Abstract

In this paper, the possibility of shaping the gain/absorption spectrum in tunable hyperbolic metamaterial (THMM) composed of subsequent layers of graphene and active/passive material by external biasing is demonstrated. For the first time it has been shown that resonance transitions between different dispersion regimes, i.e., Type I HMM→elliptic, elliptic→Type II HMM, elliptic→Type I HMM, are accompanied by interesting optical effects, such as anisotropic effective gain/absorption enhancement or electromagnetic transparency, all controllable by external voltage. We believe that this kind of tunable metamaterial could lay the foundation for a new class of active/passive media with controllable gain/absorption or electromagnetic transparency.

© 2017 Optical Society of America

1. Introduction

Hyperbolic metamaterials are uniaxial structures characterized by the permittivity tensor of the diagonal form [ε] = diag(ε||,ε||,ε). The principal components have the opposite signs ε||>0, ε<0 (Type I), ε||<0, ε>0 (Type II) [1], which leads to unclosed (hyperbolic-type) surface of dispersion in space of wave vectors, known as hyperbolic dispersion. Moreover, this kind of structures can exhibit Epsilon-Near-Zero (ENZ) behavior, i.e., effective permittivity achieving value near zero [2], which can be utilize in harmonic generation [3,4], perfect absorption [5], solitons, freezing light [6], supercoupling [7] and shaping radiation pattern of the source [8]. Further applications can be found when it comes to Type I and Type II hyperbolic dispersion offering existence of unique metamaterial states with large magnitude wavevectors (the high-k states) which are evanescent and decay exponentially in conventional media [1,9]. This feature gives rise to many device applications, such as hyperlenses [10], superlenses [9], enhanced light emission [11–13], quantum information systems [14], biochemical sensing [15], plasmon waveguiding [16], and many others as e.g., broadband super absorbers and thermal emitters [9,17].

In particular, the important consequence of unbounded dispersion of Type I and Type II HMM is a divergent photonic density of states resulting in an enhancement in the spontaneous emission of dipole emitters placed in the vicinity of HMM leading to a metamaterial-based broadband Purcell effect [18], in contrast to conventional methods based on optical resonators [19], photonic crystals cavities [20] and plasmonic aperture [21], which are all bandwidth limited. This concept has been theoretically and experimentally investigated by many research groups, and they have observed a large modification (including decay rate and pattern) of spontaneous emission of emitters (organic dyes and quantum dots) localized nearby HMM or embedded inside HMM [13].

Generally, gain-enhanced metamaterial structures have been intensively discussed in means of enhancing active imaging, ultrafast nonlinearities as well as cavity-free nanolasing [22,23]. However, studies concerning HMM structures composed of active material with optical gain were limited only to loss compensation in bulk [24] and waveguide [25] structures. Recently, it has been experimentally demonstrated that active HMM structure, i.e., gold nanorod array coated in thin film of optical gain medium composed of Rhodamine 101 doped polyvinyl alcohol (PVA), can be utilized to enhance lasing action, which could serve as a platform to achieve broadband coherent photon sources [26].

On the other hand, Tunable Hyperbolic Metamaterials (THMM) based on stimulus-sensitive functional materials allowing for active control of structure’s properties by external perturbations, i.e., electric/magnetic field or temperature, have recently attracted a widespread attention of the researchers. In this case, possibility of controlling dispersion shape of such structures gives rise to new potential applications. Especially, main efforts have been put on graphene/dielectric multilayer nanostructures showing potential for designing efficient absorbers [27–31], photonic switches [32,33], optical modulators based on reflection [34] as well as stopped light effect [35], all controllable by external electric field. Recently it has been shown that, in this kind of structures the control of dispersion regimes, i.e., Type I HMM, elliptic, Type II HMM, using external biasing is possible [36]. Moreover, the manufacturing THMM structures is possible by use of functional materials, such as semiconductors [37], conductive oxides [38], liquid crystals [39], phase-change materials [40] or gyromagnetics [41].

