Abstract

We consider emitting nanoparticles in dielectric nanocomposites with varying refractive index contrast and geometry. For that we develop a simple and universal method to calculate the emission enhancement in nanocomposites that employs solely the calculation of the effective refractive index and electric field distributions from three quasistatic calculations with orthogonal polarizations. The method is exemplified for dilute nanocomposites without electromagnetic interaction between emitting particles as well as for dense nanocomposites with strong particle interaction. We show that the radiative decay in dielectric nanocomposites is greatly affected by the shape and arrangement of its constituents and give guidelines for larger enhancement.

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

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References

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  1. P. Anger, P. Bharadwaj, and L. Novotny, “Enhancement and Quenching of Single-Molecule Fluorescence,” Phys. Rev. Lett. 96(11), 113002 (2006).
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  4. S. Ek, P. Lunnemann, Y. Chen, E. Semenova, K. Yvind, and J. Mork, “Slow-light-enhanced gain in active photonic crystal waveguides,” Nat. Commun. 5, 5039 (2014).
  5. G. M. Akselrod, C. Argyropoulos, T. B. Hoang, C. Ciracì, C. Fang, J. Huang, D. R. Smith, and M. H. Mikkelsen, “Probing the mechanisms of large Purcell enhancement in plasmonic nanoantennas,” Nat. Photonics 8(11), 835–840 (2014).
    [Crossref]
  6. T. Senden, F. T. Rabouw, and A. Meijerink, “Photonic Effects on the Radiative Decay Rate and Luminescence Quantum Yield of Doped Nanocrystals,” ACS Nano 9(2), 1801–1808 (2015).
    [Crossref] [PubMed]
  7. K. Dolgaleva, R. W. Boyd, and P. W. Milonni, “Influence of local-field effects on the radiative lifetime of liquid suspensions of Nd:YAG nanoparticles,” J. Opt. Soc. Am. B 24(3), 516–521 (2007).
    [Crossref]
  8. D. Toptygin, “Effects of the Solvent Refractive Index and Its Dispersion on the Radiative Decay Rate and Extinction Coefficient of a Fluorescent Solute,” J. Fluoresc. 13(3), 201–219 (2003).
    [Crossref]
  9. L. Rogobete, H. Schniepp, V. Sandoghdar, and C. Henkel, “Spontaneous emission in nanoscopic dielectric particles,” Opt. Lett. 28(19), 1736–1738 (2003).
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    [Crossref] [PubMed]
  12. A. N. Poddubny, P. A. Belov, and Y. S. Kivshar, “Spontaneous radiation of a finite-size dipole emitter in hyperbolic media,” Phys. Rev. A 84(2), 23807 (2011).
    [Crossref]
  13. P. Bharadwaj, B. Deutsch, and L. Novotny, “Optical Antennas,” Adv. Opt. Photonics 1(3), 438–483 (2009).
    [Crossref]
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    [Crossref]
  17. H. H. Li, “Refractive index of alkaline earth halides and its wavelength and temperature derivatives,” J. Phys. Chem. Ref. Data 9(1), 161–290 (1980).
    [Crossref]
  18. M. Daimon and A. Masumura, “High-accuracy measurements of the refractive index and its temperature coefficient of calcium fluoride in a wide wavelength range from 138 to 2326 nm,” Appl. Opt. 41(25), 5275–5281 (2002).
    [Crossref] [PubMed]
  19. T. Bellunato, M. Calvi, C. Matteuzzi, M. Musy, D. L. Perego, and B. Storaci, “Refractive index of silica aerogel: Uniformity and dispersion law,” RICH 2007(595), 183–186 (2008).
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  22. T. J. Kippenberg, A. L. Tchebotareva, J. Kalkman, A. Polman, and K. J. Vahala, “Purcell-Factor-Enhanced Scattering from Si Nanocrystals in an Optical Microcavity,” Phys. Rev. Lett. 103(2), 027406 (2009).
    [Crossref] [PubMed]
  23. I. Iorsh, A. Poddubny, A. Orlov, P. Belov, and Y. S. Kivshar, “Spontaneous emission enhancement in metal–dielectric metamaterials,” Phys. Lett. A 376(3), 185–187 (2012).
    [Crossref]
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    [Crossref]

2016 (1)

2015 (2)

T. Senden, F. T. Rabouw, and A. Meijerink, “Photonic Effects on the Radiative Decay Rate and Luminescence Quantum Yield of Doped Nanocrystals,” ACS Nano 9(2), 1801–1808 (2015).
[Crossref] [PubMed]

A. E. Krasnok, A. P. Slobozhanyuk, C. R. Simovski, S. A. Tretyakov, A. N. Poddubny, A. E. Miroshnichenko, Y. S. Kivshar, and P. A. Belov, “An antenna model for the Purcell effect,” Sci. Rep. 5(1), 12956 (2015).
[Crossref] [PubMed]

2014 (2)

S. Ek, P. Lunnemann, Y. Chen, E. Semenova, K. Yvind, and J. Mork, “Slow-light-enhanced gain in active photonic crystal waveguides,” Nat. Commun. 5, 5039 (2014).

