Abstract

An analytical description of the effects of spectral hole burning on the optical properties of active semiconductor materials is developed for fields that are slow compared to intraband relaxation times. Nonlinear gain compression and four-wave mixing effects are discussed.

© 2002 Optical Society of America

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References

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  1. See, e.g., M. N. Zervas, A. E. Willner, and S. Sasaki, eds., Optical Amplifiers and Their Applications, Vol. 16 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1997).
  2. G. Guekos, ed., Photonics Devices for Telecommunications (Springer-Verlag, Berlin, 1998).
  3. J. M. Wiesenfeld, B. Glance, J. S. Perino, and A. H. Gnauck, IEEE Photon. Technol. Lett. 5, 1300 (1993).
    [CrossRef]
  4. T. Durhuus, B. Mikkelsen, C. Joergensen, S. Lykke Danielsen, and K. E. Stubkjaer, J. Lightwave Technol. 14, 942 (1996).
    [CrossRef]
  5. D. F. Geraghty, R. B. Lee, M. Verdiell, M. Ziari, A. Mathur, and K. J. Vahala, IEEE J. Sel. Top. Quantum Electron. 3, 1146 (1997).
    [CrossRef]
  6. W. W. Chow and S. W. Koch, Semiconductor-Laser Fundamentals. Physics of the Gain Materials (Springer-Verlag, Berlin, 1999).
    [CrossRef]
  7. J. Mark and J. Moerk, Appl. Phys. Lett. 61, 2281 (1992).
    [CrossRef]
  8. J. Mark and J. Moerk, Proc. SPIE 2399, 146 (1995).
    [CrossRef]
  9. A. Uskov, J. Mark, and J. Moerk, IEEE J. Quantum Electron. 30, 1769 (1994).
    [CrossRef]
  10. R. Gutiérrez-Castrejón, L. Schares, L. Occhi, and G. Guekos, IEEE J. Quantum Electron. 36, 1476 (2000).
    [CrossRef]
  11. S. Haroche and F. Hartmann, Phys. Rev. A 6, 1280 (1972).
    [CrossRef]
  12. B. Zhao and A. Yariv, in Semiconductor Lasers I, E. Kapon, ed. (Academic, San Diego, Calif., 1999), Chap. 1, and references therein.
  13. P. M. Enders, IEEE J. Quantum Electron. 33, 580 (1997).
    [CrossRef]
  14. S. Balle, Phys. Rev. A 57, 1304 (1998).
    [CrossRef]
  15. See, e.g., R. Nagarajan and J. E. Bowers, in Semiconductor Lasers I, E. Kapon, ed. (Academic, San Diego, Calif., 1999), Chap. 3, and references therein.
  16. G. P. Agrawal, J. Appl. Phys. 63, 1232 (1988).
    [CrossRef]

2000

R. Gutiérrez-Castrejón, L. Schares, L. Occhi, and G. Guekos, IEEE J. Quantum Electron. 36, 1476 (2000).
[CrossRef]

1998

S. Balle, Phys. Rev. A 57, 1304 (1998).
[CrossRef]

1997

P. M. Enders, IEEE J. Quantum Electron. 33, 580 (1997).
[CrossRef]

D. F. Geraghty, R. B. Lee, M. Verdiell, M. Ziari, A. Mathur, and K. J. Vahala, IEEE J. Sel. Top. Quantum Electron. 3, 1146 (1997).
[CrossRef]

1996

T. Durhuus, B. Mikkelsen, C. Joergensen, S. Lykke Danielsen, and K. E. Stubkjaer, J. Lightwave Technol. 14, 942 (1996).
[CrossRef]