In this paper we propose a special class of THMM structure based on bilayers consisting of a material possessing optical gain/absorption and voltage-sensitive graphene providing tunability of complete structure. The presented analysis is focused on effects resulting from resonant electromagnetic response of complete THMM structure. In particular, it has been revealed that the change of dispersion from Type I HMM to elliptic, accompanied by sharp resonance transition of effective permittivity, leads not only to significant increase of effective gain/absorption, but also narrowing of effective bandwidth with respect to constituent gain/absorptive material. Furthermore, the wavelength of the gain/absorption maximum can be selected by proper voltage biasing. It has been also shown that the other transitions, i.e., elliptic → Type II HMM and elliptic → Type I HMM, offer two opposite effects: gain/absorption enhancement and electromagnetic transparency, respectively, both controlled by external voltage. All of considered effects are anisotropic and sensitive for wave propagation direction.

2. Theory

The single unit cell of considered THMM structure is composed of a graphene layer and a gain/absorption layer with thicknesses tgraph, tg/ab and complex permittivities εgraph, εg/ab, respectively, where their imaginary parts contribute to loss (Im(ɛ) > 0) or gain (Im(ɛ) < 0), see Fig. 1. Moreover, dispersion of both permittivities has been taken into account. Without losing the generality, the gain\absorptive material is characterized by well-defined permittivity of thulium-doped silicate glass. The considered structure consists of 6 monolayers of graphene (tgraph = 2.1 nm) and 10 nm layer of thulium doped silicate glass. What is worth noting, the thicknesses of layers have been selected to ensure existence of all three dispersion regimes [36].

 figure: Fig. 1

Fig. 1 Scheme of considered structure.

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According to [42], L.A. Falkovsky and A. A. Varlamov, the graphene’s effective permittivity can be written as:

εgraph=1jσ(ω,μc)ωεotgraph,
where ɛ0 is the vacuum permittivity and σ is the conductivity of a single-layer graphene. Moreover, frequency and chemical potential dependent conductivity of a monolayer graphene can be given by Kubo formula [42]:
σ(ω,μc)=j4πq2kBTh2(ωj2τ)[μckBT+2ln(eμ/kBT+1)]+j4πq2(ωj2τ)h20fD(ξ)fD(ξ)(ωj2τ)216(πξh)dξ,
where fD(ξ) is the Fermi-Dirac function: fD(ξ) = [exp(ξ-μC/kBT) + 1]−1, μc is the chemical potential, T is temperature, kB and h are Boltzmann and Planck’s constant, ω is the angular frequency of the incident wave, and τ is the phenomenological scattering rate, which we set equal 0.1 meV. Moreover, conductivity of multilayer graphene (up to 6 monolayers; Ngraph ≤ 6) can be described by σml = σNgraph, where Ngraph is the number of graphene layers [43]. Furthermore, chemical potential of graphene can be changed by applying external voltage, accordingly to following formula [32]:
|μc|=υFπ|a0(VgVdirac)|,
where ħ is Dirac constant, υF is the Fermi velocity of Dirac fermions in graphene (∼106 m/s), a0 = 9 × 1016 m−1V−1, Vdirac is offset bias which reflects graphene’s doping and/or its impurities. This description of conductivity is consistent to the assumption that the electronic band structure of a graphene sheet is not affected by the neighboring graphene sheets [43]. It is worth noting that, more accurate model of electrical tuning for 6-layer graphene would change the relationship between voltage and chemical potential, but will not influence obtained functionality. In our analysis we assumed pristinity of graphene monolayers, i.e., Vdirac = 0. Moreover, maximal value of biasing voltage does not exceed Vgmax = 2 V to ensure elimination of tunneling between graphene layers separated by 10 nm thick layer of thulium-doped glass material [44].

In our analysis we assume that the real part of permittivity of silica glass lowly-doped with thulium ions (1000 ppm) is determined by pure silica glass and described by empirical Sellmeier equation [45]:

Re(εg/ab(λ))1+a1λ2λ2l12+a2λ2λ2l22+a3λ2λ2l32
where, a1 = 012212122 l1 = 0.0684043, a2 = 0.4079426, l2 = 0.1162414, a3 = 0.8974794, l3 = 9.896161 are empirical coefficients describing dispersion of fused silica [45]. Moreover, the imaginary part of permittivity, responsible for gain or absorption, is determined by resonances of thulium ions and can be calculated on the basis of the McCumber theory [46]:
g(λ)=Nσem(λ),
α(λ)=Nσabs(λ),
where N is ion density and equals to 1000 ppm, which is typical value for thulium doped media corresponding to 3.1∙1025 ions/m3 [47]. and σem/abs is emission/absorption cross-section described for each optical transition by following formula [48]:

σem/abs(λ)=k=14αkexp(2(λλkΔλk)2).

