. E.

A. V. Uskov, J. R. Karin, J. E. Bowers, J. G. McInerney, and J. Le Bihan, “Effects of carrier cooling and carrier heating in saturation dynamics and pulse propagation through bulk semiconductor absorbers,” IEEE J. Quantum Electron. 34, 2162–2171 (1998).
[CrossRef]

A. V. Uskov, J. R. Karin, R. Nagarajan, and J. E. Bowers, “Dynamics of carrier heating and sweepout in waveguide saturable absorbers,” IEEE J. Sel. Top. Quantum Electron. 1, 552–561 (1995).
[CrossRef]

J. R. Karin, A. V. Uskov, R. Nagarajan, J. E. Bowers, and J. Mørk, “Carrier heating dynamics in semiconductor waveguide saturable absorbers,” Appl. Phys. Lett. 65, 2708–2711 (1994).
[CrossRef]

Calvani, R.

A. Villeneuve, M. Sundheimer, N. Finalayson, G. I. Stegeman, S. Morasca, C. Rigo, R. Calvani, and C. DeBernardi, “Two-photon absorption in In1−x−yGaxAlyAs/InP waveguides at communications wavelengths,” Appl. Phys. Lett. 56, 1865–1867 (1990).
[CrossRef]

Casey Jr., H. C.

H. C. Casey, Jr., and F. Stern, “Concentration-dependent absorption and spontaneous emission in heavily doped GaAs,” J. Appl. Phys. 47, 631–643 (1976).
[CrossRef]

Clark, M. M.

A. N. Oraevsky, M. M. Clark, and D. K. Bandy, “Many-temperature model of laser with dynamics,” Opt. Commun. 85, 360–364 (1991).
[CrossRef]

DeBernardi, C.

A. Villeneuve, M. Sundheimer, N. Finalayson, G. I. Stegeman, S. Morasca, C. Rigo, R. Calvani, and C. DeBernardi, “Two-photon absorption in In1−x−yGaxAlyAs/InP waveguides at communications wavelengths,” Appl. Phys. Lett. 56, 1865–1867 (1990).
[CrossRef]

DeFonzo, A. P.

B. N. Gomatam and A. P. DeFonzo, “Theory of hot carrier effects on non-linear gain in GaAs–GaAlAs lasers and amplifiers,” IEEE J. Quantum Electron. 26, 1689–1704 (1990).
[CrossRef]

Eastman, L. F.

C.-Y. Tsai, R. M. Spencer, Y.-H. Lo, and L. F. Eastman, “Nonlinear gain coefficients in semiconductor lasers: effects of carrier heating,” IEEE J. Quantum Electron. 32, 201–212 (1996).
[CrossRef]

Eisenstein, G.

K. L. Hall, J. Mark, E. P. Ippen, and G. Eisenstein, “Femtosecond gain dynamics in InGaAsP optical amplifiers,” Appl. Phys. Lett. 56, 1740–1742 (1990).
[CrossRef]

Finalayson, N.

A. Villeneuve, M. Sundheimer, N. Finalayson, G. I. Stegeman, S. Morasca, C. Rigo, R. Calvani, and C. DeBernardi, “Two-photon absorption in In1−x−yGaxAlyAs/InP waveguides at communications wavelengths,” Appl. Phys. Lett. 56, 1865–1867 (1990).
[CrossRef]

Fujimoto, L. G.

W. Z. Lin, L. G. Fujimoto, E. P. Ippen, and R. A. Logan, “Femtosecond carrier dynamics in GaAs,” Appl. Phys. Lett. 50, 124–126 (1987).
[CrossRef]

Gomatam, B. N.

B. N. Gomatam and A. P. DeFonzo, “Theory of hot carrier effects on non-linear gain in GaAs–GaAlAs lasers and amplifiers,” IEEE J. Quantum Electron. 26, 1689–1704 (1990).
[CrossRef]

Hagan, D. J.

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electronic nonlinear refraction in solids,” IEEE J. Quantum Electron. 27, 1296–1309 (1991).
[CrossRef]

Hall, K. L.

K. L. Hall, J. Mark, E. P. Ippen, and G. Eisenstein, “Femtosecond gain dynamics in InGaAsP optical amplifiers,” Appl. Phys. Lett. 56, 1740–1742 (1990).
[CrossRef]

Henneberger, K.

W. Schäfer and K. Henneberger, “Pulse propagation and carrier kinetics in laser excited semiconductors,” Phys. Status Solidi B 159, 59–69 (1990).
[CrossRef]

Hess, O.

O. Hess and T. Kuhn, “Maxwell–Bloch equations for spatially inhomogeneous semiconductor lasers. I. Theoretical formulation,” Phys. Rev. A 54, 3347–3359 (1996).
[CrossRef] [PubMed]

Hughes, S.

R. A. Indik, R. Binder, M. Mlejnek, J. V. Moloney, S. Hughes, A. Knorr, and S. W. Koch, “Role of plasma cooling, heating, and memory effects in subpicosecond pulse propagation in semiconductor amplifiers,” Phys. Rev. A 53, 3614–3620 (1996).
[CrossRef] [PubMed]

Hutchings, D. C.

