Abstract

Gain and refractive-index spectra for bulk and quantum-well semiconductor lasers are computed using quantum-mechanical many-body theory. The results clearly show the influence of band-gap renormalization, broadening, and Coulomb enhancement on the gain, the absorption, and the refractive-index spectra.

© 1989 Optical Society of America

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References

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  1. A. Yariv, Optical Electronics, 3rd ed. (Holt, Rinehart & Winston, New York, 1985).
  2. G. P. Agarwal, N. K. Dutta, Long-Wavelength Semiconductor Lasers (Van Nostrand Reinhold, New York, 1986).
    [CrossRef]
  3. G. H. B. Thompson, Physics of Semiconductor Laser Devices (Wiley, Chichester, UK, 1980).
  4. H. Haug, S. W. Koch, Phys. Rev. A 39, 1887 (1989).
    [CrossRef] [PubMed]
  5. See, e.g., H. Haug, ed., Optical Nonlinearities and Instabilities in Semiconductors (Academic, New York, 1988); H. Haug, S. Schmitt-Rink, Prog. Quantum Electron. 9, 3 (1984); J. Opt. Soc. Am. B 2, 1135 (1985); L. Banyai, S. W. Koch, Z. Phys. B63, 283 (1986); S. Schmitt-Rink, C. Ell, H. Haug, Phys. Rev. B 33, 1183 (1986).
    [CrossRef]
  6. J. R. Müller, R. Mewis, H. Haug, Z. Phys. B69, 231 (1987).
    [CrossRef]
  7. M. Lindberg, S. W. Koch, Phys. Rev. B 38, 3342 (1988).
    [CrossRef]
  8. M. P. Kessler, E. P. Ippen, Appl. Phys. Lett. 51, 1765 (1987).
    [CrossRef]
  9. P. R. Gaves-Morris, ed., Padé Approximants and Their Application (Academic, New York, 1973).
  10. The material parameters for bulk GaAs are ER = 4.2 meV, a0 = 12.4 nm, me = 0.0665m0, mh = 0.52m0, and Ħγ = 1ER (0.1ER) for T = 300 K (10 K). Eg = 1522 meV − 0.58T2/(T + 226 K) meV/K according to C. K. Kim, P. Lautenschlager, M. Cardona, Solid State Commun. 59, 797 (1986).
    [CrossRef]
  11. For quasi-two-dimensional GaAs we take the bulk parameters, except that Eg is increased by 120 meV. The energies are scaled to the three-dimensional Rydberg energy.

1989

H. Haug, S. W. Koch, Phys. Rev. A 39, 1887 (1989).
[CrossRef] [PubMed]

1988

M. Lindberg, S. W. Koch, Phys. Rev. B 38, 3342 (1988).
[CrossRef]

1987

M. P. Kessler, E. P. Ippen, Appl. Phys. Lett. 51, 1765 (1987).
[CrossRef]

J. R. Müller, R. Mewis, H. Haug, Z. Phys. B69, 231 (1987).
[CrossRef]

1986

The material parameters for bulk GaAs are ER = 4.2 meV, a0 = 12.4 nm, me = 0.0665m0, mh = 0.52m0, and Ħγ = 1ER (0.1ER) for T = 300 K (10 K). Eg = 1522 meV − 0.58T2/(T + 226 K) meV/K according to C. K. Kim, P. Lautenschlager, M. Cardona, Solid State Commun. 59, 797 (1986).
[CrossRef]

Agarwal, G. P.

G. P. Agarwal, N. K. Dutta, Long-Wavelength Semiconductor Lasers (Van Nostrand Reinhold, New York, 1986).
[CrossRef]

Cardona, M.

The material parameters for bulk GaAs are ER = 4.2 meV, a0 = 12.4 nm, me = 0.0665m0, mh = 0.52m0, and Ħγ = 1ER (0.1ER) for T = 300 K (10 K). Eg = 1522 meV − 0.58T2/(T + 226 K) meV/K according to C. K. Kim, P. Lautenschlager, M. Cardona, Solid State Commun. 59, 797 (1986).
[CrossRef]

Dutta, N. K.

G. P. Agarwal, N. K. Dutta, Long-Wavelength Semiconductor Lasers (Van Nostrand Reinhold, New York, 1986).
[CrossRef]

Haug, H.

H. Haug, S. W. Koch, Phys. Rev. A 39, 1887 (1989).
[CrossRef] [PubMed]

J. R. Müller, R. Mewis, H. Haug, Z. Phys. B69, 231 (1987).
[CrossRef]

Ippen, E. P.

M. P. Kessler, E. P. Ippen, Appl. Phys. Lett. 51, 1765 (1987).
[CrossRef]

Kessler, M. P.

M. P. Kessler, E. P. Ippen, Appl. Phys. Lett. 51, 1765 (1987).
[CrossRef]

Kim, C. K.

The material parameters for bulk GaAs are ER = 4.2 meV, a0 = 12.4 nm, me = 0.0665m0, mh = 0.52m0, and Ħγ = 1ER (0.1ER) for T = 300 K (10 K). Eg = 1522 meV − 0.58T2/(T + 226 K) meV/K according to C. K. Kim, P. Lautenschlager, M. Cardona, Solid State Commun. 59, 797 (1986).
[CrossRef]

Koch, S. W.