Our analysis is limited only to F34H36 (emission) and H36F34 (absorption) transitions covering spectral range from 1.5 μm to 2 μm and described by appropriate coefficients (see Table 1 in [48], S. D Jackson and T. A. King). Then, the imaginary part of permittivity is calculated by employing following relation:

Im(εg/ab)=g(λ)λRe(εg/ab).

In general, above assumptions are justified by the fact that the imaginary part of pure silica glass permittivity is negligible (in order of 10−8) in considered wavelength range, i.e., 1.5 ÷ 2 µm [45]. Moreover, the correction to real part of permittivity resulting from imaginary part appearing due to gain or losses introduced by thulium ions, and estimated with the help of Kramers-Kronig relation, is also insignificant (it is in order of 10−6).

Electromagnetic response of considered complete multilayer structure can be predicted on the basis of properties of permittivity tensor. In our analysis the components ɛ (i.e., ɛzzFig. 1), ɛ|| (i.e., ɛxx = ɛyyFig. 1) of the effective diagonal permittivity tensor are obtained using Effective Medium Theory:

ε||=tgraphεgraph+tg/abεg/abtgraph+tg/ab,
ε=εgraphεg/ab(tgraph+tg/ab)tgraphεg/ab+tg/abεgraph,
where tg is the thickness of graphene layer and εg is the graphene’s permittivity. It is assumed that the thickness of gain material/absorber layers are deep subwavelength but thick enough to avoid interaction between graphene layers [44].

Finally, the effective gain and absorption for waves propagating in complete THMM structure has been calculated with use of permittivity-based model:

g||,(λ)=Im[ε||,(λ)]λRe[|ε||,(λ)|]
α||,(λ)=Im[ε||,(λ)]λRe[|ε||,(λ)|],.
where g||/α|| and g/α describe effective gain/absorption encountered by waves propagating in “x-y” plane and along “z” axis, respectively. The characteristics revealing effective gain and absorption of complete structure are presented in next section.

3. Results and discussion

Figure 2 illustrates the real part of permittivity tensor components ɛ|| (red curve) and ɛ (blue curve) plotted versus wavelength with no biasing voltage Vg = 0 V. As we can see, for certain wavelength ranges different dispersion regimes, i.e., elliptic dispersion (ED), Type I and Type II HMM, can be obtained.

 figure: Fig. 2

Fig. 2 Real part of effective permittivity tensor components ε|| (red curve) and ε (blue curve) plotted vs. wavelength for biasing voltage Vg = 0 V, where λ0(1,3)and λ0(2) denote the resonance wavelengths of ε and ε||, respectively.

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Transitions between certain regimes are characterized by resonance wavelengths (i.e., the wavelengths for which respective component of the effective diagonal tensor equaled zero) denoted byλ0(1) (Type I HMM → ED; ɛ = 0, ɛ||>0), λ0(2) (ED → Type II HMM; ɛ|| = 0, ɛ>0) and λ0(3) (ED → Type I HMM; ɛ = 0, ɛ||>0). It is worth noting, that these resonance wavelengths can be shifted by changing the biasing voltage [36].The further analysis concerns voltage-controlled effective gain/absorption properties of complete THMM structure. First, we focus on effective gain and absorption observed for the vicinity of the transition from Type I HMM to elliptic dispersion regime with resonance wavelength λ0(1), see Fig. 2.

Figures 3(a) and 3(b) illustrate the spectral dependencies of effective gain g (encountered by waves propagating along “z” axis, i.e., perpendicularly to the structure layers - blue curves) and g|| (encountered by waves propagating in “x-y” plane - red curves) for different values of biasing voltage Vg, as well as spectral dependency of gain of constituent standalone active material (green curve).

 figure: Fig. 3

Fig. 3 Spectral dependencies of effective gain/absorption (g, g|| / α, α||) corresponding to resonance wavelengths λ0(1) for different values of biasing voltage as well as gain/absorption (g/α) of constituent material: (a) g (left axis; blue curves) for Vg = 0,3,8 mV and g (right axis; solid green curve); (b) g|| (left axis; red curves) for Vg = 0,3,8 mV and g (right axis; solid green curve); (c) α (left axis; blue curves) for Vg = 11,13,15 mV and α (right axis; dashed green curve); (d) α|| (left axis; red curves) for Vg = 11,13,15 mV and α (right axis; dashed green curve).