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electronic nonlinear refraction in solids,” IEEE J. Quantum Electron. 27, 1296–1309 (1991).
[CrossRef]

Hvam, J. M.

P. Borri, S. Scaffetti, J. Mørk, W. Langbein, J. M. Hvam, A. Mecozzi, and F. Martelli, “Measurement and calculation of the critical pulsewidth for gain saturation in semiconductor optical amplifiers,” Opt. Commun. 164, 51–55 (1999).
[CrossRef]

Indik, R. A.

R. A. Indik, R. Binder, M. Mlejnek, J. V. Moloney, S. Hughes, A. Knorr, and S. W. Koch, “Role of plasma cooling, heating, and memory effects in subpicosecond pulse propagation in semiconductor amplifiers,” Phys. Rev. A 53, 3614–3620 (1996).
[CrossRef] [PubMed]

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).
[CrossRef]

Ippen, E. P.

K. L. Hall, J. Mark, E. P. Ippen, and G. Eisenstein, “Femtosecond gain dynamics in InGaAsP optical amplifiers,” Appl. Phys. Lett. 56, 1740–1742 (1990).
[CrossRef]

W. Z. Lin, L. G. Fujimoto, E. P. Ippen, and R. A. Logan, “Femtosecond carrier dynamics in GaAs,” Appl. Phys. Lett. 50, 124–126 (1987).
[CrossRef]

M. P. Kesler and E. P. Ippen, “Subpicosecond gain dynamics in GaAlAs laser diodes,” Appl. Phys. Lett. 51, 1765–1767 (1987).
[CrossRef]

M. S. Stix, M. P. Kesler, and E. P. Ippen, “Observations of subpicosecond dynamics in GaAlAs laser diodes,” Appl. Phys. Lett. 48, 1722–1725 (1986).
[CrossRef]

Jauho, A.-P.

M. Willatzen, A. Uskov, J. Mørk, H. Olesen, B. Tromborg, and A.-P. Jauho, “Nonlinear gain suppression in semiconductor lasers due to carrier heating,” IEEE Photon. Technol. Lett. 3, 606–609 (1991).
[CrossRef]

Karin, J. R.

A. V. Uskov, J. R. Karin, J. E. Bowers, J. G. McInerney, and J. Le Bihan, “Effects of carrier cooling and carrier heating in saturation dynamics and pulse propagation through bulk semiconductor absorbers,” IEEE J. Quantum Electron. 34, 2162–2171 (1998).
[CrossRef]

A. V. Uskov, J. R. Karin, R. Nagarajan, and J. E. Bowers, “Dynamics of carrier heating and sweepout in waveguide saturable absorbers,” IEEE J. Sel. Top. Quantum Electron. 1, 552–561 (1995).
[CrossRef]

J. R. Karin, A. V. Uskov, R. Nagarajan, J. E. Bowers, and J. Mørk, “Carrier heating dynamics in semiconductor waveguide saturable absorbers,” Appl. Phys. Lett. 65, 2708–2711 (1994).
[CrossRef]

Kesler, M. P.

M. P. Kesler and E. P. Ippen, “Subpicosecond gain dynamics in GaAlAs laser diodes,” Appl. Phys. Lett. 51, 1765–1767 (1987).
[CrossRef]

M. S. Stix, M. P. Kesler, and E. P. Ippen, “Observations of subpicosecond dynamics in GaAlAs laser diodes,” Appl. Phys. Lett. 48, 1722–1725 (1986).
[CrossRef]

Knorr, A.

R. A. Indik, R. Binder, M. Mlejnek, J. V. Moloney, S. Hughes, A. Knorr, and S. W. Koch, “Role of plasma cooling, heating, and memory effects in subpicosecond pulse propagation in semiconductor amplifiers,” Phys. Rev. A 53, 3614–3620 (1996).
[CrossRef] [PubMed]

A. Knorr, R. Binder, M. Lindberg, and S. W. Koch, “Theoretical study of resonant ultrashort-pulse propagation in semiconductors,” Phys. Rev. A 46, 7179–7186 (1992).
[CrossRef] [PubMed]

Koch, S. W.

R. A. Indik, R. Binder, M. Mlejnek, J. V. Moloney, S. Hughes, A. Knorr, and S. W. Koch, “Role of plasma cooling, heating, and memory effects in subpicosecond pulse propagation in semiconductor amplifiers,” Phys. Rev. A 53, 3614–3620 (1996).
[CrossRef] [PubMed]

A. Knorr, R. Binder, M. Lindberg, and S. W. Koch, “Theoretical study of resonant ultrashort-pulse propagation in semiconductors,” Phys. Rev. A 46, 7179–7186 (1992).
[CrossRef] [PubMed]

Kuhn, T.

