OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 21, Iss. 12 — Dec. 1, 2004
  • pp: 2164–2174

Material and light-pulse parameter dependence of the nonlinear optical susceptibilities in the coherent χ(3) regime in semiconductor quantum wells

Ryu Takayama, Nai-Hang Kwong, Ilya Rumyantsev, Makoto Kuwata-Gonokami, and R. Binder  »View Author Affiliations

JOSA B, Vol. 21, Issue 12, pp. 2164-2174 (2004)

View Full Text Article

Enhanced HTML    Acrobat PDF (276 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



A detailed numerical study of the third-order nonlinear optical susceptibilities (χ(3)) of semiconductor quantum wells is presented. The dependence of χ(3) on material parameters (electron-hole mass ratio and exciton linewidths), on the light polarization configuration (co- and countercircularly polarized) and on the spectral configuration is discussed. The goal of this study is to map out the nonlinear phase shift per quantum well and a related figure of merit caused by quasi-resonant excitonic and biexcitonic nonlinearities induced by picosecond light pulses. The study is based on the dynamics-controlled truncation formalism and evaluated under the assumption that only 1s-heavy-hole excitons contribute to the nonlinearities. It includes all correlation effects (exciton–exciton scattering in the singlet and triplet channels and coherent biexciton formation in the singlet channel) that contribute within the coherent excitonic χ(3) regime.

© 2004 Optical Society of America

OCIS Codes
(190.4720) Nonlinear optics : Optical nonlinearities of condensed matter
(190.7110) Nonlinear optics : Ultrafast nonlinear optics
(230.5590) Optical devices : Quantum-well, -wire and -dot devices
(320.7130) Ultrafast optics : Ultrafast processes in condensed matter, including semiconductors

