Abstract

In this paper, we perform a coated coherent potential approximation method to investigate the transport properties of disordered media consisting of two-layered dielectric spheres whose constituent layer is dispersive. The admixture of quantum dots to polymers to a certain concentration is used as dispersive medium. We find that the dispersive inclusion of the two-layered spheres influences the transport velocities greatly and a resonant scattering taking place in a dilute disordered medium is smeared out in the corresponding densely disordered medium where the correlation effects of multiple scattering are taken into account.

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  9. A. Ioffe and A. Regel, “Non-crystalline, amorphous and liquid electronic semiconductors,” Prog. Semiconduct. 4, 237 (1960).
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    [Crossref]
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    [Crossref]
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    [Crossref]
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2008 (1)

D. Hermann, M. Diem, S. F. Mingaleev, A. García-Martín, P. Wölfle, and K. Busch, “Photonic crystals with anomalous dispersion: Unconventional propagating modes in the photonic band gap,” Phys. Rev. B 77, 035112 (2008).
[Crossref]

2007 (1)

R. Sapienza, P. D. García, J. Bertolotti, M. D. Martín, A. Blanco, L. Viña, C. López, and D. S. Wiersma, “Observation of resonant behavior in the energy velocity of diffused light,” Phys. Rev. Lett. 99, 233902 (2007).
[Crossref]

2006 (2)

M. Störzer, C. M. Aegerter, and G. Maret, “Reduced transport velocity of multiply scattered light due to resonant scattering,” Phys. Rev. E 73, 065602 (2006).
[Crossref]

M. Störzer, P. Gross, C. M. Aegerter, and G. Maret, “Observation of the critical regime near anderson localization of light,” Phys. Rev. Lett. 96, 063904 (2006).
[Crossref] [PubMed]

2005 (1)

S. Richter, M. Steinhart, H. Hofmeister, M. Zacharias, U. Gsele, N. Gaponik, A. Eychmller, A. L. Rogach, J. H. Wendorff, S. L. Schweizer, A. von Rhein, and R. B. Wehrspohn, “Quantum dot emitters in two-dimensional photonic crystals of macroporous silicon,” Appl. Phys. Lett. 87, 142107 (2005).
[Crossref]

2004 (1)

2003 (1)

1996 (1)

K. Busch and C. M. Soukoulis, “Transport properties of random media: An energy-density cpa approach,” Phys. Rev. B 54, 893–899 (1996).
[Crossref]

1995 (1)

K. Busch and C. M. Soukoulis, “Transport properties of random media: A new effective medium theory,” Phys. Rev. Lett. 75, 3442–3445 (1995).
[Crossref] [PubMed]

1994 (1)

C. M. Soukoulis, S. Datta, and E. N. Economou, “Propagation of classical waves in random media,” Phys. Rev. B 49, 3800–3810 (1994).
[Crossref]

1993 (2)

1991 (2)

Z. S. Wu and Y. P. Wang, “Electromagnetic scattering for multilayered sphere: Recursive algorithms,” Radio Sci. 26(6), 1393 (1991).
[Crossref]

M. P. van Albada, B. A. van Tiggelen, A. Lagendijk, and A. Tip, “Speed of propagation of classical waves in strongly scattering media,” Phys. Rev. Lett. 66, 3132–3135 (1991).
[Crossref] [PubMed]

1989 (1)

J. M. Drake and A. Z. Genack, “Observation of nonclassical optical diffusion,” Phys. Rev. Lett. 63, 259–262 (1989).
[Crossref] [PubMed]

1987 (1)

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[Crossref] [PubMed]

1986 (1)

E. Akkermans, P. E. Wolf, and R. Maynard, “Coherent backscattering of light by disordered media: Analysis of the peak line shape,” Phys. Rev. Lett. 56, 1471–1474 (1986).
[Crossref] [PubMed]

1985 (3)

P. W. Anderson, “The question of classical localization: a theory of white paint?” Philos. Mag. B 52, 505–509 (1985).
[Crossref]

M. P. V. Albada and A. Lagendijk, “Observation of weak localization of light in a random medium,” Phys. Rev. Lett. 55, 2692–2695 (1985).
[Crossref] [PubMed]

P.-E. Wolf and G. Maret, “Weak localization and coherent backscattering of photons in disordered media,” Phys. Rev. Lett. 55, 2696–2699 (1985).
[Crossref] [PubMed]

1984 (1)

1969 (1)

J. V. Dave, “Scattering of electromagnetic radiation by a large, absorbing sphere,” IBM J. Res. Develop. 13, 302–313 (1969).
[Crossref]

1960 (1)

A. Ioffe and A. Regel, “Non-crystalline, amorphous and liquid electronic semiconductors,” Prog. Semiconduct. 4, 237 (1960).

