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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 15 — Jul. 28, 2014
  • pp: 18290–18298
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Hyperbolic metamaterials based on quantum-dot plasmon-resonator nanocomposites

S. V. Zhukovsky, T. Ozel, E. Mutlugun, N. Gaponik, A. Eychmuller, A. V. Lavrinenko, H. V. Demir, and S. V. Gaponenko  »View Author Affiliations


Optics Express, Vol. 22, Issue 15, pp. 18290-18298 (2014)
http://dx.doi.org/10.1364/OE.22.018290


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Abstract

We theoretically demonstrate that nanocomposites made of colloidal semiconductor quantum dot monolayers placed between metal nanoparticle monolayers can function as multilayer hyperbolic metamaterials. Depending on the thickness of the spacer between the quantum dot and nanoparticle layers, the effective permittivity tensor of the nanocomposite is shown to become indefinite, resulting in increased photonic density of states and strong enhancement of quantum dot luminescence. This explains the results of recent experiments [T. Ozel et al., ACS Nano 5, 1328 (2011)] and confirms that hyperbolic metamaterials are capable of increasing the radiative decay rate of emission centers inside them. The proposed theoretical framework can also be used to design quantum-dot/nanoplasmonic composites with optimized luminescence enhancement.

© 2014 Optical Society of America

1. Introduction

Hyperbolic metamaterials (HMMs) have attracted an intense scientific interest during the recent years for several reasons. First and foremost, the material properties of such metamaterials, namely, an indefinite form of their effective permittivity tensor (such that, e.g., εx = εy < 0 and εz > 0 [1

1. D. R. Smith, D. Schurig, J. J. Mock, P. Kolinko, and P. Rye, “Partial focusing of radiation by a slab of indefinite media,” Appl. Phys. Lett. 84(13), 2244–2246 (2004). [CrossRef]

]) give rise to an unusual hyperbolic dispersion relation, ω2/c2=(kx2+ky2)/εz+kz2/εx,y [Fig. 1(a)]. Such a dispersion relation is associated with an anomalous increase of the photonic density of states (PDOS), strongly affecting many physical phenomena that rely on it: spontaneous emission [2

2. M. A. Noginov, H. Li, Yu. A. Barnakov, D. Dryden, G. Nataraj, G. Zhu, C. E. Bonner, M. Mayy, Z. Jacob, and E. E. Narimanov, “Controlling spontaneous emission with metamaterials,” Opt. Lett. 35(11), 1863–1865 (2010). [CrossRef] [PubMed]

4

4. Z. Jacob, I. I. Smolyaninov, and E.E. Narimanov, “Broadband Purcell effect: Radiative decay engineering with metamaterials,” Appl. Phys. Lett. 100(18), 181105 (2012). [CrossRef]

], blackbody radiation [5

5. C. Simovski, S. Maslovski, I. Nefedov, and S. Tretyakov, “Optimization of radiative heat transfer in hyperbolic metamaterials for thermophotovoltaic applications,” Opt. Express 21(12), 14988–15013 (2013). [CrossRef] [PubMed]

, 6

6. Y. Guo and Z. Jacob, “Thermal hyperbolic metamaterials,” Opt. Express 21(12), 15014–15019 (2013). [CrossRef] [PubMed]

], and Casimir forces [7

7. T. Morgado, S. I. Maslovski, and M. G. Silveirinha, “Ultrahigh Casimir interaction torque in nanowire systems,” Opt. Express 21(12), 14943–14955 (2013). [CrossRef] [PubMed]

]. More practical applications of HMMs include superresolution [8

8. G. D’Aguanno, N. Mattiucci, M. Bloemer, and A. Desyatnikov, “Optical vortices during a superresolution process in a metamaterial,” Phys. Rev. A 77(4), 043825 (2008). [CrossRef]

, 9

9. N. Mattiucci, G. D’Aguanno, M. Scalora, M. J. Bloemer, and C. Sibilia, “Transmission function properties for multi-layered structures: Application to super-resolution,” Opt. Express 17(20), 17517–17529 (2009). [CrossRef] [PubMed]

], far-field subwavelength imaging or “hyperlensing” [10

10. S. Ramakrishna, J. Pendry, M. Wiltshire, and W. Stewart, “Imaging the near field,” J. Mod. Opt. 50(9), 1419–1430 (2003). [CrossRef]

,11

11. Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical Hyperlens: Far-field imaging beyond the diffraction limit,” Opt. Express 14(18), 8247–8256 (2006). [CrossRef] [PubMed]

], and high broadband absorbance [12

12. N. Mattiucci, M. J. Bloemer, N. Aközbek, and G. D’Aguanno, “Impedance matched thin metamaterials make metals absorbing,” Sci. Rep. 3, 3203 (2013). [CrossRef] [PubMed]

] impervious to the detrimental effects of surface roughness [13

13. E. E. Narimanov, H. Li, Y. A. Barnakov, T. U. Tumkur, and M. A. Noginov, “Reduced reflection from roughened hyperbolic metamaterial,” Opt. Express 21(12), 14956–14961 (2013). [CrossRef] [PubMed]

]. Still other intriguing applications rely on similarities between optical dispersion relations and cosmological equations to use HMMs for tabletop optical simulation of space-time phenomena [14

14. I. I. Smolyaninov and E. E. Narimanov, “Metric signature transitions in optical metamaterials,” Phys. Rev. Lett. 105(6), 067402 (2010). [CrossRef] [PubMed]

,15

15. I. I. Smolyaninov and Yu-Ju Hung, “Modeling of time with metamaterials,” J. Opt. Soc. Am. B 28(7), 1591–1595 (2011). [CrossRef]

]. New aspects of HMM research are being uncovered (see [16

16. C. L. Cortes, W. Newman, S. Molesky, and Z. Jacob, “Quantum nanophotonics using hyperbolic metamaterials,” J. Opt. 14(6), 063001 (2012). [CrossRef]

, 17

17. V. Drachev, V. A. Podolskiy, and A. V. Kildishev, “Hyperbolic Metamaterials: new physics behind a classical problem,” Opt. Express 21(12), 15048–15064 (2013). [CrossRef] [PubMed]

] and references therein).

Fig. 1 (a) Isofrequency surfaces in the dispersion relation (kx2+ky2)/εz+kz2/εx,y=ω2/c2 for conventional anisotropic medium (εx,y,z > 0) and indefinite medium (εx,y < 0 and εz > 0). (b) Schematics of a multilayer metal-dielectric HMM. (c) Schematics of NP-spacer-NC from [31], showing the geometrical notation used in the paper.