Ryu Takayama, Nai-Hang Kwong, Ilya Rumyantsev, Makoto Kuwata-Gonokami, and R. Binder, "Material and light-pulse parameter dependence of the nonlinear optical susceptibilities in the coherent χ(3) regime in semiconductor quantum wells," J. Opt. Soc. Am. B 21, 2164-2174 (2004)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. N. Bloembergen, Nonlinear Optics (Benjamin, New York, 1971).
  2. M. D. Levenson and S. S. Kano, Introduction to Nonlinear Laser Spectroscopy (Academic, New York, 1988).
  3. R. W. Boyd, Nonlinear Optics (Academic, New York, 1992).
  4. E. Yablonovitch, C. Flytzanis, and N. Bloembergen, “Anisotropic interference of three-wave and double two-wave frequency mixing in GaAs,” Phys. Rev. Lett. 29, 865–868 (1972). [CrossRef]
  5. K. Arya and S. S. Jha, “Tight-binding bonding orbital model for third-order nonlinear optical susceptibilities in group-IV crystals,” Phys. Rev. B 20, 1611–1616 (1979). [CrossRef]
  6. R. Adair, L. L. Chase, and S. A. Payne, “Nonlinear refractive index of optical crystals,” Phys. Rev. B 39, 3337–3550 (1989). [CrossRef]
  7. M. Sheik-Bahae, D. Hutchings, D. J. Hagan, and E. W. V. Stryland, “Dispersion of bound electronic nonlinear refraction in solids,” IEEE J. Quantum Electron. 27, 1296–1309 (1991). [CrossRef]
  8. R. Grant and W. Sibbett, “Observations of ultrafast nonlinear refraction in an InGaAsP optical amplifier,” Appl. Phys. Lett. 58, 1119–1121 (1991). [CrossRef]
  9. C. T. Hultgren and E. P. Ippen, “Ultrafast refactive index dynamics in AlGaAs diode laser amplifiers,” Appl. Phys. Lett. 59, 635–637 (1991). [CrossRef]
  10. S. K. Nayak, T. Sahu, and S. P. Mohanty, “Third-order nonlinear optical susceptibilities of group IV and III–V compound semiconductors,” Physica B 191, 334–340 (1993). [CrossRef]
  11. C. Aversa, J. E. Sipe, M. Sheik-Bahae, and E. W. V. Stryland, “Third-order optical nonlinearities in semiconductors: the two-band model,” Phys. Rev. B 50, 18073–18082 (1994). [CrossRef]
  12. D. C. Hutchings and B. S. Wherrett, “Theory of the anisotropy of ultrafast nonlinear refraction in zinc-blende semiconductors,” Phys. Rev. B 52, 8150–8159 (1995). [CrossRef]
  13. C. Aversa and J. E. Sipe, “Nonlinear optical sustibilities of semiconductors: results with a length-gauge analysis,” Phys. Rev. B 52, 14636–14645 (1995). [CrossRef]
  14. J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, “The nonlinear optical properties of AlGaAs at the half band gap,” IEEE J. Quantum Electron. 33, 341–348 (1997). [CrossRef]
  15. S. K. Nayak, T. Sahu, S. P. Mohanty, and P. K. Misra, “Third-order nonlinear optical susceptibility of wide-bandgap nitrides,” Semicond. Sci. Technol. 12, 544–549 (1997). [CrossRef]
  16. E. J. Gansen, K. Jarasiunas, and A. L. Smirl, “Femtosecond all-optical polarization switching based on the virtual excitation of spin-polarized excitons in quantum wells,” Appl. Phys. Lett. 80, 971–973 (2002). [CrossRef]
  17. R. Zimmermann, Many-Particle Theory of Highly Excited Semiconductors (Teubner, Leipzig, 1988).
  18. H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors, 2nd ed. (World Scientific, Singapore, 1993).
  19. W. Schäfer and M. Wegener, Semiconductor Optics and Transport Phenomena (Springer, Berlin, 2002).
  20. Y. L. Klimontovich, D. Kremp, and W. D. Kraeft, “Kinetic theory for chemically reacting gases and partially ionized plasmas,” Adv. Chem. Phys. 68, 175–253 (1987).
  21. W. Schäfer, R. Lövenich, N. Fromer, and D. Chemla, “From coherently excited highly correlated states to incoherent relaxation processes in semiconductors,” Phys. Rev. Lett. 86, 344–347 (2001). [CrossRef] [PubMed]
  22. R. Lövenich, C. Lai, D. Hägele, D. Chemla, and W. Schäfer, “Semiconductor polarization dynamics from the coherent to the incoherent regime: theory and experiment,” Phys. Rev. B 66, 045306 (2002). [CrossRef]
  23. O. Akimoto and E. Hanamura, “Excitonic molecule. I. Calculation of the binding energy,” J. Phys. Soc. Jpn. 33, 1537–1544 (1972). [CrossRef]
