Abstract

Nanocomposites with tailored optical properties can provide a new degree of freedom for optical design. However, despite their potential these materials remain unused in bulk optical applications. Here we investigate the conditions under which they can be used for such applications using Mie theory, effective medium theories, and numerical simulations based on the finite element method. We show that due to scattering different effective medium regimes have to be distinguished, and that bulk materials can only be realized in a specific parameter range. Our analysis also enables us to quantify the range of validity of different effective medium theories, and identify design rules on how the material’s free parameters should be adjusted for specific applications.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]

2017 (1)

G. Albrecht, M. Hentschel, S. Kaiser, and H. Giessen, “Hybrid Organic-Plasmonic Nanoantennas with Enhanced Third-Harmonic Generation,” ACS Omega 2(6), 2577–2582 (2017).
[Crossref]

2016 (3)

T. Gissibl, S. Thiele, A. Herkommer, and H. Giessen, “Two-photon direct laser writing of ultracompact multi-lens objectives,” Nat. Photonics 10(8), 554–560 (2016).
[Crossref]

M. Decker and I. Staude, “Resonant dielectric nanostructures: a low-loss platform for functional nanophotonics,” J. Opt. 18(10), 103001 (2016).
[Crossref]

V. A. Markel, “Introduction to the Maxwell Garnett approximation: tutorial,” J. Opt. Soc. Am. A 33(7), 1244–1256 (2016).
[Crossref] [PubMed]

2015 (1)

M. V. Rybin, D. S. Filonov, K. B. Samusev, P. A. Belov, Y. S. Kivshar, and M. F. Limonov, “Phase diagram for the transition from photonic crystals to dielectric metamaterials,” Nat. Commun. 6(1), 10102 (2015).
[Crossref] [PubMed]

2013 (1)

P. Moitra, Y. Yang, Z. Anderson, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nat. Photonics 7(10), 791–795 (2013).
[Crossref]

2012 (1)

A. I. Kuznetsov, A. E. Miroshnichenko, Y. H. Fu, J. Zhang, and B. Luk’yanchuk, “Magnetic light,” Sci. Rep. 2(1), 492 (2012).
[Crossref] [PubMed]

2011 (1)

P. Tao, Y. Li, A. Rungta, A. Viswanath, J. Gao, B. C. Benicewicz, R. W. Siegel, and L. S. Schadler, “TiO2 nanocomposites with high refractive index and transparency,” J. Mater. Chem. 21(46), 18623–18629 (2011).
[Crossref]

2010 (2)

Y. He and T. Zeng, “First-principles study and model of dielectric functions of silver nanoparticles,” J. Phys. Chem. C 114(42), 18023–18030 (2010).
[Crossref]

P. Hartmann, R. Jedamzik, S. Reichel, and B. Schreder, “Optical glass and glass ceramic historical aspects and recent developments: a Schott view,” Appl. Opt. 49(16), D157–D176 (2010).
[Crossref]

2009 (2)

C. Lü and B. Yang, “High refractive index organic–inorganic nanocomposites: design, synthesis and application,” J. Mater. Chem. 19(19), 2884–2901 (2009).
[Crossref]

J. Liu and M. Ueda, “High refractive index polymers: fundamental research and practical applications,” J. Mater. Chem. 19(47), 8907–8919 (2009).
[Crossref]

2008 (3)

M. S. Rill, C. Plet, M. Thiel, I. Staude, G. von Freymann, S. Linden, and M. Wegener, “Photonic metamaterials by direct laser writing and silver chemical vapour deposition,” Nat. Mater. 7(7), 543–546 (2008).
[Crossref] [PubMed]

J. Petschulat, C. Menzel, A. Chipouline, C. Rockstuhl, A. Tünnermann, F. Lederer, and T. Pertsch, “Multipole approach to metamaterials,” Phys. Rev. A 78(4), 043811 (2008).
[Crossref]

C. Rockstuhl, T. Paul, F. Lederer, T. Pertsch, T. Zentgraf, T. P. Meyrath, and H. Giessen, “Transition from thin-film to bulk properties of metamaterials,” Phys. Rev. B Condens. Matter Mater. Phys. 77(3), 035126 (2008).
[Crossref]