The other important reason of the interest in HMMs is that unlike many other types of meta-materials, HMMs do not require resonant “building blocks” and can therefore be practically realized using rather simple geometries. Metal-dielectric composites as simple as subwavelength multilayers [3

3. Z. Jacob, J.-Y. Kim, G.V. Naik, A. Boltasseva, E.E. Narimanov, and V.M. Shalaev, “Engineering the photonic density of states with metamaterials,” Appl. Phys. B 100(1), 215–218 (2010). [CrossRef]

, 4

4. Z. Jacob, I. I. Smolyaninov, and E.E. Narimanov, “Broadband Purcell effect: Radiative decay engineering with metamaterials,” Appl. Phys. Lett. 100(18), 181105 (2012). [CrossRef]

] and nanorod arrays [2

2. M. A. Noginov, H. Li, Yu. A. Barnakov, D. Dryden, G. Nataraj, G. Zhu, C. E. Bonner, M. Mayy, Z. Jacob, and E. E. Narimanov, “Controlling spontaneous emission with metamaterials,” Opt. Lett. 35(11), 1863–1865 (2010). [CrossRef] [PubMed]

, 18

18. M. A. Noginov, Yu. A. Barnakov, G. Zhu, T. Tumkur, H. Li, and E. E. Narimanov, “Bulk photonic metamaterial with hyperbolic dispersion,” Appl. Phys. Lett. 94(15), 151105 (2009). [CrossRef]

] have been shown to possess salient properties of HMMs in a broad frequency range. In a series of recent experiments, it was shown that placing such metal-dielectric HMMs close to luminescent centers enhance their decay rate more strongly than what is achievable using metal or dielectric alone [2

2. M. A. Noginov, H. Li, Yu. A. Barnakov, D. Dryden, G. Nataraj, G. Zhu, C. E. Bonner, M. Mayy, Z. Jacob, and E. E. Narimanov, “Controlling spontaneous emission with metamaterials,” Opt. Lett. 35(11), 1863–1865 (2010). [CrossRef] [PubMed]

, 3

3. Z. Jacob, J.-Y. Kim, G.V. Naik, A. Boltasseva, E.E. Narimanov, and V.M. Shalaev, “Engineering the photonic density of states with metamaterials,” Appl. Phys. B 100(1), 215–218 (2010). [CrossRef]

]. However, even though these experimental results were well explained by the theory of dipole radiation in an HMM environment [19

19. O. Kidwai, S. V. Zhukovsky, and J. E. Sipe, “Dipole radiation near hyperbolic metamaterials: applicability of effective-medium approximation,” Opt. Lett. 36(13), 2530–2532 (2011). [CrossRef] [PubMed]

22

22. O. Kidwai, S. V. Zhukovsky, and J. E. Sipe, “Effective-medium approach to planar multilayer hyperbolic meta-materials: Strengths and limitations,” Phys. Rev. A 85(5), 053842 (2012). [CrossRef]

], it has proven rather difficult to distinguish whether the emission rate increase can be attributed to the increase of the radiative decay rate (i.e., the Purcell effect) or just quenching of luminescence (as happens with an emitter near a metallic surface, see [23

23. D. V. Guzatov, S. V. Vaschenko, V. V. Stankevich, A. Y. Lunevich, Y. F. Glukhov, and S. V. Gaponenko, “Plasmonic enhancement of molecular fluorescence near silver nanoparticles: theory, modeling, and experiment,” J. Phys. Chem. C 116(19), 10723–10733 (2012). [CrossRef]

]). Only in the recent work by Kim et al. [24

24. J. Kim, V. P. Drachev, Z. Jacob, G. V. Naik, A. Boltasseva, E. E. Narimanov, and V. M. Shalaev, “Improving the radiative decay rate for dye molecules with hyperbolic metamaterials,” Opt. Express 20(7), 8100–8116 (2012). [CrossRef] [PubMed]

] direct evidence of the radiative rate increase was reported.

Despite the fact that the underlying geometry of an HMM can be as simple as a metal-dielectric multilayer [Fig. 1(b)], it has proven quite challenging to fabricate an HMM with reliable characteristics. The reason is that the thicknesses of the layers involved must be sub-wavelength not only with respect to the vacuum wavelength of the incident light, but also with respect to large-wavevector bulk plasmonic waves that exist inside HMMs and substantiate the anomalously large PDOS in them [25

25. S. Zhukovsky, O. Kidwai, and J. E. Sipe, “Physical nature of volume plasmon polaritons in hyperbolic metamaterials,” Opt. Express 21(12), 14982–14987 (2013). [CrossRef] [PubMed]

]. Continuous metal films of such small thickness (on the order of a few nanometers) are difficult to fabricate using state of the art growing facilities. Depositing luminescent centers on the surface of a HMM can also be challenging and may additionally be affected by plasmonic effects in the outermost HMM layer [22

22. O. Kidwai, S. V. Zhukovsky, and J. E. Sipe, “Effective-medium approach to planar multilayer hyperbolic meta-materials: Strengths and limitations,” Phys. Rev. A 85(5), 053842 (2012). [CrossRef]

].

Here, we would like to point out another and perhaps an easier possibility to obtain a characterizable structure with HMM properties. It has been known for quite a while that layer-by-layer assembly of plasmonic nanoparticle (NP) monolayers can be realized by separating the monolayers by polyelectrolyte (PDDA) layers [26

26. O. Kulakovich, N. Strekal, A. Yaroshevich, S. Maskevich, S. Gaponenko, I. Nabiev, U. Woggon, and M. Artemyev, “Enhanced luminescence of CdSe quantum dots on gold colloids,” Nano Lett. 2(12), 1449–1452 (2002). [CrossRef]

28

28. T. Ozel, P. L. Hernandez Martinez, E. Mutlugun, O. Akin, S. Nizamoglu, I. O. Ozel, and H. V. Demir, “Observation of selective plasmon-exciton coupling in nonradiative energy transfer: Donor-selective vs. acceptor-selective plexcitons,” Nano Lett. 13(6), 3065–3071 (2013). [CrossRef] [PubMed]

]. In a densely packed monolayer of such NPs, localized plasmon resonances in each nanoparticle would couple to support ”spoof” surface plasmonic waves [29

29. M. L. Brongersma, J. W. Hartman, and H. A. Atwater, “Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit,” Phys. Rev. B 62(24), R16356 (2000). [CrossRef]

, 30

30. M. Navarro-Cìa, M. Beruete, S. Agrafiotis, F. Falcone, M. Sorolla, and S. A. Maier, “Broadband spoof plasmons and subwavelength electromagnetic energy confinement on ultrathin metafilms,” Opt. Express 17(20), 18184–18195 (2009). [CrossRef] [PubMed]

], so the monolayer may be regarded as a corrugated metallic layer. Using a similar technology, semiconductor nanocrystals (NCs), which are luminescent quantum dots, can be likewise assembled into monolayers, able to function as both dielectric and emitting layers. Alternating NP and NC monolayers is thus likely to result in HMM behavior.

