OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 8 — Apr. 13, 2009
  • pp: 6813–6828

One dimensional resonant Fibonacci quasicrystals: noncanonical linear and canonical nonlinear effects

M. Werchner, M. Schafer, M. Kira, S. W. Koch, J. Sweet, J. D. Olitzky, J. Hendrickson, B. C. Richards, G. Khitrova, H. M. Gibbs, A. N. Poddubny, E. L. Ivchenko, M. Voronov, and M. Wegener  »View Author Affiliations

Optics Express, Vol. 17, Issue 8, pp. 6813-6828 (2009)

View Full Text Article

Enhanced HTML    Acrobat PDF (410 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



A detailed experimental and theoretical study of the linear and nonlinear optical properties of different Fibonacci-spaced multiple-quantum-well structures is presented. Systematic numerical studies are performed for different average spacing and geometrical arrangement of the quantum wells. Measurements of the linear and nonlinear (carrier density dependent) reflectivity are shown to be in good agreement with the computational results. As the pump pulse energy increases, the excitation-induced dephasing broadens the exciton resonances resulting in a disappearance of sharp features and reduction in peak reflectivity.

© 2009 Optical Society of America

OCIS Codes
(190.5970) Nonlinear optics : Semiconductor nonlinear optics including MQW
(230.5590) Optical devices : Quantum-well, -wire and -dot devices
(160.5293) Materials : Photonic bandgap materials

ToC Category:
Nonlinear Optics

Original Manuscript: February 23, 2009
Revised Manuscript: March 30, 2009
Manuscript Accepted: April 1, 2009
Published: April 9, 2009

M. Werchner, M. Schafer, M. Kira, S. W. Koch, J. Sweet, J. D. Olitzky, J. Hendrickson, B. C. Richards, G. Khitrova, H. M. Gibbs, A. N. Poddubny, E. L. Ivchenko, M. Voronov, and M. Wegener, "One dimensional resonant Fibonacci quasicrystals: noncanonical linear and canonical nonlinear effects," Opt. Express 17, 6813-6828 (2009)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. D. Levine and P. J. Steinhardt, "Quasicrystals: A New Class of Ordered Structures," Phys. Rev. Lett. 53, 2477-2480 (1984). [CrossRef]
  2. C. Janot, Quasicrystals, A Primer (Clarendon Press, Oxford, UK, 1994).
  3. A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. von Freymann, "Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths," Nature Mater. 5, 942-945 (2006). [CrossRef]
  4. T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, "Transmission resonances through aperiodic arrays of subwavelength apertures," Nature 446, 517-521 (2007). [CrossRef] [PubMed]
  5. E. Yablonovitch, "Inhibited Spontaneous Emission in Solid-State Physics and Electronics," Phys. Rev. Lett. 58, 2059-2062 (1987). [CrossRef] [PubMed]
  6. S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987). [CrossRef] [PubMed]
  7. M. Kohmoto, B. Sutherland, and K. Iguchi, "Localization of optics: Quasiperiodic media," Phys. Rev. Lett. 58, 2436-2438 (1987). [CrossRef] [PubMed]
  8. L. D. Negro, M. Stolfi, Y. Yi, J. Michel, X. Duan, L. C. Kimerling, J. LeBlanc, and J. Haavisto, "Photon band gap properties and omnidirectional reflectance in Si/SiO2 Thue-Morse quasicrystals," Appl. Phys. Lett. 84, 5186-5188 (2004). [CrossRef]
  9. A. N. Poddubny, L. Pilozzi, M. M. Voronov, and E. L. Ivchenko, "Resonant Fibonacci quantum well structures in one dimension," Phys. Rev. B 77, 113306 (2008). [CrossRef]
  10. J. Hendrickson, B. C. Richards, J. Sweet, G. Khitrova, A. N. Poddubny, E. L. Ivchenko, M. Wegener, and H. M. Gibbs, "Excitonic polaritons in Fibonacci quasicrystals," Opt. Express 16, 15382-15387 (2008). [CrossRef] [PubMed]
  11. R. Merlin, K. Bajema, R. Clarke, F. Y. Juang, and P. K. Bhattacharya, "Quasiperiodic GaAs-AlAs Heterostructures," Phys. Rev. Lett. 55, 1768-1770 (1985). [CrossRef] [PubMed]
  12. M. Kohmoto and J. R. Banavar, "Quasiperiodic lattice: Electronic properties, phonon properties, and diffusion," Phys. Rev. B 34, 563-566 (1986). [CrossRef]
  13. E. L. Albuquerque and M. G. Cottam, "Theory of elementary excitations in quasiperiodic structures," Phys. Rep. 376, 225-337 (2003). [CrossRef]
  14. E. L. Ivchenko, Optical spectroscopy of semiconductor nanostructures (Alpha Science International, Harrow, UK, 2005).
  15. M. Y. Azbel, "Energy spectrum of a conduction electron in a magnetic field," Sov. Phys. JETP 19, 634-645 (1964).
  16. M. Y. Azbel, "Quantum Particle in One-Dimensional Potentials with Incommensurate Periods," Phys. Rev. Lett. 43, 1954-1957 (1979). [CrossRef]
  17. Z. Lin, M. Goda, and H. Kubo, "A family of generalized Fibonacci lattices: self-similarity and scaling of the wavefunction," J. Phys. A 28, 853-866 (1995). [CrossRef]
  18. J. M. Luck, C. Godreche, A. Janner, and T. Janssen, "The nature of the atomic surfaces of quasiperiodic selfsimilar structures," J. Phys. A 26, 1951-1999 (1993). [CrossRef]
  19. X. Fu, Y. Liu, P. Zhou, and W. Sritrakool, "Perfect self-similarity of energy spectra and gap-labeling properties in one-dimensional Fibonacci-class quasilattices," Phys. Rev. B 55, 2882-2889 (1997). [CrossRef]
  20. M. Kol’a?r, "New class of one-dimensional quasicrystals," Phys. Rev. B 47, 5489-5492 (1993). [CrossRef]
  21. M. C. Valsakumar and V. Kumar, "Diffraction from a quasi-crystalline chain," Pramana 26, 215-221 (1986). [CrossRef]
  22. Z. Lin, H. Kubo, and M. Goda, "Self-similarity and scaling of wave function for binary quasiperiodic chains associated with quadratic irrationals," Z. Phys. B: Condens Matter 98, 111-118 (1995). [CrossRef]
  23. D. Levine and P. J. Steinhardt, "Quasicrystals. I. Definition and structure," Phys. Rev. B 34, 596-616 (1986). [CrossRef]
  24. E. L. Ivchenko, A. I. Nesvizhskii, and S. Jorda, "Bragg reflection of light from quantum-well structures," Phys. Solid State 36, 1156-1161 (1994).
  25. E. L. Ivchenko, M. M. Voronov, M. V. Erementchouk, L. I. Deych, and A. A. Lisyansky, "Multiple-quantumwell-based photonic crystals with simple and compound elementary supercells," Phys. Rev. B 70, 195106 (2004). [CrossRef]
  26. M. H¨ubner, J. Kuhl, T. Stroucken, A. Knorr, S. W. Koch, R. Hey, and K. Ploog, "Collective Effects of Excitons in Multiple-Quantum-Well Bragg and Anti-Bragg Structures," Phys. Rev. Lett. 76, 4199-4202 (1996). [CrossRef] [PubMed]
  27. M. Lindberg and S.W. Koch, "Effective Bloch Equations for Semiconductors," Phys. Rev. B 38, 3342 (1988). [CrossRef]
  28. H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors (fifth ed., World Scientific Publishing, Singapore, 2009).
  29. M. Kira and S. W. Koch, "Many-body correlations and excitonic effects in semiconductor spectroscopy," Prog. Quantum Elec. 30, 155-196 (2006). [CrossRef]
  30. E. Merzbacher, Quantum Mechanics, First ed., (Wiley, New York, 1961).
  31. M. Kira, F. Jahnke, W. Hoyer, and S. W. Koch, "Quantum theory of spontaneous emission and coherent effects in semiconductor microstructures," Prog. Quantum Elec. 23, 189-279 (1999). [CrossRef]
  32. D. Hulin, A. Mysyrowicz, A. Antonetti, A. Migus, W. T. Masselink, H. Morkoc, H. M. Gibbs, and N. Peyghambarian, "An ultrafast all optical gate with subpicosecond on and off response time," Appl. Phys. Lett. 49, 749-751 (1986). [CrossRef]
  33. Z. S. Yang, N. H. Kwong, R. Binder, and A. L. Smirl, "Stopping, storing, and releasing light in quantum-well Bragg structures," J. Opt. Soc. Am. B 22, 2144-2156 (2005). [CrossRef]
  34. J. P. Prineas,W. J. Johnston, M. Yildirim, J. Zhao, and A. L. Smirl, "Tunable slow light in Bragg-spaced quantum wells," Appl. Phys. Lett. 89, 241106 (2006). [CrossRef]
  35. M. F. Yanik, W. Suh, Z. Wang, and S. Fan, "Stopping light in a waveguide with an all-optical analog of electromagnetically induced transparency," Phys. Rev. Lett. 93, 233903 (2004). [CrossRef] [PubMed]
  36. P. Chak, S. Pereira, and J. E. Sipe, "Coupled-mode theory for periodic side-coupled microcavity and photonic crystal structures," Phys. Rev. B 73, 035105 (2006). [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