O. Hess and T. Kuhn, “Maxwell–Bloch equations for spatially inhomogeneous semiconductor lasers. I. Theoretical formulation,” Phys. Rev. A 54, 3347–3359 (1996).
[CrossRef] [PubMed]

Langbein, W.

P. Borri, S. Scaffetti, J. Mørk, W. Langbein, J. M. Hvam, A. Mecozzi, and F. Martelli, “Measurement and calculation of the critical pulsewidth for gain saturation in semiconductor optical amplifiers,” Opt. Commun. 164, 51–55 (1999).
[CrossRef]

Le Bihan, J.

A. V. Uskov, J. R. Karin, J. E. Bowers, J. G. McInerney, and J. Le Bihan, “Effects of carrier cooling and carrier heating in saturation dynamics and pulse propagation through bulk semiconductor absorbers,” IEEE J. Quantum Electron. 34, 2162–2171 (1998).
[CrossRef]

Lin, W. Z.

W. Z. Lin, L. G. Fujimoto, E. P. Ippen, and R. A. Logan, “Femtosecond carrier dynamics in GaAs,” Appl. Phys. Lett. 50, 124–126 (1987).
[CrossRef]

Lindberg, M.

A. Knorr, R. Binder, M. Lindberg, and S. W. Koch, “Theoretical study of resonant ultrashort-pulse propagation in semiconductors,” Phys. Rev. A 46, 7179–7186 (1992).
[CrossRef] [PubMed]

Lo, Y.-H.

C.-Y. Tsai, R. M. Spencer, Y.-H. Lo, and L. F. Eastman, “Nonlinear gain coefficients in semiconductor lasers: effects of carrier heating,” IEEE J. Quantum Electron. 32, 201–212 (1996).
[CrossRef]

Logan, R. A.

W. Z. Lin, L. G. Fujimoto, E. P. Ippen, and R. A. Logan, “Femtosecond carrier dynamics in GaAs,” Appl. Phys. Lett. 50, 124–126 (1987).
[CrossRef]

Mark, J.

J. Mark and J. Mørk, “Subpicosecond gain dynamics in InGaAsP optical amplifiers: experiment and theory,” Appl. Phys. Lett. 61, 2281–2283 (1992).
[CrossRef]

A. V. Uskov, J. Mørk, and J. Mark, “Theory of short-pulse gain saturation in semiconductor laser amplifiers,” IEEE Photon. Technol. Lett. 4, 443–446 (1992).
[CrossRef]

K. L. Hall, J. Mark, E. P. Ippen, and G. Eisenstein, “Femtosecond gain dynamics in InGaAsP optical amplifiers,” Appl. Phys. Lett. 56, 1740–1742 (1990).
[CrossRef]

Martelli, F.

P. Borri, S. Scaffetti, J. Mørk, W. Langbein, J. M. Hvam, A. Mecozzi, and F. Martelli, “Measurement and calculation of the critical pulsewidth for gain saturation in semiconductor optical amplifiers,” Opt. Commun. 164, 51–55 (1999).
[CrossRef]

McInerney, J. G.

A. V. Uskov, J. R. Karin, J. E. Bowers, J. G. McInerney, and J. Le Bihan, “Effects of carrier cooling and carrier heating in saturation dynamics and pulse propagation through bulk semiconductor absorbers,” IEEE J. Quantum Electron. 34, 2162–2171 (1998).
[CrossRef]

Mecozzi, A.

P. Borri, S. Scaffetti, J. Mørk, W. Langbein, J. M. Hvam, A. Mecozzi, and F. Martelli, “Measurement and calculation of the critical pulsewidth for gain saturation in semiconductor optical amplifiers,” Opt. Commun. 164, 51–55 (1999).
[CrossRef]

J. Mørk and A. Mecozzi, “Theory of the ultrafast optical response of active semiconductor waveguides,” J. Opt. Soc. Am. B 13, 1803–1816 (1996).
[CrossRef]

Mlejnek, M.

R. A. Indik, R. Binder, M. Mlejnek, J. V. Moloney, S. Hughes, A. Knorr, and S. W. Koch, “Role of plasma cooling, heating, and memory effects in subpicosecond pulse propagation in semiconductor amplifiers,” Phys. Rev. A 53, 3614–3620 (1996).
[CrossRef] [PubMed]

Moloney, J. V.

R. A. Indik, R. Binder, M. Mlejnek, J. V. Moloney, S. Hughes, A. Knorr, and S. W. Koch, “Role of plasma cooling, heating, and memory effects in subpicosecond pulse propagation in semiconductor amplifiers,” Phys. Rev. A 53, 3614–3620 (1996).
[CrossRef] [PubMed]

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).
[CrossRef]

Morasca, S.

A. Villeneuve, M. Sundheimer, N. Finalayson, G. I. Stegeman, S. Morasca, C. Rigo, R. Calvani, and C. DeBernardi, “Two-photon absorption in In1−x−yGaxAlyAs/InP waveguides at communications wavelengths,” Appl. Phys. Lett. 56, 1865–1867 (1990).
[CrossRef]

Mørk, J.