2007 (2)

J. L. H. Chau, Y.-M. Lin, A.-K. Li, W.-F. Su, K.-S. Chang, S. L.-C. Hsu, and T.-L. Li, “Transparent high refractive index nanocomposite thin films,” Mater. Lett. 61(14-15), 2908–2910 (2007).
[Crossref]

S. Kubo, A. Diaz, Y. Tang, T. S. Mayer, I. C. Khoo, and T. E. Mallouk, “Tunability of the refractive index of gold nanoparticle dispersions,” Nano Lett. 7(11), 3418–3423 (2007).
[Crossref] [PubMed]

2006 (1)

M. Rong, M. Zhang, and W. Ruan, “Surface modification of nanoscale fillers for improving properties of polymer nanocomposites: a review,” Mater. Sci. Technol. 22(7), 787–796 (2006).
[Crossref]

2005 (2)

B. T. Schwartz and R. Piestun, “Dynamic properties of photonic crystals and their effective refractive index,” J. Opt. Soc. Am. B 22(9), 2018–2026 (2005).
[Crossref]

P. Mallet, C.-A. Guérin, and A. Sentenac, “Maxwell-Garnett mixing rule in the presence of multiple scattering: Derivation and accuracy,” Phys. Rev. B Condens. Matter Mater. Phys. 72(1), 014205 (2005).
[Crossref]

2003 (3)

C. L. Holloway, E. F. Kuester, J. Baker-Jarvis, and P. Kabos, “A double negative (DNG) composite medium composed of magnetodielectric spherical particles embedded in a matrix,” IEEE Trans. Antenn. Propag. 51(10), 2596–2603 (2003).
[Crossref]

R. J. Nussbaumer, W. R. Caseri, P. Smith, and T. Tervoort, “Polymer‐TiO2 Nanocomposites: A Route Towards Visually Transparent Broadband UV Filters and High Refractive Index Materials,” Macromol. Mater. Eng. 288(1), 44–49 (2003).
[Crossref]

K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The Optical Properties of Metal Nanoparticles: The Influence of Size, Shape, and Dielectric Environment,” J. Phys. Chem. B 107(3), 668–677 (2003).
[Crossref]

2000 (2)

M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap,” Phys. Rev. B Condens. Matter Mater. Phys. 62(16), 10696–10705 (2000).
[Crossref]

R. Ruppin, “Evaluation of extended Maxwell-Garnett theories,” Opt. Commun. 182(4-6), 273–279 (2000).
[Crossref]

1999 (1)

V. C. Ballenegger and T. Weber, “The Ewald–Oseen extinction theorem and extinction lengths,” Am. J. Phys. 67(7), 599–605 (1999).
[Crossref]

1996 (1)

H. Fearn, D. F. James, and P. W. Milonni, “Microscopic approach to reflection, transmission, and the Ewald–Oseen extinction theorem,” Am. J. Phys. 64(8), 986–995 (1996).
[Crossref]

1993 (1)

H. Hövel, S. Fritz, A. Hilger, U. Kreibig, and M. Vollmer, “Width of cluster plasmon resonances: Bulk dielectric functions and chemical interface damping,” Phys. Rev. B Condens. Matter 48(24), 18178–18188 (1993).
[Crossref] [PubMed]

1991 (1)

Y. Wang and N. Herron, “Nanometer-sized semiconductor clusters: materials synthesis, quantum size effects, and photophysical properties,” J. Phys. Chem. 95(2), 525–532 (1991).
[Crossref]

1989 (1)

W. T. Doyle, “Optical properties of a suspension of metal spheres,” Phys. Rev. B Condens. Matter 39(14), 9852–9858 (1989).
[Crossref] [PubMed]

1986 (1)

C. F. Bohren, “Applicability of effective-medium theories to problems of scattering and absorption by nonhomogeneous atmospheric particles,” J. Atmos. Sci. 43(5), 468–475 (1986).
[Crossref]

1982 (1)

D. Aspnes, “Local‐field effects and effective‐medium theory: a microscopic perspective,” Am. J. Phys. 50(8), 704–709 (1982).
[Crossref]

1970 (1)

G. Russakoff, “A derivation of the macroscopic Maxwell equations,” Am. J. Phys. 38(10), 1188–1195 (1970).
[Crossref]

1908 (1)

G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys. 330(3), 377–445 (1908).
[Crossref]

Albrecht, G.

