OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: Henry van Driel
  • Vol. 27, Iss. 2 — Feb. 1, 2010
  • pp: 168–178

Theoretical investigation of the role of optically induced carrier pulsations in wave mixing in semiconductor optical amplifiers

Simeon N. Kaunga-Nyirenda, Michal P. Dlubek, Andrew J. Phillips, Jun Jun Lim, Eric C. Larkins, and Slawomir Sujecki  »View Author Affiliations

JOSA B, Vol. 27, Issue 2, pp. 168-178 (2010)

View Full Text Article

Enhanced HTML    Acrobat PDF (476 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



A theoretical investigation of the role of interband effects in wave mixing in semiconductor optical amplifiers (SOA) is reported. Carrier density modulation (CDM) caused by optical wave beating in SOAs is examined along with its dependence on different operating parameters. Unlike most wave mixing theories, in which the existence and form of carrier pulsations are assumed a priori, we model the carrier dynamics and optical propagation in the time domain directly without invoking such an assumption. The dependence of CDM on the bias current, input power, and detuning between the pump and probe waves is investigated. Selected simulation results are verified experimentally. Good qualitative agreement is obtained between simulations and experiments for nearly degenerate wave mixing (restricted to 3 GHz by experimental limitations).

© 2010 Optical Society of America

OCIS Codes
(190.5970) Nonlinear optics : Semiconductor nonlinear optics including MQW
(250.5980) Optoelectronics : Semiconductor optical amplifiers
(190.4223) Nonlinear optics : Nonlinear wave mixing

ToC Category:
Nonlinear Optics

Original Manuscript: September 4, 2009
Manuscript Accepted: October 26, 2009
Published: January 7, 2010