1958 (1)

J. K. Percus and G. J. Yevick, “Analysis of classical statistical mechanics by means of collective coordinates,” Phys. Rev. 110, 1–13 (1958).
[Crossref]

1955 (1)

E. P. Wigner, “Lower limit for the energy derivative of the scattering phase shift,” Phys. Rev. 98, 145–147 (1955).
[Crossref]

Aegerter, C. M.

M. Störzer, P. Gross, C. M. Aegerter, and G. Maret, “Observation of the critical regime near anderson localization of light,” Phys. Rev. Lett. 96, 063904 (2006).
[Crossref] [PubMed]

M. Störzer, C. M. Aegerter, and G. Maret, “Reduced transport velocity of multiply scattered light due to resonant scattering,” Phys. Rev. E 73, 065602 (2006).
[Crossref]

Akkermans, E.

E. Akkermans, P. E. Wolf, and R. Maynard, “Coherent backscattering of light by disordered media: Analysis of the peak line shape,” Phys. Rev. Lett. 56, 1471–1474 (1986).
[Crossref] [PubMed]

E. Akkermans and G. Montambaux, Mesoscopic Physics of Electrons and Photons (Cambridge University Press, 2007).
[Crossref]

Albada, M. P. V.

M. P. V. Albada and A. Lagendijk, “Observation of weak localization of light in a random medium,” Phys. Rev. Lett. 55, 2692–2695 (1985).
[Crossref] [PubMed]

Anderson, P. W.

P. W. Anderson, “The question of classical localization: a theory of white paint?” Philos. Mag. B 52, 505–509 (1985).
[Crossref]

P. W. Anderson, “Absence of diffusion in certain random lattices,” Phys. Rev.109, 1492–1505 (1958).
[Crossref]

Barber, P. W.

Bertolotti, J.

R. Sapienza, P. D. García, J. Bertolotti, M. D. Martín, A. Blanco, L. Viña, C. López, and D. S. Wiersma, “Observation of resonant behavior in the energy velocity of diffused light,” Phys. Rev. Lett. 99, 233902 (2007).
[Crossref]

Blanco, A.

R. Sapienza, P. D. García, J. Bertolotti, M. D. Martín, A. Blanco, L. Viña, C. López, and D. S. Wiersma, “Observation of resonant behavior in the energy velocity of diffused light,” Phys. Rev. Lett. 99, 233902 (2007).
[Crossref]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, Inc, 1998).
[Crossref]

Busch, K.

D. Hermann, M. Diem, S. F. Mingaleev, A. García-Martín, P. Wölfle, and K. Busch, “Photonic crystals with anomalous dispersion: Unconventional propagating modes in the photonic band gap,” Phys. Rev. B 77, 035112 (2008).
[Crossref]

K. Busch and C. M. Soukoulis, “Transport properties of random media: An energy-density cpa approach,” Phys. Rev. B 54, 893–899 (1996).
[Crossref]

K. Busch and C. M. Soukoulis, “Transport properties of random media: A new effective medium theory,” Phys. Rev. Lett. 75, 3442–3445 (1995).
[Crossref] [PubMed]

Conwell, P. R.

Datta, S.

C. M. Soukoulis, S. Datta, and E. N. Economou, “Propagation of classical waves in random media,” Phys. Rev. B 49, 3800–3810 (1994).
[Crossref]

Dave, J. V.

J. V. Dave, “Scattering of electromagnetic radiation by a large, absorbing sphere,” IBM J. Res. Develop. 13, 302–313 (1969).
[Crossref]

Diem, M.

D. Hermann, M. Diem, S. F. Mingaleev, A. García-Martín, P. Wölfle, and K. Busch, “Photonic crystals with anomalous dispersion: Unconventional propagating modes in the photonic band gap,” Phys. Rev. B 77, 035112 (2008).
[Crossref]

Drake, J. M.

J. M. Drake and A. Z. Genack, “Observation of nonclassical optical diffusion,” Phys. Rev. Lett. 63, 259–262 (1989).
[Crossref] [PubMed]

Du, H.