1995

J. Mark and J. Moerk, Proc. SPIE 2399, 146 (1995).
[CrossRef]

1994

A. Uskov, J. Mark, and J. Moerk, IEEE J. Quantum Electron. 30, 1769 (1994).
[CrossRef]

1993

J. M. Wiesenfeld, B. Glance, J. S. Perino, and A. H. Gnauck, IEEE Photon. Technol. Lett. 5, 1300 (1993).
[CrossRef]

1992

J. Mark and J. Moerk, Appl. Phys. Lett. 61, 2281 (1992).
[CrossRef]

1988

G. P. Agrawal, J. Appl. Phys. 63, 1232 (1988).
[CrossRef]

1972

S. Haroche and F. Hartmann, Phys. Rev. A 6, 1280 (1972).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, J. Appl. Phys. 63, 1232 (1988).
[CrossRef]

Balle, S.

S. Balle, Phys. Rev. A 57, 1304 (1998).
[CrossRef]

Bowers, J. E.

See, e.g., R. Nagarajan and J. E. Bowers, in Semiconductor Lasers I, E. Kapon, ed. (Academic, San Diego, Calif., 1999), Chap. 3, and references therein.

Chow, W. W.

W. W. Chow and S. W. Koch, Semiconductor-Laser Fundamentals. Physics of the Gain Materials (Springer-Verlag, Berlin, 1999).
[CrossRef]

Danielsen, S. Lykke

T. Durhuus, B. Mikkelsen, C. Joergensen, S. Lykke Danielsen, and K. E. Stubkjaer, J. Lightwave Technol. 14, 942 (1996).
[CrossRef]

Durhuus, T.

T. Durhuus, B. Mikkelsen, C. Joergensen, S. Lykke Danielsen, and K. E. Stubkjaer, J. Lightwave Technol. 14, 942 (1996).
[CrossRef]

Enders, P. M.

P. M. Enders, IEEE J. Quantum Electron. 33, 580 (1997).
[CrossRef]

Geraghty, D. F.

D. F. Geraghty, R. B. Lee, M. Verdiell, M. Ziari, A. Mathur, and K. J. Vahala, IEEE J. Sel. Top. Quantum Electron. 3, 1146 (1997).
[CrossRef]

Glance, B.

J. M. Wiesenfeld, B. Glance, J. S. Perino, and A. H. Gnauck, IEEE Photon. Technol. Lett. 5, 1300 (1993).
[CrossRef]

Gnauck, A. H.

J. M. Wiesenfeld, B. Glance, J. S. Perino, and A. H. Gnauck, IEEE Photon. Technol. Lett. 5, 1300 (1993).
[CrossRef]

Guekos, G.

R. Gutiérrez-Castrejón, L. Schares, L. Occhi, and G. Guekos, IEEE J. Quantum Electron. 36, 1476 (2000).
[CrossRef]

Gutiérrez-Castrejón, R.

R. Gutiérrez-Castrejón, L. Schares, L. Occhi, and G. Guekos, IEEE J. Quantum Electron. 36, 1476 (2000).
[CrossRef]

Haroche, S.

S. Haroche and F. Hartmann, Phys. Rev. A 6, 1280 (1972).
[CrossRef]

Hartmann, F.

S. Haroche and F. Hartmann, Phys. Rev. A 6, 1280 (1972).
[CrossRef]

Joergensen, C.

T. Durhuus, B. Mikkelsen, C. Joergensen, S. Lykke Danielsen, and K. E. Stubkjaer, J. Lightwave Technol. 14, 942 (1996).
[CrossRef]

Koch, S. W.

W. W. Chow and S. W. Koch, Semiconductor-Laser Fundamentals. Physics of the Gain Materials (Springer-Verlag, Berlin, 1999).
[CrossRef]

Lee, R. B.

D. F. Geraghty, R. B. Lee, M. Verdiell, M. Ziari, A. Mathur, and K. J. Vahala, IEEE J. Sel. Top. Quantum Electron. 3, 1146 (1997).
[CrossRef]

Mark, J.