G. M. Akselrod, C. Argyropoulos, T. B. Hoang, C. Ciracì, C. Fang, J. Huang, D. R. Smith, and M. H. Mikkelsen, “Probing the mechanisms of large Purcell enhancement in plasmonic nanoantennas,” Nat. Photonics 8(11), 835–840 (2014).
[Crossref]

2012 (1)

I. Iorsh, A. Poddubny, A. Orlov, P. Belov, and Y. S. Kivshar, “Spontaneous emission enhancement in metal–dielectric metamaterials,” Phys. Lett. A 376(3), 185–187 (2012).
[Crossref]

2011 (1)

A. N. Poddubny, P. A. Belov, and Y. S. Kivshar, “Spontaneous radiation of a finite-size dipole emitter in hyperbolic media,” Phys. Rev. A 84(2), 23807 (2011).
[Crossref]

2009 (2)

P. Bharadwaj, B. Deutsch, and L. Novotny, “Optical Antennas,” Adv. Opt. Photonics 1(3), 438–483 (2009).
[Crossref]

T. J. Kippenberg, A. L. Tchebotareva, J. Kalkman, A. Polman, and K. J. Vahala, “Purcell-Factor-Enhanced Scattering from Si Nanocrystals in an Optical Microcavity,” Phys. Rev. Lett. 103(2), 027406 (2009).
[Crossref] [PubMed]

2008 (1)

T. Bellunato, M. Calvi, C. Matteuzzi, M. Musy, D. L. Perego, and B. Storaci, “Refractive index of silica aerogel: Uniformity and dispersion law,” RICH 2007(595), 183–186 (2008).

2007 (2)

G. A. Kumar, C. W. Chen, J. Ballato, and R. E. Riman, “Optical Characterization of Infrared Emitting Rare-Earth-Doped Fluoride Nanocrystals and Their Transparent Nanocomposites,” Chem. Mater. 19(6), 1523–1528 (2007).
[Crossref]

K. Dolgaleva, R. W. Boyd, and P. W. Milonni, “Influence of local-field effects on the radiative lifetime of liquid suspensions of Nd:YAG nanoparticles,” J. Opt. Soc. Am. B 24(3), 516–521 (2007).
[Crossref]

2006 (1)

P. Anger, P. Bharadwaj, and L. Novotny, “Enhancement and Quenching of Single-Molecule Fluorescence,” Phys. Rev. Lett. 96(11), 113002 (2006).
[Crossref] [PubMed]

2003 (2)

D. Toptygin, “Effects of the Solvent Refractive Index and Its Dispersion on the Radiative Decay Rate and Extinction Coefficient of a Fluorescent Solute,” J. Fluoresc. 13(3), 201–219 (2003).
[Crossref]

L. Rogobete, H. Schniepp, V. Sandoghdar, and C. Henkel, “Spontaneous emission in nanoscopic dielectric particles,” Opt. Lett. 28(19), 1736–1738 (2003).
[Crossref] [PubMed]

2002 (3)

M. Daimon and A. Masumura, “High-accuracy measurements of the refractive index and its temperature coefficient of calcium fluoride in a wide wavelength range from 138 to 2326 nm,” Appl. Opt. 41(25), 5275–5281 (2002).
[Crossref] [PubMed]

M. Pelton, J. Vukovic, G. S. Solomon, A. Scherer, and Y. Yamamoto, “Three-dimensionally confined modes in micropost microcavities: quality factors and Purcell factors,” IEEE J. Quantum Electron. 38(2), 170–177 (2002).
[Crossref]

A. A. Krokhin, P. Halevi, and J. Arriaga, “Long-wavelength limit (homogenization) for two-dimensional photonic crystals,” Phys. Rev. B 65(11), 115208 (2002).
[Crossref]

1980 (1)

H. H. Li, “Refractive index of alkaline earth halides and its wavelength and temperature derivatives,” J. Phys. Chem. Ref. Data 9(1), 161–290 (1980).
[Crossref]

1946 (1)

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).

Akselrod, G. M.

G. M. Akselrod, C. Argyropoulos, T. B. Hoang, C. Ciracì, C. Fang, J. Huang, D. R. Smith, and M. H. Mikkelsen, “Probing the mechanisms of large Purcell enhancement in plasmonic nanoantennas,” Nat. Photonics 8(11), 835–840 (2014).
[Crossref]

Anger, P.

P. Anger, P. Bharadwaj, and L. Novotny, “Enhancement and Quenching of Single-Molecule Fluorescence,” Phys. Rev. Lett. 96(11), 113002 (2006).
[Crossref] [PubMed]

Argyropoulos, C.