P. Borri, S. Scaffetti, J. Mørk, W. Langbein, J. M. Hvam, A. Mecozzi, and F. Martelli, “Measurement and calculation of the critical pulsewidth for gain saturation in semiconductor optical amplifiers,” Opt. Commun. 164, 51–55 (1999).
[CrossRef]

J. Mørk and A. Mecozzi, “Theory of the ultrafast optical response of active semiconductor waveguides,” J. Opt. Soc. Am. B 13, 1803–1816 (1996).
[CrossRef]

J. R. Karin, A. V. Uskov, R. Nagarajan, J. E. Bowers, and J. Mørk, “Carrier heating dynamics in semiconductor waveguide saturable absorbers,” Appl. Phys. Lett. 65, 2708–2711 (1994).
[CrossRef]

A. V. Uskov, J. Mørk, and J. Mark, “Theory of short-pulse gain saturation in semiconductor laser amplifiers,” IEEE Photon. Technol. Lett. 4, 443–446 (1992).
[CrossRef]

J. Mark and J. Mørk, “Subpicosecond gain dynamics in InGaAsP optical amplifiers: experiment and theory,” Appl. Phys. Lett. 61, 2281–2283 (1992).
[CrossRef]

M. Willatzen, A. Uskov, J. Mørk, H. Olesen, B. Tromborg, and A.-P. Jauho, “Nonlinear gain suppression in semiconductor lasers due to carrier heating,” IEEE Photon. Technol. Lett. 3, 606–609 (1991).
[CrossRef]

Mycielski, J.

D. Bimberg and J. Mycielski, “The recombination-induced temperature change of no-equilibrium charge carriers,” J. Phys. C 19, 2363–2373 (1986).
[CrossRef]

D. Bimberg and J. Mycielski, “Recombination-induced heating of free carriers in a semiconductor,” Phys. Rev. B 31, 5490–5493 (1985).
[CrossRef]

Nagarajan, R.

A. V. Uskov, J. R. Karin, R. Nagarajan, and J. E. Bowers, “Dynamics of carrier heating and sweepout in waveguide saturable absorbers,” IEEE J. Sel. Top. Quantum Electron. 1, 552–561 (1995).
[CrossRef]

J. R. Karin, A. V. Uskov, R. Nagarajan, J. E. Bowers, and J. Mørk, “Carrier heating dynamics in semiconductor waveguide saturable absorbers,” Appl. Phys. Lett. 65, 2708–2711 (1994).
[CrossRef]

Ning, C. Z.

Olesen, H.

M. Willatzen, A. Uskov, J. Mørk, H. Olesen, B. Tromborg, and A.-P. Jauho, “Nonlinear gain suppression in semiconductor lasers due to carrier heating,” IEEE Photon. Technol. Lett. 3, 606–609 (1991).
[CrossRef]

Oraevsky, A. N.

T. V. Sarkisyan, A. N. Oraevsky, A. T. Rosenberger, R. L. Rolleigh, and D. K. Bandy, “Nonlinear gain and carrier temperature dynamics in semiconductor laser media,” J. Opt. Soc. Am. B 15, 1107–1119 (1998).
[CrossRef]

A. N. Oraevsky, T. V. Sarkisyan, and D. K. Bandy, “Nonlinear gain and bistable regime of free-running oscillation in a semiconductor laser,” Laser Phys. 7, 920–927 (1997).

A. N. Oraevsky, T. Sarkisyan, and D. K. Bandy, “Dynamics of the temperature of a recombining ensemble of fermions,” JETP Lett. 62, 673–676 (1995).

A. N. Oraevsky, M. M. Clark, and D. K. Bandy, “Many-temperature model of laser with dynamics,” Opt. Commun. 85, 360–364 (1991).
[CrossRef]

Rigo, C.

A. Villeneuve, M. Sundheimer, N. Finalayson, G. I. Stegeman, S. Morasca, C. Rigo, R. Calvani, and C. DeBernardi, “Two-photon absorption in In1−x−yGaxAlyAs/InP waveguides at communications wavelengths,” Appl. Phys. Lett. 56, 1865–1867 (1990).
[CrossRef]

Rivlin, L. A.

L. A. Rivlin, “Dynamics and emission spectra of semiconductor lasers,” J. Sov. Laser Res. 7, 57–206 (1986).
[CrossRef]

Rolleigh, R. L.

Rosenberger, A. T.

Sarkisyan, T.

A. N. Oraevsky, T. Sarkisyan, and D. K. Bandy, “Dynamics of the temperature of a recombining ensemble of fermions,” JETP Lett. 62, 673–676 (1995).

Sarkisyan, T. V.

T. V. Sarkisyan, A. N. Oraevsky, A. T. Rosenberger, R. L. Rolleigh, and D. K. Bandy, “Nonlinear gain and carrier temperature dynamics in semiconductor laser media,” J. Opt. Soc. Am. B 15, 1107–1119 (1998).
[CrossRef]

A. N. Oraevsky, T. V. Sarkisyan, and D. K. Bandy, “Nonlinear gain and bistable regime of free-running oscillation in a semiconductor laser,” Laser Phys. 7, 920–927 (1997).