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First of all, we can notice strong anisotropy of gain, i.e., g achieves much higher values than g||. The effective gain g|| is approximately one order of magnitude greater in relation to gain of constituent material, while their bandwidths do not differ much, see Fig. 3(b). What is more, the biasing voltage does not influence g|| The situation changes dramatically for g, which behaves in very interesting manner. In this case, the maximum of effective gain g exceeds the gain of constituent material a few orders of magnitude, while the effective bandwidth is two orders of magnitude narrower. These effects result from sharp resonance transition of Re(ɛ) observed for the wavelength λ0(1) at which Type I HMM dispersion changes into elliptic, see Fig. 2, since the resonance transition shape of Re(ɛ), by Kramers-Kronig relation, mostly determines Im(ɛ) and both parts of complex permittivity ɛ contribute to effective gain g. It is worth underlining that due to the fact that resonance wavelength λ0(1) can be shifted by applying external voltage, thus we can select, by proper biasing, the wavelength for which the maximum effective gain appears. Naturally, the range of tunability is limited by gain bandwidth of constituent material as well as tunable properties of employed THMM structure [36]. Sufficient value of voltage biasing enables also to shift the resonance wavelength λ0(1) to the spectral range where absorption of constituent material occurs. Figures 3(c) and 3(d) show spectral dependencies of effective absorption α and α||, respectively, for different values of biasing voltage, and absorption of constituent material α illustrated by dashed green curve. Once again, we can observe effects characteristic for the sharp resonant transition, i.e., narrowing of the bandwidth and significant increase of the maximum, appearing for α see Fig. 3(c). Similarly, we can select, by proper voltage biasing, the wavelength for which maximum effective absorption α appears. Again, tunability is limited by loss bandwidth of constituent material and tunable properties of employed structure. What is more, the spectral behavior of α|| remains similar to absorption of constituent material and does not depend on applied voltage. Moreover, α|| achieves much lower values than α and the structure reveals loss anisotropy, see Figs. 3(c)-3(d). Analogous characteristics revealing spectral dependencies of effective gain and absorption are obtained for the transition with the resonance wavelength λ0(2), i.e., ED → Type II HMM, see Figs. 4(a)-4(d).

 figure: Fig. 4

Fig. 4 Spectral dependencies of effective gain/absorption (g, g|| / α, α||) corresponding to resonance wavelengths λ0(2)for different values of biasing voltage as well as gain/absorption (g/α) of constituent material: (a) g (left axis; blue curves) for Vg = 0.55,0.75,0.9 V and g (right axis; solid green curve); (b) g|| (left axis; red curves) for Vg = 0.55,0.75,0.9 V and g (right axis; solid green curve); (c) α (left axis; blue curves) for Vg = 1.1,1.2,1.4 V and α (right axis; dashed green curve); (d) α|| (left axis; red curves) for Vg = 1.1,1.2,1.4 V and α (right axis; dashed green curve).

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In contrast to the characteristics for the previously discussed transition, g|| and α|| reveal controllable resonant-like and are greater than g and α, respectively. In this case g and α exhibit similar spectral dependence as gain and absorption of constituent material and they are practically insensitive to the applied voltage. Although, the effective gain g|| and absorption α|| peaks are significantly lower and broader than that obtained for g and α for the Type I HMM → elliptic transition, but still considerable enhancement, with respect to constituent material, is observed. Once more, anisotropy of the THMM structure is confined.