G. M. Akselrod, C. Argyropoulos, T. B. Hoang, C. Ciracì, C. Fang, J. Huang, D. R. Smith, and M. H. Mikkelsen, “Probing the mechanisms of large Purcell enhancement in plasmonic nanoantennas,” Nat. Photonics 8(11), 835–840 (2014).
[Crossref]

Arriaga, J.

A. A. Krokhin, P. Halevi, and J. Arriaga, “Long-wavelength limit (homogenization) for two-dimensional photonic crystals,” Phys. Rev. B 65(11), 115208 (2002).
[Crossref]

Ballato, J.

G. A. Kumar, C. W. Chen, J. Ballato, and R. E. Riman, “Optical Characterization of Infrared Emitting Rare-Earth-Doped Fluoride Nanocrystals and Their Transparent Nanocomposites,” Chem. Mater. 19(6), 1523–1528 (2007).
[Crossref]

Bellunato, T.

T. Bellunato, M. Calvi, C. Matteuzzi, M. Musy, D. L. Perego, and B. Storaci, “Refractive index of silica aerogel: Uniformity and dispersion law,” RICH 2007(595), 183–186 (2008).

Belov, P.

I. Iorsh, A. Poddubny, A. Orlov, P. Belov, and Y. S. Kivshar, “Spontaneous emission enhancement in metal–dielectric metamaterials,” Phys. Lett. A 376(3), 185–187 (2012).
[Crossref]

Belov, P. A.

A. E. Krasnok, A. P. Slobozhanyuk, C. R. Simovski, S. A. Tretyakov, A. N. Poddubny, A. E. Miroshnichenko, Y. S. Kivshar, and P. A. Belov, “An antenna model for the Purcell effect,” Sci. Rep. 5(1), 12956 (2015).
[Crossref] [PubMed]

A. N. Poddubny, P. A. Belov, and Y. S. Kivshar, “Spontaneous radiation of a finite-size dipole emitter in hyperbolic media,” Phys. Rev. A 84(2), 23807 (2011).
[Crossref]

Bharadwaj, P.

P. Bharadwaj, B. Deutsch, and L. Novotny, “Optical Antennas,” Adv. Opt. Photonics 1(3), 438–483 (2009).
[Crossref]

P. Anger, P. Bharadwaj, and L. Novotny, “Enhancement and Quenching of Single-Molecule Fluorescence,” Phys. Rev. Lett. 96(11), 113002 (2006).
[Crossref] [PubMed]

Boyd, R. W.

Calvi, M.

T. Bellunato, M. Calvi, C. Matteuzzi, M. Musy, D. L. Perego, and B. Storaci, “Refractive index of silica aerogel: Uniformity and dispersion law,” RICH 2007(595), 183–186 (2008).

Chen, C. W.

G. A. Kumar, C. W. Chen, J. Ballato, and R. E. Riman, “Optical Characterization of Infrared Emitting Rare-Earth-Doped Fluoride Nanocrystals and Their Transparent Nanocomposites,” Chem. Mater. 19(6), 1523–1528 (2007).
[Crossref]

Chen, Y.

S. Ek, P. Lunnemann, Y. Chen, E. Semenova, K. Yvind, and J. Mork, “Slow-light-enhanced gain in active photonic crystal waveguides,” Nat. Commun. 5, 5039 (2014).

Ciracì, C.

G. M. Akselrod, C. Argyropoulos, T. B. Hoang, C. Ciracì, C. Fang, J. Huang, D. R. Smith, and M. H. Mikkelsen, “Probing the mechanisms of large Purcell enhancement in plasmonic nanoantennas,” Nat. Photonics 8(11), 835–840 (2014).
[Crossref]

Daimon, M.

Deutsch, B.

P. Bharadwaj, B. Deutsch, and L. Novotny, “Optical Antennas,” Adv. Opt. Photonics 1(3), 438–483 (2009).
[Crossref]

Dolgaleva, K.

Ek, S.

S. Ek, P. Lunnemann, Y. Chen, E. Semenova, K. Yvind, and J. Mork, “Slow-light-enhanced gain in active photonic crystal waveguides,” Nat. Commun. 5, 5039 (2014).

Fang, C.

G. M. Akselrod, C. Argyropoulos, T. B. Hoang, C. Ciracì, C. Fang, J. Huang, D. R. Smith, and M. H. Mikkelsen, “Probing the mechanisms of large Purcell enhancement in plasmonic nanoantennas,” Nat. Photonics 8(11), 835–840 (2014).
[Crossref]

Halevi, P.

A. A. Krokhin, P. Halevi, and J. Arriaga, “Long-wavelength limit (homogenization) for two-dimensional photonic crystals,” Phys. Rev. B 65(11), 115208 (2002).
[Crossref]

Henkel, C.