Economou, E. N.

C. M. Soukoulis, S. Datta, and E. N. Economou, “Propagation of classical waves in random media,” Phys. Rev. B 49, 3800–3810 (1994).
[Crossref]

Eychmller, A.

S. Richter, M. Steinhart, H. Hofmeister, M. Zacharias, U. Gsele, N. Gaponik, A. Eychmller, A. L. Rogach, J. H. Wendorff, S. L. Schweizer, A. von Rhein, and R. B. Wehrspohn, “Quantum dot emitters in two-dimensional photonic crystals of macroporous silicon,” Appl. Phys. Lett. 87, 142107 (2005).
[Crossref]

Gaponik, N.

S. Richter, M. Steinhart, H. Hofmeister, M. Zacharias, U. Gsele, N. Gaponik, A. Eychmller, A. L. Rogach, J. H. Wendorff, S. L. Schweizer, A. von Rhein, and R. B. Wehrspohn, “Quantum dot emitters in two-dimensional photonic crystals of macroporous silicon,” Appl. Phys. Lett. 87, 142107 (2005).
[Crossref]

García, P. D.

R. Sapienza, P. D. García, J. Bertolotti, M. D. Martín, A. Blanco, L. Viña, C. López, and D. S. Wiersma, “Observation of resonant behavior in the energy velocity of diffused light,” Phys. Rev. Lett. 99, 233902 (2007).
[Crossref]

García-Martín, A.

D. Hermann, M. Diem, S. F. Mingaleev, A. García-Martín, P. Wölfle, and K. Busch, “Photonic crystals with anomalous dispersion: Unconventional propagating modes in the photonic band gap,” Phys. Rev. B 77, 035112 (2008).
[Crossref]

Genack, A. Z.

J. M. Drake and A. Z. Genack, “Observation of nonclassical optical diffusion,” Phys. Rev. Lett. 63, 259–262 (1989).
[Crossref] [PubMed]

Gross, P.

M. Störzer, P. Gross, C. M. Aegerter, and G. Maret, “Observation of the critical regime near anderson localization of light,” Phys. Rev. Lett. 96, 063904 (2006).
[Crossref] [PubMed]

Gsele, U.

S. Richter, M. Steinhart, H. Hofmeister, M. Zacharias, U. Gsele, N. Gaponik, A. Eychmller, A. L. Rogach, J. H. Wendorff, S. L. Schweizer, A. von Rhein, and R. B. Wehrspohn, “Quantum dot emitters in two-dimensional photonic crystals of macroporous silicon,” Appl. Phys. Lett. 87, 142107 (2005).
[Crossref]

Hermann, D.

D. Hermann, M. Diem, S. F. Mingaleev, A. García-Martín, P. Wölfle, and K. Busch, “Photonic crystals with anomalous dispersion: Unconventional propagating modes in the photonic band gap,” Phys. Rev. B 77, 035112 (2008).
[Crossref]

Hofmeister, H.

S. Richter, M. Steinhart, H. Hofmeister, M. Zacharias, U. Gsele, N. Gaponik, A. Eychmller, A. L. Rogach, J. H. Wendorff, S. L. Schweizer, A. von Rhein, and R. B. Wehrspohn, “Quantum dot emitters in two-dimensional photonic crystals of macroporous silicon,” Appl. Phys. Lett. 87, 142107 (2005).
[Crossref]

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, Inc, 1998).
[Crossref]

Iglesias, J. E.

Ioffe, A.

A. Ioffe and A. Regel, “Non-crystalline, amorphous and liquid electronic semiconductors,” Prog. Semiconduct. 4, 237 (1960).

John, S.

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[Crossref] [PubMed]

Lagendijk, A.

B. A. van Tiggelen and A. Lagendijk, “Rigorous Treatment of the Speed of Diffusing Classical Waves,” Europhys. Lett. 23, 311–316 (1993).
[Crossref]

M. P. van Albada, B. A. van Tiggelen, A. Lagendijk, and A. Tip, “Speed of propagation of classical waves in strongly scattering media,” Phys. Rev. Lett. 66, 3132–3135 (1991).
[Crossref] [PubMed]

M. P. V. Albada and A. Lagendijk, “Observation of weak localization of light in a random medium,” Phys. Rev. Lett. 55, 2692–2695 (1985).
[Crossref] [PubMed]

Lenke, R.