Indeed, a recent experimental paper by T. Ozel et al. [31

31. T. Ozel, S. Nizamoglu, M. A. Sefunc, O. Samarskaya, I. O. Ozel, E. Mutlugun, V. Lesnyak, N. Gaponik, A. Eychmuller, S. V. Gaponenko, and H. V. Demir, “Anisotropic emission from multilayered plasmon resonator nanocomposites of isotropic semiconductor quantum dots,” ACS Nano 5(2), 1328–1334 (2011). [CrossRef] [PubMed]

] reported that the luminescence from NCs was increased by a factor of 4 when placed into such a multilayer arrangement. Interestingly, the enhancement was only seen when the NC and NP layers were separated by thin dielectric spacer layers [Fig. 1(c)]. Even though an explanation based on the increased plasmon-exciton coupling between NCs and NPs was given and confirmed by time-domain numerical simulations, the role of the dielectric spacer layers was not very well understood.

2. Nanocrystal/nanoparticle composites as multilayer hyperbolic metamaterials

We begin by considering an infinitely periodic system shown in Fig. 1(c) where a number (mp) of monolayers of gold NPs with diameter dp = 15 nm alternate with a number (mq) of monolayers of semiconductor (CdTe) NC quantum dots with diameter dq = 5.5 nm, separated by dielectric spacers with varied thickness ds. The dielectric constants of gold, CdTe, and the spacer material are denoted by εp, εq, and εs, respectively.

We will follow the standard multilayer homogenization procedure [32

32. K. Dolgaleva and R. W. Boyd, “Local-field effects in nanostructured photonic materials,” Adv. Opt. Photon. 4(1), 1–77 (2012). [CrossRef]

] where the effective permittivity components of a subwavelength multilayer are determined by the relations
εx=εy=2dsεs+mpdpε¯p+mqdqε¯q2ds+mpdp+mqdq,εz1=2dsεs1+mpdpε¯p1+mqdqε¯q12ds+mpdp+mqdq.
(1)
The averaged permittivity ε̄q of a dielectric NC monolayer can be estimated from the Bruggeman formula (see [32

32. K. Dolgaleva and R. W. Boyd, “Local-field effects in nanostructured photonic materials,” Adv. Opt. Photon. 4(1), 1–77 (2012). [CrossRef]

]):
fqεqε¯qεq+2ε¯q+(1fq)1ε¯q1+2ε¯q=0
(2)
The plasmonic NP monolayer can be assumed to be above the percolation threshold to have conductive coupling between the NPs, so that the entire monolayer can be treated using the Drude model with the diluted metal assumption, with the resulting averaged permittivity
ε¯p=1fpωp2ω2iγω
(3)
where ωp and γ are the standard Drude plasma and collision frequency for the metal. The factors fp,q are volume filling fractions of the particle material (metal for NPs and semiconductor for NCs) within each monolayer; for the triangular lattice, fq,p=π2/(83). Finally, the permittivity of the PDDA/PSS spacer layers is εs = 2.4 [33

33. J. H. Kim, J. H. Hwang, and T. Y. Lim, “A layer-by-layer self-assembly method for organic-inorganic hybrid multilayer thin films,” J. Ceram. Process. Res. 10(6), 770–773 (2009).

].

For mp = mq = 3 and the materials used in [31

31. T. Ozel, S. Nizamoglu, M. A. Sefunc, O. Samarskaya, I. O. Ozel, E. Mutlugun, V. Lesnyak, N. Gaponik, A. Eychmuller, S. V. Gaponenko, and H. V. Demir, “Anisotropic emission from multilayered plasmon resonator nanocomposites of isotropic semiconductor quantum dots,” ACS Nano 5(2), 1328–1334 (2011). [CrossRef] [PubMed]

], the resulting permittivity tensor components are shown in Fig. 2. It can be seen at once that the parallel component εx,y varies slowly and remains negative, whereas the real part of the perpendicular component εz changes sign at Reεz1=0, which happens at ds between 1 and 5 nm, depending on the wavelength.

Fig. 2 Plots of the real part of (a) εx = εy and (b) εz depending on the spacer thickness ds and the incident light wavelength λ for the structure shown in Fig. 1(c). The green dashed line in (b) shows the singularity where Reεz1=0.

Therefore, the functionality of the entire material crucially depends on the spacer. Without it (ds = 0), the material is effectively a strongly anisotropic metal with |εz| ≫ |εx,y| and εz < εx,y < 0. As any metal, such a material would quench the luminescence from the NCs compared to the case when NPs are absent. Conversely, adding the spacer results in |εz| ≫ |εx,y| but εx,y < 0 < εz, and the material becomes an HMM. Thus, a significant increase of the decay rate of the NCs (including the increase of radiative decay) would be expected.

We note that we have regarded a passive metal-dielectric structure with dipole emitters embedded in it, whereas in [31

31. T. Ozel, S. Nizamoglu, M. A. Sefunc, O. Samarskaya, I. O. Ozel, E. Mutlugun, V. Lesnyak, N. Gaponik, A. Eychmuller, S. V. Gaponenko, and H. V. Demir, “Anisotropic emission from multilayered plasmon resonator nanocomposites of isotropic semiconductor quantum dots,” ACS Nano 5(2), 1328–1334 (2011). [CrossRef] [PubMed]

] the structure is active, with quantum dots used both as a constituent portion of HMM and as an ensemble of luminescent probes. A similar approach has been applied to examine radiative decay of emitters in a photonic crystal [34

34. M. Fujita, S. Takahashi, Y. Tanaka, T. Asano, and S. Noda., “Simultaneous inhibition and redistribution of spontaneous light emission in photonic crystals,” Science 308(5726), 1296–1298 (2005). [CrossRef] [PubMed]

]. The latter was examined in more detail than the emergent notion of HMM. Notably, when a probe position was scanned from the depth of the structure to its surface or even slightly (10 nm) above, the enhancement effect of a photonic crystal density of states on radiative lifetime was shown to persist steadily with smooth position dependence [35

35. A. F. Koenderink, M. Kafesaki, C. M. Soukolis, and V. Sandoghdar, “Spontaneous emission in the near field of two-dimensional photonic crystals,” Opt. Lett. 30(23), 3210–3212 (2005). [CrossRef] [PubMed]

]. Given that multilayer HMMs act as photonic crystals for large-wavevector metamaterial modes [25

25. S. Zhukovsky, O. Kidwai, and J. E. Sipe, “Physical nature of volume plasmon polaritons in hyperbolic metamaterials,” Opt. Express 21(12), 14982–14987 (2013). [CrossRef] [PubMed]

], we expect that the considered homogenization is an adequate representation of the structure in [31

31. T. Ozel, S. Nizamoglu, M. A. Sefunc, O. Samarskaya, I. O. Ozel, E. Mutlugun, V. Lesnyak, N. Gaponik, A. Eychmuller, S. V. Gaponenko, and H. V. Demir, “Anisotropic emission from multilayered plasmon resonator nanocomposites of isotropic semiconductor quantum dots,” ACS Nano 5(2), 1328–1334 (2011). [CrossRef] [PubMed]

] for the purpose of establishing the plausibility of the hypothesis regarding the HMM properties of the structures under consideration.