Simeon N. Kaunga-Nyirenda, Michal P. Dlubek, Andrew J. Phillips, Jun Jun Lim, Eric C. Larkins, and Slawomir Sujecki, "Theoretical investigation of the role of optically induced carrier pulsations in wave mixing in semiconductor optical amplifiers," J. Opt. Soc. Am. B 27, 168-178 (2010)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. T. Mukai, Y. Yamamoto, and T. Kimura, “Optical amplification by semiconductor lasers,” Semicond. Semimetals 22, 265-317 (1985). [CrossRef]
  2. D. F. Geraghty, R. B. Lee, K. J. Vahala, M. Verdiell, M. Ziari, and A. Mathur, “Wavelength conversion up to 18 nm at 10 Gb/s by four-wave mixing in a semiconductor optical amplifier,” IEEE Photon. Technol. Lett. 9, 452-454 (1997). [CrossRef]
  3. J. H. Caulfield, C. S. Vikram, and A. Zavalin, “Optical logic redux,” Optik (Stuttgart) 117, 199-209 (2006). [CrossRef]
  4. K. E. Stubkjaer, “Semiconductor optical amplifier-based all-optical gates for high-speed optical processing,” IEEE J. Sel. Top. Quantum Electron. 6, 1428-1435 (2000). [CrossRef]
  5. G. P. Agrawal, “Four-wave mixing and phase conjugation in semiconductor laser medium,” Opt. Lett. 12, 260-262 (1987). [CrossRef] [PubMed]
  6. P. G. Eliseev and V. V. Luc, “Semiconductor optical amplifiers: multifunctional possibilities, photoresponse and phase shift properties,” Pure Appl. Opt. 4, 295-313 (1995). [CrossRef]
  7. D. Nesset, T. Kelly, and D. Marcenac, “All-optical wavelength conversion using SOA nonlinearities,” IEEE Commun. Mag. 36, 56-61 (1998). [CrossRef]
  8. M. Kovačević and A. Acampora, “Benefits of wavelength translation in all-optical clear-channel networks,” IEEE J. Sel. Areas Commun. 14, 868-880 (1995).
  9. J. Yates, J. Lacey, M. Rumsewicz, and M. Summerfield, “Performance of networks using wavelength converters based on four-wave mixing in semiconductor optical amplifiers,” J. Lightwave Technol. 17, 782-791 (1999). [CrossRef]
  10. K. J. Vahala, J. Zhou, D. Geraghty, R. Lee, M. Newkirk, and B. Miller, “Four-wave mixing in semiconductor travelling-wave amplifiers for wavelength conversion in all-optical networks,” Int. J. High Speed Electron. Syst. 7, 153-177 (1996). [CrossRef]
  11. S. Bischoff, A. Buxens, H. N. Poulsen, A. T. Clausen, and J. Mørk, “Bidirectional four-wave mixing in semiconductor optical amplifiers: theory and experiment,” J. Lightwave Technol. 17, 1617-1625 (1999). [CrossRef]
  12. T. Baba, “Photonic crystals remember the light,” Nat. Photonics 1, 11-12 (2007). [CrossRef]
  13. E. Suhir, “Microelectronics and photonics--the future,” Microelectron. J. 31, 839-851 (2000). [CrossRef]
  14. D. L. Mills, Nonlinear Optics: Basic Concepts (Springer-Verlag, 1991).
  15. M. Sheik-Bahae and M. P. Hasselbeck, “Third-order optical nonlinearities,” in OSA Handbook of Optics. IV, M.Bass, ed. (Mc-GrawHill, 2001), pp. 17.1-17.34.
  16. R. Paiella, G. Hunziker, U. Koren, and K. J. Vahala, “Polarization-dependent optical nonlinearities of multiquantum-well laser amplifiers,” IEEE J. Sel. Top. Quantum Electron. 3, 529-540 (1997). [CrossRef]
  17. S. Hoffmann, M. Hofmann, E. Bründermann, M. Havenith, M. Matus, J. V. Moloney, A. S. Moskalenko, M. Kira, S. W. Koch, S. Saito, and K. Sakai, “Four-wave mixing and direct terahertz emission with two-color semiconductor lasers,” Appl. Phys. Lett. 84, 3585-3587 (2004). [CrossRef]
  18. G. P. Agrawal, “Population pulsations and nondegenerate four-wave mixing in semiconductor lasers and amplifiers,” J. Opt. Soc. Am. B 5, 147-159 (1988). [CrossRef]
  19. Y. R. Shen, “Basic considerations of four-wave mixing and dynamic gratings,” IEEE J. Quantum Electron. QE-22, 1196-1203 (1986). [CrossRef]
  20. 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]
  21. P. J. Bream, S. Sujecki, and E. C. Larkins, “Nonequilibrium gain and nonlinear optical response of QWs for functional photonic devices,” presented at the 6th International Conference on Numerical Simulation of Optoelectronic Devices, Nanyang Technological University, Singapore, 11-14 September 2006.
  22. T. Mukai and T. Saitoh, “Detuning characterisitcs and conversion efficiency of nearly degenerate four-wave mixing in a 1.5-μm travelling-wave semiconductor laser amplifier,” IEEE J. Quantum Electron. 26, 865-875 (1990). [CrossRef]
  23. M. A. Summerfield and R. S. Tucker, “Frequency-domain model for multiwave mixing in bulk semiconductor optical amplifiers,” IEEE J. Sel. Top. Quantum Electron. 5, 839-850 (1999). [CrossRef]
  24. W. M. Yee and K. A. Shore, “Nearly degenerate four-wave mixing in laser diodes with nonuniform longitudinal gain distribution,” J. Opt. Soc. Am. B 11, 1221-1228 (1994). [CrossRef]
  25. R. Nietzke, P. Panknin, W. Elsasser, and E. O. Gobel, “Four-wave mixing in GaAs/AlGaAs semiconductor lasers,” IEEE J. Quantum Electron. 25, 1399-1406 (1989). [CrossRef]