Hoang, T. B.

G. M. Akselrod, C. Argyropoulos, T. B. Hoang, C. Ciracì, C. Fang, J. Huang, D. R. Smith, and M. H. Mikkelsen, “Probing the mechanisms of large Purcell enhancement in plasmonic nanoantennas,” Nat. Photonics 8(11), 835–840 (2014).
[Crossref]

Huang, J.

G. M. Akselrod, C. Argyropoulos, T. B. Hoang, C. Ciracì, C. Fang, J. Huang, D. R. Smith, and M. H. Mikkelsen, “Probing the mechanisms of large Purcell enhancement in plasmonic nanoantennas,” Nat. Photonics 8(11), 835–840 (2014).
[Crossref]

Iorsh, I.

I. Iorsh, A. Poddubny, A. Orlov, P. Belov, and Y. S. Kivshar, “Spontaneous emission enhancement in metal–dielectric metamaterials,” Phys. Lett. A 376(3), 185–187 (2012).
[Crossref]

Kalkman, J.

T. J. Kippenberg, A. L. Tchebotareva, J. Kalkman, A. Polman, and K. J. Vahala, “Purcell-Factor-Enhanced Scattering from Si Nanocrystals in an Optical Microcavity,” Phys. Rev. Lett. 103(2), 027406 (2009).
[Crossref] [PubMed]

Kippenberg, T. J.

T. J. Kippenberg, A. L. Tchebotareva, J. Kalkman, A. Polman, and K. J. Vahala, “Purcell-Factor-Enhanced Scattering from Si Nanocrystals in an Optical Microcavity,” Phys. Rev. Lett. 103(2), 027406 (2009).
[Crossref] [PubMed]

Kivshar, Y. S.

A. E. Krasnok, A. P. Slobozhanyuk, C. R. Simovski, S. A. Tretyakov, A. N. Poddubny, A. E. Miroshnichenko, Y. S. Kivshar, and P. A. Belov, “An antenna model for the Purcell effect,” Sci. Rep. 5(1), 12956 (2015).
[Crossref] [PubMed]

I. Iorsh, A. Poddubny, A. Orlov, P. Belov, and Y. S. Kivshar, “Spontaneous emission enhancement in metal–dielectric metamaterials,” Phys. Lett. A 376(3), 185–187 (2012).
[Crossref]

A. N. Poddubny, P. A. Belov, and Y. S. Kivshar, “Spontaneous radiation of a finite-size dipole emitter in hyperbolic media,” Phys. Rev. A 84(2), 23807 (2011).
[Crossref]

Krasnok, A. E.

A. E. Krasnok, A. P. Slobozhanyuk, C. R. Simovski, S. A. Tretyakov, A. N. Poddubny, A. E. Miroshnichenko, Y. S. Kivshar, and P. A. Belov, “An antenna model for the Purcell effect,” Sci. Rep. 5(1), 12956 (2015).
[Crossref] [PubMed]

Krokhin, A. A.

A. A. Krokhin, P. Halevi, and J. Arriaga, “Long-wavelength limit (homogenization) for two-dimensional photonic crystals,” Phys. Rev. B 65(11), 115208 (2002).
[Crossref]

Kumar, G. A.

G. A. Kumar, C. W. Chen, J. Ballato, and R. E. Riman, “Optical Characterization of Infrared Emitting Rare-Earth-Doped Fluoride Nanocrystals and Their Transparent Nanocomposites,” Chem. Mater. 19(6), 1523–1528 (2007).
[Crossref]

Li, H. H.

H. H. Li, “Refractive index of alkaline earth halides and its wavelength and temperature derivatives,” J. Phys. Chem. Ref. Data 9(1), 161–290 (1980).
[Crossref]

Lunnemann, P.

S. Ek, P. Lunnemann, Y. Chen, E. Semenova, K. Yvind, and J. Mork, “Slow-light-enhanced gain in active photonic crystal waveguides,” Nat. Commun. 5, 5039 (2014).

Masumura, A.

Matteuzzi, C.

T. Bellunato, M. Calvi, C. Matteuzzi, M. Musy, D. L. Perego, and B. Storaci, “Refractive index of silica aerogel: Uniformity and dispersion law,” RICH 2007(595), 183–186 (2008).

Meijerink, A.

T. Senden, F. T. Rabouw, and A. Meijerink, “Photonic Effects on the Radiative Decay Rate and Luminescence Quantum Yield of Doped Nanocrystals,” ACS Nano 9(2), 1801–1808 (2015).
[Crossref] [PubMed]

Mikkelsen, M. H.

G. M. Akselrod, C. Argyropoulos, T. B. Hoang, C. Ciracì, C. Fang, J. Huang, D. R. Smith, and M. H. Mikkelsen, “Probing the mechanisms of large Purcell enhancement in plasmonic nanoantennas,” Nat. Photonics 8(11), 835–840 (2014).
[Crossref]

Milonni, P. W.