R. Lenke and G. Maret, “Multiple scattering of light: Coherent backscattering and transmission,” in Scattering in Polymeric and Colloidal Systems, W. Brown and K. Mortensen, eds. (Gordon and Breach Science Publishers, 2000).

López, C.

R. Sapienza, P. D. García, J. Bertolotti, M. D. Martín, A. Blanco, L. Viña, C. López, and D. S. Wiersma, “Observation of resonant behavior in the energy velocity of diffused light,” Phys. Rev. Lett. 99, 233902 (2007).
[Crossref]

Maret, G.

M. Störzer, P. Gross, C. M. Aegerter, and G. Maret, “Observation of the critical regime near anderson localization of light,” Phys. Rev. Lett. 96, 063904 (2006).
[Crossref] [PubMed]

M. Störzer, C. M. Aegerter, and G. Maret, “Reduced transport velocity of multiply scattered light due to resonant scattering,” Phys. Rev. E 73, 065602 (2006).
[Crossref]

P.-E. Wolf and G. Maret, “Weak localization and coherent backscattering of photons in disordered media,” Phys. Rev. Lett. 55, 2696–2699 (1985).
[Crossref] [PubMed]

R. Lenke and G. Maret, “Multiple scattering of light: Coherent backscattering and transmission,” in Scattering in Polymeric and Colloidal Systems, W. Brown and K. Mortensen, eds. (Gordon and Breach Science Publishers, 2000).

Martín, M. D.

R. Sapienza, P. D. García, J. Bertolotti, M. D. Martín, A. Blanco, L. Viña, C. López, and D. S. Wiersma, “Observation of resonant behavior in the energy velocity of diffused light,” Phys. Rev. Lett. 99, 233902 (2007).
[Crossref]

Maynard, R.

E. Akkermans, P. E. Wolf, and R. Maynard, “Coherent backscattering of light by disordered media: Analysis of the peak line shape,” Phys. Rev. Lett. 56, 1471–1474 (1986).
[Crossref] [PubMed]

Mingaleev, S. F.

D. Hermann, M. Diem, S. F. Mingaleev, A. García-Martín, P. Wölfle, and K. Busch, “Photonic crystals with anomalous dispersion: Unconventional propagating modes in the photonic band gap,” Phys. Rev. B 77, 035112 (2008).
[Crossref]

Montambaux, G.

E. Akkermans and G. Montambaux, Mesoscopic Physics of Electrons and Photons (Cambridge University Press, 2007).
[Crossref]

Pecharroman, C.

Percus, J. K.

J. K. Percus and G. J. Yevick, “Analysis of classical statistical mechanics by means of collective coordinates,” Phys. Rev. 110, 1–13 (1958).
[Crossref]

Regel, A.

A. Ioffe and A. Regel, “Non-crystalline, amorphous and liquid electronic semiconductors,” Prog. Semiconduct. 4, 237 (1960).

Richter, S.

S. Richter, M. Steinhart, H. Hofmeister, M. Zacharias, U. Gsele, N. Gaponik, A. Eychmller, A. L. Rogach, J. H. Wendorff, S. L. Schweizer, A. von Rhein, and R. B. Wehrspohn, “Quantum dot emitters in two-dimensional photonic crystals of macroporous silicon,” Appl. Phys. Lett. 87, 142107 (2005).
[Crossref]

Rogach, A. L.

S. Richter, M. Steinhart, H. Hofmeister, M. Zacharias, U. Gsele, N. Gaponik, A. Eychmller, A. L. Rogach, J. H. Wendorff, S. L. Schweizer, A. von Rhein, and R. B. Wehrspohn, “Quantum dot emitters in two-dimensional photonic crystals of macroporous silicon,” Appl. Phys. Lett. 87, 142107 (2005).
[Crossref]

Rushforth, C. K.

Sapienza, R.

R. Sapienza, P. D. García, J. Bertolotti, M. D. Martín, A. Blanco, L. Viña, C. López, and D. S. Wiersma, “Observation of resonant behavior in the energy velocity of diffused light,” Phys. Rev. Lett. 99, 233902 (2007).
[Crossref]

Schweizer, S. L.

S. Richter, M. Steinhart, H. Hofmeister, M. Zacharias, U. Gsele, N. Gaponik, A. Eychmller, A. L. Rogach, J. H. Wendorff, S. L. Schweizer, A. von Rhein, and R. B. Wehrspohn, “Quantum dot emitters in two-dimensional photonic crystals of macroporous silicon,” Appl. Phys. Lett. 87, 142107 (2005).
[Crossref]

Sheng, P.

