Abstract

A comprehensive numerical study of the influence of electron-hole scattering on optical dephasing and related pulse propagation phenomena in semiconductor waveguide media is presented. The material equations incorporate a hierarchy of incoherent scattering mechanisms including inscattering and outscattering and higher-order polarization scattering processes into the optical polarization; these mechanisms are treated on the level of quantum Boltzmann equations. For optically excited semiconductor absorbers a dramatic increase of the dephasing time of the optical polarization is demonstrated theoretically for excitation conditions near the band edge, in comparison with excitation high into the continuum. These results are applied to model pulse propagation high above the band gap and at the exciton resonance, which display qualitatively different behavior. For the semiconductor amplifier it is shown that the inscattering mechanisms are important for an accurate description of linear gain spectra. Nonlinear pulse propagation is also studied for excitation at the peak gain of the optical amplifier.

© 1997 Optical Society of America

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References

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  1. See H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors, 3rd ed. (World Scientific, Singapore, 1994), and references therein.
  2. A. Knorr, R. Binder, E. Wright, and S. Koch, Opt. Lett. 18, 1538 (1993).
    [Crossref]
  3. T. Rappen, U.-G. Peter, M. Wegener, and W. Schäfer, Phys. Rev. B 49, 10774 (1994).
    [Crossref]
  4. F. Rossi, S. Haas, and T. Kuhn, Phys. Rev. Lett. 72, 152 (1994).
    [Crossref] [PubMed]
  5. W. Schäfer and K. Henneberger, Phys. Stat. Sol. B 159, 59 (1990).
    [Crossref]
  6. R. Binder, D. C. Scott, A. E. Paul, M. Lindberg, K. Henneberger, and S. W. Koch, Phys. Rev. B 45, 1107 (1992).
    [Crossref]
  7. D. C. Scott, R. Binder, and S. W. Koch, Phys. Rev. Lett. 69, 347 (1992).
    [Crossref] [PubMed]
  8. M. Lindberg, R. Binder, and S. W. Koch, Phys. Rev. A 45, 1865 (1992).
    [Crossref] [PubMed]
  9. S. T. Cundiff, A. Knorr, J. Feldmann, S. W. Koch, E. O. Göbel, and H. Nickel, Phys. Rev. Lett. 73, 1178 (1994).
    [Crossref] [PubMed]
  10. W. W. Chow, S. W. Koch, and M. Sargent, Semiconductor-Laser Physics (Springer, Berlin, 1994).
  11. R. Binder, S. W. Koch, M. Lindberg, and N. Peyghambarian, Phys. Rev. Lett. 65, 899 (1990).
    [Crossref] [PubMed]
  12. A. Knorr, R. Binder, M. Lindberg, and S. W. Koch, Phys. Rev. A 46, 7179 (1992).
    [Crossref] [PubMed]
  13. M. Yamanishi and Y. Lee, IEEE J. Quantum Electron. QE-14, 367 (1987).
    [Crossref]
  14. R. A. Indik, M. Mlejnek, J. V. Moloney, R. Binder, S. Hughes, A. Knorr, and S. W. Koch, Phys. Rev. A 53, 3614 (1996).
    [Crossref] [PubMed]
  15. T. Ohtoshi and M. Yamanishi, IEEE J. Quantum Electron. 27, 46 (1991).
    [Crossref]
  16. R. Indik, A. Knorr, R. Binder, J. Moloney, and S. W. Koch, Opt. Lett. 19, 966 (1994).
    [Crossref] [PubMed]

1996 (1)

R. A. Indik, M. Mlejnek, J. V. Moloney, R. Binder, S. Hughes, A. Knorr, and S. W. Koch, Phys. Rev. A 53, 3614 (1996).
[Crossref] [PubMed]

1994 (4)

R. Indik, A. Knorr, R. Binder, J. Moloney, and S. W. Koch, Opt. Lett. 19, 966 (1994).
[Crossref] [PubMed]

T. Rappen, U.-G. Peter, M. Wegener, and W. Schäfer, Phys. Rev. B 49, 10774 (1994).
[Crossref]

F. Rossi, S. Haas, and T. Kuhn, Phys. Rev. Lett. 72, 152 (1994).
[Crossref] [PubMed]

S. T. Cundiff, A. Knorr, J. Feldmann, S. W. Koch, E. O. Göbel, and H. Nickel, Phys. Rev. Lett. 73, 1178 (1994).
[Crossref] [PubMed]