Finally, the spectral dependencies of effective absorption α|| and α, observed for the third transition (i.e., ED → Type I HMM) with the resonance wavelength λ0(3), are shown in Figs. 5(a)–5(b). The α|| possess similar dependence as in the case of transition with λ0(1), i.e., the same bandwidth as the constituent material and loss enhancement. However, α behaves in different and interesting manner. We observe effective absorption α equaled zero for resonance wavelengthλ0(3), which leads to the electromagnetic transparency. Again, by proper biasing we can select the wavelength at which the structure becomes lossless. We can expect that the same transparency effect for this resonance transition will be observed in THMM structure with gain, however achieving this effect requires shifting λ0(3) to the gain band of the constituent material.

 figure: Fig. 5

Fig. 5 Spectral dependencies of effective absorption (α, α||) corresponding to resonance wavelengths λ0(3)for different values of biasing voltage as well as absorption (α) of constituent material: (c) α (left axis; blue curves) for Vg = 0,0.5,1 mV and α (right axis; dashed green curve); (d) α|| (left axis; red curves) for Vg = 0,0.5,1 mV and α (right axis; dashed green curve).

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4. Conclusions

To conclude, we show that THMM structure composed of active material and functional material offers possibility of controllable modification of gain/absorption bandwidth of constituent active medium as well as controllable electromagnetic transparency. Hyperbolic metamaterials, in general, exhibits broadband enhancement effect, confirmed in many scientific studies [12–14,18], which are consistent with our results. Our study also divulges interesting effects appearing in the vicinity of resonance wavelengths connected with transitions between different dispersion regimes. In particular, in case of Type I HMM → ED transition we can observe strong enhancement of effective gain or absorption, encountered by waves propagating along “z” axis, with significantly narrowed bandwidth and weaker broadband enhancement in “x-y” plane. The situation changes for the ED → Type II HMM transition where broadband gain/loss enhancement occurs for wave propagating along “z” axis and stronger enhancement with narrowed bandwidth is obtained for propagation in plane ”x-y”. Other distinct property appears for the third transition, i.e., ED → Type I, HMM which reveals electromagnetic transparency for wave propagating along “z” axis, while for “x-y” we observe moderate broadband enhancement effect. What is noteworthy, by proper biasing of complete structure we can select the wavelength at which the maximum effective gain or absorption appears for waves propagating perpendicularly or parallel to the structure’s layers depending on the transition between certain dispersion regimes. The voltage controlling occurs for resonant transitions for which we observe narrowing of the effective gain/loss bandwidth. Similarly, it is also possible to select wavelength at which electromagnetic transparency appears, while the third transition is considered.

It is worth to underline that, all described effects are a result of dispersion regimes transitions, achievable in HMM structures based on various materials. Thus, replacing graphene by any stimulus-sensitive material providing negative permittivity (e.g., vanadium oxide [37], indium tin oxide [38], nematic liquid crystal [39]) and thulium-doped silica glass by any absorptive/amplifying dielectric material (e.g., dye-doped PMMA) should not influence desired functionality.

In particular, the manufacturing of layered structures consisting of several graphene sheets separated by dielectric layers is technologically achievable by using, e.g., well-developed CVD, MBE methods and cleavage techniques [49,50]. This opens possibility of realization a new class of tunable active/passive media based on THMM structures composed of absorptive/amplifying material paving foundation for platform of novel controllable photonic devices.

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44. R. Mroczyński, N. Kwietniewski, M. Ćwil, P. Hoffmann, R. B. Beck, and J. Jakubowski, “Improvement of electro-physical properties of ultra-thin PECVD silicon oxynitride layers by high-temperature annealing,” Vacuum 82(10), 1013–1019 (2008). [CrossRef]  

45. I. H. Malitson, “Interspecimen comparison of the refractive index of fused silica,” J. Opt. Soc. Am. 55(10), 1205–1209 (1965). [CrossRef]  

46. D. E. McCumber, “Einstein relations connecting broadband emission and absorption spectra,” Phys. Rev. 136(4A), A954–A957 (1964). [CrossRef]  

47. S. D. Jackson and T. A. King, “Theoretical modeling of Tm-doped silica fiber lasers,” J. Lightwave Technol. 17(5), 948–956 (1999). [CrossRef]  

48. P. Peterka, I. Kasik, A. Dhar, B. Dussardier, and W. Blanc, “Theoretical modeling of fiber laser at 810 nm based on thulium-doped silica fibers with enhanced 3H4 level lifetime,” Opt. Express 19(3), 2773–2781 (2011). [CrossRef]   [PubMed]  

49. I. V. Iorsh, I. S. Mukhin, I. V. Shadrivov, P. A. Belov, and Y. S. Kivshar, “Hyperbolic metamaterials based on multilayer graphene structures,” Phys. Rev. B 87(7), 075416 (2013). [CrossRef]  

50. Y.-C. Chang, C.-H. Liu, C.-H. Liu, S. Zhang, S. R. Marder, E. E. Narimanov, Z. Zhong, and T. B. Norris, “Realization of mid-infrared graphene hyperbolic metamaterials,” Nat. Commun. 7(10568), 10568 (2016). [CrossRef]   [PubMed]  

References

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  1. Y. Guo, W. Newman, C. L. Cortes, and Z. Jacob, “Applications of Hyperbolic Metamaterial Substrates,” Adv. Optoelectron. 2012, 452502 (2012).
    [Crossref]
  2. H. Wang, H. Zhao, H. Su, G. Hu, and J. Zhang, “Active tuning of epsilon-near-zero point of hyperbolic metamaterial at visible and near-infrared regimes,” Appl. Phys. Express 9(9), 092201 (2016).
    [Crossref]
  3. M. A. Vincenti, D. De Ceglia, A. Ciattoni, and M. Scalora, “Singularity-driven second- and third-harmonic generation at-near-zero crossing points,” Phys. Rev. A 84(6), 063826 (2011).
    [Crossref]
  4. C. Argyropoulos, G. D’Aguanno, and A. Alǔ, “Giant second-harmonic generation efficiency and ideal phase matching with a double ε-near-zero cross-slit metamaterial,” Phys. Rev. B 89(23), 235401 (2014).
    [Crossref]
  5. J. Park, J.-H. Kang, X. Liu, and M. L. Brongersma, “Electrically Tunable Epsilon-Near-Zero (ENZ) Metafilm Absorbers,” Sci. Rep. 5(1), 15754 (2015).
    [Crossref] [PubMed]
  6. A. Marini and F. J. de Abajo, “Self-organization of frozen light in near-zero-index media with cubic nonlinearity,” Sci. Rep. 6(1), 20088 (2016).
    [Crossref] [PubMed]
  7. M. G. Silveirinha and N. Engheta, “Theory of supercoupling, squeezing wave energy, and field confinement in narrow channels and tight bends using ε- near-zero metamaterials,” Phys. Rev. B 76(24), 245109 (2007).
    [Crossref]
  8. A. Alǔ, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B 75(15), 155410 (2007).
    [Crossref]
  9. L. Ferrari, C. Wu, D. Lepage, X. Zhang, and Z. Liu, “Hyperbolic metamaterials and their applications,” Prog. Quantum Electron. 40, 1–40 (2015).
    [Crossref]
  10. Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
    [Crossref] [PubMed]
  11. Y. He, S. He, and X. Yang, “Optical field enhancement in nanoscale slot waveguides of hyperbolic metamaterials,” Opt. Lett. 37(14), 2907–2909 (2012).
    [Crossref] [PubMed]
  12. K. V. Sreekanth, T. Biaglow, and G. Strangi, “Directional spontaneous emission enhancement in hyperbolic metamaterials,” J. Appl. Phys. 114(13), 134306 (2013).
    [Crossref]
  13. L. Ferrari, D. Lu, D. Lepage, and Z. Liu, “Enhanced spontaneous emission inside hyperbolic metamaterials,” Opt. Express 22(4), 4301–4306 (2014).
    [Crossref] [PubMed]
  14. W. D. Newman, C. L. Cortes, and Z. Jacob, “Enhanced and directional single-photon emission in hyperbolic metamaterials,” J. Opt. Soc. Am. B 30(4), 766–775 (2013).
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  15. N. Vasilantonakis, G. A. Wurtz, V. A. Podolskiy, and A. V. Zayats, “Refractive index sensing with hyperbolic metamaterials: strategies for biosensing and nonlinearity enhancement,” Opt. Express 23(11), 14329–14343 (2015).
    [Crossref] [PubMed]
  16. S. Ishii, M. Y. Shalaginov, V. E. Babicheva, A. Boltasseva, and A. V. Kildishev, “Plasmonic waveguides cladded by hyperbolic metamaterials,” Opt. Lett. 39(16), 4663–4666 (2014).
    [Crossref] [PubMed]
  17. Y. Guo, C. L. Cortes, S. Molesky, and Z. Jacob, “Broadband super-Planckian thermal emission from hyperbolic metamaterials,” Appl. Phys. Lett. 101(13), 131106 (2012).