3. Enhancement of emission from nanocrystals

The Fresnel coefficients can be calculated using the transfer matrix method for multilayer structures with both finite [20

20. A. N. Poddubny, P. A. Belov, and Yu. S. Kivshar, “Spontaneous radiation of a finite-size dipole emitter in hyperbolic media,” Phys. Rev. A 84(2), 023807 (2011). [CrossRef]

, 21

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

] and infinite [22

22. O. Kidwai, S. V. Zhukovsky, and J. E. Sipe, “Effective-medium approach to planar multilayer hyperbolic meta-materials: Strengths and limitations,” Phys. Rev. A 85(5), 053842 (2012). [CrossRef]

] number of periods. The salient properties of HMMs stem from the existence of high-κ band where HMM supports propagating waves and ImRp is significantly non-zero [25

25. S. Zhukovsky, O. Kidwai, and J. E. Sipe, “Physical nature of volume plasmon polaritons in hyperbolic metamaterials,” Opt. Express 21(12), 14982–14987 (2013). [CrossRef] [PubMed]

]. In a homogeneous HMM, it would span from κc=(ω/c)εz all the way to infinity. In multilayers with finite layer thickness, however, the high-κ band will be limited by the thickest layer, in our case 3dp [3

3. Z. Jacob, J.-Y. Kim, G.V. Naik, A. Boltasseva, E.E. Narimanov, and V.M. Shalaev, “Engineering the photonic density of states with metamaterials,” Appl. Phys. B 100(1), 215–218 (2010). [CrossRef]

, 19

19. O. Kidwai, S. V. Zhukovsky, and J. E. Sipe, “Dipole radiation near hyperbolic metamaterials: applicability of effective-medium approximation,” Opt. Lett. 36(13), 2530–2532 (2011). [CrossRef] [PubMed]

, 22

22. O. Kidwai, S. V. Zhukovsky, and J. E. Sipe, “Effective-medium approach to planar multilayer hyperbolic meta-materials: Strengths and limitations,” Phys. Rev. A 85(5), 053842 (2012). [CrossRef]

].

Indeed, Figs. 3(a) and 3(b) show the existence of such a band for ds = 8 nm in stark contrast with its absence for ds = 0. Comparing the reflection properties of the structures with finite number of periods N [Fig. 3(c)], we see that the overall character of the band is preserved for finite N, and the spectrum for N = 5 qualitatively coincides with that for N = ∞.

Fig. 3 High-κ wave vector dependencies of ImRp for (a) ds = 0, N = ∞; (b) ds = 8 nm, N = ∞; (c) ds = 8 nm and N = 2, 3, 5.

To be able to compare the spontaneous emission enhancement of Eq. (4) with the luminescence enhancement in [31

31. T. Ozel, S. Nizamoglu, M. A. Sefunc, O. Samarskaya, I. O. Ozel, E. Mutlugun, V. Lesnyak, N. Gaponik, A. Eychmuller, S. V. Gaponenko, and H. V. Demir, “Anisotropic emission from multilayered plasmon resonator nanocomposites of isotropic semiconductor quantum dots,” ACS Nano 5(2), 1328–1334 (2011). [CrossRef] [PubMed]

], one needs to distinguish between the radiative (enhancement) and non-radiative (quenching) Purcell factor. To do so, we have artificially negated all losses in the system; the resulting enhancement thus has to be purely radiative. Even though the action of an HMM on an emitter is very likely to result in coupling to large-wavevector modes that do not couple outside of the structure in the ideal case, making the luminescence enhancement hard to observe, the associated emission enhancement is still radiative from the physical point of view because modes in the metamaterial are external with respect to the emitter. Indeed, luminescence enhancement was reported to accompany the lifetime shortening of emitters placed close to multilayer HMMs [24

24. J. Kim, V. P. Drachev, Z. Jacob, G. V. Naik, A. Boltasseva, E. E. Narimanov, and V. M. Shalaev, “Improving the radiative decay rate for dye molecules with hyperbolic metamaterials,” Opt. Express 20(7), 8100–8116 (2012). [CrossRef] [PubMed]

]. Hence, the rate between b(ds ≠ 0) and b(ds = 0) can be regared as an estimate of the luminescence enhancement factor due to the HMM character of the infinite-period NP-spacer-NC nanocomposite. Shown in Fig. 4 for two different orientations of the emitting dipole, it is seen that the enhancement grows as ds becomes larger, and then falls back towards unity as spacer layers become so thick that the high-κ band is suppressed. It can be seen that for ds < 10 nm, the enhancement is markedly stronger at shorter wavelength for one of the orientation of the emitting dipoles, explaining a slight blue shift of the luminescence peak in experiments [31

31. T. Ozel, S. Nizamoglu, M. A. Sefunc, O. Samarskaya, I. O. Ozel, E. Mutlugun, V. Lesnyak, N. Gaponik, A. Eychmuller, S. V. Gaponenko, and H. V. Demir, “Anisotropic emission from multilayered plasmon resonator nanocomposites of isotropic semiconductor quantum dots,” ACS Nano 5(2), 1328–1334 (2011). [CrossRef] [PubMed]

]. It can also be seen that the enhancement is different for the different orientation of the emitter, confirming the observed anisotropy in photoluminescence spectra [31

31. T. Ozel, S. Nizamoglu, M. A. Sefunc, O. Samarskaya, I. O. Ozel, E. Mutlugun, V. Lesnyak, N. Gaponik, A. Eychmuller, S. V. Gaponenko, and H. V. Demir, “Anisotropic emission from multilayered plasmon resonator nanocomposites of isotropic semiconductor quantum dots,” ACS Nano 5(2), 1328–1334 (2011). [CrossRef] [PubMed]

].

Fig. 4 Ratio of decay rate for the structure with and without spacer [β = b(ds)/b(ds = 0)] in absence of material losses and therefore corresponding to the radiative rate enhancement for (a) parallel (f = 1, f = 0) and (b) perpendicular (f = 1, f = 0) orientation of the emitting dipole. The middle column shows the 2D dependence β(ds, λ); the left column shows β(ds) at three wavelengths; the right column shows β(λ) for three values of ds.