Scaffetti, S.

P. Borri, S. Scaffetti, J. Mørk, W. Langbein, J. M. Hvam, A. Mecozzi, and F. Martelli, “Measurement and calculation of the critical pulsewidth for gain saturation in semiconductor optical amplifiers,” Opt. Commun. 164, 51–55 (1999).
[CrossRef]

Schäfer, W.

W. Schäfer and K. Henneberger, “Pulse propagation and carrier kinetics in laser excited semiconductors,” Phys. Status Solidi B 159, 59–69 (1990).
[CrossRef]

Sheik-Bahae, M.

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electronic nonlinear refraction in solids,” IEEE J. Quantum Electron. 27, 1296–1309 (1991).
[CrossRef]

Spencer, R. M.

C.-Y. Tsai, R. M. Spencer, Y.-H. Lo, and L. F. Eastman, “Nonlinear gain coefficients in semiconductor lasers: effects of carrier heating,” IEEE J. Quantum Electron. 32, 201–212 (1996).
[CrossRef]

Stegeman, G. I.

A. Villeneuve, M. Sundheimer, N. Finalayson, G. I. Stegeman, S. Morasca, C. Rigo, R. Calvani, and C. DeBernardi, “Two-photon absorption in In1−x−yGaxAlyAs/InP waveguides at communications wavelengths,” Appl. Phys. Lett. 56, 1865–1867 (1990).
[CrossRef]

Stern, F.

H. C. Casey, Jr., and F. Stern, “Concentration-dependent absorption and spontaneous emission in heavily doped GaAs,” J. Appl. Phys. 47, 631–643 (1976).
[CrossRef]

Stix, M. S.

M. S. Stix, M. P. Kesler, and E. P. Ippen, “Observations of subpicosecond dynamics in GaAlAs laser diodes,” Appl. Phys. Lett. 48, 1722–1725 (1986).
[CrossRef]

Sundheimer, M.

A. Villeneuve, M. Sundheimer, N. Finalayson, G. I. Stegeman, S. Morasca, C. Rigo, R. Calvani, and C. DeBernardi, “Two-photon absorption in In1−x−yGaxAlyAs/InP waveguides at communications wavelengths,” Appl. Phys. Lett. 56, 1865–1867 (1990).
[CrossRef]

Takahashi, T.

M. Willatzen, T. Takahashi, and Y. Arakawa, “Nonlinear gain effects due to carrier heating and spectral hole burning in strained-quantum well lasers,” IEEE Photon. Technol. Lett. 4, 682–685 (1992).
[CrossRef]

Tolstikhin, V. I.

V. I. Tolstikhin and M. Willander, “Carrier heating effects in dynamic-single-frequency GaInAsP–InP laser diodes,” IEEE J. Quantum Electron. 31, 814–833 (1995).
[CrossRef]

Tromborg, B.

M. Willatzen, A. Uskov, J. Mørk, H. Olesen, B. Tromborg, and A.-P. Jauho, “Nonlinear gain suppression in semiconductor lasers due to carrier heating,” IEEE Photon. Technol. Lett. 3, 606–609 (1991).
[CrossRef]

Tsai, C.-Y.

C.-Y. Tsai, R. M. Spencer, Y.-H. Lo, and L. F. Eastman, “Nonlinear gain coefficients in semiconductor lasers: effects of carrier heating,” IEEE J. Quantum Electron. 32, 201–212 (1996).
[CrossRef]

Uskov, A.

M. Willatzen, A. Uskov, J. Mørk, H. Olesen, B. Tromborg, and A.-P. Jauho, “Nonlinear gain suppression in semiconductor lasers due to carrier heating,” IEEE Photon. Technol. Lett. 3, 606–609 (1991).
[CrossRef]

Uskov, A. V.

A. V. Uskov, J. R. Karin, J. E. Bowers, J. G. McInerney, and J. Le Bihan, “Effects of carrier cooling and carrier heating in saturation dynamics and pulse propagation through bulk semiconductor absorbers,” IEEE J. Quantum Electron. 34, 2162–2171 (1998).
[CrossRef]

A. V. Uskov, J. R. Karin, R. Nagarajan, and J. E. Bowers, “Dynamics of carrier heating and sweepout in waveguide saturable absorbers,” IEEE J. Sel. Top. Quantum Electron. 1, 552–561 (1995).
[CrossRef]

J. R. Karin, A. V. Uskov, R. Nagarajan, J. E. Bowers, and J. Mørk, “Carrier heating dynamics in semiconductor waveguide saturable absorbers,” Appl. Phys. Lett. 65, 2708–2711 (1994).
[CrossRef]

A. V. Uskov, J. Mørk, and J. Mark, “Theory of short-pulse gain saturation in semiconductor laser amplifiers,” IEEE Photon. Technol. Lett. 4, 443–446 (1992).
[CrossRef]

Van Stryland, E. W.