1993 (1)

1992 (4)

A. Knorr, R. Binder, M. Lindberg, and S. W. Koch, Phys. Rev. A 46, 7179 (1992).
[Crossref] [PubMed]

R. Binder, D. C. Scott, A. E. Paul, M. Lindberg, K. Henneberger, and S. W. Koch, Phys. Rev. B 45, 1107 (1992).
[Crossref]

D. C. Scott, R. Binder, and S. W. Koch, Phys. Rev. Lett. 69, 347 (1992).
[Crossref] [PubMed]

M. Lindberg, R. Binder, and S. W. Koch, Phys. Rev. A 45, 1865 (1992).
[Crossref] [PubMed]

1991 (1)

T. Ohtoshi and M. Yamanishi, IEEE J. Quantum Electron. 27, 46 (1991).
[Crossref]

1990 (2)

W. Schäfer and K. Henneberger, Phys. Stat. Sol. B 159, 59 (1990).
[Crossref]

R. Binder, S. W. Koch, M. Lindberg, and N. Peyghambarian, Phys. Rev. Lett. 65, 899 (1990).
[Crossref] [PubMed]

1987 (1)

M. Yamanishi and Y. Lee, IEEE J. Quantum Electron. QE-14, 367 (1987).
[Crossref]

Binder, R.

R. A. Indik, M. Mlejnek, J. V. Moloney, R. Binder, S. Hughes, A. Knorr, and S. W. Koch, Phys. Rev. A 53, 3614 (1996).
[Crossref] [PubMed]

R. Indik, A. Knorr, R. Binder, J. Moloney, and S. W. Koch, Opt. Lett. 19, 966 (1994).
[Crossref] [PubMed]

A. Knorr, R. Binder, E. Wright, and S. Koch, Opt. Lett. 18, 1538 (1993).
[Crossref]

R. Binder, D. C. Scott, A. E. Paul, M. Lindberg, K. Henneberger, and S. W. Koch, Phys. Rev. B 45, 1107 (1992).
[Crossref]

D. C. Scott, R. Binder, and S. W. Koch, Phys. Rev. Lett. 69, 347 (1992).
[Crossref] [PubMed]

M. Lindberg, R. Binder, and S. W. Koch, Phys. Rev. A 45, 1865 (1992).
[Crossref] [PubMed]

A. Knorr, R. Binder, M. Lindberg, and S. W. Koch, Phys. Rev. A 46, 7179 (1992).
[Crossref] [PubMed]

R. Binder, S. W. Koch, M. Lindberg, and N. Peyghambarian, Phys. Rev. Lett. 65, 899 (1990).
[Crossref] [PubMed]

Chow, W. W.

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

Cundiff, S. T.

S. T. Cundiff, A. Knorr, J. Feldmann, S. W. Koch, E. O. Göbel, and H. Nickel, Phys. Rev. Lett. 73, 1178 (1994).
[Crossref] [PubMed]

Feldmann, J.

S. T. Cundiff, A. Knorr, J. Feldmann, S. W. Koch, E. O. Göbel, and H. Nickel, Phys. Rev. Lett. 73, 1178 (1994).
[Crossref] [PubMed]

Göbel, E. O.

S. T. Cundiff, A. Knorr, J. Feldmann, S. W. Koch, E. O. Göbel, and H. Nickel, Phys. Rev. Lett. 73, 1178 (1994).
[Crossref] [PubMed]

Haas, S.

F. Rossi, S. Haas, and T. Kuhn, Phys. Rev. Lett. 72, 152 (1994).
[Crossref] [PubMed]

Haug, H.

See H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors, 3rd ed. (World Scientific, Singapore, 1994), and references therein.

Henneberger, K.

R. Binder, D. C. Scott, A. E. Paul, M. Lindberg, K. Henneberger, and S. W. Koch, Phys. Rev. B 45, 1107 (1992).
[Crossref]

W. Schäfer and K. Henneberger, Phys. Stat. Sol. B 159, 59 (1990).
[Crossref]

Hughes, S.

R. A. Indik, M. Mlejnek, J. V. Moloney, R. Binder, S. Hughes, A. Knorr, and S. W. Koch, Phys. Rev. A 53, 3614 (1996).
[Crossref] [PubMed]

Indik, R.