P. Sheng, Introduction to Wave Scattering, Localization, and Mesoscopic Phenomena (Springer, Heidelberger, 2006), 2nd ed.

Soukoulis, C. M.

K. Busch and C. M. Soukoulis, “Transport properties of random media: An energy-density cpa approach,” Phys. Rev. B 54, 893–899 (1996).
[Crossref]

K. Busch and C. M. Soukoulis, “Transport properties of random media: A new effective medium theory,” Phys. Rev. Lett. 75, 3442–3445 (1995).
[Crossref] [PubMed]

C. M. Soukoulis, S. Datta, and E. N. Economou, “Propagation of classical waves in random media,” Phys. Rev. B 49, 3800–3810 (1994).
[Crossref]

Steinhart, M.

S. Richter, M. Steinhart, H. Hofmeister, M. Zacharias, U. Gsele, N. Gaponik, A. Eychmller, A. L. Rogach, J. H. Wendorff, S. L. Schweizer, A. von Rhein, and R. B. Wehrspohn, “Quantum dot emitters in two-dimensional photonic crystals of macroporous silicon,” Appl. Phys. Lett. 87, 142107 (2005).
[Crossref]

Störzer, M.

M. Störzer, P. Gross, C. M. Aegerter, and G. Maret, “Observation of the critical regime near anderson localization of light,” Phys. Rev. Lett. 96, 063904 (2006).
[Crossref] [PubMed]

M. Störzer, C. M. Aegerter, and G. Maret, “Reduced transport velocity of multiply scattered light due to resonant scattering,” Phys. Rev. E 73, 065602 (2006).
[Crossref]

Tip, A.

M. P. van Albada, B. A. van Tiggelen, A. Lagendijk, and A. Tip, “Speed of propagation of classical waves in strongly scattering media,” Phys. Rev. Lett. 66, 3132–3135 (1991).
[Crossref] [PubMed]

Tweer, R.

R. Tweer, “Vielfachstreuung von licht in systemen dicht gepackter mie-streuer: Auf dem weg zur anderson-lokalisierung?” Ph.D. thesis (2002).

van Albada, M. P.

M. P. van Albada, B. A. van Tiggelen, A. Lagendijk, and A. Tip, “Speed of propagation of classical waves in strongly scattering media,” Phys. Rev. Lett. 66, 3132–3135 (1991).
[Crossref] [PubMed]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover Publications, Inc. New York, 1981).

van Tiggelen, B. A.

B. A. van Tiggelen and A. Lagendijk, “Rigorous Treatment of the Speed of Diffusing Classical Waves,” Europhys. Lett. 23, 311–316 (1993).
[Crossref]

M. P. van Albada, B. A. van Tiggelen, A. Lagendijk, and A. Tip, “Speed of propagation of classical waves in strongly scattering media,” Phys. Rev. Lett. 66, 3132–3135 (1991).
[Crossref] [PubMed]

Viña, L.

R. Sapienza, P. D. García, J. Bertolotti, M. D. Martín, A. Blanco, L. Viña, C. López, and D. S. Wiersma, “Observation of resonant behavior in the energy velocity of diffused light,” Phys. Rev. Lett. 99, 233902 (2007).
[Crossref]

von Rhein, A.

S. Richter, M. Steinhart, H. Hofmeister, M. Zacharias, U. Gsele, N. Gaponik, A. Eychmller, A. L. Rogach, J. H. Wendorff, S. L. Schweizer, A. von Rhein, and R. B. Wehrspohn, “Quantum dot emitters in two-dimensional photonic crystals of macroporous silicon,” Appl. Phys. Lett. 87, 142107 (2005).
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[Crossref]

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S. Richter, M. Steinhart, H. Hofmeister, M. Zacharias, U. Gsele, N. Gaponik, A. Eychmller, A. L. Rogach, J. H. Wendorff, S. L. Schweizer, A. von Rhein, and R. B. Wehrspohn, “Quantum dot emitters in two-dimensional photonic crystals of macroporous silicon,” Appl. Phys. Lett. 87, 142107 (2005).
[Crossref]

Wendorff, J. H.