  24. E. Hanamura, “Giant two-photon absorption due to excitonic molecule,” Solid State Commun. 12, 951–953 (1973). [CrossRef]
  25. E. Hanamura and H. Haug, “Condensation effects of excitons,” Phys. Rep. 33, 209–284 (1977). [CrossRef]
  26. M. Kuwata-Gonokami and T. Saiki, “Giant optical nonlinearity of exciton and biexciton system in semiconductors,” in Nonlinear Optics—Proceedings of the Fifth Toyota Conference on Nonlinear Optical Materials, S. Miyata, ed. (North-Holland, Amsterdam, 1992), pp. 329–334.
  27. A. Ivanov and H. Haug, “Self-consistent theory of the biexciton optical nonlinearity,” Phys. Rev. B 48, 1490–1504 (1993). [CrossRef]
  28. A. Ivanov, M. Hasuo, N. Nagasawa, and H. Haug, “Two-photon generation of excitonic molecules in CuCl: an exactly solvable bipolariton model and high-precision experiments,” Phys. Rev. B 52, 11017–11033 (1995). [CrossRef]
  29. M. Combescot and R. Combescot, “Excitonic stark shift: a coupling to semivirtual biexcitons,” Phys. Rev. Lett. 61, 117–120 (1988). [CrossRef] [PubMed]
  30. M. Combescot and R. Combescot, “Optical stark effect of the exciton: biexcitonic origin of the shift,” Phys. Rev. B 40, 3788–3801 (1989). [CrossRef]
  31. M. Combescot, “Optical stark effect of the exciton. II. Polarization effects and exciton splitting,” Phys. Rev. B 41, 3517–3517 (1990). [CrossRef]
  32. B. F. Feuerbacher, J. Kuhl, and K. Ploog, “Biexitonic contribution to the degenerate-four-wave-mixing signal from a GaAs/AlxGa1−xAs quantum well,” Phys. Rev. B 43, 2439–2441 (1991). [CrossRef]
  33. S. Bar-Ad and I. Bar-Joseph, “Exciton spin dynamics in GaAs heterostructures,” Phys. Rev. Lett. 68, 349–352 (1992). [CrossRef] [PubMed]
  34. E. J. Mayer, G. O. Smith, V. Heuckeroth, J. Kuhl, K. Bott, A. Schulze, T. Meier, D. Bennhardt, S. W. Koch, P. Thomas, R. Hey, and K. Ploog, “Evidence of biexcitonic contributions to four-wave mixing in GaAs quantum wells,” Phys. Rev. B 50, 14730–14733 (1994). [CrossRef]
  35. S. Patkar, A. E. Paul, W. Sha, J. A. Bolger, and A. L. Smirl, “Degree and state of polarization of the time-integrated coherent four-wave mixing signal from semiconductor multiple quantum wells,” Phys. Rev. B 51, 10789–10794 (1995). [CrossRef]
  36. A. E. Paul, J. A. Bolger, A. L. Smirl, and J. G. Pellegrino, “Time-resolved measurements of the polarization state of four-wave mixing signals from GaAs multiple quantum wells,” J. Opt. Soc. Am. B 13, 1016–1025 (1996). [CrossRef]
  37. M. Kuwata-Gonokami, S. Inoue, H. Suzuura, M. Shirane, and R. Shimano, “Parametric scattering of cavity polaritons,” Phys. Rev. Lett. 79, 1341–1344 (1997). [CrossRef]
  38. V. M. Axt, K. Victor, and T. Kuhn, “Exciton-exciton continuum and its contribution to four-wave mixing signals,” Phys. Status Solidi B 206, 189–196 (1998). [CrossRef]
  39. M. Shirane, C. Ramkumar, Y. P. Svirko, H. Suzuura, S. Inoue, R. Shimano, T. Someya, H. Sakaki, and M. Kuwata-Gonokami, “Degenerate four-wave mixing measurements on an exciton-photon coupled system in a semiconductor microcavity,” Phys. Rev. B 58, 7978–7985 (1998). [CrossRef]
  40. H. Suzuura, Y. Svirko, and M. Kuwata-Gonokami, “Four-wave mixing theory in a cavity-polariton system,” Solid State Commun. 108, 289–293 (1998). [CrossRef]
  41. Y. P. Svirko, M. Shirane, H. Suzuura, and M. Kuwata-Gonokami, “Four-wave mixing theory at the excitonic resonance: weakly interacting boson model,” J. Phys. Soc. Jpn. 68, 647–682 (1999). [CrossRef]
  42. H. P. Wagner, A. Schätz, W. Langbein, J. M. Hvam, and A. L. Smirl, “Interaction-induced effects in the nonlinear coherent response of quantum-well excitons,” Phys. Rev. B 60, 4454–4457 (1999). [CrossRef]
  43. M. Kuwata-Gonokami, T. Aoki, C. Ramkumar, R. Shimano, and Y. Svirko, “Role of exciton–exciton interaction on resonant third-order nonlinear optical responses,” J. Lumin. 87–89, 162–167 (2000). [CrossRef]
  44. Y. Svirko and M. Kuwata-Gonokami, “Signatures of the excitonic memory effects in four-wave mixing processes in cavity polaritons,” Phys. Rev. B 62, 6912–6915 (2000). [CrossRef]