G. Albrecht, M. Hentschel, S. Kaiser, and H. Giessen, “Hybrid Organic-Plasmonic Nanoantennas with Enhanced Third-Harmonic Generation,” ACS Omega 2(6), 2577–2582 (2017).
[Crossref]

Anderson, Z.

P. Moitra, Y. Yang, Z. Anderson, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nat. Photonics 7(10), 791–795 (2013).
[Crossref]

Aspnes, D.

D. Aspnes, “Local‐field effects and effective‐medium theory: a microscopic perspective,” Am. J. Phys. 50(8), 704–709 (1982).
[Crossref]

Baker-Jarvis, J.

C. L. Holloway, E. F. Kuester, J. Baker-Jarvis, and P. Kabos, “A double negative (DNG) composite medium composed of magnetodielectric spherical particles embedded in a matrix,” IEEE Trans. Antenn. Propag. 51(10), 2596–2603 (2003).
[Crossref]

Ballenegger, V. C.

V. C. Ballenegger and T. Weber, “The Ewald–Oseen extinction theorem and extinction lengths,” Am. J. Phys. 67(7), 599–605 (1999).
[Crossref]

Belov, P. A.

M. V. Rybin, D. S. Filonov, K. B. Samusev, P. A. Belov, Y. S. Kivshar, and M. F. Limonov, “Phase diagram for the transition from photonic crystals to dielectric metamaterials,” Nat. Commun. 6(1), 10102 (2015).
[Crossref] [PubMed]

Benicewicz, B. C.

P. Tao, Y. Li, A. Rungta, A. Viswanath, J. Gao, B. C. Benicewicz, R. W. Siegel, and L. S. Schadler, “TiO2 nanocomposites with high refractive index and transparency,” J. Mater. Chem. 21(46), 18623–18629 (2011).
[Crossref]

Bohren, C. F.

C. F. Bohren, “Applicability of effective-medium theories to problems of scattering and absorption by nonhomogeneous atmospheric particles,” J. Atmos. Sci. 43(5), 468–475 (1986).
[Crossref]

Briggs, D. P.

P. Moitra, Y. Yang, Z. Anderson, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nat. Photonics 7(10), 791–795 (2013).
[Crossref]

Caseri, W. R.

R. J. Nussbaumer, W. R. Caseri, P. Smith, and T. Tervoort, “Polymer‐TiO2 Nanocomposites: A Route Towards Visually Transparent Broadband UV Filters and High Refractive Index Materials,” Macromol. Mater. Eng. 288(1), 44–49 (2003).
[Crossref]

Chang, K.-S.

J. L. H. Chau, Y.-M. Lin, A.-K. Li, W.-F. Su, K.-S. Chang, S. L.-C. Hsu, and T.-L. Li, “Transparent high refractive index nanocomposite thin films,” Mater. Lett. 61(14-15), 2908–2910 (2007).
[Crossref]

Chau, J. L. H.

J. L. H. Chau, Y.-M. Lin, A.-K. Li, W.-F. Su, K.-S. Chang, S. L.-C. Hsu, and T.-L. Li, “Transparent high refractive index nanocomposite thin films,” Mater. Lett. 61(14-15), 2908–2910 (2007).
[Crossref]

Chipouline, A.

J. Petschulat, C. Menzel, A. Chipouline, C. Rockstuhl, A. Tünnermann, F. Lederer, and T. Pertsch, “Multipole approach to metamaterials,” Phys. Rev. A 78(4), 043811 (2008).
[Crossref]

Coronado, E.

K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The Optical Properties of Metal Nanoparticles: The Influence of Size, Shape, and Dielectric Environment,” J. Phys. Chem. B 107(3), 668–677 (2003).
[Crossref]

Decker, M.

M. Decker and I. Staude, “Resonant dielectric nanostructures: a low-loss platform for functional nanophotonics,” J. Opt. 18(10), 103001 (2016).
[Crossref]

Diaz, A.