The calculated values of the enhancement factor are between 1.5 and 2.0 (Fig. 4). For comparison with the theoretical modeling we recall the results of experimental studies of luminescence lifetime parameters for the multilayer structure and for its individual components. The lifetime for a sole quantum dot layer was measured to be 7.66 ± 0.24 ns. The lifetime of a single period of the structure, i.e. a quantum dot layer over a metal Au nanoparticles layer separated by a dielectric spacer was measured to be 5.31 ± 0.17 ns. The 5-period structure was found to feature 2.85 ± 0.11 ns [31

31. T. Ozel, S. Nizamoglu, M. A. Sefunc, O. Samarskaya, I. O. Ozel, E. Mutlugun, V. Lesnyak, N. Gaponik, A. Eychmuller, S. V. Gaponenko, and H. V. Demir, “Anisotropic emission from multilayered plasmon resonator nanocomposites of isotropic semiconductor quantum dots,” ACS Nano 5(2), 1328–1334 (2011). [CrossRef] [PubMed]

]. Therefore one can see that the typical plasmonic enhancement of decay rate known for single-layered metal-dielectric (semiconductor) structures (see, e.g. [23

23. D. V. Guzatov, S. V. Vaschenko, V. V. Stankevich, A. Y. Lunevich, Y. F. Glukhov, and S. V. Gaponenko, “Plasmonic enhancement of molecular fluorescence near silver nanoparticles: theory, modeling, and experiment,” J. Phys. Chem. C 116(19), 10723–10733 (2012). [CrossRef]

, 36

36. S. V. Gaponenko, Introduction to Nanophotonics (Cambridge University Press, 2010). [CrossRef]

]) cannot be responsible for the lifetime modification observed for the 5-period structure. For the reasonable comparison with the modeling, experimental results for lifetime in the periodic structure should be compared with the reference data for a single dot-spacer-metal period rather than with intrinsic lifetime of sole quantum dot layer. Comparing 2.85 versus 5.31 ns one arrives at 1.86-fold reduction in the lifetime and, accordingly 1.86-fold enhancement of the decay rate. This falls into the theoretically predicted values of decay rate enhancement, β = 1.5...2, presented in Fig. 4.

Therefore, we can conclude that the observed 1.86-fold increase in the decay rate reasonably agrees with the theoretical modeling and cannot be attributed entirely to the plasmonic effect in a single layer; rather, it is the result of the fact that the multilayer structure acquires the properties of a hyperbolic medium. This conclusion is additionally supported by the growing anisotropy of emission in terms of more strongly polarized emission for a larger number of layers. This observation means again that the multilayer structure does gain additional features which do not reduce to simple sum of the properties inherent in a single period. We bear in mind the this semi-qualitative analysis is by no means exhaustive, and further experiments shall be performed to examine the complicated spatially-angular features of output luminescence owing to specific HMM modes. These experiments are planned with thicker structures since the approximately 400 nm thickness of the structure examined may not demonstrate HMM mode properties to their full extent.

On the other hand, we expect that an even greater agreement with the experimental results can be obtained by using a more refined model, which would take into account the positions of individual NCs within the structure [21

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

] by generalizing it to account for finite-N structures. Another potential source of disagreements is the spoof character of SPPs in a highly corrugated NP monolayer compared to a smooth layer, potentially leading to a stronger field confinement and a more pronounced PDOS increase as a result. We believe that these two approximations are the strongest simplifications involved in the present model, and going beyond them is an interesting topic for further studies.

It also becomes clear that the HMM character of the structure, and hence the predicted photoluminescence enhancement, becomes stronger if the high-κ band (see Fig. 3) is more pronounced. Hence, we can use the presented theoretical findings to further optimize the composite design using this criterion. As mentioned above, we know that the high-κ band is wider for structures with thinner layers, so it can be expected that lowering mp from 3 to 1 would improve the response of the structure. It can also be seen that lower |εz| brings the high-κ band towards the smaller κ, making it less susceptible to the NC size cut-off in Eq. (4).

Figure 5 shows that indeed, lowering mq from 3 to 1 significantly increases both the width of the high-κ band and the magnitude of ImR inside it [cf. Figs. 3(b), 5(a), and 5(d)]. As established above, this can drastically boost the spontaneous emission and NC luminescence enhancement. On the contrary, lowering mq [cf. Figs. 5(a)–5(c)] does not influence the HMM band much, although it does make it more pronounced at the higher-wavelength edge. This is because of the overall decrease of losses in the material due to the reduction of the overall content of CdTe. One can note, however, that many HMM characteristics were shown to be robust against the presence of ohmic losses in the metal [9

9. N. Mattiucci, G. D’Aguanno, M. Scalora, M. J. Bloemer, and C. Sibilia, “Transmission function properties for multi-layered structures: Application to super-resolution,” Opt. Express 17(20), 17517–17529 (2009). [CrossRef] [PubMed]

, 22

22. O. Kidwai, S. V. Zhukovsky, and J. E. Sipe, “Effective-medium approach to planar multilayer hyperbolic meta-materials: Strengths and limitations,” Phys. Rev. A 85(5), 053842 (2012). [CrossRef]

].

Fig. 5 Same as Fig. 3(b) but for different number of NP and NC monolayers mp and mq.

4. Conclusions

We have demonstrated that nanocomposites consisting of layers of self-assembled colloidal semiconductor quantum dots arranged between layers of likewise assembled metal nanoparticles [Fig. 1(c)] can function as multilayer HMMs. Depending on the geometric parameters of the composite, such as the number of quantum dot and nanoparticle layers, as well as the thickness of the spacer layer between quantum dots and nanoparticles, the effective permittivity tensor of the entire nanocomposite may become indefinite (see Fig. 2). This leads to an increase in the photonic density of states, in turn resulting in strong enhancement and pronounced polarization anisotropy of quantum dot luminescence [24

24. J. Kim, V. P. Drachev, Z. Jacob, G. V. Naik, A. Boltasseva, E. E. Narimanov, and V. M. Shalaev, “Improving the radiative decay rate for dye molecules with hyperbolic metamaterials,” Opt. Express 20(7), 8100–8116 (2012). [CrossRef] [PubMed]

]. This offers an alternative explanation of the results of recent experiments [31

31. T. Ozel, S. Nizamoglu, M. A. Sefunc, O. Samarskaya, I. O. Ozel, E. Mutlugun, V. Lesnyak, N. Gaponik, A. Eychmuller, S. V. Gaponenko, and H. V. Demir, “Anisotropic emission from multilayered plasmon resonator nanocomposites of isotropic semiconductor quantum dots,” ACS Nano 5(2), 1328–1334 (2011). [CrossRef] [PubMed]

]. At the same time, these results allow to see these experiments in new light, directly confirming that HMMs are capable of increasing the radiative decay rate of emission centers placed inside them, in the same way as the more recent demonstration by Kim et al in [24

24. J. Kim, V. P. Drachev, Z. Jacob, G. V. Naik, A. Boltasseva, E. E. Narimanov, and V. M. Shalaev, “Improving the radiative decay rate for dye molecules with hyperbolic metamaterials,” Opt. Express 20(7), 8100–8116 (2012). [CrossRef] [PubMed]

].