H. Haug, S. W. Koch, Phys. Rev. A 39, 1887 (1989).
[CrossRef] [PubMed]

M. Lindberg, S. W. Koch, Phys. Rev. B 38, 3342 (1988).
[CrossRef]

Lautenschlager, P.

The material parameters for bulk GaAs are ER = 4.2 meV, a0 = 12.4 nm, me = 0.0665m0, mh = 0.52m0, and Ħγ = 1ER (0.1ER) for T = 300 K (10 K). Eg = 1522 meV − 0.58T2/(T + 226 K) meV/K according to C. K. Kim, P. Lautenschlager, M. Cardona, Solid State Commun. 59, 797 (1986).
[CrossRef]

Lindberg, M.

M. Lindberg, S. W. Koch, Phys. Rev. B 38, 3342 (1988).
[CrossRef]

Mewis, R.

J. R. Müller, R. Mewis, H. Haug, Z. Phys. B69, 231 (1987).
[CrossRef]

Müller, J. R.

J. R. Müller, R. Mewis, H. Haug, Z. Phys. B69, 231 (1987).
[CrossRef]

Thompson, G. H. B.

G. H. B. Thompson, Physics of Semiconductor Laser Devices (Wiley, Chichester, UK, 1980).

Yariv, A.

A. Yariv, Optical Electronics, 3rd ed. (Holt, Rinehart & Winston, New York, 1985).

Appl. Phys. Lett.

M. P. Kessler, E. P. Ippen, Appl. Phys. Lett. 51, 1765 (1987).
[CrossRef]

Phys. Rev. A

H. Haug, S. W. Koch, Phys. Rev. A 39, 1887 (1989).
[CrossRef] [PubMed]

Phys. Rev. B

M. Lindberg, S. W. Koch, Phys. Rev. B 38, 3342 (1988).
[CrossRef]

Solid State Commun.

The material parameters for bulk GaAs are ER = 4.2 meV, a0 = 12.4 nm, me = 0.0665m0, mh = 0.52m0, and Ħγ = 1ER (0.1ER) for T = 300 K (10 K). Eg = 1522 meV − 0.58T2/(T + 226 K) meV/K according to C. K. Kim, P. Lautenschlager, M. Cardona, Solid State Commun. 59, 797 (1986).
[CrossRef]

Z. Phys.

J. R. Müller, R. Mewis, H. Haug, Z. Phys. B69, 231 (1987).
[CrossRef]

Other

P. R. Gaves-Morris, ed., Padé Approximants and Their Application (Academic, New York, 1973).

See, e.g., H. Haug, ed., Optical Nonlinearities and Instabilities in Semiconductors (Academic, New York, 1988); H. Haug, S. Schmitt-Rink, Prog. Quantum Electron. 9, 3 (1984); J. Opt. Soc. Am. B 2, 1135 (1985); L. Banyai, S. W. Koch, Z. Phys. B63, 283 (1986); S. Schmitt-Rink, C. Ell, H. Haug, Phys. Rev. B 33, 1183 (1986).
[CrossRef]

A. Yariv, Optical Electronics, 3rd ed. (Holt, Rinehart & Winston, New York, 1985).

G. P. Agarwal, N. K. Dutta, Long-Wavelength Semiconductor Lasers (Van Nostrand Reinhold, New York, 1986).
[CrossRef]

G. H. B. Thompson, Physics of Semiconductor Laser Devices (Wiley, Chichester, UK, 1980).

For quasi-two-dimensional GaAs we take the bulk parameters, except that Eg is increased by 120 meV. The energies are scaled to the three-dimensional Rydberg energy.

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Figures (5)

Fig. 1
Fig. 1

(a) Gain/absorption and (b) refractive-index spectra for bulk GaAs at room temperature and plasma densities of 2 × 1018 (curve 1), 5 × 1018 (curve 2), and 1 × 1019 cm−3 (curve 3).

Fig. 2
Fig. 2

(a) Gain/absorption and (b) refractive-index spectra for room-temperature bulk GaAs at a density of 2 × 1018 cm−3. The dashed curves are the results without Coulomb enhancement.

Fig. 3
Fig. 3

(a) Gain/absorption and (b) refractive-index spectra for quasi-two-dimensional GaAs at room temperature for the plasma densities of 2 × 1012 (curve 1), 4 × 1012 (curve 2), and 6 × 1012 cm−3 (curve 3).

Fig. 4
Fig. 4

Quasi-two-dimensional GaAs (a) gain/absorption and (b) refractive-index spectra for room temperature and a plasma density of 4 × 1012 cm−3. The dashed curves are the results without Coulomb enhancement.

Fig. 5
Fig. 5

(a) Bulk GaAs and (b) quasi-two-dimensional GaAs gain/absorption spectra for a density of 2 × 1018 (a) and 4 × 1012 cm−3 (b) and temperatures of T = 10 K (dotted curves) and T = 300 K (solid curves).

Equations (4)

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[ t + i Δ eff ( k ) + γ ] P ( k ) = i [ 1 - f h ( k ) - f e ( k ) ] × [ d k E ( t ) + k 0 V s ( k - k ) P ( k ) ] .
χ ( ω ) = 1 V k χ 0 ( k , ω ) 1 - q 1 ( k , ω ) ,
χ 0 ( ω ) = k χ 0 ( k , ω ) = k d k [ f e ( k ) + f h ( k ) - 1 ] ω - Δ eff ( k ) + j γ
q 1 ( k , ω ) = 1 d k 1 V k V s ( k - k ) χ 0 ( k , ω ) ,

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