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electronic nonlinear refraction in solids,” IEEE J. Quantum Electron. 27, 1296–1309 (1991).
[CrossRef]

Villeneuve, A.

A. Villeneuve, M. Sundheimer, N. Finalayson, G. I. Stegeman, S. Morasca, C. Rigo, R. Calvani, and C. DeBernardi, “Two-photon absorption in In1−x−yGaxAlyAs/InP waveguides at communications wavelengths,” Appl. Phys. Lett. 56, 1865–1867 (1990).
[CrossRef]

Willander, M.

V. I. Tolstikhin and M. Willander, “Carrier heating effects in dynamic-single-frequency GaInAsP–InP laser diodes,” IEEE J. Quantum Electron. 31, 814–833 (1995).
[CrossRef]

Willatzen, M.

M. Willatzen, T. Takahashi, and Y. Arakawa, “Nonlinear gain effects due to carrier heating and spectral hole burning in strained-quantum well lasers,” IEEE Photon. Technol. Lett. 4, 682–685 (1992).
[CrossRef]

M. Willatzen, A. Uskov, J. Mørk, H. Olesen, B. Tromborg, and A.-P. Jauho, “Nonlinear gain suppression in semiconductor lasers due to carrier heating,” IEEE Photon. Technol. Lett. 3, 606–609 (1991).
[CrossRef]

Appl. Phys. Lett.

M. S. Stix, M. P. Kesler, and E. P. Ippen, “Observations of subpicosecond dynamics in GaAlAs laser diodes,” Appl. Phys. Lett. 48, 1722–1725 (1986).
[CrossRef]

W. Z. Lin, L. G. Fujimoto, E. P. Ippen, and R. A. Logan, “Femtosecond carrier dynamics in GaAs,” Appl. Phys. Lett. 50, 124–126 (1987).
[CrossRef]

M. P. Kesler and E. P. Ippen, “Subpicosecond gain dynamics in GaAlAs laser diodes,” Appl. Phys. Lett. 51, 1765–1767 (1987).
[CrossRef]

K. L. Hall, J. Mark, E. P. Ippen, and G. Eisenstein, “Femtosecond gain dynamics in InGaAsP optical amplifiers,” Appl. Phys. Lett. 56, 1740–1742 (1990).
[CrossRef]

J. Mark and J. Mørk, “Subpicosecond gain dynamics in InGaAsP optical amplifiers: experiment and theory,” Appl. Phys. Lett. 61, 2281–2283 (1992).
[CrossRef]

A. Villeneuve, M. Sundheimer, N. Finalayson, G. I. Stegeman, S. Morasca, C. Rigo, R. Calvani, and C. DeBernardi, “Two-photon absorption in In1−x−yGaxAlyAs/InP waveguides at communications wavelengths,” Appl. Phys. Lett. 56, 1865–1867 (1990).
[CrossRef]

J. R. Karin, A. V. Uskov, R. Nagarajan, J. E. Bowers, and J. Mørk, “Carrier heating dynamics in semiconductor waveguide saturable absorbers,” Appl. Phys. Lett. 65, 2708–2711 (1994).
[CrossRef]

IEEE J. Quantum Electron.

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electronic nonlinear refraction in solids,” IEEE J. Quantum Electron. 27, 1296–1309 (1991).
[CrossRef]

B. N. Gomatam and A. P. DeFonzo, “Theory of hot carrier effects on non-linear gain in GaAs–GaAlAs lasers and amplifiers,” IEEE J. Quantum Electron. 26, 1689–1704 (1990).
[CrossRef]

V. I. Tolstikhin and M. Willander, “Carrier heating effects in dynamic-single-frequency GaInAsP–InP laser diodes,” IEEE J. Quantum Electron. 31, 814–833 (1995).
[CrossRef]

C.-Y. Tsai, R. M. Spencer, Y.-H. Lo, and L. F. Eastman, “Nonlinear gain coefficients in semiconductor lasers: effects of carrier heating,” IEEE J. Quantum Electron. 32, 201–212 (1996).
[CrossRef]

A. V. Uskov, J. R. Karin, J. E. Bowers, J. G. McInerney, and J. Le Bihan, “Effects of carrier cooling and carrier heating in saturation dynamics and pulse propagation through bulk semiconductor absorbers,” IEEE J. Quantum Electron. 34, 2162–2171 (1998).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

A. V. Uskov, J. R. Karin, R. Nagarajan, and J. E. Bowers, “Dynamics of carrier heating and sweepout in waveguide saturable absorbers,” IEEE J. Sel. Top. Quantum Electron. 1, 552–561 (1995).
[CrossRef]

IEEE Photon. Technol. Lett.

