Rabi-oscillation-enhanced frequency conversion in quantum-dot semiconductor optical amplifiers

  • Benjamin LingnauEmail author
  • Kathy Lüdge
Part of the following topical collections:
  1. 2017 Numerical Simulation of Optoelectronic Devices


We investigate the nonlinear light propagation in InAs/InGaAs quantum-dot-in-a-well semiconductor optical amplifiers in the limit of strong optical excitation where Rabi oscillations are excited in the active medium. The amplifier is analyzed in a degenerate four-wave-mixing setup and characterized by its frequency conversion and creation performance. Our simulations show that the interplay between the nonlinear four-wave-mixing process and the coherent Rabi oscillations greatly influences the frequency conversion process. Rabi oscillations can be resonantly excited by the correct choice of the frequency detuning between pump and probe signals, which greatly enhances the nonlinear frequency conversion efficiency at frequencies up to several THz. We furthermore show that the coherent pulse shaping of ultrashort optical pulses in the quantum-dot medium can greatly enhance their spectral bandwidth, potentially allowing for ultra-broad-band frequency comb generation.


Quantum-dot semiconductor optical amplifiers Four-wave mixing Rabi oscillations 



This work was supported by the Deutsche Forschungsgemeinschaft within CRC787.

Supplementary material

11082_2018_1380_MOESM1_ESM.pdf (15 kb)
Supplementary material 1 (pdf 14 KB)


