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]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [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]

M. Kira and S. W. Koch, ”Many-body correlations and excitonic effects in semiconductor spectroscopy,” Prog. Quantum Elec. 30, 155–296 (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]

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 electro-magnetically induced transparency,” Phys. Rev. Lett. 93, 233903 (2004).
[Crossref] [PubMed]

E. L. Ivchenko, M. M. Voronov, M. V. Erementchouk, L. I. Deych, and A. A. Lisyansky, “Multiple-quantum-well-based photonic crystals with simple and compound elementary supercells,” Phys. Rev. B 70, 195106 (2004).
[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]

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, 1891961).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. Hübner, 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, H. Kubo, and M. Goda, “Self-similarity and scaling of wave function for binary quasiperiodic chains associated with quadratic irrationals,” Z. Phys. B: Condensed 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]

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 self-similar structures,” J. Phys. A 26, 1951–1999 (1993).
[Crossref]

M. Kolář, “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. Hulin, A. Mysyrowicz, A. Antonetti, A. Migus, W. T. Masselink, H. Morkoc, H. M. Gibbs, and N. Peygham-barian, “An ultrafast all optical gate with subpicosecond on and off response time,” Appl. Phys. Lett. 49, 7491961).751 (1986).
[Crossref]

D. Levine and P. J. Steinhardt, “Quasicrystals. I. Definition and structure,” Phys. Rev. B 34, 596–616 (1986).
[Crossref]

1985 (1)

R. Merlin, K. Bajema, R. Clarke, F. Y. Juang, and P. K. Bhattacharya, “Quasiperiodic GaAs-AlAs Heterostruc-tures,” 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. Peygham-barian, “An ultrafast all optical gate with subpicosecond on and off response time,” Appl. Phys. Lett. 49, 7491961).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 Heterostruc-tures,” 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 Heterostruc-tures,” 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 Heterostruc-tures,” 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-quantum-well-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-quantum-well-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 electro-magnetically induced transparency,” Phys. Rev. Lett. 93, 233903 (2004).
[Crossref] [PubMed]

Freymann, G. von

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]

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. Peygham-barian, “An ultrafast all optical gate with subpicosecond on and off response time,” Appl. Phys. Lett. 49, 7491961).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: Condensed 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 self-similar structures,” J. Phys. A 26, 1951–1999 (1993).
[Crossref]

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]

Haug, H.

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

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. Hübner, 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, 1891961).279 (1999).
[Crossref]

Hübner, M.

M. Hübner, 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]

Hulin, D.

D. Hulin, A. Mysyrowicz, A. Antonetti, A. Migus, W. T. Masselink, H. Morkoc, H. M. Gibbs, and N. Peygham-barian, “An ultrafast all optical gate with subpicosecond on and off response time,” Appl. Phys. Lett. 49, 7491961).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.

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]

E. L. Ivchenko, M. M. Voronov, M. V. Erementchouk, L. I. Deych, and A. A. Lisyansky, “Multiple-quantum-well-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).

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

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, 1891961).279 (1999).
[Crossref]

Janner, A.

J. M. Luck, C. Godreche, A. Janner, and T. Janssen, “The nature of the atomic surfaces of quasiperiodic self-similar structures,” J. Phys. A 26, 1951–1999 (1993).
[Crossref]

Janot, C.

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

Janssen, T.

J. M. Luck, C. Godreche, A. Janner, and T. Janssen, “The nature of the atomic surfaces of quasiperiodic self-similar 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 Heterostruc-tures,” 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, 155–296 (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, 1891961).279 (1999).
[Crossref]

Knorr, A.

M. Hübner, 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, 155–296 (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, 1891961).279 (1999).
[Crossref]

M. Hübner, 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]

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

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]

Kolár, M.

M. Kolář, “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: Condensed 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. Hübner, 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: Condensed 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-quantum-well-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 self-similar 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. Peygham-barian, “An ultrafast all optical gate with subpicosecond on and off response time,” Appl. Phys. Lett. 49, 7491961).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 Heterostruc-tures,” Phys. Rev. Lett. 55, 1768–1770 (1985).
[Crossref] [PubMed]

Merzbacher, E.

E. Merzbacher, Quantum Mechanics (first ed., Wiley, New York, 1961).

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. Peygham-barian, “An ultrafast all optical gate with subpicosecond on and off response time,” Appl. Phys. Lett. 49, 7491961).751 (1986).
[Crossref]

Morkoc, H.

D. Hulin, A. Mysyrowicz, A. Antonetti, A. Migus, W. T. Masselink, H. Morkoc, H. M. Gibbs, and N. Peygham-barian, “An ultrafast all optical gate with subpicosecond on and off response time,” Appl. Phys. Lett. 49, 7491961).751 (1986).
[Crossref]

Mysyrowicz, A.

D. Hulin, A. Mysyrowicz, A. Antonetti, A. Migus, W. T. Masselink, H. Morkoc, H. M. Gibbs, and N. Peygham-barian, “An ultrafast all optical gate with subpicosecond on and off response time,” Appl. Phys. Lett. 49, 7491961).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]

Peygham-barian, N.

D. Hulin, A. Mysyrowicz, A. Antonetti, A. Migus, W. T. Masselink, H. Morkoc, H. M. Gibbs, and N. Peygham-barian, “An ultrafast all optical gate with subpicosecond on and off response time,” Appl. Phys. Lett. 49, 7491961).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. Hübner, 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, 21441961).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. Hübner, 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 electro-magnetically 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]

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-quantum-well-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 electro-magnetically 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 electro-magnetically 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)

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]

D. Hulin, A. Mysyrowicz, A. Antonetti, A. Migus, W. T. Masselink, H. Morkoc, H. M. Gibbs, and N. Peygham-barian, “An ultrafast all optical gate with subpicosecond on and off response time,” Appl. Phys. Lett. 49, 7491961).751 (1986).
[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 self-similar 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]

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]

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. Kolář, “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-quantum-well-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]

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 electro-magnetically induced transparency,” Phys. Rev. Lett. 93, 233903 (2004).
[Crossref] [PubMed]

M. Hübner, 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]

D. Levine and P. J. Steinhardt, “Quasicrystals: A New Class of Ordered Structures,” Phys. Rev. Lett. 53, 2477–2480 (1984).
[Crossref]

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]

R. Merlin, K. Bajema, R. Clarke, F. Y. Juang, and P. K. Bhattacharya, “Quasiperiodic GaAs-AlAs Heterostruc-tures,” Phys. Rev. Lett. 55, 1768–1770 (1985).
[Crossref] [PubMed]

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

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, 155–296 (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, 1891961).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: Condensed Matter (1)

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: Condensed Matter 98, 111–118 (1995).
[Crossref]

Other (4)

E. Merzbacher, Quantum Mechanics (first ed., Wiley, New York, 1961).

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

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

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)

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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.

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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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