S. Kubo, A. Diaz, Y. Tang, T. S. Mayer, I. C. Khoo, and T. E. Mallouk, “Tunability of the refractive index of gold nanoparticle dispersions,” Nano Lett. 7(11), 3418–3423 (2007).
[Crossref] [PubMed]

Doyle, W. T.

W. T. Doyle, “Optical properties of a suspension of metal spheres,” Phys. Rev. B Condens. Matter 39(14), 9852–9858 (1989).
[Crossref] [PubMed]

Fearn, H.

H. Fearn, D. F. James, and P. W. Milonni, “Microscopic approach to reflection, transmission, and the Ewald–Oseen extinction theorem,” Am. J. Phys. 64(8), 986–995 (1996).
[Crossref]

Filonov, D. S.

M. V. Rybin, D. S. Filonov, K. B. Samusev, P. A. Belov, Y. S. Kivshar, and M. F. Limonov, “Phase diagram for the transition from photonic crystals to dielectric metamaterials,” Nat. Commun. 6(1), 10102 (2015).
[Crossref] [PubMed]

Fritz, S.

H. Hövel, S. Fritz, A. Hilger, U. Kreibig, and M. Vollmer, “Width of cluster plasmon resonances: Bulk dielectric functions and chemical interface damping,” Phys. Rev. B Condens. Matter 48(24), 18178–18188 (1993).
[Crossref] [PubMed]

Fu, Y. H.

A. I. Kuznetsov, A. E. Miroshnichenko, Y. H. Fu, J. Zhang, and B. Luk’yanchuk, “Magnetic light,” Sci. Rep. 2(1), 492 (2012).
[Crossref] [PubMed]

Gao, J.

P. Tao, Y. Li, A. Rungta, A. Viswanath, J. Gao, B. C. Benicewicz, R. W. Siegel, and L. S. Schadler, “TiO2 nanocomposites with high refractive index and transparency,” J. Mater. Chem. 21(46), 18623–18629 (2011).
[Crossref]

Giessen, H.

G. Albrecht, M. Hentschel, S. Kaiser, and H. Giessen, “Hybrid Organic-Plasmonic Nanoantennas with Enhanced Third-Harmonic Generation,” ACS Omega 2(6), 2577–2582 (2017).
[Crossref]

T. Gissibl, S. Thiele, A. Herkommer, and H. Giessen, “Two-photon direct laser writing of ultracompact multi-lens objectives,” Nat. Photonics 10(8), 554–560 (2016).
[Crossref]

C. Rockstuhl, T. Paul, F. Lederer, T. Pertsch, T. Zentgraf, T. P. Meyrath, and H. Giessen, “Transition from thin-film to bulk properties of metamaterials,” Phys. Rev. B Condens. Matter Mater. Phys. 77(3), 035126 (2008).
[Crossref]

Gissibl, T.

T. Gissibl, S. Thiele, A. Herkommer, and H. Giessen, “Two-photon direct laser writing of ultracompact multi-lens objectives,” Nat. Photonics 10(8), 554–560 (2016).
[Crossref]

Guérin, C.-A.

P. Mallet, C.-A. Guérin, and A. Sentenac, “Maxwell-Garnett mixing rule in the presence of multiple scattering: Derivation and accuracy,” Phys. Rev. B Condens. Matter Mater. Phys. 72(1), 014205 (2005).
[Crossref]

Hartmann, P.

He, Y.

Y. He and T. Zeng, “First-principles study and model of dielectric functions of silver nanoparticles,” J. Phys. Chem. C 114(42), 18023–18030 (2010).
[Crossref]

Hentschel, M.

G. Albrecht, M. Hentschel, S. Kaiser, and H. Giessen, “Hybrid Organic-Plasmonic Nanoantennas with Enhanced Third-Harmonic Generation,” ACS Omega 2(6), 2577–2582 (2017).
[Crossref]

Herkommer, A.

T. Gissibl, S. Thiele, A. Herkommer, and H. Giessen, “Two-photon direct laser writing of ultracompact multi-lens objectives,” Nat. Photonics 10(8), 554–560 (2016).
[Crossref]

Herron, N.