M. Willatzen, T. Takahashi, and Y. Arakawa, “Nonlinear gain effects due to carrier heating and spectral hole burning in strained-quantum well lasers,” IEEE Photon. Technol. Lett. 4, 682–685 (1992).
[CrossRef]

A. V. Uskov, J. Mørk, and J. Mark, “Theory of short-pulse gain saturation in semiconductor laser amplifiers,” IEEE Photon. Technol. Lett. 4, 443–446 (1992).
[CrossRef]

M. Willatzen, A. Uskov, J. Mørk, H. Olesen, B. Tromborg, and A.-P. Jauho, “Nonlinear gain suppression in semiconductor lasers due to carrier heating,” IEEE Photon. Technol. Lett. 3, 606–609 (1991).
[CrossRef]

J. Appl. Phys.

H. C. Casey, Jr., and F. Stern, “Concentration-dependent absorption and spontaneous emission in heavily doped GaAs,” J. Appl. Phys. 47, 631–643 (1976).
[CrossRef]

J. Opt. Soc. Am. B

J. Phys. C

D. Bimberg and J. Mycielski, “The recombination-induced temperature change of no-equilibrium charge carriers,” J. Phys. C 19, 2363–2373 (1986).
[CrossRef]

J. Sov. Laser Res.

L. A. Rivlin, “Dynamics and emission spectra of semiconductor lasers,” J. Sov. Laser Res. 7, 57–206 (1986).
[CrossRef]

JETP Lett.

A. N. Oraevsky, T. Sarkisyan, and D. K. Bandy, “Dynamics of the temperature of a recombining ensemble of fermions,” JETP Lett. 62, 673–676 (1995).

Laser Phys.

A. N. Oraevsky, T. V. Sarkisyan, and D. K. Bandy, “Nonlinear gain and bistable regime of free-running oscillation in a semiconductor laser,” Laser Phys. 7, 920–927 (1997).

Opt. Commun.

A. N. Oraevsky, M. M. Clark, and D. K. Bandy, “Many-temperature model of laser with dynamics,” Opt. Commun. 85, 360–364 (1991).
[CrossRef]

P. Borri, S. Scaffetti, J. Mørk, W. Langbein, J. M. Hvam, A. Mecozzi, and F. Martelli, “Measurement and calculation of the critical pulsewidth for gain saturation in semiconductor optical amplifiers,” Opt. Commun. 164, 51–55 (1999).
[CrossRef]

Phys. Rev. A

R. A. Indik, R. Binder, M. Mlejnek, J. V. Moloney, S. Hughes, A. Knorr, and S. W. Koch, “Role of plasma cooling, heating, and memory effects in subpicosecond pulse propagation in semiconductor amplifiers,” Phys. Rev. A 53, 3614–3620 (1996).
[CrossRef] [PubMed]

A. Knorr, R. Binder, M. Lindberg, and S. W. Koch, “Theoretical study of resonant ultrashort-pulse propagation in semiconductors,” Phys. Rev. A 46, 7179–7186 (1992).
[CrossRef] [PubMed]

C. M. Bowden and G. P. Agrawal, “Bloch–Maxwell formulation for semiconductors: effects of coherent Coulomb exchange,” Phys. Rev. A 51, 4132–4139 (1995).
[CrossRef] [PubMed]

O. Hess and T. Kuhn, “Maxwell–Bloch equations for spatially inhomogeneous semiconductor lasers. I. Theoretical formulation,” Phys. Rev. A 54, 3347–3359 (1996).
[CrossRef] [PubMed]

Phys. Rev. B

D. Bimberg and J. Mycielski, “Recombination-induced heating of free carriers in a semiconductor,” Phys. Rev. B 31, 5490–5493 (1985).
[CrossRef]

Phys. Status Solidi B

W. Schäfer and K. Henneberger, “Pulse propagation and carrier kinetics in laser excited semiconductors,” Phys. Status Solidi B 159, 59–69 (1990).
[CrossRef]

Other

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

G. H. B. Thompson, Physics of Semiconductor Laser Devices (Wiley, New York, 1980).

G. P. Agrawal and N. K. Dutta, Semiconductor Lasers (Van Nostrand Reinhold, New York, 1993).

L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley, New York, 1995).

S. L. Chuang, Physics of Optoelectronic Devices (Wiley, New York, 1995), p. 358.

L. A. Rivlin, A. T. Semenov, and S. D. Yakubovich, Dinamika i Spektry Izlucheniya Poluprovodnikovykh Lazerov (Radio Svyaz, Moscow, 1983) (in Russian).

Semiconductors: Group IV Elements and III–V Compounds, O. Madelung, ed. (Springer-Verlag, Berlin, 1991), pp. 101–113.

H. C. Casey, Jr., and M. B. Panish, Heterostructure Part B: Materials and Operating Characteristics (Academic, New York, 1978).

V. M. Galitskii and V. F. Elesin, Resonant Interaction of Electromagnetic Fields with Semiconductors (Energoatomizdat, Moscow, 1986) (in Russian).

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Figures (10)

Fig. 1
Fig. 1

Gain [Eq. (9)] as a function of photon energy for fixed temperature or chemical potential. Equation (10) is used for G(ω). Curves a and b correspond to different temperatures (Ta>Tb), and curves b and c correspond to different chemical potentials (μb<μc).

