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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 52, Iss. 14 — May. 10, 2013
  • pp: 3156–3165

Four-wave mixing in quantum dot semiconductor optical amplifiers

Ahmed H. Flayyih and Amin H. Al-Khursan  »View Author Affiliations

Applied Optics, Vol. 52, Issue 14, pp. 3156-3165 (2013)

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The theory of four-wave mixing (FWM) in the quantum dot (QD) semiconductor optical amplifiers (SOAs) is discussed by combining the QD rate equations system, the quantum-mechanical density-matrix theory, and the pulse propagation in QD SOAs including the three region of QD structure ground state (GS), excited state (ES), and wetting layer. Also, relations for differential gain, gain integral, and nonlinear susceptibility of both pump, probe, and signal pulses were discussed. Gain and differential gain have been calculated for QD structure. FWM efficiency and its components [spectral hole burning (SHB), carrier heating, and carrier density pulsation] are calculated. It is found that inclusion of ES in the formulas and in the calculations is essential since it works as a carrier reservoir for GS. It is found that QD SOA with enough capture time from ES to GS will reduce the SHB component, and so it is suitable for telecommunication applications that require symmetric conversion and independent detuning.

© 2013 Optical Society of America

OCIS Codes
(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing
(350.4238) Other areas of optics : Nanophotonics and photonic crystals

ToC Category:
Nonlinear Optics

Original Manuscript: January 15, 2013
Revised Manuscript: April 1, 2013
Manuscript Accepted: April 1, 2013
Published: May 7, 2013

Ahmed H. Flayyih and Amin H. Al-Khursan, "Four-wave mixing in quantum dot semiconductor optical amplifiers," Appl. Opt. 52, 3156-3165 (2013)

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  1. T. W. Berg, J. Mørk, and J. M. Hvam, “Gain dynamics and saturation in semiconductor quantum dot amplifiers,” New J. Phys. 6, 178 (2004). [CrossRef]
  2. J. Kim, M. Laemmlin, C. Meuer, D. Bimberg, and G. Eisenstein, “Static gain saturation model of quantum-dot semiconductor optical amplifiers,” IEEE J. Quantum Electron. 44, 658–666 (2008). [CrossRef]
  3. J. Kim, C. Meuer, D. Bimberg, and G. Eisenstein, “Numerical simulation of temporal and spectral variation of gain and phase recovery in quantum-dot semiconductor optical amplifiers,” IEEE J. Quantum Electron. 46, 405–413 (2010). [CrossRef]
  4. D. Nielsen and S. L. Chuang, “Four-wave mixing and wavelength conversion in quantum dots,” Phys. Rev. B 81, 035305 (2010). [CrossRef]
  5. C. Wang, F. Grillot, and J. Even, “Impacts of wetting layer and excited state on the modulation response of quantum-dot lasers”, IEEE J. Quantum Electron. 48, 1144–1150(2012). [CrossRef]
  6. O. Qasaimeh, “Characteristics of cross-gain (XG) wavelength conversion in quantum dot semiconductor optical amplifiers,” IEEE Photon. Technol. Lett. 16, 542–544 (2004). [CrossRef]
  7. Y. Ben-Ezra, M. Haridim, and B. I. Lembrikov, “Theoretical analysis of gain-recovery time and chirp in QD-SOA,” IEEE Photon. Technol. Lett. 17, 1803–1805 (2005). [CrossRef]
  8. Y. Ben-Ezra, B. I. Lembrikov, and M. Haridim, “Acceleration of gain recovery and dynamics of electrons in QD-SOA,” IEEE J. Quantum Electron. 41, 1268–1273 (2005). [CrossRef]
  9. T. W. Berg and J. Mørk, “Saturation and noise properties of quantum-dot optical amplifiers,” IEEE J. Quantum Electron. 40, 1527–1539 (2004). [CrossRef]
  10. S. Grosse, J. H. Sandman, G. von Plessen, J. Feldman, H. Lipsanen, M. Sopanen, J. Tulkki, and J. Ahopelto, “Carrier relaxation dynamics in quantum dots: scattering mechanisms and state-filing effects,” Phys. Rev. B 55, 4473–4476(1997). [CrossRef]
  11. M. Sugawara, H. Ebe, N. Hatori, M. Ishida, Y. Arakawa, T. Akiyama, K. Otsubo, and Y. Nakata, “Theory of optical signal amplification and processing by quantum-dot semiconductor optical amplifiers,” Phys. Rev. B 69, 235332 (2004). [CrossRef]
  12. T. W. Berg, S. Bischoff, I. Magnusdottir, and J. Mørk, “Ultrafast gain recovery and modulation limitations in self-assembled quantum-dot devices,” IEEE Photon. Technol. Lett. 13, 541–543 (2001). [CrossRef]
  13. F. Grillot and M. Gioannini, “Spectral analysis of 1.55 μm InAs–InP(113)B quantum-dot lasers based on a multipopulation rate equations mode,” IEEE J. Quantum Electron. 45, 872–878 (2009). [CrossRef]
  14. M. Gioannini and I. Montrosset, “Numerical analysis of the frequency chirp in quantum-dot semiconductor lasers,” IEEE J. Quantum Electron. 43, 941–949 (2007). [CrossRef]
  15. D. Bimberg, N. Kistaedter, N. N. Ledentsov, Z. Alferov, P. Kopev, and V. Ustinov, “InGaAs-GaAs quantum-dot lasers,” IEEE J. Quantum Electron. 3, 196–205 (1997). [CrossRef]
  16. R. Maram, Q. H. Baghban, H. Rasooli, S. R. Ghorbani, and A. Rostami, “Equivalent circuit model of quantum dot semiconductor optical amplifiers: dynamic behavior and saturation properties,” J. Opt. A 11, 105205 (2009). [CrossRef]
  17. A. Uskov, J. Mork, and J. Mark, “Wave mixing in semiconductor laser amplifiers due to carrier heating and spectral-hole burning,” IEEE J. Quantum Electron. 30, 1769–1781 (1994). [CrossRef]
  18. M. Shtaif and G. Eisenstein, “Analytical solution of wave mixing between short optical pulses in a semiconductor optical amplifier,” Appl. Phys. Lett. 66, 1458 (1995). [CrossRef]
  19. S. S. Mikhrin, A. R. Kovsh, I. L. Krestnikov, A. V. Kozhukhov, D. A. Livshits, N. N. Ledentsov, Y. M. Shernyakov, I. I. Novikov, M. V. Maximov, V. M. Ustinov, and Z. I. Alferov, “High power temperature-insensitive 1.3 μm InAs/InGaAs/GaAs quantum dot lasers,” Semicond. Sci. Technol. 20, 340–342 (2005). [CrossRef]
  20. T. Akiyama, H. Kuwatsuka, N. Hatori, Y. Nakata, H. Ebe, and M. Sugawara, “Symmetric highly efficient (∼0  dB) wavelength conversion based on four-wave mixing in quantum dot optical amplifiers,” IEEE Photon. Technol. Lett. 14, 1139 (2002). [CrossRef]
  21. M. Sugawara, T. Akiyama, N. Hatori, Y. Nakata, K. Otsubo, and H. Ebe, “Quantum-dot semiconductor optical amplifiers,” Proc. SPIE 4905, 259–275 (2002). [CrossRef]

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