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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 5 — Mar. 11, 2013
  • pp: 5715–5736

Nonlinear pulse propagation in a quantum dot laser

O. Karni, A. Capua, G. Eisenstein, D. Franke, J. Kreissl, H. Kuenzel, D. Arsenijević, H. Schmeckebier, M. Stubenrauch, M. Kleinert, D. Bimberg, C. Gilfert, and J. P Reithmaier  »View Author Affiliations

Optics Express, Vol. 21, Issue 5, pp. 5715-5736 (2013)

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We investigate the nonlinear propagation of an ultra-short, 150 fs, optical pulse along the waveguide of a quantum dot (QD) laser operating above threshold. We demonstrate that among the various nonlinear processes experienced by the propagating pulse, four-wave mixing (FWM) between the pulse and the two oscillating counter-propagating cw fields of the laser is the dominant one. FWM has two important consequences. One is the creation of a spectral hole located in the vicinity of the cw oscillating frequency. The width of the spectral hole is determined by an effective carrier and gain relaxation time. The second is a modification of the shape of the trailing edge of the pulse. The wave mixing involves first and second order processes which result in a complicated interaction among several fields inside the cavity, some of which are cw while the others are time varying, all propagating in both directions. The nonlinear pulse propagation is analyzed using two complementary theoretical approaches. One is a semi-analytical model which considers only the wave mixing interaction between six field components, three of which propagate in each direction (two cw fields and four time-varying signals). This model predicts the deformation of the tail of the output signal by a secondary idler wave, produced in a cascaded FWM process, which co-propagates with the original injected pulse. The second approach is a finite-difference time-domain simulation, which considers also additional nonlinear effects, such as gain saturation and self–phase modulation. The theoretical results are confirmed by a series of experiments in which the time dependent amplitude and phase of the pulse after propagation are measured using the cross-frequency-resolved optical gating technique.

© 2013 OSA

OCIS Codes
(140.5960) Lasers and laser optics : Semiconductor lasers
(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing
(250.5980) Optoelectronics : Semiconductor optical amplifiers
(320.0320) Ultrafast optics : Ultrafast optics
(320.2250) Ultrafast optics : Femtosecond phenomena
(320.7100) Ultrafast optics : Ultrafast measurements
(190.4223) Nonlinear optics : Nonlinear wave mixing
(250.4390) Optoelectronics : Nonlinear optics, integrated optics
(250.5590) Optoelectronics : Quantum-well, -wire and -dot devices

ToC Category:
Lasers and Laser Optics

Original Manuscript: November 5, 2012
Revised Manuscript: January 17, 2013
Manuscript Accepted: February 5, 2013
Published: March 1, 2013

O. Karni, A. Capua, G. Eisenstein, D. Franke, J. Kreissl, H. Kuenzel, D. Arsenijević, H. Schmeckebier, M. Stubenrauch, M. Kleinert, D. Bimberg, C. Gilfert, and J. P Reithmaier, "Nonlinear pulse propagation in a quantum dot laser," Opt. Express 21, 5715-5736 (2013)