Acknowledgments

The authors thank F. J. Arregui for helpful suggestions. This work has been partially supported by the Basic Research Foundation of Belarus. S.V. Z. wishes to acknowledge financial support from the People Programme (Marie Curie Actions) of the European Union’s 7th Framework (EU FP7) Programme FP7-PEOPLE-2011-IIF under REA grant agreement No. 302009 (Project HyPHONE). N.G., A.E., and H.V. D acknowledge partial financial support from EU FP7 Network of Excellence “Nanophotonics for Energy Efficiency (N4E)”. H.V.D., E.M., and T.O. gratefully acknowledge Singapore National Research Foundation (NRF) under programs NRF-RF-2009-09 and NRF-CRP-6-2010-02, as well as TÜBA -- Turkish Academy of Sciences..

References and links

1.

D. R. Smith, D. Schurig, J. J. Mock, P. Kolinko, and P. Rye, “Partial focusing of radiation by a slab of indefinite media,” Appl. Phys. Lett. 84(13), 2244–2246 (2004). [CrossRef]

2.

M. A. Noginov, H. Li, Yu. A. Barnakov, D. Dryden, G. Nataraj, G. Zhu, C. E. Bonner, M. Mayy, Z. Jacob, and E. E. Narimanov, “Controlling spontaneous emission with metamaterials,” Opt. Lett. 35(11), 1863–1865 (2010). [CrossRef] [PubMed]

3.

Z. Jacob, J.-Y. Kim, G.V. Naik, A. Boltasseva, E.E. Narimanov, and V.M. Shalaev, “Engineering the photonic density of states with metamaterials,” Appl. Phys. B 100(1), 215–218 (2010). [CrossRef]

4.

Z. Jacob, I. I. Smolyaninov, and E.E. Narimanov, “Broadband Purcell effect: Radiative decay engineering with metamaterials,” Appl. Phys. Lett. 100(18), 181105 (2012). [CrossRef]

5.

C. Simovski, S. Maslovski, I. Nefedov, and S. Tretyakov, “Optimization of radiative heat transfer in hyperbolic metamaterials for thermophotovoltaic applications,” Opt. Express 21(12), 14988–15013 (2013). [CrossRef] [PubMed]

6.

Y. Guo and Z. Jacob, “Thermal hyperbolic metamaterials,” Opt. Express 21(12), 15014–15019 (2013). [CrossRef] [PubMed]

7.

T. Morgado, S. I. Maslovski, and M. G. Silveirinha, “Ultrahigh Casimir interaction torque in nanowire systems,” Opt. Express 21(12), 14943–14955 (2013). [CrossRef] [PubMed]

8.

G. D’Aguanno, N. Mattiucci, M. Bloemer, and A. Desyatnikov, “Optical vortices during a superresolution process in a metamaterial,” Phys. Rev. A 77(4), 043825 (2008). [CrossRef]

9.

N. Mattiucci, G. D’Aguanno, M. Scalora, M. J. Bloemer, and C. Sibilia, “Transmission function properties for multi-layered structures: Application to super-resolution,” Opt. Express 17(20), 17517–17529 (2009). [CrossRef] [PubMed]

10.

S. Ramakrishna, J. Pendry, M. Wiltshire, and W. Stewart, “Imaging the near field,” J. Mod. Opt. 50(9), 1419–1430 (2003). [CrossRef]

11.

Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical Hyperlens: Far-field imaging beyond the diffraction limit,” Opt. Express 14(18), 8247–8256 (2006). [CrossRef] [PubMed]

12.

N. Mattiucci, M. J. Bloemer, N. Aközbek, and G. D’Aguanno, “Impedance matched thin metamaterials make metals absorbing,” Sci. Rep. 3, 3203 (2013). [CrossRef] [PubMed]

13.

E. E. Narimanov, H. Li, Y. A. Barnakov, T. U. Tumkur, and M. A. Noginov, “Reduced reflection from roughened hyperbolic metamaterial,” Opt. Express 21(12), 14956–14961 (2013). [CrossRef] [PubMed]

14.

I. I. Smolyaninov and E. E. Narimanov, “Metric signature transitions in optical metamaterials,” Phys. Rev. Lett. 105(6), 067402 (2010). [CrossRef] [PubMed]

15.

I. I. Smolyaninov and Yu-Ju Hung, “Modeling of time with metamaterials,” J. Opt. Soc. Am. B 28(7), 1591–1595 (2011). [CrossRef]

16.

C. L. Cortes, W. Newman, S. Molesky, and Z. Jacob, “Quantum nanophotonics using hyperbolic metamaterials,” J. Opt. 14(6), 063001 (2012). [CrossRef]

17.

V. Drachev, V. A. Podolskiy, and A. V. Kildishev, “Hyperbolic Metamaterials: new physics behind a classical problem,” Opt. Express 21(12), 15048–15064 (2013). [CrossRef] [PubMed]

18.

M. A. Noginov, Yu. A. Barnakov, G. Zhu, T. Tumkur, H. Li, and E. E. Narimanov, “Bulk photonic metamaterial with hyperbolic dispersion,” Appl. Phys. Lett. 94(15), 151105 (2009). [CrossRef]

19.

O. Kidwai, S. V. Zhukovsky, and J. E. Sipe, “Dipole radiation near hyperbolic metamaterials: applicability of effective-medium approximation,” Opt. Lett. 36(13), 2530–2532 (2011). [CrossRef] [PubMed]

20.

A. N. Poddubny, P. A. Belov, and Yu. S. Kivshar, “Spontaneous radiation of a finite-size dipole emitter in hyperbolic media,” Phys. Rev. A 84(2), 023807 (2011). [CrossRef]

21.

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

22.

O. Kidwai, S. V. Zhukovsky, and J. E. Sipe, “Effective-medium approach to planar multilayer hyperbolic meta-materials: Strengths and limitations,” Phys. Rev. A 85(5), 053842 (2012). [CrossRef]

23.

D. V. Guzatov, S. V. Vaschenko, V. V. Stankevich, A. Y. Lunevich, Y. F. Glukhov, and S. V. Gaponenko, “Plasmonic enhancement of molecular fluorescence near silver nanoparticles: theory, modeling, and experiment,” J. Phys. Chem. C 116(19), 10723–10733 (2012). [CrossRef]

24.

J. Kim, V. P. Drachev, Z. Jacob, G. V. Naik, A. Boltasseva, E. E. Narimanov, and V. M. Shalaev, “Improving the radiative decay rate for dye molecules with hyperbolic metamaterials,” Opt. Express 20(7), 8100–8116 (2012). [CrossRef] [PubMed]

25.