S. Richter, M. Steinhart, H. Hofmeister, M. Zacharias, U. Gsele, N. Gaponik, A. Eychmller, A. L. Rogach, J. H. Wendorff, S. L. Schweizer, A. von Rhein, and R. B. Wehrspohn, “Quantum dot emitters in two-dimensional photonic crystals of macroporous silicon,” Appl. Phys. Lett. 87, 142107 (2005).
[Crossref]

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R. Sapienza, P. D. García, J. Bertolotti, M. D. Martín, A. Blanco, L. Viña, C. López, and D. S. Wiersma, “Observation of resonant behavior in the energy velocity of diffused light,” Phys. Rev. Lett. 99, 233902 (2007).
[Crossref]

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E. P. Wigner, “Lower limit for the energy derivative of the scattering phase shift,” Phys. Rev. 98, 145–147 (1955).
[Crossref]

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W. J. Wiscombe, “Mie scattering calculations: Advances in technique and fast, vector-speed computer codes,” Tech. rep., NCAR Technical Note NCAR/TN-140+STR (National Center for Atmospheric Research, Boulder, Colo. 80307) (1979).

Wolf, P. E.

E. Akkermans, P. E. Wolf, and R. Maynard, “Coherent backscattering of light by disordered media: Analysis of the peak line shape,” Phys. Rev. Lett. 56, 1471–1474 (1986).
[Crossref] [PubMed]

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P.-E. Wolf and G. Maret, “Weak localization and coherent backscattering of photons in disordered media,” Phys. Rev. Lett. 55, 2696–2699 (1985).
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D. Hermann, M. Diem, S. F. Mingaleev, A. García-Martín, P. Wölfle, and K. Busch, “Photonic crystals with anomalous dispersion: Unconventional propagating modes in the photonic band gap,” Phys. Rev. B 77, 035112 (2008).
[Crossref]

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Z. S. Wu and Y. P. Wang, “Electromagnetic scattering for multilayered sphere: Recursive algorithms,” Radio Sci. 26(6), 1393 (1991).
[Crossref]

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[Crossref]

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S. Richter, M. Steinhart, H. Hofmeister, M. Zacharias, U. Gsele, N. Gaponik, A. Eychmller, A. L. Rogach, J. H. Wendorff, S. L. Schweizer, A. von Rhein, and R. B. Wehrspohn, “Quantum dot emitters in two-dimensional photonic crystals of macroporous silicon,” Appl. Phys. Lett. 87, 142107 (2005).
[Crossref]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

S. Richter, M. Steinhart, H. Hofmeister, M. Zacharias, U. Gsele, N. Gaponik, A. Eychmller, A. L. Rogach, J. H. Wendorff, S. L. Schweizer, A. von Rhein, and R. B. Wehrspohn, “Quantum dot emitters in two-dimensional photonic crystals of macroporous silicon,” Appl. Phys. Lett. 87, 142107 (2005).
[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

Phys. Rev. (2)

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[Crossref]

J. K. Percus and G. J. Yevick, “Analysis of classical statistical mechanics by means of collective coordinates,” Phys. Rev. 110, 1–13 (1958).
[Crossref]

Phys. Rev. B (3)

K. Busch and C. M. Soukoulis, “Transport properties of random media: An energy-density cpa approach,” Phys. Rev. B 54, 893–899 (1996).
[Crossref]

D. Hermann, M. Diem, S. F. Mingaleev, A. García-Martín, P. Wölfle, and K. Busch, “Photonic crystals with anomalous dispersion: Unconventional propagating modes in the photonic band gap,” Phys. Rev. B 77, 035112 (2008).
[Crossref]

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[Crossref]

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M. Störzer, C. M. Aegerter, and G. Maret, “Reduced transport velocity of multiply scattered light due to resonant scattering,” Phys. Rev. E 73, 065602 (2006).
[Crossref]

Phys. Rev. Lett. (9)

R. Sapienza, P. D. García, J. Bertolotti, M. D. Martín, A. Blanco, L. Viña, C. López, and D. S. Wiersma, “Observation of resonant behavior in the energy velocity of diffused light,” Phys. Rev. Lett. 99, 233902 (2007).
[Crossref]

M. P. van Albada, B. A. van Tiggelen, A. Lagendijk, and A. Tip, “Speed of propagation of classical waves in strongly scattering media,” Phys. Rev. Lett. 66, 3132–3135 (1991).
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[Crossref] [PubMed]

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[Crossref] [PubMed]

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[Crossref] [PubMed]

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[Crossref] [PubMed]

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[Crossref]

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Figures (6)

Fig. 1
Fig. 1

Effective dielectric constants for the dispersive material constructed by polymer doped with quantum dots for three different concentrations η = 0.001, 0.005, 0.01, respectively. r is the radius of the mantel layer.