  45. V. M. Axt and A. Stahl, “A dynamics-controlled truncation scheme for the hierarchy of density matrices in semiconductor optics,” Z. Phys. B: Condens. Matter 93, 195–204 (1994). [CrossRef]
  46. V. M. Axt and A. Stahl, “The role of the biexciton in a dynamic density matrix theory of the semiconductor band edge,” Z. Phys. B: Condens. Matter 93, 205–211 (1994). [CrossRef]
  47. M. Z. Maialle and L. J. Sham, “Exciton spin dynamics and polarized luminescence in quantum wells,” Surf. Sci. 305, 256–262 (1994). [CrossRef]
  48. M. Lindberg, Y. Z. Hu, R. Binder, and S. W. Koch, “χ(3) formalism in optically excited semiconductors and its applications in four-wave-mixing spectroscopy,” Phys. Rev. B 50, 18060–18072 (1994). [CrossRef]
  49. K. Victor, V. Axt, and A. Stahl, “Hierachy of density matrices in coherent semiconductor optics,” Phys. Rev. B 51, 14164–14175 (1995). [CrossRef]
  50. T. Östreich, K. Schönhammer, and L. J. Sham, “Exciton–exciton correlation in the nonlinear opical regime,” Phys. Rev. Lett. 74, 4698–4701 (1995). [CrossRef]
  51. T. Östreich, K. Schönhammer, and L. Sham, “Theory of exciton–exciton correlation in nonlinear optical response,” Phys. Rev. B 58, 12920–12936 (1998). [CrossRef]
  52. V. M. Axt and S. Mukamel, “Influence of a photon bath on electronic correlations and optical response in molecular aggregates,” Nonlinear Opti. Mater. 101, 1–32 (1998). [CrossRef]
  53. C. Sieh, T. Meier, F. Jahnke, A. Knorr, S. W. Koch, P. Brick, M. Hübner, C. Ell, J. Prineas, G. Khitrova, and H. Gibbs, “Coulomb memory signatures in the excitonic optical stark effect,” Phys. Rev. Lett. 82, 3112–3115 (1999). [CrossRef]
  54. N. H. Kwong and R. Binder, “Green’s function approach to the dynamics-controlled truncation formalism: derivation of the χ(3) equations of motion,” Phys. Rev. B 61, 8341–8358 (2000). [CrossRef]
  55. S. W. Koch, M. Kira, and T. Meier, “Correlation effects in the excitonic optical properties of semiconductors,” J. Opt. B: Quantum Semiclassical Opt. 3, R29–R45 (2001). [CrossRef]
  56. R. Takayama, N. H. Kwong, I. Rumyantsev, M. Kuwata-Gonokami, and R. Binder, “T-matrix analysis of biexcitonic correlations in the nonlinear optical response of semiconductor quantum wells,” Eur. Phys. J. B 25, 445–462 (2002). [CrossRef]
  57. W. Schäfer, D. Kim, J. Shah, T. Damen, J. Cunningham, K. Goossen, L. Pfeiffer, and K. Köhler, “Femtosecond coherent fields induced by many-particle correlations in transient four-wave mixing,” Phys. Rev. B 53, 16429–16443 (1996). [CrossRef]
  58. P. Kner, S. Bar-Ad, M. V. Marquezini, D. S. Chemla, and W. Schäfer, “Magnetically enhanced exciton–exciton correlations in semiconductors,” Phys. Rev. Lett. 78, 1319–1322 (1997). [CrossRef]
  59. G. Bartels, G. Cho, T. Dekorsy, H. Kurz, A. Stahl, and K. Köhler, “Coherent signature of differential transmission signals in semiconductors: theory and experiments,” Phys. Rev. B 55, 16404–16413 (1997). [CrossRef]
  60. P. Kner, W. Schäfer, R. Lövenich, and D. S. Chemla, “Coherence of four-particle correlations in semiconductors,” Phys. Rev. Lett. 81, 5386–5389 (1998). [CrossRef]
  61. P. Kner, S. Bar-Ad, M. Marquezini, D. Chemla, R. Lövenich, and W. Schäfer, “Effect of magnetoexciton correlations on the coherent emission of semiconductors,” Phys. Rev. B 60, 4731–4748 (1999). [CrossRef]
  62. S. W. Koch, C. Sieh, T. Meier, F. Jahnke, A. Knorr, P. Brick, M. Hubner, C. Ell, J. Prineas, G. Khitrova, and H. M. Gibbs, “Theory of coherent effects in semiconductors,” J. Lumin. 83, 1–6 (1999). [CrossRef]
  63. T. Meier, S. W. Koch, M. Phillips, and H. Wang, “Strong coupling of heavy- and light-hole excitons induced by many-body correlations,” Phys. Rev. B 62, 12605–12608 (2000). [CrossRef]
  64. U. Neukirch, S. R. Bolton, L. J. Sham, and D. S. Chemla, “Electronic four-particle correlations in semiconductors: renormalization of coherent pump-probe oscillations,” Phys. Rev. B 61, R7835–R7837 (2000). [CrossRef]
  65. S. R. Bolton, U. Neukirch, L. J. Sham, D. S. Chemla, and V. M. Axt, “Demonstration of sixth-order coulomb correlations in a semiconductor single quantum well,” Phys. Rev. Lett. 85, 2002–2005 (2000). [CrossRef] [PubMed]