  1. Akiyama, T., Kuwatsuka, H., Hatori, N., Nakata, Y., Ebe, H., Sugawara, M.: Symmetric highly efficient (~ 0 dB) wavelength conversion based on four-wave mixing in quantum dot optical amplifiers. IEEE Photonics Technol. Lett. 14(8), 1139–1141 (2002)ADSCrossRefGoogle Scholar
  2. Allen, L., Eberly, J.H.: Optical Resonance and Two-Level Atoms, Dover books on Physics and Chemistry. Dover, New York (1975)Google Scholar
  3. Arkhipov, R.M., Arkhipov, M.V., Babushkin, I., Rosanov, N.N.: Formation and erasure of population difference gratings in the coherent interaction of a resonant medium with extremely short optical pulses. Opt. Spectrosc. 125(5), 758–764 (2016)ADSCrossRefGoogle Scholar
  4. Bardella, P., Columbo, L., Gioannini, M.: Self-generation of optical frequency comb in single section quantum dot Fabry-Perot lasers: a theoretical study. Opt. Express 25(21), 26234–26252 (2017)ADSCrossRefGoogle Scholar
  5. Birkedal, D., Leosson, K., Hvam, J.M.: Long lived coherence in self-assembled quantum dots. Phys. Rev. Lett. 87, 227401 (2001). ADSCrossRefGoogle Scholar
  6. Borri, P., Langbein, W., Schneider, S., Woggon, U., Sellin, R.L., Ouyang, D., Bimberg, D.: Ultralong dephasing time in InGaAs quantum dots. Phys. Rev. Lett. 87(15), 157401 (2001). ADSCrossRefGoogle Scholar
  7. Capua, A., Karni, O., Eisenstein, G., Reithmaier, J.P.: Rabi oscillations in a room-temperature quantum dash semiconductor optical amplifier. Phys. Rev. B 90, 045305 (2014). ADSCrossRefGoogle Scholar
  8. Chow, W.W., Koch, S.W.: Theory of semiconductor quantum-dot laser dynamics. IEEE J. Quantum Electron. 41, 495–505 (2005). ADSCrossRefGoogle Scholar
  9. Contestabile, G., Maruta, A., Kitayama, K.: Four wave mixing in quantum dot semiconductor optical amplifiers. IEEE J. Quantum Electron. 50(5), 379–389 (2014). ADSCrossRefGoogle Scholar
  10. Crisp, M.D.: Adiabatic-following approximation. Phys. Rev. A 8, 2128–2135 (1973). ADSCrossRefGoogle Scholar
  11. Diez, S., Schmidt, C., Ludwig, R., Weber, H.G., Obermann, K., Kindt, S., Koltchanov, I., Petermann, K.: Four-wave mixing in semiconductor optical amplifiers for frequency conversion and fast optical switching. IEEE J. Sel. Top. Quantum Electron. 3(5), 1131–1145 (1997). CrossRefGoogle Scholar
  12. Elmirghani, J.M.H., Mouftah, H.T.: All-optical wavelength conversion: technologies and applications in DWDM networks. IEEE Commun. Mag. 38(3), 86–92 (2000). CrossRefGoogle Scholar
  13. Ghosh, S., Bhattacharya, P., Stoner, E., Singh, J., Jiang, H., Nuttinck, S., Laskar, J.: Temperature-dependent measurement of auger recombination in self-organized In0.4Ga0.6As/GaAs quantum dots. Appl. Phys. Lett. 79(6), 722–724 (2001). ADSCrossRefGoogle Scholar
  14. Haug, A.: Auger recombination in quantum well semiconductors: calculation with realistic energy bands. Semicond. Sci. Technol. 7(11), 1337–1340 (1992)ADSCrossRefGoogle Scholar
  15. Hausser, S., Fuchs, G., Hangleiter, A., Streubel, K., Tsang, W.T.: Auger recombination in bulk and quantum well InGaAas. Appl. Phys. Lett. 56(10), 913–915 (1990). ADSCrossRefGoogle Scholar
  16. Henry, C.H.: Theory of the linewidth of semiconductor lasers. IEEE J. Quantum Electron. 18(2), 259–264 (1982)ADSCrossRefGoogle Scholar
  17. Herzog, B., Lingnau, B., Kolarczik, M., Kaptan, Y., Bimberg, D., Maadorf, A., Pohl, U.W., Rosales, R., Schulze, J.H., Strittmatter, A., Weyers, M., Woggon, U., Lüdge, K., Owschimikow, N.: Strong amplitude-phase coupling in submonolayer quantum dots. Appl. Phys. Lett. 109, 201102 (2016). ADSCrossRefGoogle Scholar
  18. Hoffmann, M., Sieber, O.D., Wittwer, V.J., Krestnikov, I.L., Livshits, D.A., Barbarin, Y., Südmeyer, T., Keller, U.: Femtosecond high-power quantum dot vertical external cavity surface emitting laser. Opt. Express 19(9), 8108–8116 (2011). ADSCrossRefGoogle Scholar
  19. Javaloyes, J., Balle, S.: Multimode dynamics in bidirectional laser cavities by folding space into time delay. Opt. Express 20(8), 8496–8502 (2012)ADSCrossRefGoogle Scholar
  20. Kibria, R., Austin, M.W.: All optical signal-processing techniques utilizing four wave mixing. Photonics 2(1), 200–213 (2015). CrossRefGoogle Scholar
  21. Kolarczik, M., Owschimikow, N., Korn, J., Lingnau, B., Kaptan, Y., Bimberg, D., Schöll, E., Lüdge, K., Woggon, U.: Quantum coherence induces pulse shape modification in a semiconductor optical amplifier at room temperature. Nat. Commun. 4, 2953 (2013)ADSCrossRefGoogle Scholar
  22. Lingnau, B.: Nonlinear and Nonequilibrium Dynamics of Quantum-Dot Optoelectronic Devices, Springer Theses. Springer, Cham (2015)CrossRefGoogle Scholar
  23. Lingnau, B., Lüdge, K.: Quantum-dot semiconductor optical amplifiers. In: Piprek, J. (ed.) Handbook of Optoelectronic Device Modeling and Simulation, Vol. 1 of Series in Optics and Optoelectronics, Chap. 23. CRC Press, Boca Raton (2017)Google Scholar