Miroshnichenko, A. E.

A. E. Krasnok, A. P. Slobozhanyuk, C. R. Simovski, S. A. Tretyakov, A. N. Poddubny, A. E. Miroshnichenko, Y. S. Kivshar, and P. A. Belov, “An antenna model for the Purcell effect,” Sci. Rep. 5(1), 12956 (2015).
[Crossref] [PubMed]

Mork, J.

S. Ek, P. Lunnemann, Y. Chen, E. Semenova, K. Yvind, and J. Mork, “Slow-light-enhanced gain in active photonic crystal waveguides,” Nat. Commun. 5, 5039 (2014).

Musy, M.

T. Bellunato, M. Calvi, C. Matteuzzi, M. Musy, D. L. Perego, and B. Storaci, “Refractive index of silica aerogel: Uniformity and dispersion law,” RICH 2007(595), 183–186 (2008).

Novotny, L.

P. Bharadwaj, B. Deutsch, and L. Novotny, “Optical Antennas,” Adv. Opt. Photonics 1(3), 438–483 (2009).
[Crossref]

P. Anger, P. Bharadwaj, and L. Novotny, “Enhancement and Quenching of Single-Molecule Fluorescence,” Phys. Rev. Lett. 96(11), 113002 (2006).
[Crossref] [PubMed]

Orlov, A.

I. Iorsh, A. Poddubny, A. Orlov, P. Belov, and Y. S. Kivshar, “Spontaneous emission enhancement in metal–dielectric metamaterials,” Phys. Lett. A 376(3), 185–187 (2012).
[Crossref]

Pelton, M.

M. Pelton, J. Vukovic, G. S. Solomon, A. Scherer, and Y. Yamamoto, “Three-dimensionally confined modes in micropost microcavities: quality factors and Purcell factors,” IEEE J. Quantum Electron. 38(2), 170–177 (2002).
[Crossref]

Perego, D. L.

T. Bellunato, M. Calvi, C. Matteuzzi, M. Musy, D. L. Perego, and B. Storaci, “Refractive index of silica aerogel: Uniformity and dispersion law,” RICH 2007(595), 183–186 (2008).

Poddubny, A.

I. Iorsh, A. Poddubny, A. Orlov, P. Belov, and Y. S. Kivshar, “Spontaneous emission enhancement in metal–dielectric metamaterials,” Phys. Lett. A 376(3), 185–187 (2012).
[Crossref]

Poddubny, A. N.

A. E. Krasnok, A. P. Slobozhanyuk, C. R. Simovski, S. A. Tretyakov, A. N. Poddubny, A. E. Miroshnichenko, Y. S. Kivshar, and P. A. Belov, “An antenna model for the Purcell effect,” Sci. Rep. 5(1), 12956 (2015).
[Crossref] [PubMed]

A. N. Poddubny, P. A. Belov, and Y. S. Kivshar, “Spontaneous radiation of a finite-size dipole emitter in hyperbolic media,” Phys. Rev. A 84(2), 23807 (2011).
[Crossref]

Polman, A.

T. J. Kippenberg, A. L. Tchebotareva, J. Kalkman, A. Polman, and K. J. Vahala, “Purcell-Factor-Enhanced Scattering from Si Nanocrystals in an Optical Microcavity,” Phys. Rev. Lett. 103(2), 027406 (2009).
[Crossref] [PubMed]

Purcell, E. M.

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).

Rabouw, F. T.

T. Senden, F. T. Rabouw, and A. Meijerink, “Photonic Effects on the Radiative Decay Rate and Luminescence Quantum Yield of Doped Nanocrystals,” ACS Nano 9(2), 1801–1808 (2015).
[Crossref] [PubMed]

Riman, R. E.

G. A. Kumar, C. W. Chen, J. Ballato, and R. E. Riman, “Optical Characterization of Infrared Emitting Rare-Earth-Doped Fluoride Nanocrystals and Their Transparent Nanocomposites,” Chem. Mater. 19(6), 1523–1528 (2007).
[Crossref]

Rogobete, L.

Sandoghdar, V.

Scherer, A.

M. Pelton, J. Vukovic, G. S. Solomon, A. Scherer, and Y. Yamamoto, “Three-dimensionally confined modes in micropost microcavities: quality factors and Purcell factors,” IEEE J. Quantum Electron. 38(2), 170–177 (2002).
[Crossref]

Schniepp, H.

Semenova, E.

S. Ek, P. Lunnemann, Y. Chen, E. Semenova, K. Yvind, and J. Mork, “Slow-light-enhanced gain in active photonic crystal waveguides,” Nat. Commun. 5, 5039 (2014).

Senden, T.