    [Crossref]
  18. 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]
  19. A. Faraon, P. E. Barclay, C. Santori, K.-M. C. Fu, and R. G. Beausoleil, “Resonant enhancement of the zero-phonon emission from a colour centre in a diamond cavity,” Nat. Photonics 5(5), 301–305 (2011).
    [Crossref]
  20. A. Faraon, C. Santori, Z. Huang, V. M. Acosta, and R. G. Beausoleil, “Coupling of Nitrogen-Vacancy Centers to Photonic Crystal Cavities in Monocrystalline Diamond,” Phys. Rev. Lett. 109(3), 033604 (2012).
    [Crossref] [PubMed]
  21. J. T. Choy, B. J. M. Hausmann, T. M. Babinec, I. Bulu, M. Khan, P. Maletinsky, A. Yacoby, and M. Loncar, “Enhanced single-photon emission from a diamond–silver aperture,” Nat. Photonics 5(12), 738–743 (2011).
    [Crossref]
  22. O. Hess, J. B. Pendry, S. A. Maier, R. F. Oulton, J. M. Hamm, and K. L. Tsakmakidis, “Active nanoplasmonic metamaterials,” Nat. Mater. 11(7), 573–584 (2012).
    [Crossref] [PubMed]
  23. A. Pusch, S. Wuestner, J. M. Hamm, K. L. Tsakmakidis, and O. Hess, “Coherent amplification and noise in gain-enhanced nanoplasmonic metamaterials: a Maxwell-Bloch Langevin approach,” ACS Nano 6(3), 2420–2431 (2012).
    [Crossref] [PubMed]
  24. J. Zhang, H. Jiang, B. Gralak, S. Enoch, G. Tayeb, and M. Lequime, “Compensation of loss to approach −1 effective index by gain in metal-dielectric stacks,” Eur. Phys. J. Appl. Phys. 46(3), 1–6 (2008).
    [Crossref]
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    [Crossref] [PubMed]
  26. R. Chandrasekar, Z. Wang, X. Meng, A. Lagutchev, Y. L. Kim, A. Wei, A. Boltasseva, and V. M. Shalaev, “Lasing action with gold nanorod hyperbolic metamaterials,” in Conference on Lasers and Electro-Optics CLEO: Applications and Technology (2016), paper JTh4A.4.
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    [Crossref] [PubMed]
  28. R. Ning, S. Liu, H. Zhang, B. Bian, and X. Kong, “A wide-angle broadband absorber in graphene-based hyperbolic metamaterials,” Eur. Phys. J. Appl. Phys. 68(2), 20401 (2014).
    [Crossref]
  29. R. Ning, S. Liu, H. Zhang, B. Bian, and X. Kong, “Tunable absorption in graphene-based hyperbolic metamaterials for mid-infrared range,” Physica B 457, 144–148 (2015).
    [Crossref]
  30. R. Ning, S. Liu, H. Zhang, and Z. Jiao, “Dual-gated tunable absorption in graphene-based hyperbolic metamaterials,” AIP Adv. 5(6), 067106 (2015).
    [Crossref]
  31. M. A. Othman, C. Guclu, and F. Capolino, “Graphene-based tunable hyperbolic metamaterials and enhanced near-field absorption,” Opt. Express 21(6), 7614–7632 (2013).
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  32. A. Al Sayem, A. Shahriar, M. R. C. Mahdy, and M. S. Rahman, “Control of reflection through epsilon near zero graphene based anisotropic metamaterial,” in Proceedings of IEEE Conference on Electrical and Computer Engineering (IEEE,2014), pp. 812–815.
  33. M. A. K. Othman, C. Guclu, and F. Capolino, “Graphene-dielectric composite metamaterials: evolution from elliptic to hyperbolic wavevector dispersion and the transverse epsilon-near-zero condition,” J. Nanophotonics 7(1), 073089 (2013).
    [Crossref]
  34. M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
    [Crossref] [PubMed]