Indik, R. A.

R. A. Indik, M. Mlejnek, J. V. Moloney, R. Binder, S. Hughes, A. Knorr, and S. W. Koch, Phys. Rev. A 53, 3614 (1996).
[Crossref] [PubMed]

Knorr, A.

R. A. Indik, M. Mlejnek, J. V. Moloney, R. Binder, S. Hughes, A. Knorr, and S. W. Koch, Phys. Rev. A 53, 3614 (1996).
[Crossref] [PubMed]

R. Indik, A. Knorr, R. Binder, J. Moloney, and S. W. Koch, Opt. Lett. 19, 966 (1994).
[Crossref] [PubMed]

S. T. Cundiff, A. Knorr, J. Feldmann, S. W. Koch, E. O. Göbel, and H. Nickel, Phys. Rev. Lett. 73, 1178 (1994).
[Crossref] [PubMed]

A. Knorr, R. Binder, E. Wright, and S. Koch, Opt. Lett. 18, 1538 (1993).
[Crossref]

A. Knorr, R. Binder, M. Lindberg, and S. W. Koch, Phys. Rev. A 46, 7179 (1992).
[Crossref] [PubMed]

Koch, S.

Koch, S. W.

R. A. Indik, M. Mlejnek, J. V. Moloney, R. Binder, S. Hughes, A. Knorr, and S. W. Koch, Phys. Rev. A 53, 3614 (1996).
[Crossref] [PubMed]

R. Indik, A. Knorr, R. Binder, J. Moloney, and S. W. Koch, Opt. Lett. 19, 966 (1994).
[Crossref] [PubMed]

S. T. Cundiff, A. Knorr, J. Feldmann, S. W. Koch, E. O. Göbel, and H. Nickel, Phys. Rev. Lett. 73, 1178 (1994).
[Crossref] [PubMed]

M. Lindberg, R. Binder, and S. W. Koch, Phys. Rev. A 45, 1865 (1992).
[Crossref] [PubMed]

R. Binder, D. C. Scott, A. E. Paul, M. Lindberg, K. Henneberger, and S. W. Koch, Phys. Rev. B 45, 1107 (1992).
[Crossref]

D. C. Scott, R. Binder, and S. W. Koch, Phys. Rev. Lett. 69, 347 (1992).
[Crossref] [PubMed]

A. Knorr, R. Binder, M. Lindberg, and S. W. Koch, Phys. Rev. A 46, 7179 (1992).
[Crossref] [PubMed]

R. Binder, S. W. Koch, M. Lindberg, and N. Peyghambarian, Phys. Rev. Lett. 65, 899 (1990).
[Crossref] [PubMed]

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

See H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors, 3rd ed. (World Scientific, Singapore, 1994), and references therein.

Kuhn, T.

F. Rossi, S. Haas, and T. Kuhn, Phys. Rev. Lett. 72, 152 (1994).
[Crossref] [PubMed]

Lee, Y.

M. Yamanishi and Y. Lee, IEEE J. Quantum Electron. QE-14, 367 (1987).
[Crossref]

Lindberg, M.

M. Lindberg, R. Binder, and S. W. Koch, Phys. Rev. A 45, 1865 (1992).
[Crossref] [PubMed]

R. Binder, D. C. Scott, A. E. Paul, M. Lindberg, K. Henneberger, and S. W. Koch, Phys. Rev. B 45, 1107 (1992).
[Crossref]

A. Knorr, R. Binder, M. Lindberg, and S. W. Koch, Phys. Rev. A 46, 7179 (1992).
[Crossref] [PubMed]

R. Binder, S. W. Koch, M. Lindberg, and N. Peyghambarian, Phys. Rev. Lett. 65, 899 (1990).
[Crossref] [PubMed]

Mlejnek, M.

R. A. Indik, M. Mlejnek, J. V. Moloney, R. Binder, S. Hughes, A. Knorr, and S. W. Koch, Phys. Rev. A 53, 3614 (1996).
[Crossref] [PubMed]

Moloney, J.

Moloney, J. V.

R. A. Indik, M. Mlejnek, J. V. Moloney, R. Binder, S. Hughes, A. Knorr, and S. W. Koch, Phys. Rev. A 53, 3614 (1996).
[Crossref] [PubMed]

Nickel, H.