J. Mark and J. Moerk, Proc. SPIE 2399, 146 (1995).
[CrossRef]

A. Uskov, J. Mark, and J. Moerk, IEEE J. Quantum Electron. 30, 1769 (1994).
[CrossRef]

J. Mark and J. Moerk, Appl. Phys. Lett. 61, 2281 (1992).
[CrossRef]

Mathur, A.

D. F. Geraghty, R. B. Lee, M. Verdiell, M. Ziari, A. Mathur, and K. J. Vahala, IEEE J. Sel. Top. Quantum Electron. 3, 1146 (1997).
[CrossRef]

Mikkelsen, B.

T. Durhuus, B. Mikkelsen, C. Joergensen, S. Lykke Danielsen, and K. E. Stubkjaer, J. Lightwave Technol. 14, 942 (1996).
[CrossRef]

Moerk, J.

J. Mark and J. Moerk, Proc. SPIE 2399, 146 (1995).
[CrossRef]

A. Uskov, J. Mark, and J. Moerk, IEEE J. Quantum Electron. 30, 1769 (1994).
[CrossRef]

J. Mark and J. Moerk, Appl. Phys. Lett. 61, 2281 (1992).
[CrossRef]

Nagarajan, R.

See, e.g., R. Nagarajan and J. E. Bowers, in Semiconductor Lasers I, E. Kapon, ed. (Academic, San Diego, Calif., 1999), Chap. 3, and references therein.

Occhi, L.

R. Gutiérrez-Castrejón, L. Schares, L. Occhi, and G. Guekos, IEEE J. Quantum Electron. 36, 1476 (2000).
[CrossRef]

Perino, J. S.

J. M. Wiesenfeld, B. Glance, J. S. Perino, and A. H. Gnauck, IEEE Photon. Technol. Lett. 5, 1300 (1993).
[CrossRef]

Schares, L.

R. Gutiérrez-Castrejón, L. Schares, L. Occhi, and G. Guekos, IEEE J. Quantum Electron. 36, 1476 (2000).
[CrossRef]

Stubkjaer, K. E.

T. Durhuus, B. Mikkelsen, C. Joergensen, S. Lykke Danielsen, and K. E. Stubkjaer, J. Lightwave Technol. 14, 942 (1996).
[CrossRef]

Uskov, A.

A. Uskov, J. Mark, and J. Moerk, IEEE J. Quantum Electron. 30, 1769 (1994).
[CrossRef]

Vahala, K. J.

D. F. Geraghty, R. B. Lee, M. Verdiell, M. Ziari, A. Mathur, and K. J. Vahala, IEEE J. Sel. Top. Quantum Electron. 3, 1146 (1997).
[CrossRef]

Verdiell, M.

D. F. Geraghty, R. B. Lee, M. Verdiell, M. Ziari, A. Mathur, and K. J. Vahala, IEEE J. Sel. Top. Quantum Electron. 3, 1146 (1997).
[CrossRef]

Wiesenfeld, J. M.

J. M. Wiesenfeld, B. Glance, J. S. Perino, and A. H. Gnauck, IEEE Photon. Technol. Lett. 5, 1300 (1993).
[CrossRef]

Yariv, A.

B. Zhao and A. Yariv, in Semiconductor Lasers I, E. Kapon, ed. (Academic, San Diego, Calif., 1999), Chap. 1, and references therein.

Zhao, B.

B. Zhao and A. Yariv, in Semiconductor Lasers I, E. Kapon, ed. (Academic, San Diego, Calif., 1999), Chap. 1, and references therein.

Ziari, M.

D. F. Geraghty, R. B. Lee, M. Verdiell, M. Ziari, A. Mathur, and K. J. Vahala, IEEE J. Sel. Top. Quantum Electron. 3, 1146 (1997).
[CrossRef]

Appl. Phys. Lett.

J. Mark and J. Moerk, Appl. Phys. Lett. 61, 2281 (1992).
[CrossRef]

IEEE J. Quantum Electron.