  26. I. Koltchanov, S. Kindt, K. Petermann, S. Diez, R. Ludwig, R. Schnabel, and H. G. Weber, “Analytical theory of terahertz four-wave mixing in semiconductor-laser amplifiers,” Appl. Phys. Lett. 68, 2787-2789 (1996). [CrossRef]
  27. G. P. Agrawal and N. K. Dutta, Long-Wavelength Semiconductor Lasers (Van Nostrand Reinhold, 1986).
  28. J. M. Tang and K. A. Shore, “Carrier diffusion and depletion effects on multiwave mixing in semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron. 3, 1280-1286 (1997). [CrossRef]
  29. S. Diez, C. Schmidt, R. Ludwig, H. G. Weber, K. Obermann, S. Kindt, I. Koltchanov, and K. Petermann, “Four-wave mixing in semiconductor optical amplifiers for frequency conversion and fast optical switching,” IEEE J. Sel. Top. Quantum Electron. 3, 1131-1145 (1997). [CrossRef]
  30. H. Jang, S. Hur, Y. Kim, and J. Jeong, “Theoretical investigation of optical wavelength conversion techniques for DPSK modulation formats using FWM in SOAs and frequency comb in 10 Gb/s transmission systems,” J. Lightwave Technol. 23, 2638-2646 (2005). [CrossRef]
  31. C. Politi, D. Klonidis, and M. J. O'Mahony, “Dynamic behaviour of wavelength converters based on FWM in SOAs,” IEEE J. Quantum Electron. 42, 108-125 (2006). [CrossRef]
  32. N. K. Das, Y. Yamayoshi, and H. Kawagushi, “Analysis of basic four-wave mixing characteristics in a semiconductor optical amplifier by finite-difference beam propagation method,” IEEE J. Quantum Electron. 36, 1184-1192 (2000). [CrossRef]
  33. G. Toptchiyski, S. Kindt, K. Petermann, E. Hillinger, S. Diez, and H. G. Weber, “Time-domain modeling of semiconductor optical amplifiers for OTDM applications,” J. Lightwave Technol. 17, 2577-2583 (1999). [CrossRef]
  34. E. M. Pratt. and J. E. Carroll, “Gain modelling and particle balance in semiconductor lasers,” IEE Proc.: Optoelectron. 147, 77-82 (2000). [CrossRef]
  35. K. Inoue, T. Mukai, and T. Saitoh, “Nearly degenerate four-wave mixing in a traveling-wave semiconductor laser amplifier,” Appl. Phys. Lett. 51, 1051-1053 (1987). [CrossRef]
  36. X. Li and J. Park, “Time-domain modeling and simulation of the broadband behavior of semiconductor optical amplifiers,” Proc. SPIE 5248, 227-239 (2003). [CrossRef]
  37. J. K. White, J. V. Moloney, A. Gavrielides, V. Kovanis, A. Hohl, and R. Kalmus, “Multilongitudinal-mode dynamics in a semiconductor laser subject to optical injection,” IEEE J. Quantum Electron. 34, 1469-1473 (1998). [CrossRef]
  38. Z. Dai, R. Michalzik, P. Unger, and K. J. Ebeling, “Numerical simulation of broad-area high-power semiconductor laser amplifiers,” IEEE J. Quantum Electron. 33, 2240-2254 (1997). [CrossRef]
  39. V. I. Tolstikhin, “Carrier charge imbalance and optical properties of separate confinement heterostructure quantum well lasers,” J. Appl. Phys. 87, 7342-7348 (2000). [CrossRef]
  40. M. J. Connelly, “Wideband semiconductor optical amplifier steady-state numerical model,” IEEE J. Quantum Electron. 37, 439-447 (2001). [CrossRef]
  41. P. S. Zory, Quantum Well Lasers (Academic, 1993).
  42. I. Vurgaftman, J. R. Meyer, and L. R. Ram-Mohan, “Band parameters for III-V compound semiconductors and their alloys,” Appl. Sci. Res., Sect. B 89, 5815-5875 (2001).
  43. W. W. Chow and S. W. Koch, Semiconductor-LaserFundamentals: Physics of Gain Materials (Springer-Verlag, 1999).
  44. J. Wang and H. Schweizer, “A quantitative comparison of the classical rate-equation model with the carrier heating model on dynamics of the quantum-well laser: the role of carrier energy relaxation, electron-hole interaction, and Auger effect,” IEEE J. Quantum Electron. 33, 1350-1359 (1997). [CrossRef]
  45. D. C. Hutchings, M. Sheik-bahae, D. J. Hagan, and E. W. V. Stryland, “Kramers-Kronig relations in nonlinear optics,” Opt. Quantum Electron. 24, 1-30 (1992). [CrossRef]
  46. R. W. Boyd, Nonlinear Optics (Academic, 2003).
  47. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C++ (Cambridge Univ. Press, 2002).
  48. Y. L. Wong and J. E. Carroll, “A travelling-wave rate equation analysis for semiconductor lasers,” Solid-State Electron. 30, 13-19 (1987). [CrossRef]
  49. D. J. Jones, L. M. Zhang, J. E. Carroll, and D. D. Marcenac, “Dynamics of monolithic passively mode-locked semiconductor lasers,” IEEE J. Quantum Electron. 31, 1051-1058 (1995). [CrossRef]
  50. S. W. Smith, Digital Signal Processing: A Practical Guide for Engineers and Scientists (Newnes, 2002).
  51. A. E. Kelly, I. F. Lealman, L. J. Rivers, S. D. Perrin, and M. Silver, “Polarisation insensitive, 25 dB gain semiconductor laser amplifier without antireflection coatings,” Electron. Lett. 32, 1835-1836 (1996). [CrossRef]
  52. I. F. Lealman, Centre for Integrated Photonics (CIP), B55, Adastral Park, Martlesham Heath, Ipswich, IP5 3RE, UK (Private communication, 2009).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited