Abstract

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

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    [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).
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    [CrossRef] [PubMed]
  7. M. Kohmoto, B. Sutherland, and K. Iguchi, "Localization of optics: Quasiperiodic media," Phys. Rev. Lett. 58, 2436-2438 (1987).
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    [CrossRef]
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    [CrossRef]
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    [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]

2008 (2)

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]

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]

2007 (1)

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]

2006 (4)

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]

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]

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]

M. Kira and S. W. Koch, "Many-body correlations and excitonic effects in semiconductor spectroscopy," Prog. Quantum Elec. 30, 155-196 (2006).
[CrossRef]

2005 (1)

2004 (3)

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]

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]

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]

2003 (1)

E. L. Albuquerque and M. G. Cottam, "Theory of elementary excitations in quasiperiodic structures," Phys. Rep. 376, 225-337 (2003).
[CrossRef]

1999 (1)

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]

1997 (1)

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]

1996 (1)

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]

1995 (2)

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]

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]

1994 (1)

E. L. Ivchenko, A. I. Nesvizhskii, and S. Jorda, "Bragg reflection of light from quantum-well structures," Phys. Solid State 36, 1156-1161 (1994).

1993 (2)

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]

M. Kol’a?r, "New class of one-dimensional quasicrystals," Phys. Rev. B 47, 5489-5492 (1993).
[CrossRef]

1988 (1)

M. Lindberg and S.W. Koch, "Effective Bloch Equations for Semiconductors," Phys. Rev. B 38, 3342 (1988).
[CrossRef]

1987 (3)

E. Yablonovitch, "Inhibited Spontaneous Emission in Solid-State Physics and Electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987).
[CrossRef] [PubMed]

M. Kohmoto, B. Sutherland, and K. Iguchi, "Localization of optics: Quasiperiodic media," Phys. Rev. Lett. 58, 2436-2438 (1987).
[CrossRef] [PubMed]

1986 (4)

M. C. Valsakumar and V. Kumar, "Diffraction from a quasi-crystalline chain," Pramana 26, 215-221 (1986).
[CrossRef]

M. Kohmoto and J. R. Banavar, "Quasiperiodic lattice: Electronic properties, phonon properties, and diffusion," Phys. Rev. B 34, 563-566 (1986).
[CrossRef]

D. Levine and P. J. Steinhardt, "Quasicrystals. I. Definition and structure," Phys. Rev. B 34, 596-616 (1986).
[CrossRef]

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]

1985 (1)

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]

1984 (1)

D. Levine and P. J. Steinhardt, "Quasicrystals: A New Class of Ordered Structures," Phys. Rev. Lett. 53, 2477-2480 (1984).
[CrossRef]

1979 (1)

M. Y. Azbel, "Quantum Particle in One-Dimensional Potentials with Incommensurate Periods," Phys. Rev. Lett. 43, 1954-1957 (1979).
[CrossRef]

1964 (1)

M. Y. Azbel, "Energy spectrum of a conduction electron in a magnetic field," Sov. Phys. JETP 19, 634-645 (1964).

Agrawal, A.

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]

Albuquerque, E. L.

E. L. Albuquerque and M. G. Cottam, "Theory of elementary excitations in quasiperiodic structures," Phys. Rep. 376, 225-337 (2003).
[CrossRef]

Antonetti, A.

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]

Azbel, M. Y.

M. Y. Azbel, "Quantum Particle in One-Dimensional Potentials with Incommensurate Periods," Phys. Rev. Lett. 43, 1954-1957 (1979).
[CrossRef]

M. Y. Azbel, "Energy spectrum of a conduction electron in a magnetic field," Sov. Phys. JETP 19, 634-645 (1964).

Bajema, K.

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]

Banavar, J. R.

M. Kohmoto and J. R. Banavar, "Quasiperiodic lattice: Electronic properties, phonon properties, and diffusion," Phys. Rev. B 34, 563-566 (1986).
[CrossRef]

Bhattacharya, P. K.

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]

Binder, R.

Cademartiri, L.

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]

Chak, P.

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]

Clarke, R.

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]

Cottam, M. G.

E. L. Albuquerque and M. G. Cottam, "Theory of elementary excitations in quasiperiodic structures," Phys. Rep. 376, 225-337 (2003).
[CrossRef]

Deych, L. I.

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]

Duan, X.

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]

Erementchouk, M. V.

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]

Fan, S.

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]

Fu, X.

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]

Gibbs, H. M.

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]

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]

Goda, M.

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]

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]

Godreche, C.

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]

H¨ubner, M.

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]

Haavisto, J.

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]

Hendrickson, J.

Hermatschweiler, M.

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]

Hey, R.

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]

Hoyer, W.

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]

Hulin, D.

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]

Iguchi, K.

M. Kohmoto, B. Sutherland, and K. Iguchi, "Localization of optics: Quasiperiodic media," Phys. Rev. Lett. 58, 2436-2438 (1987).
[CrossRef] [PubMed]

Ivchenko, E. L.

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]

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]

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]

E. L. Ivchenko, A. I. Nesvizhskii, and S. Jorda, "Bragg reflection of light from quantum-well structures," Phys. Solid State 36, 1156-1161 (1994).

Jahnke, F.

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]

Janner, A.

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]

Janssen, T.

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]

John, S.

S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987).
[CrossRef] [PubMed]

Johnston, W. J.

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]

Jorda, S.

E. L. Ivchenko, A. I. Nesvizhskii, and S. Jorda, "Bragg reflection of light from quantum-well structures," Phys. Solid State 36, 1156-1161 (1994).

Juang, F. Y.

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]

Khitrova, G.

Kimerling, L. C.

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]

Kira, M.

M. Kira and S. W. Koch, "Many-body correlations and excitonic effects in semiconductor spectroscopy," Prog. Quantum Elec. 30, 155-196 (2006).
[CrossRef]

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]

Knorr, A.

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]

Koch, S. W.

M. Kira and S. W. Koch, "Many-body correlations and excitonic effects in semiconductor spectroscopy," Prog. Quantum Elec. 30, 155-196 (2006).
[CrossRef]

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]

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]

Koch, S.W.

M. Lindberg and S.W. Koch, "Effective Bloch Equations for Semiconductors," Phys. Rev. B 38, 3342 (1988).
[CrossRef]

Kohmoto, M.

M. Kohmoto, B. Sutherland, and K. Iguchi, "Localization of optics: Quasiperiodic media," Phys. Rev. Lett. 58, 2436-2438 (1987).
[CrossRef] [PubMed]

M. Kohmoto and J. R. Banavar, "Quasiperiodic lattice: Electronic properties, phonon properties, and diffusion," Phys. Rev. B 34, 563-566 (1986).
[CrossRef]

Kol’a?r, M.

M. Kol’a?r, "New class of one-dimensional quasicrystals," Phys. Rev. B 47, 5489-5492 (1993).
[CrossRef]

Kubo, H.

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]

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]

Kuhl, J.

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]

Kumar, V.

M. C. Valsakumar and V. Kumar, "Diffraction from a quasi-crystalline chain," Pramana 26, 215-221 (1986).
[CrossRef]

Kwong, N. H.

LeBlanc, J.

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]

Ledermann, A.

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]

Levine, D.

D. Levine and P. J. Steinhardt, "Quasicrystals. I. Definition and structure," Phys. Rev. B 34, 596-616 (1986).
[CrossRef]

D. Levine and P. J. Steinhardt, "Quasicrystals: A New Class of Ordered Structures," Phys. Rev. Lett. 53, 2477-2480 (1984).
[CrossRef]

Lin, Z.

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]

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]

Lindberg, M.

M. Lindberg and S.W. Koch, "Effective Bloch Equations for Semiconductors," Phys. Rev. B 38, 3342 (1988).
[CrossRef]

Lisyansky, A. A.

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]

Liu, Y.

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]

Luck, J. M.

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]

Masselink, W. T.

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]

Matsui, T.

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]

Merlin, R.

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]

Michel, J.

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]

Migus, A.

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]

Morkoc, H.

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]

Mysyrowicz, A.

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]

Nahata, A.

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]

Negro, L. D.

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]

Nesvizhskii, A. I.

E. L. Ivchenko, A. I. Nesvizhskii, and S. Jorda, "Bragg reflection of light from quantum-well structures," Phys. Solid State 36, 1156-1161 (1994).

Ozin, G. A.

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]

Pereira, S.

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]

Peyghambarian, N.

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]

Pilozzi, L.

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]

Ploog, K.

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]

Poddubny, A. N.

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]

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]

Prineas, J. P.

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]

Richards, B. C.

Sipe, J. E.

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]

Smirl, A. L.

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]

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]

Sritrakool, W.

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]

Steinhardt, P. J.

D. Levine and P. J. Steinhardt, "Quasicrystals. I. Definition and structure," Phys. Rev. B 34, 596-616 (1986).
[CrossRef]

D. Levine and P. J. Steinhardt, "Quasicrystals: A New Class of Ordered Structures," Phys. Rev. Lett. 53, 2477-2480 (1984).
[CrossRef]

Stolfi, M.

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]

Stroucken, T.

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]

Suh, W.

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]

Sutherland, B.

M. Kohmoto, B. Sutherland, and K. Iguchi, "Localization of optics: Quasiperiodic media," Phys. Rev. Lett. 58, 2436-2438 (1987).
[CrossRef] [PubMed]

Sweet, J.

Toninelli, C.

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]

Valsakumar, M. C.

M. C. Valsakumar and V. Kumar, "Diffraction from a quasi-crystalline chain," Pramana 26, 215-221 (1986).
[CrossRef]

Vardeny, Z. V.

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]

von Freymann, G.

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]

Voronov, M. M.

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]

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]

Wang, Z.

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]

Wegener, M.

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]

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]

Wiersma, D. S.

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]

Yablonovitch, E.

E. Yablonovitch, "Inhibited Spontaneous Emission in Solid-State Physics and Electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

Yang, Z. S.

Yanik, M. F.

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]

Yi, Y.

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]

Yildirim, M.

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]

Zhao, J.

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]

Zhou, P.

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]

Appl. Phys. Lett. (3)

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]

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]

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]

J. Opt. Soc. Am. B (1)

J. Phys. A (2)

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]

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]

Nature (1)

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]

Nature Mater. (1)

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]

Opt. Express (1)

Phys. Rep. (1)

E. L. Albuquerque and M. G. Cottam, "Theory of elementary excitations in quasiperiodic structures," Phys. Rep. 376, 225-337 (2003).
[CrossRef]

Phys. Rev. B (8)

M. Kohmoto and J. R. Banavar, "Quasiperiodic lattice: Electronic properties, phonon properties, and diffusion," Phys. Rev. B 34, 563-566 (1986).
[CrossRef]

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]

M. Kol’a?r, "New class of one-dimensional quasicrystals," Phys. Rev. B 47, 5489-5492 (1993).
[CrossRef]

D. Levine and P. J. Steinhardt, "Quasicrystals. I. Definition and structure," Phys. Rev. B 34, 596-616 (1986).
[CrossRef]

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]

M. Lindberg and S.W. Koch, "Effective Bloch Equations for Semiconductors," Phys. Rev. B 38, 3342 (1988).
[CrossRef]

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]

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]

Phys. Rev. Lett. (8)

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]

E. Yablonovitch, "Inhibited Spontaneous Emission in Solid-State Physics and Electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987).
[CrossRef] [PubMed]

M. Kohmoto, B. Sutherland, and K. Iguchi, "Localization of optics: Quasiperiodic media," Phys. Rev. Lett. 58, 2436-2438 (1987).
[CrossRef] [PubMed]

D. Levine and P. J. Steinhardt, "Quasicrystals: A New Class of Ordered Structures," Phys. Rev. Lett. 53, 2477-2480 (1984).
[CrossRef]

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]

M. Y. Azbel, "Quantum Particle in One-Dimensional Potentials with Incommensurate Periods," Phys. Rev. Lett. 43, 1954-1957 (1979).
[CrossRef]

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]

Phys. Solid State (1)

E. L. Ivchenko, A. I. Nesvizhskii, and S. Jorda, "Bragg reflection of light from quantum-well structures," Phys. Solid State 36, 1156-1161 (1994).

Pramana (1)

M. C. Valsakumar and V. Kumar, "Diffraction from a quasi-crystalline chain," Pramana 26, 215-221 (1986).
[CrossRef]

Prog. Quantum Elec. (2)

M. Kira and S. W. Koch, "Many-body correlations and excitonic effects in semiconductor spectroscopy," Prog. Quantum Elec. 30, 155-196 (2006).
[CrossRef]

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]

Sov. Phys. JETP (1)

M. Y. Azbel, "Energy spectrum of a conduction electron in a magnetic field," Sov. Phys. JETP 19, 634-645 (1964).

Z. Phys. B: Condens Matter (1)

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[CrossRef]

Other (4)

E. L. Ivchenko, Optical spectroscopy of semiconductor nanostructures (Alpha Science International, Harrow, UK, 2005).

H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors (fifth ed., World Scientific Publishing, Singapore, 2009).

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C. Janot, Quasicrystals, A Primer (Clarendon Press, Oxford, UK, 1994).

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Figures (10)

Fig. 1.
Fig. 1.

Experimental setup

Fig. 2.
Fig. 2.

Linear fits (blue line) to measured data (shaded area) for (a) a single QW (FIB10) and (b) for 54 Fibonacci-spaced QWs (FIB13) using a frequency-dependent dephasing γ(ω) and identical fit parameters. For both samples, theory and experiment agree excellently.

Fig. 3.
Fig. 3.

Very good agreement between (a) computed and (b) experimental nonlinear reflectance is obtained for FIB13. Theory used densities n = 1 × 109 cm-2 (shaded area), n = 5 × 109 cm-2 (red line), n = 2 × 1010 cm-2 (blue line), and n = 5 × 1010 cm-2 (black line) while in the experiment the pump power was P = 76.6μW (shaded area),P = 871μW (red line), P = 3.7mW (blue line), P = 11.1mW (black line). An average spacing of D 0 = 0.5016λ is deduced from the fit parameters. The real part (c) and the imaginary part of the corresponding computed susceptibilities (d) show broadening and bleaching with elevated carrier densities.

Fig. 4.
Fig. 4.

The spectra of the experimentally applied pulses (shaded areas) are shown together with the computed absorption probability in frame (a) for low (blue line) and high (red line) excitation. The corresponding true absorption (b) is plotted for on-resonance and above-resonance excitation, showing that in both cases most of the absorption generates free carriers. Nonlinear reflectances obtained by above-band pumps are shown in frame (c). The spectra look very similar to those obtained by pumping resonantly.

Fig. 5.
Fig. 5.

Calculated reflectance spectra using the full QW susceptibility (shaded area) and with the real part (blue line), imaginary part (red line), or total susceptibility (black line) set to zero. Fine structures are introduced by the real part of the susceptibility while the imaginary part makes them partially vanish again.

Fig. 6.
Fig. 6.

Deviations of 54QW reflectance spectra from the fit spectrum (D 0 = 0.5016λ and ρ 0 = 1.643) are shown in dependence of (a) the average distance D and (b) the ratio of layer thicknesses ρ= L o/S o. A strong dependence on D is found while a certain robustnest against changes in ρ is observed.

Fig. 7.
Fig. 7.

For (a) the first Bragg resonance with (h,h′) = (F 1 ,F 0) = (1,0) as well as an average spacing D 0 =0.5016λ, and (b) the second Bragg resonance with (h,h′) = (F 2,F 1) = (1,1) as well as D = 0.8115λ, the reflectance is shown for different ratios L/S, while the respective average spacing is kept constant.

Fig. 8.
Fig. 8.

Structure factors for the Bragg resonances, (h,h′) = (F 1 ,F 0) = (1,0) plotted in red and (h,h′) = (F 2,F 1) = (1,1) plotted in blue.

Fig. 9.
Fig. 9.

Reflectance for 54QWs: (a) computations with parameters according to FIB13 (shaded area), FIB13 with ARC (red line), constant refractive index everywhere but same optical lengths as FIB13 (blue line), and optical-length periodic spacing (black line) with same average spacing D = 0.5016λ as FIB13. Obtaining the dip in all spectra suggests the dip to be caused by the uniform average spacing. (b) For D = 0.4992λ, there is no dip in the spectrum of periodically spaced 54QWs (black line) while there is one for Fibonacci-spaced QWs (area).

Fig. 10.
Fig. 10.

Reflectance close to the 1s-hh-resonance position as a function of QW number and energy for parameters according to FIB13.

Tables (2)

Tables Icon

Table 1. Comparison of spacers for periodic Bragg spacing (ρ = 1) and canonical Fibonacci spacing (ρ = τ) for the first three Bragg resonances, j = 1,2,3.

Tables Icon

Table 2. Layer widths and refractive indices used in the analysis of the samples. The sample FIB10 contains only “cap” and “buffer and substrate” layers while the sample FIB13 contains additional “large spacer” and “small spacer” layers, producing a Fibonacci-spaced chain of QWs. The layers in both samples can be categorized into seven types. The refractive indices of only four layer types (indicated by a *) out of these seven were changed to match theory with experiment. The barriers are Al0.3Ga0.7As, the spacers are Al0.04Ga0.96As, the QWs and adjuster are GaAs, and the AlAs/GaAs SL is a six times repetition of 2 nm AlAs followed by 2 nm GaAs.

Equations (19)

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z m = z 0 + m d ¯ + r ( m ) ,
r ( m ) = Δ { m t + φ } ,
S p = d ¯ + Δ / t and L p = d ¯ + Δ ( 1 / t 1 ) .
d ¯ = S p + ( L p S p ) / t .
N S N L = t 1 .
L σ ( L ) = M 1 M 2 M α + β ,
S σ ( S ) = N 1 N 2 N γ + δ .
f ( q ) = lim N f ( q , N ) , f ( q , N ) = 1 N m = 1 N e 2 i q z m .
f ( q ) = h , h = δ 2 q , G hh , f hh ,
G hh′ = 2 π d ¯ ( h + h′ t ) ,
f hh′ = sin S hh′ S hh′ e i θ hh′ , θ hh′ = ( z 0 + Δ { φ } ) G hh′ + S hh′ ,
S hh′ = π Δ h d ¯ + π h′ ( 1 + Δ t d ¯ ) = πh′ + Δ 2 G hh′ .
L LS , S L .
t = τ ( 5 + 1 ) / 2 1.618 ,
Δ = S p L p , φ = 0 , d = S p + ( L p S p ) / τ .
q ( ω 0 ) d ¯ = π ( h + h′ τ ) ,
χ ( ω ) = P ( ω ) ε 0 E ( ω ) , P ( ω ) = d cv Ү k P k ( ω ) ,
γ bg ( ω ) = γ bg exp ( ( h ¯ ω E x + Δ E cut ) / C ) + 1
ε = ω 1 , s , hh Δ ω 1 , s , hh + Δ R ( ω ) R 0 ( ω ) ω 1 , s , hh Δ ω 1 , s , hh + Δ R 0 ( ω ) .

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