S. T. Cundiff, A. Knorr, J. Feldmann, S. W. Koch, E. O. Göbel, and H. Nickel, Phys. Rev. Lett. 73, 1178 (1994).
[Crossref] [PubMed]

Ohtoshi, T.

T. Ohtoshi and M. Yamanishi, IEEE J. Quantum Electron. 27, 46 (1991).
[Crossref]

Paul, A. E.

R. Binder, D. C. Scott, A. E. Paul, M. Lindberg, K. Henneberger, and S. W. Koch, Phys. Rev. B 45, 1107 (1992).
[Crossref]

Peter, U.-G.

T. Rappen, U.-G. Peter, M. Wegener, and W. Schäfer, Phys. Rev. B 49, 10774 (1994).
[Crossref]

Peyghambarian, N.

R. Binder, S. W. Koch, M. Lindberg, and N. Peyghambarian, Phys. Rev. Lett. 65, 899 (1990).
[Crossref] [PubMed]

Rappen, T.

T. Rappen, U.-G. Peter, M. Wegener, and W. Schäfer, Phys. Rev. B 49, 10774 (1994).
[Crossref]

Rossi, F.

F. Rossi, S. Haas, and T. Kuhn, Phys. Rev. Lett. 72, 152 (1994).
[Crossref] [PubMed]

Sargent, M.

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

Schäfer, W.

T. Rappen, U.-G. Peter, M. Wegener, and W. Schäfer, Phys. Rev. B 49, 10774 (1994).
[Crossref]

W. Schäfer and K. Henneberger, Phys. Stat. Sol. B 159, 59 (1990).
[Crossref]

Scott, D. C.

R. Binder, D. C. Scott, A. E. Paul, M. Lindberg, K. Henneberger, and S. W. Koch, Phys. Rev. B 45, 1107 (1992).
[Crossref]

D. C. Scott, R. Binder, and S. W. Koch, Phys. Rev. Lett. 69, 347 (1992).
[Crossref] [PubMed]

Wegener, M.

T. Rappen, U.-G. Peter, M. Wegener, and W. Schäfer, Phys. Rev. B 49, 10774 (1994).
[Crossref]

Wright, E.

Yamanishi, M.

T. Ohtoshi and M. Yamanishi, IEEE J. Quantum Electron. 27, 46 (1991).
[Crossref]

M. Yamanishi and Y. Lee, IEEE J. Quantum Electron. QE-14, 367 (1987).
[Crossref]

IEEE J. Quantum Electron. (2)

M. Yamanishi and Y. Lee, IEEE J. Quantum Electron. QE-14, 367 (1987).
[Crossref]

T. Ohtoshi and M. Yamanishi, IEEE J. Quantum Electron. 27, 46 (1991).
[Crossref]

Opt. Lett. (2)

Phys. Rev. A (3)

M. Lindberg, R. Binder, and S. W. Koch, Phys. Rev. A 45, 1865 (1992).
[Crossref] [PubMed]

A. Knorr, R. Binder, M. Lindberg, and S. W. Koch, Phys. Rev. A 46, 7179 (1992).
[Crossref] [PubMed]

R. A. Indik, M. Mlejnek, J. V. Moloney, R. Binder, S. Hughes, A. Knorr, and S. W. Koch, Phys. Rev. A 53, 3614 (1996).
[Crossref] [PubMed]

Phys. Rev. B (2)

R. Binder, D. C. Scott, A. E. Paul, M. Lindberg, K. Henneberger, and S. W. Koch, Phys. Rev. B 45, 1107 (1992).
[Crossref]

T. Rappen, U.-G. Peter, M. Wegener, and W. Schäfer, Phys. Rev. B 49, 10774 (1994).
[Crossref]

Phys. Rev. Lett. (4)

F. Rossi, S. Haas, and T. Kuhn, Phys. Rev. Lett. 72, 152 (1994).
[Crossref] [PubMed]

D. C. Scott, R. Binder, and S. W. Koch, Phys. Rev. Lett. 69, 347 (1992).
[Crossref] [PubMed]

S. T. Cundiff, A. Knorr, J. Feldmann, S. W. Koch, E. O. Göbel, and H. Nickel, Phys. Rev. Lett. 73, 1178 (1994).
[Crossref] [PubMed]

R. Binder, S. W. Koch, M. Lindberg, and N. Peyghambarian, Phys. Rev. Lett. 65, 899 (1990).
[Crossref] [PubMed]

Phys. Stat. Sol. B (1)

W. Schäfer and K. Henneberger, Phys. Stat. Sol. B 159, 59 (1990).
[Crossref]

Other (2)

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

See H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors, 3rd ed. (World Scientific, Singapore, 1994), and references therein.