  24. Lingnau, B., Lüdge, K., Chow, W.W., Schöll, E.: Failure of the \(\alpha\)-factor in describing dynamical instabilities and chaos in quantum-dot lasers. Phys. Rev. E 86(6), 065201(R) (2012). ADSCrossRefGoogle Scholar
  25. Lingnau, B., Chow, W.W., Lüdge, K.: Amplitude-phase coupling and chirp in quantum-dot lasers: influence of charge carrier scattering dynamics. Opt. Express 22(5), 4867–4879 (2014)ADSCrossRefGoogle Scholar
  26. Lingnau, B., Herzog, B., Kolarczik, M., Woggon, U., Lüdge, K., Owschimikow, N.: Dynamic phase response and amplitude-phase coupling of self-assembled semiconductor quantum dots. Appl. Phys. Lett. 110, 241102 (2017)ADSCrossRefGoogle Scholar
  27. Majer, N., Lüdge, K., Schöll, E.: Cascading enables ultrafast gain recovery dynamics of quantum dot semiconductor optical amplifiers. Phys. Rev. B 82, 235301 (2010)ADSCrossRefGoogle Scholar
  28. Majer, N., Dommers-Völkel, S., Gomis-Bresco, J., Woggon, U., Lüdge, K., Schöll, E.: Impact of carrier-carrier scattering and carrier heating on pulse train dynamics of quantum dot semiconductor optical amplifiers. Appl. Phys. Lett. 99, 131102 (2011). ADSCrossRefGoogle Scholar
  29. McCall, S.L., Hahn, E.L.: Self-induced transparency. Phys. Rev. 183(2), 457–485 (1969). ADSCrossRefGoogle Scholar
  30. Meuer, C., Schmeckebier, H., Fiol, G., Arsenijević, D., Kim, J., Eisenstein, G., Bimberg, D.: Cross-gain modulation and four-wave mixing for wavelength conversion in undoped and p-doped 1.3-μm quantum dot semiconductor optical amplifiers. IEEE Photonics J. 2(2), 141–151 (2010)CrossRefGoogle Scholar
  31. Moelbjerg, A., Kaer, P., Lorke, M., Mørk, J.: Resonance fluorescence from semiconductor quantum dots: beyond the mollow triplet. Phys. Rev. Lett. 108, 017401 (2012). ADSCrossRefGoogle Scholar
  32. Nielsen, D., Chuang, S.L.: Four-wave mixing and wavelength conversion in quantum dots. Phys. Rev. B 81, 035305 (2010). ADSCrossRefGoogle Scholar
  33. Nielsen, T.R., Gartner, P., Lorke, M., Seebeck, J., Jahnke, F.: Coulomb scattering in nitride-based self-assembled quantum dot systems. Phys. Rev. B 72(23), 235311 (2005). ADSCrossRefGoogle Scholar
  34. Politi, C., Klonidis, D., O’Mahony, M.J.: Waveband converters based on four-wave mixing in soas. J. Lightwave Technol. 24(3), 1203–1217 (2006). ADSCrossRefGoogle Scholar
  35. Press, W.H., Flannery, B.P., Teukolsky, S.A., Vettering, W.T.: Numerical Recipes, 3rd edn. Cambridge University Press, Cambridge (2007)Google Scholar
  36. Scheller, M., Wang, T.L., Kunert, B., Stolz, W., Koch, S.W., Moloney, J.V.: Passively modelocked vecsel emitting 682 fs pulses with 5.1 W of average output power. Electron. Lett. 48(10), 588–589 (2012). CrossRefGoogle Scholar
  37. Schliesser, A., Picque, N., Hänsch, T.W.: Mid-infrared frequency combs. Nat Photonics 6(7), 440–449 (2012). ADSCrossRefGoogle Scholar
  38. Schmeckebier, H., Meuer, C., Arsenijević, D., Fiol, G., Schmidt-Langhorst, C., Schubert, C., Eisenstein, G., Bimberg, D.: Wide-range wavelength conversion of 40-Gb/s NRZ-DPSK signals using a 1.3-μm quantum-dot semiconductor optical amplifier. IEEE Photonics Technol. Lett. 24(13), 1163–1165 (2012)ADSCrossRefGoogle Scholar
  39. Schmeckebier, H., Lingnau, B., König, S., Lüdge, K., Meuer, C., Zeghuzi, A., Arsenijević, D., Stubenrauch, M., Bonk, R., Koos, C., Schubert, C., Pfeiffer, T., Bimberg, D.: Ultra-broadband bidirectional dual-band quantum-dot semiconductor optical amplifier. In: Optical Fiber Communication Conference and Exposition Tu3I.7 (2015).
  40. Scully, M.O.: Quantum Optics. Cambridge University Press, Cambridge (1997)CrossRefGoogle Scholar
  41. Stubkjaer, K.E.: Semiconductor optical amplifier-based all-optical gates for high-speed optical processing. IEEE J. Sel. Top. Quantum Electron. 6(6), 1428–1435 (2000). CrossRefGoogle Scholar
  42. Sugawara, M., Ebe, H., Hatori, N., Ishida, M., Arakawa, Y., Akiyama, T., Otsubo, K., Nakata, Y.: Theory of optical signal amplification and processing by quantum-dot semiconductor optical amplifiers. Phys. Rev. B 69(23), 235332 (2004). ADSCrossRefGoogle Scholar
  43. Udem, T., Holzwarth, R., Hänsch, T.W.: Optical frequency metrology. Nature 416, 233–237 (2002)ADSCrossRefGoogle Scholar
  44. Ye, J., Schnatz, H., Hollberg, L.: Optical frequency combs: from frequency metrology to optical phase control. IEEE J. Sel. Top. Quantum Electron. 9(4), 1041–1058 (2003). CrossRefGoogle Scholar
  45. Yoo, S.J.B.: Wavelength conversion technologies for WDM network applications. J. Lightwave Technol. 14(6), 955–966 (1996). ADSCrossRefGoogle Scholar
  46. Zajnulina, M., Lingnau, B., Lüdge, K.: Four-wave mixing in quantum dot semiconductor optical amplifiers: a detailed analysis of the nonlinear effects. IEEE J. Sel. Top. Quantum Electron. 23(6), 3000112 (2017). CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institut für Theoretische PhysikTechnische Universität BerlinBerlinGermany

Personalised recommendations