S. Zhukovsky, O. Kidwai, and J. E. Sipe, “Physical nature of volume plasmon polaritons in hyperbolic metamaterials,” Opt. Express 21(12), 14982–14987 (2013). [CrossRef] [PubMed]

26.

O. Kulakovich, N. Strekal, A. Yaroshevich, S. Maskevich, S. Gaponenko, I. Nabiev, U. Woggon, and M. Artemyev, “Enhanced luminescence of CdSe quantum dots on gold colloids,” Nano Lett. 2(12), 1449–1452 (2002). [CrossRef]

27.

M. Lunz, V. A. Gerard, Y. K. Gunko, V. Lesnyak, N. Gaponik, A. S. Susha, A. L. Rogach, and A. L. Bradley, “Surface plasmon enhanced energy transfer between donor and acceptor CdTe nanocrystal quantum dot monolayers,” Nano Lett. 11(8), 3341–3345 (2011). [CrossRef] [PubMed]

28.

T. Ozel, P. L. Hernandez Martinez, E. Mutlugun, O. Akin, S. Nizamoglu, I. O. Ozel, and H. V. Demir, “Observation of selective plasmon-exciton coupling in nonradiative energy transfer: Donor-selective vs. acceptor-selective plexcitons,” Nano Lett. 13(6), 3065–3071 (2013). [CrossRef] [PubMed]

29.

M. L. Brongersma, J. W. Hartman, and H. A. Atwater, “Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit,” Phys. Rev. B 62(24), R16356 (2000). [CrossRef]

30.

M. Navarro-Cìa, M. Beruete, S. Agrafiotis, F. Falcone, M. Sorolla, and S. A. Maier, “Broadband spoof plasmons and subwavelength electromagnetic energy confinement on ultrathin metafilms,” Opt. Express 17(20), 18184–18195 (2009). [CrossRef] [PubMed]

31.

T. Ozel, S. Nizamoglu, M. A. Sefunc, O. Samarskaya, I. O. Ozel, E. Mutlugun, V. Lesnyak, N. Gaponik, A. Eychmuller, S. V. Gaponenko, and H. V. Demir, “Anisotropic emission from multilayered plasmon resonator nanocomposites of isotropic semiconductor quantum dots,” ACS Nano 5(2), 1328–1334 (2011). [CrossRef] [PubMed]

32.

K. Dolgaleva and R. W. Boyd, “Local-field effects in nanostructured photonic materials,” Adv. Opt. Photon. 4(1), 1–77 (2012). [CrossRef]

33.

J. H. Kim, J. H. Hwang, and T. Y. Lim, “A layer-by-layer self-assembly method for organic-inorganic hybrid multilayer thin films,” J. Ceram. Process. Res. 10(6), 770–773 (2009).

34.

M. Fujita, S. Takahashi, Y. Tanaka, T. Asano, and S. Noda., “Simultaneous inhibition and redistribution of spontaneous light emission in photonic crystals,” Science 308(5726), 1296–1298 (2005). [CrossRef] [PubMed]

35.

A. F. Koenderink, M. Kafesaki, C. M. Soukolis, and V. Sandoghdar, “Spontaneous emission in the near field of two-dimensional photonic crystals,” Opt. Lett. 30(23), 3210–3212 (2005). [CrossRef] [PubMed]

36.

S. V. Gaponenko, Introduction to Nanophotonics (Cambridge University Press, 2010). [CrossRef]

OCIS Codes
(160.1190) Materials : Anisotropic optical materials
(160.3918) Materials : Metamaterials
(160.4236) Materials : Nanomaterials
(250.5590) Optoelectronics : Quantum-well, -wire and -dot devices

ToC Category:
Metamaterials

History
Original Manuscript: March 21, 2014
Revised Manuscript: May 27, 2014
Manuscript Accepted: July 6, 2014
Published: July 22, 2014

Citation
S. V. Zhukovsky, T. Ozel, E. Mutlugun, N. Gaponik, A. Eychmuller, A. V. Lavrinenko, H. V. Demir, and S. V. Gaponenko, "Hyperbolic metamaterials based on quantum-dot plasmon-resonator nanocomposites," Opt. Express 22, 18290-18298 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-15-18290