T. Senden, F. T. Rabouw, and A. Meijerink, “Photonic Effects on the Radiative Decay Rate and Luminescence Quantum Yield of Doped Nanocrystals,” ACS Nano 9(2), 1801–1808 (2015).
[Crossref] [PubMed]

Simovski, C. R.

A. E. Krasnok, A. P. Slobozhanyuk, C. R. Simovski, S. A. Tretyakov, A. N. Poddubny, A. E. Miroshnichenko, Y. S. Kivshar, and P. A. Belov, “An antenna model for the Purcell effect,” Sci. Rep. 5(1), 12956 (2015).
[Crossref] [PubMed]

Slobozhanyuk, A. P.

A. E. Krasnok, A. P. Slobozhanyuk, C. R. Simovski, S. A. Tretyakov, A. N. Poddubny, A. E. Miroshnichenko, Y. S. Kivshar, and P. A. Belov, “An antenna model for the Purcell effect,” Sci. Rep. 5(1), 12956 (2015).
[Crossref] [PubMed]

Smith, D. R.

G. M. Akselrod, C. Argyropoulos, T. B. Hoang, C. Ciracì, C. Fang, J. Huang, D. R. Smith, and M. H. Mikkelsen, “Probing the mechanisms of large Purcell enhancement in plasmonic nanoantennas,” Nat. Photonics 8(11), 835–840 (2014).
[Crossref]

Solomon, G. S.

M. Pelton, J. Vukovic, G. S. Solomon, A. Scherer, and Y. Yamamoto, “Three-dimensionally confined modes in micropost microcavities: quality factors and Purcell factors,” IEEE J. Quantum Electron. 38(2), 170–177 (2002).
[Crossref]

Storaci, B.

T. Bellunato, M. Calvi, C. Matteuzzi, M. Musy, D. L. Perego, and B. Storaci, “Refractive index of silica aerogel: Uniformity and dispersion law,” RICH 2007(595), 183–186 (2008).

Tchebotareva, A. L.

T. J. Kippenberg, A. L. Tchebotareva, J. Kalkman, A. Polman, and K. J. Vahala, “Purcell-Factor-Enhanced Scattering from Si Nanocrystals in an Optical Microcavity,” Phys. Rev. Lett. 103(2), 027406 (2009).
[Crossref] [PubMed]

Toptygin, D.

D. Toptygin, “Effects of the Solvent Refractive Index and Its Dispersion on the Radiative Decay Rate and Extinction Coefficient of a Fluorescent Solute,” J. Fluoresc. 13(3), 201–219 (2003).
[Crossref]

Tretyakov, S. A.

A. E. Krasnok, A. P. Slobozhanyuk, C. R. Simovski, S. A. Tretyakov, A. N. Poddubny, A. E. Miroshnichenko, Y. S. Kivshar, and P. A. Belov, “An antenna model for the Purcell effect,” Sci. Rep. 5(1), 12956 (2015).
[Crossref] [PubMed]

Tsakmakidis, K. L.

Vahala, K. J.

T. J. Kippenberg, A. L. Tchebotareva, J. Kalkman, A. Polman, and K. J. Vahala, “Purcell-Factor-Enhanced Scattering from Si Nanocrystals in an Optical Microcavity,” Phys. Rev. Lett. 103(2), 027406 (2009).
[Crossref] [PubMed]

Vukovic, J.

M. Pelton, J. Vukovic, G. S. Solomon, A. Scherer, and Y. Yamamoto, “Three-dimensionally confined modes in micropost microcavities: quality factors and Purcell factors,” IEEE J. Quantum Electron. 38(2), 170–177 (2002).
[Crossref]

Yablonovitch, E.

Yamamoto, Y.

M. Pelton, J. Vukovic, G. S. Solomon, A. Scherer, and Y. Yamamoto, “Three-dimensionally confined modes in micropost microcavities: quality factors and Purcell factors,” IEEE J. Quantum Electron. 38(2), 170–177 (2002).
[Crossref]

Yvind, K.

S. Ek, P. Lunnemann, Y. Chen, E. Semenova, K. Yvind, and J. Mork, “Slow-light-enhanced gain in active photonic crystal waveguides,” Nat. Commun. 5, 5039 (2014).

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ACS Nano (1)

T. Senden, F. T. Rabouw, and A. Meijerink, “Photonic Effects on the Radiative Decay Rate and Luminescence Quantum Yield of Doped Nanocrystals,” ACS Nano 9(2), 1801–1808 (2015).
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P. Bharadwaj, B. Deutsch, and L. Novotny, “Optical Antennas,” Adv. Opt. Photonics 1(3), 438–483 (2009).
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Appl. Opt. (1)

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M. Pelton, J. Vukovic, G. S. Solomon, A. Scherer, and Y. Yamamoto, “Three-dimensionally confined modes in micropost microcavities: quality factors and Purcell factors,” IEEE J. Quantum Electron. 38(2), 170–177 (2002).
[Crossref]

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D. Toptygin, “Effects of the Solvent Refractive Index and Its Dispersion on the Radiative Decay Rate and Extinction Coefficient of a Fluorescent Solute,” J. Fluoresc. 13(3), 201–219 (2003).
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S. Ek, P. Lunnemann, Y. Chen, E. Semenova, K. Yvind, and J. Mork, “Slow-light-enhanced gain in active photonic crystal waveguides,” Nat. Commun. 5, 5039 (2014).