Y. Wang and N. Herron, “Nanometer-sized semiconductor clusters: materials synthesis, quantum size effects, and photophysical properties,” J. Phys. Chem. 95(2), 525–532 (1991).
[Crossref]

Hilger, A.

H. Hövel, S. Fritz, A. Hilger, U. Kreibig, and M. Vollmer, “Width of cluster plasmon resonances: Bulk dielectric functions and chemical interface damping,” Phys. Rev. B Condens. Matter 48(24), 18178–18188 (1993).
[Crossref] [PubMed]

Holloway, C. L.

C. L. Holloway, E. F. Kuester, J. Baker-Jarvis, and P. Kabos, “A double negative (DNG) composite medium composed of magnetodielectric spherical particles embedded in a matrix,” IEEE Trans. Antenn. Propag. 51(10), 2596–2603 (2003).
[Crossref]

Hövel, H.

H. Hövel, S. Fritz, A. Hilger, U. Kreibig, and M. Vollmer, “Width of cluster plasmon resonances: Bulk dielectric functions and chemical interface damping,” Phys. Rev. B Condens. Matter 48(24), 18178–18188 (1993).
[Crossref] [PubMed]

Hsu, S. L.-C.

J. L. H. Chau, Y.-M. Lin, A.-K. Li, W.-F. Su, K.-S. Chang, S. L.-C. Hsu, and T.-L. Li, “Transparent high refractive index nanocomposite thin films,” Mater. Lett. 61(14-15), 2908–2910 (2007).
[Crossref]

James, D. F.

H. Fearn, D. F. James, and P. W. Milonni, “Microscopic approach to reflection, transmission, and the Ewald–Oseen extinction theorem,” Am. J. Phys. 64(8), 986–995 (1996).
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Jedamzik, R.

Kabos, P.