Fig. 2
Fig. 2

Behavior of (a) the dimensionless gain coefficient and of (b) the carrier temperature, influenced by 0.1- and 1.0-pJ pulses with (solid curve) and without (dotted curve) FCA and TPA in an initially absorbing (g<0) medium.

Fig. 3
Fig. 3

Behavior of (a) the dimensionless gain coefficient and of (b) the carrier temperature, influenced by a 0.1-pJ pulse with FCA and TPA (solid curve), without FCA (dashed curve), without TPA (dashed–dotted curve), and without both (dotted curve) in an initially transparent (g=0) medium.

Fig. 4
Fig. 4

Behavior of (a) the dimensionless gain coefficient and of (b) the carrier temperature, influenced by a 1-pJ pulse with FCA and TPA (solid curve), without FCA (dashed curve), without TPA (dashed–dotted curve), and without both (dotted curve) in an initially transparent (g=0) medium.

Fig. 5
Fig. 5

Behavior of (a) the dimensionless gain coefficient and of (b) the carrier temperature, influenced by a 1-pJ pulse with FCA and TPA (solid curve), and without both (dotted curve) in an initially amplifying (g>0) medium.

Fig. 6
Fig. 6

Behavior of (a) the dimensionless gain coefficient and of (b) the carrier temperature, influenced by a 5-pJ pulse with FCA and TPA (solid curve), without FCA (dashed curve), without TPA (dashed–dotted curve), and without both (dotted curve) in an initially absorbing (g<0) medium.

Fig. 7
Fig. 7

Behavior of (a) the dimensionless gain coefficient and of (b) the carrier temperature, influenced by a 25-pJ pulse with FCA and TPA (solid curve), without FCA (dashed curve), without TPA (dashed–dotted curve), and without both (dotted curve) in an initially absorbing (g<0) medium.

Fig. 8
Fig. 8

Behavior of (a) the dimensionless gain coefficient and of (b) the carrier temperature, influenced by a 5-pJ pulse with FCA and TPA (solid curve), without FCA (dashed curve), without TPA (dashed–dotted curve), and without both (dotted curve) in an initially amplifying (g>0) medium.

Fig. 9
Fig. 9

Behavior of (a) the dimensionless gain coefficient and of (b) the carrier temperature, influenced by a 25-pJ pulse with FCA and TPA (solid curve), without FCA (dashed curve), without TPA (dashed–dotted curve) and without both (dotted curve) in an initially amplifying (g>0) medium.

Fig. 10
Fig. 10

Behavior of the carrier density influenced by (a) 5-pJ and (b) 25-pJ pulses with FCA and TPA (solid curve), without FCA (dashed curve), without TPA (dashed–dotted curve), and without both (dotted curve) in an initially amplifying (g>0) medium.

Equations (28)

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

dNpdt=-1τpNp+ΓνgrgNp+Γβsp Nτs-νgrsFCANNp-νgrsTPANp2+κNpx,
dNdt=J-Nτe-νgrgNp+νgrsTPANp2,
dUdt=Q-Uτs-U-U1τ1-ωνgrgNp+ωνgrsFCANNp+2ωνgrsTPANp2,
g=C0(ω, Tl)|M|2ρr[f(μe, Te)+f(μh, Th)-1]=g(ω,Tl,Te,Th,μe,μh).
f(εe,μe,Te)-12+f(εh,μh,Th)-12
=12tanhμe-εe2kBTe+tanhμh-εh2kBTh,
εe=εg+(ω-εg)m¯/me,
-εh=(ω-εg)m¯/mh,
εe=εg-(mh/me)εh.
μe=εg-(mh/me)μh.
12tanhμe-εe2kBTe+tanhmemh μe-εe2kBTh.
f(εe, μe, Te)+f(εh, μh, Th)-112tanhμe-εe2kBTe,
g=G(ω)tanhμ-ε2kBT,
G(ω)=ngr π2c2τsω2n3ρ0 expωεt,
N(μ, T)=ρ(ε)f(ε, μ, T)dε,
U(μ, T)=ρ(ε)f(ε, μ, T)εdε.
Ul=ρ(ε)f(ε, μ(Tl), Tl)εdε.
f(ε, μ, T)=1-0.5 exp[(ε-μ)/kBT]εμ0.5 exp[(μ-ε)/kBT]ε>μ.
N(μ,θ)=ρ0εt1-θ2expμεt,
U(μ,θ)=Nμ+εt (3θ2-1)1-θ2,
Q=Jμ˜+εt (3θl2-1)1-θl2,
μ˜=εt lnN˜ (1-θl2)ρ0εt.
Q=JεtlnJτs (1-θl2)ρ0εt-1-3θl21-θl2.
εg(N)=εg-1.6×10-8N1/3,
β2=K Epn2εg32 ωεg-13/2ωεg-5.
Npx(t)=WπΔτexp-tΔτ2,
E=c·ωNpx(x, y, t)dxdydt,
Ex=Wωsc,

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