A. Uskov, J. Mark, and J. Moerk, IEEE J. Quantum Electron. 30, 1769 (1994).
[CrossRef]

R. Gutiérrez-Castrejón, L. Schares, L. Occhi, and G. Guekos, IEEE J. Quantum Electron. 36, 1476 (2000).
[CrossRef]

P. M. Enders, IEEE J. Quantum Electron. 33, 580 (1997).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

D. F. Geraghty, R. B. Lee, M. Verdiell, M. Ziari, A. Mathur, and K. J. Vahala, IEEE J. Sel. Top. Quantum Electron. 3, 1146 (1997).
[CrossRef]

IEEE Photon. Technol. Lett.

J. M. Wiesenfeld, B. Glance, J. S. Perino, and A. H. Gnauck, IEEE Photon. Technol. Lett. 5, 1300 (1993).
[CrossRef]

J. Appl. Phys.

G. P. Agrawal, J. Appl. Phys. 63, 1232 (1988).
[CrossRef]

J. Lightwave Technol.

T. Durhuus, B. Mikkelsen, C. Joergensen, S. Lykke Danielsen, and K. E. Stubkjaer, J. Lightwave Technol. 14, 942 (1996).
[CrossRef]

Phys. Rev. A

S. Balle, Phys. Rev. A 57, 1304 (1998).
[CrossRef]

S. Haroche and F. Hartmann, Phys. Rev. A 6, 1280 (1972).
[CrossRef]

Proc. SPIE

J. Mark and J. Moerk, Proc. SPIE 2399, 146 (1995).
[CrossRef]

Other

W. W. Chow and S. W. Koch, Semiconductor-Laser Fundamentals. Physics of the Gain Materials (Springer-Verlag, Berlin, 1999).
[CrossRef]

See, e.g., M. N. Zervas, A. E. Willner, and S. Sasaki, eds., Optical Amplifiers and Their Applications, Vol. 16 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1997).

G. Guekos, ed., Photonics Devices for Telecommunications (Springer-Verlag, Berlin, 1998).

B. Zhao and A. Yariv, in Semiconductor Lasers I, E. Kapon, ed. (Academic, San Diego, Calif., 1999), Chap. 1, and references therein.

See, e.g., R. Nagarajan and J. E. Bowers, in Semiconductor Lasers I, E. Kapon, ed. (Academic, San Diego, Calif., 1999), Chap. 3, and references therein.

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Figures (2)

Fig. 1
Fig. 1

Gain spectrum at T=350 K for two carrier densities, N=9Nt (lower pair of curves) and N=12Nt (upper curves) for photon densities A2=0 (solid curves) and A2=0.1 (dashed curves). Unsaturated transparency, N=5Nt.

Fig. 2
Fig. 2

Spectrum of the material response in the degenerate limit under pulsed conditions (see text for details).

Equations (10)

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

dtnk=-nk-n¯kτk,n+igkApk*-A*pk,
dthk=-hk-h¯kτk,h+igkApk*-A*pk,
dtpk=-Γkpk-igknk+hk-1A,
pk=-igk-tdt exp-Γkt-tAtn¯k+h¯k-1+igk-tdtexp-t-tτk,n+exp-t-tτk,h×Atpk*t-A*tpkt.
pkt=gkAtn¯k+h¯k-1Ω-ωk-iγkΩ-ωk2+γk2+γk2kAt2,
Bt=AtΛt+12Λtft+Λt-12Λtf*t,
ft=g2Vkn¯k+h¯k-1Ω-ωk+iγΛt
=mμ2πW2ln1-bu+iΛt+n=01u+iΛtn+1Fcn+Fvn,
ft=mμ2πW2-2 ln1-Du+iΛt+ln1-bu+iΛt,
GΩ,Nmμ20πW21Λtπ2+arctanuΛt×expacD-1expacD-1+expacu+expavD-1expavD-1+expavu-1.

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