C. L. Holloway, E. F. Kuester, J. Baker-Jarvis, and P. Kabos, “A double negative (DNG) composite medium composed of magnetodielectric spherical particles embedded in a matrix,” IEEE Trans. Antenn. Propag. 51(10), 2596–2603 (2003).
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G. Albrecht, M. Hentschel, S. Kaiser, and H. Giessen, “Hybrid Organic-Plasmonic Nanoantennas with Enhanced Third-Harmonic Generation,” ACS Omega 2(6), 2577–2582 (2017).
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K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The Optical Properties of Metal Nanoparticles: The Influence of Size, Shape, and Dielectric Environment,” J. Phys. Chem. B 107(3), 668–677 (2003).
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S. Kubo, A. Diaz, Y. Tang, T. S. Mayer, I. C. Khoo, and T. E. Mallouk, “Tunability of the refractive index of gold nanoparticle dispersions,” Nano Lett. 7(11), 3418–3423 (2007).
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M. V. Rybin, D. S. Filonov, K. B. Samusev, P. A. Belov, Y. S. Kivshar, and M. F. Limonov, “Phase diagram for the transition from photonic crystals to dielectric metamaterials,” Nat. Commun. 6(1), 10102 (2015).
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P. Moitra, Y. Yang, Z. Anderson, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nat. Photonics 7(10), 791–795 (2013).
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S. Kubo, A. Diaz, Y. Tang, T. S. Mayer, I. C. Khoo, and T. E. Mallouk, “Tunability of the refractive index of gold nanoparticle dispersions,” Nano Lett. 7(11), 3418–3423 (2007).
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C. L. Holloway, E. F. Kuester, J. Baker-Jarvis, and P. Kabos, “A double negative (DNG) composite medium composed of magnetodielectric spherical particles embedded in a matrix,” IEEE Trans. Antenn. Propag. 51(10), 2596–2603 (2003).
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S. Kubo, A. Diaz, Y. Tang, T. S. Mayer, I. C. Khoo, and T. E. Mallouk, “Tunability of the refractive index of gold nanoparticle dispersions,” Nano Lett. 7(11), 3418–3423 (2007).
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J. Petschulat, C. Menzel, A. Chipouline, C. Rockstuhl, A. Tünnermann, F. Lederer, and T. Pertsch, “Multipole approach to metamaterials,” Phys. Rev. A 78(4), 043811 (2008).
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M. V. Rybin, D. S. Filonov, K. B. Samusev, P. A. Belov, Y. S. Kivshar, and M. F. Limonov, “Phase diagram for the transition from photonic crystals to dielectric metamaterials,” Nat. Commun. 6(1), 10102 (2015).
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P. Tao, Y. Li, A. Rungta, A. Viswanath, J. Gao, B. C. Benicewicz, R. W. Siegel, and L. S. Schadler, “TiO2 nanocomposites with high refractive index and transparency,” J. Mater. Chem. 21(46), 18623–18629 (2011).
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J. L. H. Chau, Y.-M. Lin, A.-K. Li, W.-F. Su, K.-S. Chang, S. L.-C. Hsu, and T.-L. Li, “Transparent high refractive index nanocomposite thin films,” Mater. Lett. 61(14-15), 2908–2910 (2007).
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S. Kubo, A. Diaz, Y. Tang, T. S. Mayer, I. C. Khoo, and T. E. Mallouk, “Tunability of the refractive index of gold nanoparticle dispersions,” Nano Lett. 7(11), 3418–3423 (2007).
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P. Tao, Y. Li, A. Rungta, A. Viswanath, J. Gao, B. C. Benicewicz, R. W. Siegel, and L. S. Schadler, “TiO2 nanocomposites with high refractive index and transparency,” J. Mater. Chem. 21(46), 18623–18629 (2011).
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R. J. Nussbaumer, W. R. Caseri, P. Smith, and T. Tervoort, “Polymer‐TiO2 Nanocomposites: A Route Towards Visually Transparent Broadband UV Filters and High Refractive Index Materials,” Macromol. Mater. Eng. 288(1), 44–49 (2003).
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M. S. Rill, C. Plet, M. Thiel, I. Staude, G. von Freymann, S. Linden, and M. Wegener, “Photonic metamaterials by direct laser writing and silver chemical vapour deposition,” Nat. Mater. 7(7), 543–546 (2008).
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P. Moitra, Y. Yang, Z. Anderson, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nat. Photonics 7(10), 791–795 (2013).
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P. Tao, Y. Li, A. Rungta, A. Viswanath, J. Gao, B. C. Benicewicz, R. W. Siegel, and L. S. Schadler, “TiO2 nanocomposites with high refractive index and transparency,” J. Mater. Chem. 21(46), 18623–18629 (2011).
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M. S. Rill, C. Plet, M. Thiel, I. Staude, G. von Freymann, S. Linden, and M. Wegener, “Photonic metamaterials by direct laser writing and silver chemical vapour deposition,” Nat. Mater. 7(7), 543–546 (2008).
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C. Lü and B. Yang, “High refractive index organic–inorganic nanocomposites: design, synthesis and application,” J. Mater. Chem. 19(19), 2884–2901 (2009).
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P. Moitra, Y. Yang, Z. Anderson, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nat. Photonics 7(10), 791–795 (2013).
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Y. He and T. Zeng, “First-principles study and model of dielectric functions of silver nanoparticles,” J. Phys. Chem. C 114(42), 18023–18030 (2010).
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C. Rockstuhl, T. Paul, F. Lederer, T. Pertsch, T. Zentgraf, T. P. Meyrath, and H. Giessen, “Transition from thin-film to bulk properties of metamaterials,” Phys. Rev. B Condens. Matter Mater. Phys. 77(3), 035126 (2008).
[Crossref]

Zhang, J.

A. I. Kuznetsov, A. E. Miroshnichenko, Y. H. Fu, J. Zhang, and B. Luk’yanchuk, “Magnetic light,” Sci. Rep. 2(1), 492 (2012).
[Crossref] [PubMed]

Zhang, M.

M. Rong, M. Zhang, and W. Ruan, “Surface modification of nanoscale fillers for improving properties of polymer nanocomposites: a review,” Mater. Sci. Technol. 22(7), 787–796 (2006).
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Zhao, L. L.