Fig. 2
Fig. 2

Scheme of the coated CPA as an effective medium theory. Different colorful spheres in (a) indicate different materials with different refractive indices. The effective dielectric constant ɛ̄ is calculated by the effective medium theory, Ψl represents the vectorial field in lth layer, and Ψi represents the vectorial incident field. The dashed volume in (b) indicates the averaged counterpart of the coated spheres.

Fig. 3
Fig. 3

Calculated scattering efficiency factors for two-layered spheres whose core layers are dispersive. The dielectric constant of the core layer, i.e ɛcore is determined by incident wavelengths and the concentration of QDs (a) η = 0, (b) η = 0.001, (c) η = 0.005 and (d) η = 0.01 respectively.

Fig. 4
Fig. 4

Numerical comparisons between the Qscas calculated by the coated CPA method and those calculated by the Maxwell-Garnett theory.

Fig. 5
Fig. 5

Calculated scattering efficiency factors Qsca for two-layered spheres under considerations and transport velocities of electromagnetic energy for optical disordered medium composed of the two-layered spheres with f = 60%. The radia of the core layer are r1 = 0.5r2 in (a) and (c), r1 = 0.9r2 in (b) and (d), respectively. Numerical results for systems with different values of the concentration η, i.e η = 0, η = 0.001, η = 0.005 and η = 0.01 are indicated by the blue, red, black and green lines respectively.

Fig. 6
Fig. 6

(a) Calculated scattering efficiency factor for a single scattering of a two-layered sphere with r1 = 0.5r2 and η = 0.01. Figs. (b–d) show the transport velocities of electromagnetic energy for disordered media composed of two-layered spheres with r1 = 0.5r2, η = 0.01 and volume fractions f = 1%, 30%, 50%, respectively.

Equations (28)