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  1. K. L. Hall, J. Mark, E. P. Ippen, and G. Eisenstein, “Femtosecond gain dynamics in InGaAsP optical amplifiers,” Appl. Phys. Lett.56(18), 1740–1742 (1990). [CrossRef]
  2. P. Borri, W. Langbein, J. M. Hvam, F. Heinrichsdorff, M.-H. Mao, and D. Bimberg, “Ultrafast gain dynamics in InAs-InGaAs quantum-dot amplifiers,” IEEE Photon. Technol. Lett.12(6), 594–596 (2000). [CrossRef]
  3. A. Capua, G. Eisenstein, and J. P. Reithmaier, “A nearly instantaneous gain response in quantum dash based optical amplifiers,” Appl. Phys. Lett.97(13), 131108 (2010). [CrossRef]
  4. 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(8), 1769–1781 (1994). [CrossRef]
  5. A. Capua, V. Mikhelashvili, G. Eisenstein, J. P. Reithmaier, A. Somers, A. Forchel, M. Calligaro, O. Parillaud, and M. Krakowski, “Direct observation of the coherent spectral hole in the noise spectrum of a saturated InAs/InP quantum dash amplifier operating near 1550 nm,” Opt. Express16(3), 2141–2146 (2008). [CrossRef] [PubMed]
  6. J. Zimmermann, S. T. Cundiff, G. von Plessen, J. Feldmann, M. Arzberger, G. Böhm, M.-C. Amann, and G. Abstreiter, “Dark pulse formation in a quantum-dot laser,” Appl. Phys. Lett.79(1), 18–20 (2001). [CrossRef]
  7. C. Sun, B. Golubovic, H. Choi, C. A. Wang, and J. G. Fujimoto, “Femtosecond investigations of spectral hole burning in semiconductor lasers,” Appl. Phys. Lett.66(13), 1650–1652 (1995). [CrossRef]
  8. G. P. Agrawal, “Population pulsations and nondegenerate four-wave mixing in semiconductor lasers and amplifiers,” J. Opt. Soc. Am. B5(1), 147–159 (1988). [CrossRef]
  9. M. Shtaif and G. Eisenstein, “Analytical solution of wave mixing between short optical pulses in a semiconductor optical amplifier,” Appl. Phys. Lett.66(12), 1458–1460 (1995). [CrossRef]
  10. A. Mecozzi and J. Mork, “Saturation effects in nondegenerate four-wave mixing between short optical pulses in semiconductor laser amplifiers,” IEEE J. Sel. Top. Quantum Electron.3(5), 1190–1207 (1997). [CrossRef]
  11. A. Bilenca, R. Alizon, V. Mikhelashvili, D. Dahan, G. Eisenstein, R. Schwertberger, D. Gold, J. P. Reithmaier, and A. Forchel, “Broad-band wavelength conversion based on cross-gain modulation and four-wave mixing in InAs-InP quantum-dash semiconductor optical amplifiers operating at 1550 nm,” IEEE Photon. Technol. Lett.15(4), 563–565 (2003).
  12. P. Agrawal and N. A. Olsson, “Self-phase modulation and spectral broadening of optical pulses in semiconductor laser amplifiers,” IEEE J. Quantum Electron.25(11), 2297–2306 (1989). [CrossRef]
  13. S. Linden, H. Giessen, and J. Kuhl, “XFROG — A new method for amplitude and phase characterization of weak ultrashort pulses,” Phys. Status Solidi, B Basic Res.206(1), 119–124 (1998). [CrossRef]
  14. A. Capua, A. Saal, O. Karni, G. Eisenstein, J. P. Reithmaier, and K. Yvind, “Complex characterization of short-pulse propagation through InAs/InP quantum-dash optical amplifiers: from the quasi-linear to the two-photon-dominated regime,” Opt. Express20(1), 347–353 (2012). [CrossRef] [PubMed]
  15. R. Trebino, Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses (Kluwer Academic Publishers, Norwell, 2002).
  16. C. H. Henry, “Theory of the linewidth of semiconductor lasers,” IEEE J. Quantum Electron.18(2), 259–264 (1982). [CrossRef]
  17. M. Shtaif and G. Eisenstein, “Noise properties of nonlinear semiconductor optical amplifiers,” Opt. Lett.21(22), 1851–1853 (1996). [CrossRef] [PubMed]
  18. A. P. Bogatov, P. G. Eliseev, and B. N. Sverdlov, “Anomalous interaction of spectral modes in a semiconductor laser,” IEEE J. Quantum Electron.11(7), 510–515 (1975). [CrossRef]
  19. A. Bilenca and G. Eisenstein, “On the noise properties of linear and nonlinear quantum-dot semiconductor optical amplifiers: the impact of inhomogeneously broadened gain and fast carrier dynamics,” IEEE J. Quantum Electron.40(6), 690–702 (2004). [CrossRef]
  20. G. M. Slavcheva, J. M. Arnold, and R. W. Ziolkowski, “FDTD simulation of the nonlinear gain dynamics in active optical waveguides and semiconductor microcavities,” IEEE J. Sel. Top. Quantum Electron.10(5), 1052–1062 (2004). [CrossRef]
  21. J. E. Kim, E. Malic, M. Richter, A. Wilms, and A. Knorr, “Maxwell–bloch equation approach for describing the microscopic dynamics of quantum-dot surface-emitting structures,” IEEE J. Quantum Electron.46(7), 1115–1126 (2010). [CrossRef]
  22. J. Kim, C. Meuer, D. Bimberg, and G. Eisenstein, “Role of carrier reservoirs on the slow phase recovery of quantum dot semiconductor optical amplifiers,” Appl. Phys. Lett.94(4), 041112 (2009). [CrossRef]

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