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References

  1. D. R. Smith, D. Schurig, J. J. Mock, P. Kolinko, and P. Rye, “Partial focusing of radiation by a slab of indefinite media,” Appl. Phys. Lett.84(13), 2244–2246 (2004). [CrossRef]
  2. M. A. Noginov, H. Li, Yu. A. Barnakov, D. Dryden, G. Nataraj, G. Zhu, C. E. Bonner, M. Mayy, Z. Jacob, and E. E. Narimanov, “Controlling spontaneous emission with metamaterials,” Opt. Lett.35(11), 1863–1865 (2010). [CrossRef] [PubMed]
  3. Z. Jacob, J.-Y. Kim, G.V. Naik, A. Boltasseva, E.E. Narimanov, and V.M. Shalaev, “Engineering the photonic density of states with metamaterials,” Appl. Phys. B100(1), 215–218 (2010). [CrossRef]
  4. Z. Jacob, I. I. Smolyaninov, and E.E. Narimanov, “Broadband Purcell effect: Radiative decay engineering with metamaterials,” Appl. Phys. Lett.100(18), 181105 (2012). [CrossRef]
  5. C. Simovski, S. Maslovski, I. Nefedov, and S. Tretyakov, “Optimization of radiative heat transfer in hyperbolic metamaterials for thermophotovoltaic applications,” Opt. Express21(12), 14988–15013 (2013). [CrossRef] [PubMed]
  6. Y. Guo and Z. Jacob, “Thermal hyperbolic metamaterials,” Opt. Express21(12), 15014–15019 (2013). [CrossRef] [PubMed]
  7. T. Morgado, S. I. Maslovski, and M. G. Silveirinha, “Ultrahigh Casimir interaction torque in nanowire systems,” Opt. Express21(12), 14943–14955 (2013). [CrossRef] [PubMed]
  8. G. D’Aguanno, N. Mattiucci, M. Bloemer, and A. Desyatnikov, “Optical vortices during a superresolution process in a metamaterial,” Phys. Rev. A77(4), 043825 (2008). [CrossRef]
  9. N. Mattiucci, G. D’Aguanno, M. Scalora, M. J. Bloemer, and C. Sibilia, “Transmission function properties for multi-layered structures: Application to super-resolution,” Opt. Express17(20), 17517–17529 (2009). [CrossRef] [PubMed]
  10. S. Ramakrishna, J. Pendry, M. Wiltshire, and W. Stewart, “Imaging the near field,” J. Mod. Opt.50(9), 1419–1430 (2003). [CrossRef]
  11. Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical Hyperlens: Far-field imaging beyond the diffraction limit,” Opt. Express14(18), 8247–8256 (2006). [CrossRef] [PubMed]
  12. N. Mattiucci, M. J. Bloemer, N. Aközbek, and G. D’Aguanno, “Impedance matched thin metamaterials make metals absorbing,” Sci. Rep.3, 3203 (2013). [CrossRef] [PubMed]
  13. E. E. Narimanov, H. Li, Y. A. Barnakov, T. U. Tumkur, and M. A. Noginov, “Reduced reflection from roughened hyperbolic metamaterial,” Opt. Express21(12), 14956–14961 (2013). [CrossRef] [PubMed]
  14. I. I. Smolyaninov and E. E. Narimanov, “Metric signature transitions in optical metamaterials,” Phys. Rev. Lett.105(6), 067402 (2010). [CrossRef] [PubMed]
  15. I. I. Smolyaninov and Yu-Ju Hung, “Modeling of time with metamaterials,” J. Opt. Soc. Am. B28(7), 1591–1595 (2011). [CrossRef]
  16. C. L. Cortes, W. Newman, S. Molesky, and Z. Jacob, “Quantum nanophotonics using hyperbolic metamaterials,” J. Opt.14(6), 063001 (2012). [CrossRef]
  17. V. Drachev, V. A. Podolskiy, and A. V. Kildishev, “Hyperbolic Metamaterials: new physics behind a classical problem,” Opt. Express21(12), 15048–15064 (2013). [CrossRef] [PubMed]
  18. M. A. Noginov, Yu. A. Barnakov, G. Zhu, T. Tumkur, H. Li, and E. E. Narimanov, “Bulk photonic metamaterial with hyperbolic dispersion,” Appl. Phys. Lett.94(15), 151105 (2009). [CrossRef]
  19. O. Kidwai, S. V. Zhukovsky, and J. E. Sipe, “Dipole radiation near hyperbolic metamaterials: applicability of effective-medium approximation,” Opt. Lett.36(13), 2530–2532 (2011). [CrossRef] [PubMed]
  20. A. N. Poddubny, P. A. Belov, and Yu. S. Kivshar, “Spontaneous radiation of a finite-size dipole emitter in hyperbolic media,” Phys. Rev. A84(2), 023807 (2011). [CrossRef]
  21. I. Iorsh, A. Poddubny, A. Orlov, P. Belov, and Yu. Kivshar, “Spontaneous emission enhancement in metal-dielectric metamaterials,” Phys. Lett. A376(3), 185–187 (2012). [CrossRef]
  22. O. Kidwai, S. V. Zhukovsky, and J. E. Sipe, “Effective-medium approach to planar multilayer hyperbolic meta-materials: Strengths and limitations,” Phys. Rev. A85(5), 053842 (2012). [CrossRef]
  23. D. V. Guzatov, S. V. Vaschenko, V. V. Stankevich, A. Y. Lunevich, Y. F. Glukhov, and S. V. Gaponenko, “Plasmonic enhancement of molecular fluorescence near silver nanoparticles: theory, modeling, and experiment,” J. Phys. Chem. C116(19), 10723–10733 (2012). [CrossRef]
  24. J. Kim, V. P. Drachev, Z. Jacob, G. V. Naik, A. Boltasseva, E. E. Narimanov, and V. M. Shalaev, “Improving the radiative decay rate for dye molecules with hyperbolic metamaterials,” Opt. Express20(7), 8100–8116 (2012). [CrossRef] [PubMed]
  25. S. Zhukovsky, O. Kidwai, and J. E. Sipe, “Physical nature of volume plasmon polaritons in hyperbolic metamaterials,” Opt. Express21(12), 14982–14987 (2013). [CrossRef] [PubMed]
  26. O. Kulakovich, N. Strekal, A. Yaroshevich, S. Maskevich, S. Gaponenko, I. Nabiev, U. Woggon, and M. Artemyev, “Enhanced luminescence of CdSe quantum dots on gold colloids,” Nano Lett.2(12), 1449–1452 (2002). [CrossRef]
  27. M. Lunz, V. A. Gerard, Y. K. Gunko, V. Lesnyak, N. Gaponik, A. S. Susha, A. L. Rogach, and A. L. Bradley, “Surface plasmon enhanced energy transfer between donor and acceptor CdTe nanocrystal quantum dot monolayers,” Nano Lett.11(8), 3341–3345 (2011). [CrossRef] [PubMed]
  28. T. Ozel, P. L. Hernandez Martinez, E. Mutlugun, O. Akin, S. Nizamoglu, I. O. Ozel, and H. V. Demir, “Observation of selective plasmon-exciton coupling in nonradiative energy transfer: Donor-selective vs. acceptor-selective plexcitons,” Nano Lett.13(6), 3065–3071 (2013). [CrossRef] [PubMed]
  29. M. L. Brongersma, J. W. Hartman, and H. A. Atwater, “Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit,” Phys. Rev. B62(24), R16356 (2000). [CrossRef]
  30. M. Navarro-Cìa, M. Beruete, S. Agrafiotis, F. Falcone, M. Sorolla, and S. A. Maier, “Broadband spoof plasmons and subwavelength electromagnetic energy confinement on ultrathin metafilms,” Opt. Express17(20), 18184–18195 (2009). [CrossRef] [PubMed]
  31. T. Ozel, S. Nizamoglu, M. A. Sefunc, O. Samarskaya, I. O. Ozel, E. Mutlugun, V. Lesnyak, N. Gaponik, A. Eychmuller, S. V. Gaponenko, and H. V. Demir, “Anisotropic emission from multilayered plasmon resonator nanocomposites of isotropic semiconductor quantum dots,” ACS Nano5(2), 1328–1334 (2011). [CrossRef] [PubMed]
  32. K. Dolgaleva and R. W. Boyd, “Local-field effects in nanostructured photonic materials,” Adv. Opt. Photon.4(1), 1–77 (2012). [CrossRef]
  33. J. H. Kim, J. H. Hwang, and T. Y. Lim, “A layer-by-layer self-assembly method for organic-inorganic hybrid multilayer thin films,” J. Ceram. Process. Res.10(6), 770–773 (2009).
  34. M. Fujita, S. Takahashi, Y. Tanaka, T. Asano, and S. Noda., “Simultaneous inhibition and redistribution of spontaneous light emission in photonic crystals,” Science308(5726), 1296–1298 (2005). [CrossRef] [PubMed]
  35. A. F. Koenderink, M. Kafesaki, C. M. Soukolis, and V. Sandoghdar, “Spontaneous emission in the near field of two-dimensional photonic crystals,” Opt. Lett.30(23), 3210–3212 (2005). [CrossRef] [PubMed]
  36. S. V. Gaponenko, Introduction to Nanophotonics (Cambridge University Press, 2010). [CrossRef]

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