  66. P. Brick, C. Ell, S. Chatterjee, G. Khitrova, H. M. Gibbs, T. Meier, C. Sieh, and S. W. Koch, “Influence of light holes on the heavy-hole excitonic optical stark effect,” Phys. Rev. B 64, 075323 (2001). [CrossRef]
  67. N. H. Kwong, R. Takayama, I. Rumyantsev, M. Kuwata-Gonokami, and R. Binder, “Third-order exciton-correlation and nonlinear cavity-polariton effects in semiconductor microcavities,” Phys. Rev. B 64, 045316 (2001). [CrossRef]
  68. N. H. Kwong, R. Takayama, I. Rumyantsev, M. Kuwata-Gonokami, and R. Binder, “Evidence of nonperturbative continuum correlations in two-dimensional exciton systems in semiconductor microcavities,” Phys. Rev. Lett. 87, 027402 (2001). [CrossRef]
  69. V. M. Axt, B. Haase, and U. Neukirch, “Influence of two-pair continuum correlations following resonant excitation of excitons,” Phys. Rev. Lett. 86, 4620–4623 (2001). [CrossRef] [PubMed]
  70. V. M. Axt, S. R. Bolton, U. Neukirch, L. J. Sham, and D. S. Chemla, “Evidence of six-particle Coulomb correlations in six-wave-mixing signals from a semiconductor quantum well,” Phys. Rev. B 63, 115303 (2001). [CrossRef]
  71. W. Langbein, T. Meier, S. Koch, and J. Hvam, “Spectral signatures of χ(5) processes in four-wave mixing of homogeneously broadened excitons,” J. Opt. Soc. Am. B 18, 1318–1325 (2001). [CrossRef]
  72. M. E. Donovan, A. Schülzgen, J. Lee, P.-A. Blanche, N. Peyghambarian, G. Khitrova, H. M. Gibbs, I. Rumyantsev, N. H. Kwong, R. Takayama, Z. S. Yang, and R. Binder, “Evidence for intervalence band coherences in semiconductor quantum wells via coherently coupled optical stark shifts,” Phys. Rev. Lett. 87, 237402 (2001). [CrossRef] [PubMed]
  73. O. Madelung, ed., Semiconductors—Basic Data, 2nd ed. (CRC Press, Boca Raton, Fla., 1996).
  74. L. I. Berger, Semiconductor Materials (CRC Press, Boca Raton, Fla., 1997).
  75. H. Ishihara, “Anomalous size dependence of optical nonlinearities due to excitonic coherence,” J. Phys.: Condens. Matter 16, R247–R273 (2004).
  76. A. V. Filinov, M. Bonitz, and Y. E. Lozovik, “Path integral Monte Carlo simulations of bound states in semiconductor quantum wells: excitons, trions and biexcitons,” in Progress in Nonequilibrium Green’s Functions II, M. Bonitz and D. Semkat, eds. (World Scientific, Singapore, 2004).
  77. D. Dvorak, W. A. Schroeder, D. R. Andersen, A. L. Smirl, and B. S. Wherrett, “Measurement of the anisotropy of two-photon absorption coefficients in zincblende semiconductors,” IEEE J. Quantum Electron. 30, 256–269 (1994). [CrossRef]
  78. W. A. Schroeder, D. S. McCallum, D. R. Harken, M. D. Dvorak, D. R. Anderson, A. L. Smirl, and B. W. Wherrett, “Intrinsic and induced anisotropy of nonlinear absorption and refraction in zinc blende semiconductors,” J. Opt. Soc. Am. B 12, 401–415 (1995). [CrossRef]
  79. M. Lindberg, R. Binder, Y. Z. Hu, and S. W. Koch, “Dipole selection rules in multiband semiconductors,” Phys. Rev. B 49, 16942–16951 (1994). [CrossRef]
  80. J. A. Bolger, A. E. Paul, and A. L. Smirl, “Ultrafast ellipsometry of coherent processes and exciton–exciton interactions in quantum wells at negative delays,” Phys. Rev. B 54, 11666–11671 (1996). [CrossRef]
  81. R. Lövenich, “Elektron-Elektron-Wechselwirkung in Halbleitern,” Ph.D. dissertation (John von Neumann-Institut für Computing, Jülich, Germany, 2000) (in German).
  82. R. Binder, I. Rumyantsev, N. H. Kwong, and R. Takayama, “On the identification of intervalence-band coherences in semiconductor quantum wells,” Phys. Status Solidi B 221, 169–178 (2000). [CrossRef]
  83. F. Meier and B. Zakharchenya, eds., Optical Orientation (North-Holland, Amsterdam, 1984).
  84. G. Khitrova, H. M. Gibbs, F. Jahnke, M. Kira, and S. W. Koch, “Nonlinear optics of normal-mode coupling semiconductor microcavities,” Rev. Mod. Phys. 71, 1591–1639 (1999). [CrossRef]

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.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited