Optical and Quantum Electronics

, Volume 47, Issue 7, pp 2141–2153 | Cite as

Theoretical analysis of carrier heating effect in semiconductor optical amplifiers

  • Mingjun Xia
  • H. Ghafouri-Shiraz


This paper reports an accurate and simple analytical method to study carrier heating effect in semiconductor optical amplifiers using both Fermi–Dirac integrals of 3/2 and 1/2 orders. Global approximations for Fermi–Dirac integrals of 3/2 and 1/2 orders are adopted to obtain the analytical expression for the carrier temperature. The amplification of a single strong pico-second pulse having different peak powers is studied both with and without carrier heating effect. It has been found carrier heating impose more distortion on the amplified pulse, including suppressing the peak power value, increasing the peak temporal shift and broadening the bandwidth of amplified output signals. Also, when the input signal peak power or the pump current increases because of carrier heating effect the carrier temperature increases too. We have studied the amplification of 80 Gbit/s pico-second pulse sequences and found an increase in the peak value of the amplified output signal due to the pronounced fast gain recovery process induced by the carrier heating effect.


Semiconductor optical amplifiers Carrier heating effect Nonlinear optics Optical communication 


  1. Aymerich-Humet, F.X., Mestres, S., Millan, J.: An analytical approximation for the Fermi–Dirac integral \(F_{3/2} (\eta )\). Solid State Electron. 24, 981–982 (1981)ADSCrossRefGoogle Scholar
  2. Adachi, S.: GaAs and Related Materials, pp. 135–170. World Scientific, Singapore (1994)Google Scholar
  3. Blakemore, J.S.: Semiconductors Statistics, pp. 343–357. Pergamon, New York (1962). Appendices B and CGoogle Scholar
  4. Blakemore, J.S.: Approximations for Fermi–Dirac integrals, especially the function \(f_{1/2} (\eta )\) used to describe elctron density in a semiconductor. Solid State Electron. 2, 1067–1076 (1982)ADSCrossRefGoogle Scholar
  5. Bednarczyk, D., Bednarczyk, J.: The approximation of the Fermi–Dirac integral \(F_{1/2} (\eta )\). Phys. Lett. A 64, 409–410 (1978)ADSCrossRefGoogle Scholar
  6. Coldren, L.A., Corzine, S.W.: Diode Lasers and Photonic Integrated Circuits, pp. 529–544. Wiley, New York (1995)Google Scholar
  7. Chao, C.Y.-P., Chuang, S.L.: Spin-orbit-coupling effects on the valence-band structure of strained semiconductor quantum wells. Phys. Rev. B 46, 4110–4122 (1992)Google Scholar
  8. Connelly, M.J.: Wideband semiconductor optical amplifier steady-state numerical model. IEEE J. Quantum Electron. 37, 439–447 (2001)ADSCrossRefGoogle Scholar
  9. Chuang, S.L.: Physics of Optoelectronic Devices, pp. 707–711. Wiley, New York (1995)Google Scholar
  10. Dailey, J.M., Koch, T.L.: Impact of carrier heating on SOA transmission dynamics for wavelength conversion. IEEE Photon. Technol. Lett. 19, 1078–1080 (2007)Google Scholar
  11. Dailey, J., Koch, T.: Simple rules for optimizing asymmetries in SOA-based Mach–Zehnder wavelength converters. Lightw. Technol. 27, 1480–1488 (2009)CrossRefGoogle Scholar
  12. Gomatam, B.N., DeFonzo, A.P.: Theory of hot carriers effects on nonlinear gain in GaAs/GaAlAs lasers and amplifiers. IEEE J. Quantum Electron. 26, 1689–1704 (1990)ADSCrossRefGoogle Scholar
  13. Ghafouri-Shiraz, H., Tan, P.W., Aruga, T.: Picosecond pulse amplification in tapered-waveguide laser-diode amplifiers. IEEE J. Sel. Top. Quantum Electron. 3, 210–217 (1997)CrossRefGoogle Scholar
  14. Ghafouri-Shiraz, H., Tan, P.W.: Study of a novel laser diode amplifier structure. Semicond. Sci. Technol. 11, 1443–1449 (1996)Google Scholar
  15. Hall, K.L., Lenz, G., Darwish, A.M., Ippen, E.P.: Subpicosecond gain and index nonlinearities in InGaAsP diode lasers. Opt. Commun. 111, 589–612 (1994)ADSCrossRefGoogle Scholar
  16. Hussain, K., Datta, P.K.: Effect of including intraband phenomena in the semiconductor optical amplifier model for propagation of short pulses. Appl. Opt. 52, 7171–7177 (2013)ADSCrossRefGoogle Scholar
  17. Mecozzi, A.: Mørk, J.: Saturation induced by picosecond pulses in semiconductor optical amplifiers. J. Opt. Soc. Am. B 14, 761–770 (1997)ADSCrossRefGoogle Scholar
  18. Nambu, Y., Tomita, A.: Spectral hole-burning and carrier heating effect on the transient optical nonlinearity of highly carrier-injected semiconductor. IEEE J. Quantum Electron. 30, 1981–1994 (1994)ADSCrossRefGoogle Scholar
  19. Nilsson, N.G.: Empirical approximations for the Fermi energy of a semiconductor with parabolic bands. Appl. Phys. Lett. 33, 653–654 (1978)ADSCrossRefGoogle Scholar
  20. Occhi, L., Ito, Y., Kawaguchi, H., Schares, L., Eckner, J., Guekos, G.: Intraband gain dynamics in bulk semiconductor optical amplifiers: measurements and simulations. IEEE J. Quantum Electron. 38, 54–60 (2000)ADSCrossRefGoogle Scholar
  21. Qin, C., Huang, X., Zhang, X.: Gain recovery acceleration by enhancing differential gain in quantum well semiconductor optical amplifiers. IEEE Quantum Electron. 47, 1443–1450 (2011)ADSCrossRefGoogle Scholar
  22. Tolstikhin, V., Willander, M.: Carrier heating effect in dynamic single-frequency GaInAsP-InP laser diodes. IEEE J. Quantum Electron. 31, 814–833 (1995)ADSCrossRefGoogle Scholar
  23. Uskov, A.V., Meuer, C., Schmeckebier, H., Bimberg, D.: Auger capture induced carrier heating in quantum dot lasers and amplifiers. Appl. Phys. Express 4, 022202 (2011)ADSCrossRefGoogle Scholar
  24. Uskov, A.V., Karin, J.R., Bowers, J.E., McInerney, J.G., Bihan, J.L.: 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)ADSCrossRefGoogle Scholar
  25. Xia, M., Ghafouri-Shiraz, H.: Analysis of carrier heating effect in quantum well semiconductor optical amplifiers considering holes’ non-parabolic density of states. Opt. Quantum Electron. (2014). doi: 10.1007/s11082-014-0049-2
  26. Yariv, A.: Optical Electronics, pp. 552–585. HWR International, New York (1985)Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.School of Electronic, Electrical and System EngineeringUniversity of BirminghamBirminghamUK

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