K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The Optical Properties of Metal Nanoparticles: The Influence of Size, Shape, and Dielectric Environment,” J. Phys. Chem. B 107(3), 668–677 (2003).
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ACS Omega (1)

G. Albrecht, M. Hentschel, S. Kaiser, and H. Giessen, “Hybrid Organic-Plasmonic Nanoantennas with Enhanced Third-Harmonic Generation,” ACS Omega 2(6), 2577–2582 (2017).
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Ann. Phys. (1)

G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys. 330(3), 377–445 (1908).
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Appl. Opt. (1)

IEEE Trans. Antenn. Propag. (1)

C. L. Holloway, E. F. Kuester, J. Baker-Jarvis, and P. Kabos, “A double negative (DNG) composite medium composed of magnetodielectric spherical particles embedded in a matrix,” IEEE Trans. Antenn. Propag. 51(10), 2596–2603 (2003).
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J. Mater. Chem. (3)

P. Tao, Y. Li, A. Rungta, A. Viswanath, J. Gao, B. C. Benicewicz, R. W. Siegel, and L. S. Schadler, “TiO2 nanocomposites with high refractive index and transparency,” J. Mater. Chem. 21(46), 18623–18629 (2011).
[Crossref]

C. Lü and B. Yang, “High refractive index organic–inorganic nanocomposites: design, synthesis and application,” J. Mater. Chem. 19(19), 2884–2901 (2009).
[Crossref]

J. Liu and M. Ueda, “High refractive index polymers: fundamental research and practical applications,” J. Mater. Chem. 19(47), 8907–8919 (2009).
[Crossref]

J. Opt. (1)

M. Decker and I. Staude, “Resonant dielectric nanostructures: a low-loss platform for functional nanophotonics,” J. Opt. 18(10), 103001 (2016).
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J. Opt. Soc. Am. A (1)

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

J. Phys. Chem. (1)

Y. Wang and N. Herron, “Nanometer-sized semiconductor clusters: materials synthesis, quantum size effects, and photophysical properties,” J. Phys. Chem. 95(2), 525–532 (1991).
[Crossref]

J. Phys. Chem. B (1)

K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The Optical Properties of Metal Nanoparticles: The Influence of Size, Shape, and Dielectric Environment,” J. Phys. Chem. B 107(3), 668–677 (2003).
[Crossref]

J. Phys. Chem. C (1)

Y. He and T. Zeng, “First-principles study and model of dielectric functions of silver nanoparticles,” J. Phys. Chem. C 114(42), 18023–18030 (2010).
[Crossref]

Macromol. Mater. Eng. (1)

R. J. Nussbaumer, W. R. Caseri, P. Smith, and T. Tervoort, “Polymer‐TiO2 Nanocomposites: A Route Towards Visually Transparent Broadband UV Filters and High Refractive Index Materials,” Macromol. Mater. Eng. 288(1), 44–49 (2003).
[Crossref]

Mater. Lett. (1)

J. L. H. Chau, Y.-M. Lin, A.-K. Li, W.-F. Su, K.-S. Chang, S. L.-C. Hsu, and T.-L. Li, “Transparent high refractive index nanocomposite thin films,” Mater. Lett. 61(14-15), 2908–2910 (2007).
[Crossref]

Mater. Sci. Technol. (1)

M. Rong, M. Zhang, and W. Ruan, “Surface modification of nanoscale fillers for improving properties of polymer nanocomposites: a review,” Mater. Sci. Technol. 22(7), 787–796 (2006).
[Crossref]

Nano Lett. (1)

S. Kubo, A. Diaz, Y. Tang, T. S. Mayer, I. C. Khoo, and T. E. Mallouk, “Tunability of the refractive index of gold nanoparticle dispersions,” Nano Lett. 7(11), 3418–3423 (2007).
[Crossref] [PubMed]

Nat. Commun. (1)

M. V. Rybin, D. S. Filonov, K. B. Samusev, P. A. Belov, Y. S. Kivshar, and M. F. Limonov, “Phase diagram for the transition from photonic crystals to dielectric metamaterials,” Nat. Commun. 6(1), 10102 (2015).
[Crossref] [PubMed]

Nat. Mater. (1)

M. S. Rill, C. Plet, M. Thiel, I. Staude, G. von Freymann, S. Linden, and M. Wegener, “Photonic metamaterials by direct laser writing and silver chemical vapour deposition,” Nat. Mater. 7(7), 543–546 (2008).
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Figures (6)