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Figures (5)

Fig. 1
Fig. 1

(a) Excited carrier density for excitation at 16Ex above the band gap. The dotted curve corresponds to the P˙k|out contributions to dephasing only, the solid curve includes P˙k|in scattering (see text), and the dashed curve includes higher-order PP-scattering contributions to dephasing. For comparison, also shown is the purely coherent case, which exhibits Rabi flopping. (b) Same as for (a) for excitation at the band gap E=Eg. (c) Same as (a) for excitation E=Eg-Ex (exciton resonance).

Fig. 2
Fig. 2

(a) Scattering contributions [Eq. (4)] that affect the rate of change of optical polarization for the excitation E=Eg +Ex. The dotted curve represents the usual P˙k|out scattering, and the solid curve corresponds to the P˙k|in scattering. The dashed curve depicts the sum of the two, corresponding to the overall dephasing of the optical polarization. The units of scattering (inverse nanoseconds) are dictated by the value of the polarizations Pk. (b) Electron distributions fe,k at 0 fs and +300 fs, respectively. Excitation is at E=Eg+Ex and only P˙k|in is accounted for. (c) Same as (b), using all scattering mechanisms for the calculation of the optical dephasing.

Fig. 3
Fig. 3

(a) Pulse irradiance profiles for propagation through the semiconductor amplifier for the excitation 16Ex above the band gap and (b) at the exciton resonance.

Fig. 4
Fig. 4

Gain spectra calculated by including only P˙k|out outscattering (solid curve) and with inscattering and outscattering -P˙k|out, P˙k|in (dashed curve) for the respective carrier densities (a) 1.0×1012cm-2, (b) 1.5×1012cm-2.

Fig. 5
Fig. 5

(a) Distribution functions for the electrons at the front face of the amplifier, before the pulse (t=-), during the pulse (t=-80 fs), and after the pulse (t=). The final distribution is shown for two cases: The dotted curve includes all scattering mechanisms, and the dashed–dotted curve includes only the outscattering in the polarization calculations. (b) Temporal variation of carrier density at the front face of the amplifier. The solid curve corresponds to outscattering contributions only, and the dashed and the dotted lines incorporate inscattering and PP scattering, respectively. (c) Pulse irradiance profiles for propagation through the amplifier.

Equations (16)

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

Pkt=-iΔkPk-iΩk(fke+fkh-1)+Pktscatt,
fke/ht=iPk*Ωk-iPkΩk*+fke/htscatt,
Δk=εk-ω0-1q[Vk-q(fqe+fqh)+(Vq-Vq0)]
E(ζ, η)ζ=i4μ0ω02Γk0Lqwkdcv(k)Pk,
Pktscatt=-Pktout+Pktin,
PktoutΓoutp(k, f)Pk,
PktinqΓinp(k, q, f)Pk+q,
fkatscatt=Γina(k, f)[1-fka]-Γouta(k, f)fka+(PkΩk*|scatt+c.c.),
Γina(k, f)=πk,qb=e,h2|V(q)|2fk+qa[(1-fkb)fk-qb-Pk-q*Pk+c.c.]δ[a(k)+b(k)-a(|k+q|)-b(|k-q|)],
Ωk*|scatt=πk,qb=e,h2|V(q)|2(fk-qb-fkb)Pk+q*×δ[a˜(k)+b(k)-a˜(|k+q|)-b(|k-q|)],
Pktscatt=-Γoutp(k, f)Pk+qΓinp(k, q, f)Pk+q,
Γout,kp=12a=e,h(Γout,ka+Γin,ka),
Γinp(k, q, n)=πkba=eh2|V(q)|2[(1-fka)fk-qb(1-fkb)+fkafkb(1-fk-qb)-Pk*Pk-q]×δ[a(k)+b(k)-a(|k+q|)-b(|k-q|)],
G(ω)=1zln I(ω)I0(ω),
E(ω)=E0(ω)+i2μoω2kLqwP(ω)z.
G(ω)=4μoω2kLqwIm [P*(ω)E0(ω)-P(ω)E0*(ω)]|E0(ω)|2.

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