Nat. Photonics (1)

G. M. Akselrod, C. Argyropoulos, T. B. Hoang, C. Ciracì, C. Fang, J. Huang, D. R. Smith, and M. H. Mikkelsen, “Probing the mechanisms of large Purcell enhancement in plasmonic nanoantennas,” Nat. Photonics 8(11), 835–840 (2014).
[Crossref]

Opt. Express (1)

Opt. Lett. (1)

Phys. Lett. A (1)

I. Iorsh, A. Poddubny, A. Orlov, P. Belov, and Y. S. Kivshar, “Spontaneous emission enhancement in metal–dielectric metamaterials,” Phys. Lett. A 376(3), 185–187 (2012).
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A. N. Poddubny, P. A. Belov, and Y. S. Kivshar, “Spontaneous radiation of a finite-size dipole emitter in hyperbolic media,” Phys. Rev. A 84(2), 23807 (2011).
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T. J. Kippenberg, A. L. Tchebotareva, J. Kalkman, A. Polman, and K. J. Vahala, “Purcell-Factor-Enhanced Scattering from Si Nanocrystals in an Optical Microcavity,” Phys. Rev. Lett. 103(2), 027406 (2009).
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T. Bellunato, M. Calvi, C. Matteuzzi, M. Musy, D. L. Perego, and B. Storaci, “Refractive index of silica aerogel: Uniformity and dispersion law,” RICH 2007(595), 183–186 (2008).

Sci. Rep. (1)

A. E. Krasnok, A. P. Slobozhanyuk, C. R. Simovski, S. A. Tretyakov, A. N. Poddubny, A. E. Miroshnichenko, Y. S. Kivshar, and P. A. Belov, “An antenna model for the Purcell effect,” Sci. Rep. 5(1), 12956 (2015).
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Figures (6)

Fig. 1
Fig. 1 (a) A dipole J 1 at r= r 1 emits into a structured medium. It produces a plane wave far away from the source at r= r 2 . The emitting material is drawn in red. (b) The medium is artificially separated into two regions: nanostructured (inside the green perimeter) and homogeneous (outside). The plane wave has an amplitude E 1 at r= r 2 . (c) Reversed case. A test dipole J 2 oriented along E 1 produces a field E 2 at the position of the original dipole and a field E 2 ' at the green boundary.
Fig. 2
Fig. 2 (a) Emission enhancement factor vs host refractive index of an emitter in a spherical particle (Eq. (10)). (b) Emission enhancement factor vs host refractive index of an emitter in a platelet. Equation (13) is the blue line, Eq. (14) the red and Eq. (15) the green. The luminescent material has refractive index 1.43 is colored red in the sketch.
Fig. 3
Fig. 3 We investigate two representative periodic 3D nanocomposites with 50/50 material split. (a) Emitting cubes inside a passive material. (b) Passive cubes inside an emitting material.
Fig. 4
Fig. 4 (a) Emission enhancement factor vs refractive index of the passive material. For the blue line the emitting material is inside the cubes, for the red line its outside. The inset shows the effective refractive index of the two structures. (b) Electric field enhancement factor for a bias in vertical direction. Outside the cube is the emitting material with n = 1.43 and inside is the passive material with n = 3.5. (c) as (b) but with emitting material inside and passive material outside. Since a quasi-static approximation is validthe exact dimensions of the structure don’t affect the result. For the fields in (b) and (c) an inner cube with 10nm long edges was considered.
Fig. 5
Fig. 5 (a) A dipole at r= r 1 emits into a structured medium. It produces the electric field far away from the source at r= r 2 . The medium is artificially separated into two regions: nanostructured and homogeneous. (b) A test dipole oriented along e θ . (c) A test dipole oriented along e φ . The emitting material is drawn in red.
Fig. 6
Fig. 6 Eigenmode solver boundary conditions: In the horizontal direction periodic boundary conditions with a phase shift of Δϕ are used. In the vertical direction the tangential electric field is set to zero. In the remaining orthogonal direction, the tangential magnetic field is zero. These boundary conditions yield a plane wave traveling in horizontal direction with electric field polarized in vertical direction. To obtain the solution for another electric field polarization the boundary conditions need to be switched accordingly. Each volume edge has a length of a.