Fig. 1
Fig. 1 Attenuation coefficient as a function of the wavelength and dinc/λ for TiO2 spheres at dinc = 140nm in a vacuum (a) and relative contribution of the different multipoles (b) for a dilute suspension at f = 0.1% (ED, MD, EQ, MQ denote the electric (E) and magnetic (M) dipoles (D) and quadrupoles (Q), respectively). The shaded area in (a) corresponds to the “total attenuation in the visible” regime. The different colors in (b) highlight the regimes in which different multipole orders must be considered.
Fig. 2
Fig. 2 Total (spectrally integrated) attenuation in the visible regime for TiO2 (a) and gold (c) nanoparticles at f = 0.1% in PMMA as a function of the particle size. Mieext, Miescat, and Mieabs denote the total attenuation, scattering, and absorption losses as obtained from Mie theory, respectively. In (b) and (d) the relative weight of the multipoles ( γ tot i / γ tot ext ) are shown. Green area: response solely defined by electric dipole; yellow area: magnetic dipole plays a role; red area: At least one of the quadrupoles has to be considered. The inset of (a) illustrates that for TiO2 scattering plays a role for sizes over 2 nm, and dominates over absorption for sizes larger than 5 nm.
Fig. 3
Fig. 3 Transmission of a coherent beam of light through a 1 mm thick slab of a TiO2-nanocomposite in PMMA for different particle sizes and f = 12.5% (obtained from I(d)/ I 0 =exp(γz)) and the MGMm theory). The transmissivity rapidly decreases as the size is increased due to scattering. The dotted line illustrates, that for a corresponding gold-nanocomposite at f = 2.5%, the transmission is zero at all particle sizes because of the large amount of absorption.
Fig. 4
Fig. 4 Effective medium regimes, and suitable effective medium theories (MG – Maxwell-Garnett; MGM – Maxwell-Garnett-Mie; MGMm Maxwell-Garnett-Mie with magnetic dipole response). Note that the “magnetic” regime within the “restricted effective medium” regime only exists if the magnetic dipole dominates over the electric quadrupole.
Fig. 5
Fig. 5 2D FEM simulations visualizing the propagation of a Gaussian beam (λ = 800nm) in the effective medium regimes at an area fraction of f = 40% for TiO2 in PMMA. The beam can propagate unaffected through an “unrestricted effective” medium, but is quickly separated into different bundles in a “restricted” medium. In a heterogeneous material the directionality is completely lost after several wavelengths.
Fig. 6
Fig. 6 (a) nd and νd as a function of the particle size for TiO2 nanoparticles in PMMA at f = 12%: nd depends only weakly on the particle size, whereas the tail of the electric dipole resonance starts to affect νd for dinc>10nm. The magnetic dipole contributes for dinc>70nm. (b) nd and νd as a function of the volume fraction at dinc = 4nm. Adjusting the volume fraction changes the optical properties along a trajectory defined by the constituent materials.

Equations (10)

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σ ext Mie = λ 2 2π n=0 ( 2n+1 )Re( a n + b n ),   
σ scat Mie = λ 2 2π n=0 ( 2n+1 )( | a n | 2 + | b n | 2 ),
γ Mie ext = N σ ext Mie Single scattering = 8f 4 3 π d inc 3 σ ext Mie ,
ϵ eff = ϵ h 1+ 16f d inc 3 α inc 1 8f d inc 3 α inc ,
α inc Mie =i 3 ( d inc /2 ) 3 2 x 3 a 1 ,
α inc stat = ( d inc /2 ) 3 ϵ inc ϵ h ϵ inc +2 ϵ h ,
μ eff = x 3 +3if b 1 x 3 3 2 if b 1 . 
γ eff ext = 4π λ Im( n eff ).
n eff = ϵ eff n h ( 1+2πNRe( α inc ) ) Re( n eff ) +i n h 2πNIm( α inc ) Im( n eff ) +Ο( ( nα ) 2 ), 
γ tot i = 400 nm 800 nm γ i ext ( λ )dλ,

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