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ɛ c o r e = ɛ m ( 1 + 3 η β ( ω ) 1 η β ( ω ) )
ɛ Q D = 1 + ω p 2 ω 0 2 ω 2 i γ ω
0 R c d 3 r ρ E ( 1 ) ( r ) = 0 R c d 3 r ρ E ( 2 ) ( r )
ρ E ( r ) = 1 2 [ ɛ ( r ) | E ( r ) | 2 + μ | H ( r ) | 2 ]
ɛ ¯ = ( 1 f ) ɛ 3 + f S 1 1 f + f S 2
S 1 = 3 ɛ 3 ɛ 2 ( ɛ 1 ( 1 + 2 ξ ) + 2 ɛ 2 ( 1 ξ ) ) / Θ
S 2 = 3 ɛ 3 ( ɛ 1 ( 1 ξ ) + ɛ 2 ( 2 + ξ ) ) / Θ
Θ = ( ɛ 1 + 2 ɛ 2 ) ( ɛ 2 + 2 ɛ 3 ) + 2 ξ ( ɛ 2 ɛ 3 ) ( ɛ 1 ɛ 2 )
E 1 = n = 1 E n ( c n M o 1 n ( 1 ) i d n N e 1 n ( 1 ) )
H 1 = k 1 ω μ 1 n = 1 E n ( d n M e 1 n ( 1 ) + i c n N o 1 n ( 1 ) )
E n = E 0 i n 2 n + 1 n ( n + 1 )
E l = n = 1 E n ( f n ( l ) M o 1 n ( 1 ) i g n ( l ) N e 1 n ( 1 ) + v n ( l ) M o 1 n ( 2 ) i w n ( l ) N e 1 n ( 2 ) )
H l = k l ω μ l n = 1 E n ( g n ( l ) M e 1 n ( 1 ) + i f n ( l ) N o 1 n ( 1 ) + w n ( l ) M e 1 n ( 2 ) + i v n ( l ) N o 1 n ( 2 ) )
E ( 1 ) = E 1 ( 1 ) + E 2 ( 1 ) + E 3 ( 1 )
E 1 ( 1 ) = 1 2 ω 2 c 2 ɛ 1 n = 1 ( | c n | 2 + | d n | 2 ) 1 k 1 3 0 k 1 r 1 ρ 2 d ρ W n ( j n , j n ; ρ )
W n ( z n , z n ¯ ; r ) = ( 2 n + 1 ) z n ( r ) z n ¯ ( r ) + ( n + 1 ) z n 1 ( r ) z n 1 ¯ ( r ) + n z n + 1 ( r ) z n + 1 ¯ ( r )
E 2 ( 1 ) = 1 2 ω 2 c 2 ɛ 2 n = 1 1 k 2 3 k 2 r 1 k 2 r 2 ρ 2 d ρ [ ( | f n ( 2 ) | 2 + | g n ( 2 ) | 2 ) W n ( j n , j n ; ρ ) + ( | v n ( 2 ) | 2 + | w n ( 2 ) | 2 ) W n ( n n , n n ; ρ ) + 2 ( | f n ( 2 ) v n ( 2 ) | + | g n ( 2 ) w n ( 2 ) | ) W n ( j n , n n ; ρ ) ]
f n ( 2 ) = ψ n ( m 1 x ) χ n ( m 2 x ) [ G 1 n ( m 1 x ) ( m 2 / m 1 ) G 2 n ( m 2 x ) ] c n ϕ n ( m 1 , m 2 ; x ) c n
v n ( 2 ) = ψ n ( m 1 x ) ψ n ( m 2 x ) [ G 1 n ( m 1 x ) ( m 2 / m 1 ) G 1 n ( m 2 x ) ] c n ζ n ( m 1 , m 2 ; x ) c n
g n ( 2 ) = ψ n ( m 1 x ) χ n ( m 2 x ) [ ( m 2 / m 1 ) G 1 n ( m 1 x ) G 2 n ( m 2 x ) ] d n γ n ( m 1 , m 2 ; x ) d n
w n ( 2 ) = ψ n ( m 1 x ) ψ n ( m 2 x ) [ ( m 2 / m 1 ) G 1 n ( m 1 x ) G 1 n ( m 2 x ) ] d n η n ( m 1 , m 2 ; x ) d n
G 1 n ( m 1 x ) = ψ n ( m 1 x ) / ψ n ( m 1 x ) , G 2 n ( m 1 x ) = χ n ( m 1 x ) / χ n ( m 1 x )
E 3 ( 1 ) = 1 2 ω 2 c 3 ɛ 3 n = 1 1 k 3 3 k 3 r 2 k 3 R c ρ 2 d ρ [ ( | f n ( 3 ) | 2 + | g n ( 3 ) | 2 ) W n ( j n , j n ; ρ ) + ( | v n ( 3 ) | 2 + | w n ( 3 ) | 2 ) W n ( n n , n n ; ρ ) + 2 ( | f n ( 3 ) v n ( 3 ) | + | g n ( 3 ) w n ( 3 ) | ) W n ( j n , n n ; ρ ) ]
( f n ( 3 ) v n ( 3 ) g n ( 3 ) w n ( 3 ) ) = ( ϕ n ( m 2 , m 3 ; y ) ς n ( m 2 , m 3 ; y ) 0 0 ζ n ( m 2 , m 3 ; y ) ϑ n ( m 2 , m 3 ; y ) 0 0 0 0 γ n ( m 2 , m 3 ; y ) ϖ n ( m 2 , m 3 ; y ) 0 0 η n ( m 2 , m 3 ; y ) ρ n ( m 2 , m 3 ; y ) ) ( f n ( 2 ) v n ( 2 ) g n ( 2 ) w n ( 2 ) )
ς n ( m 2 , m 3 ; y ) χ n ( m 2 y ) χ n ( m 3 y ) [ ( m 3 / m 2 ) G 2 n ( m 3 y ) G 2 n ( m 2 y ) ]
ϑ n ( m 2 , m 3 ; y ) χ n ( m 2 y ) ψ n ( m 3 y ) [ ( m 3 / m 2 ) G 1 n ( m 3 y ) G 2 n ( m 2 y ) ]
ϖ n ( m 2 , m 3 ; y ) χ n ( m 2 y ) χ n ( m 3 y ) [ G 2 n ( m 3 y ) ( m 3 / m 2 ) G 2 n ( m 2 y ) ]
ρ n ( m 2 , m 3 ; y ) χ n ( m 2 y ) ψ n ( m 3 y ) [ G 1 n ( m 3 y ) ( m 3 / m 2 ) G 2 n ( m 2 y ) ] )

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