Equations (28)

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J 1 E 2  dV= E 1 J 2  dV.
e J1 E 2 ( r 1 )= E 1 ( r 2 ),
E 1 ( r 2 )= e J1 E 2 ( r 1 ) | E 2 ' | 1 4π ϵ 0 k 0 2 e jk( r 1 r 2 ) | r 1 r 2 | | J 1 | ω .
P rad,nc = n eff ( | e J1 E 2 x | 2 | E 2,x ' | 2 + | e J1 E 2 y | 2 | E 2,z ' | 2 + | e J1 E 2 z | 2 | E 2,z ' | 2 ) k 0 4 12π Z 0 ε 0 2 | J 1 | 2 ω 2 ,
P rad,vac = k 0 4 12π Z 0 ϵ 0 2 | J 1 | 2 ω 2 .
f nc = n eff ( | e J1 E 2 x | 2 | E 2,x ' | 2 + | e J1 E 2 y | 2 | E 2,z ' | 2 + | e J1 E 2 z | 2 | E 2,z ' | 2 ).
f unpol = 1 3 n eff ( | E 2 x | 2 | E 2,x ' | 2 + | E 2 y | 2 | E 2,y ' | 2 + | E 2 z | 2 | E 2,z ' | 2 ).
E 2 = 3 n host 2 2 n host 2 + n emitter 2 E 2 ' ,
f sphere = n host | E 2 | 2 | E 2 ' | 2 = n host ( 3 n host 2 2 n host 2 + n emitter 2 ) 2 ,
E 2, = n host 2 n emitter 2 E 2, '
E 2, = E 2, ' .
f plate, = n host | E 2, | 2 | E 2, ' | 2 = n host n host 4 n emitter 4
f plate, = n host | E 2, | 2 | E 2, ' | 2 = n host .
f plate,unpol = 1 3 n host n host 4 n emitter 4 + 2 3 n host .
e J1 E 2 θ ( r 1 )= e θ E 1 ( r 2 )= E 1,θ ( r 2 ),
e J1 E 2 φ ( r 1 )= e φ E 1 ( r 2 )= E 1,φ ( r 2 ).
E 2 θ ( r 1 )=( cos( θ )cos( φ ) E 2 x | E 2,x ' | +cos( θ )sin( φ ) E 2 y | E 2,y ' | sin( θ ) E 2 z | E 2,z ' | ) 1 4π ϵ 0 ( ω c 0 ) 2 e jk( r 1 r 2 ) | r 1 r 2 | | J 1 | ω ,
E 2 φ ( r 1 )=( sin( ϕ ) E 2 x | E 2,x ' | +cos( ϕ ) E 2 y | E 2,y ' | ) 1 4π ϵ 0 ( ω c 0 ) 2 e jk( r 1 r 2 ) | r 1 r 2 | | J 1 | ω .
E 1,θ ( r 2 )=( cos( θ )cos( φ ) e J1 E 2 x | E 2,x ' | +cos( θ )sin( φ ) e J1 E 2 y | E 2,y ' | sin( θ ) e J1 E 2 z | E 2,z ' | ) 1 4π ϵ 0 ( ω c 0 ) 2 e jk( r 1 r 2 ) | r 1 r 2 | | J 1 | ω ,
E 1,φ ( r 2 )=( sin( ϕ ) e J1 E 2 x | E 2,x ' | +cos( ϕ ) e J1 E 2 y | E 2,y ' | ) 1 4π ϵ 0 ( ω c 0 ) 2 e jk( r 1 r 2 ) | r 1 r 2 | | J 1 | ω .
I( θ,φ )= n eff 2 Z 0 ( | E 1,θ | 2 + | E 1,φ | 2 ).
P dipole = 0 2π 0 π n 2 Z 0 ( | E 1,θ | 2 + | E 1,φ | 2 ) r 1 sin( θ )dθdφ.
P dipole = n eff 2 Z 0 8π 3 ( 1 4π ϵ 0 ( ω c 0 ) 2 | J 1 | ω ) 2 ( | e J1 E 2 x | 2 | E 2,x ' | 2 + | e J1 E 2 y | 2 | E 2,z ' | 2 + | e J1 E 2 z | 2 | E 2,z ' | 2 ).
f dipole = n eff ( | e J1 E 2 x | 2 | E 2,x ' | 2 + | e J1 E 2 y | 2 | E 2,z ' | 2 + | e J1 E 2 z | 2 | E 2,z ' | 2 ).
f unpol = 1 3 n eff ( | E 2 x | 2 | E 2,x ' | 2 + | E 2 y | 2 | E 2,z ' | 2 + | E 2 z | 2 | E 2,z ' | 2 ).
k= ω c 0 n eff = Δϕ a ,
P mode = n eff 2 Z 0 | E avg | 2 .
P mode = v g a W E ω c 0 n eff 1 a W E

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