  35. A. Tyszka-Zawadzka, B. Janaszek, and P. Szczepański, “Tunable slow light in graphene-based hyperbolic metamaterial waveguide operating in SCLU telecom bands,” Optics Express, in press (2017).
  36. B. Janaszek, A. Tyszka-Zawadzka, and P. Szczepański, “Tunable graphene-based hyperbolic metamaterial operating in SCLU telecom bands,” Opt. Express 24(21), 24129–24136 (2016).
    [Crossref] [PubMed]
  37. S. Prayakarao, B. Mendoza, A. Devine, C. Kyaw, R. B. van Dover, V. Liberman, and M. A. Noginov, “Tunable VO2/Au hyperbolic metamaterial,” Appl. Phys. Lett. 109(6), 061105 (2016).
    [Crossref]
  38. G. T. Paradakis and H. A. Atwater, “Field-effect induced tunability in hyperbolic metamaterials,” Phys. Rev. B 92(18), 184101 (2015).
    [Crossref]
  39. Z. Cao, X. Xiang, C. Yang, Y. Zhang, Z. Peng, and L. Xuan, “Analysis of tunable characteristics of liquid-crystal-based hyperbolic metamaterials,” Liq. Cryst. 43(12), 1753–1759 (2016).
    [Crossref]
  40. H. N. S. Krishnamoorthy, Y. Zhou, S. Ramanathan, E. Narimanov, and V. M. Menon, “Tunable hyperbolic metamaterials utilizing phase change heterostructures,” Appl. Phys. Lett. 104(12), 121101 (2014).
    [Crossref]
  41. W. Li, Z. Liu, X. Zhang, and X. Jiang, “Switchable hyperbolic metamaterials with magnetic control,” Appl. Phys. Lett. 100(16), 161108 (2012).
    [Crossref]
  42. L. A. Falkovsky and A. A. Varlamov, “Space-time dispersion of graphene conductivity,” Eur. Phys. J. B 56(4), 281–284 (2007).
    [Crossref]
  43. Y. Xiang, J. Guo, X. Dai, S. Wen, and D. Tang, “Engineered surface Bloch waves in graphene-based hyperbolic metamaterials,” Opt. Express 22(3), 3054–3062 (2014).
    [Crossref] [PubMed]
  44. R. Mroczyński, N. Kwietniewski, M. Ćwil, P. Hoffmann, R. B. Beck, and J. Jakubowski, “Improvement of electro-physical properties of ultra-thin PECVD silicon oxynitride layers by high-temperature annealing,” Vacuum 82(10), 1013–1019 (2008).
    [Crossref]
  45. I. H. Malitson, “Interspecimen comparison of the refractive index of fused silica,” J. Opt. Soc. Am. 55(10), 1205–1209 (1965).
    [Crossref]
  46. D. E. McCumber, “Einstein relations connecting broadband emission and absorption spectra,” Phys. Rev. 136(4A), A954–A957 (1964).
    [Crossref]
  47. S. D. Jackson and T. A. King, “Theoretical modeling of Tm-doped silica fiber lasers,” J. Lightwave Technol. 17(5), 948–956 (1999).
    [Crossref]
  48. P. Peterka, I. Kasik, A. Dhar, B. Dussardier, and W. Blanc, “Theoretical modeling of fiber laser at 810 nm based on thulium-doped silica fibers with enhanced 3H4 level lifetime,” Opt. Express 19(3), 2773–2781 (2011).
    [Crossref] [PubMed]
  49. I. V. Iorsh, I. S. Mukhin, I. V. Shadrivov, P. A. Belov, and Y. S. Kivshar, “Hyperbolic metamaterials based on multilayer graphene structures,” Phys. Rev. B 87(7), 075416 (2013).
    [Crossref]
  50. Y.-C. Chang, C.-H. Liu, C.-H. Liu, S. Zhang, S. R. Marder, E. E. Narimanov, Z. Zhong, and T. B. Norris, “Realization of mid-infrared graphene hyperbolic metamaterials,” Nat. Commun. 7(10568), 10568 (2016).
    [Crossref] [PubMed]

2016 (6)

H. Wang, H. Zhao, H. Su, G. Hu, and J. Zhang, “Active tuning of epsilon-near-zero point of hyperbolic metamaterial at visible and near-infrared regimes,” Appl. Phys. Express 9(9), 092201 (2016).
[Crossref]

A. Marini and F. J. de Abajo, “Self-organization of frozen light in near-zero-index media with cubic nonlinearity,” Sci. Rep. 6(1), 20088 (2016).
[Crossref] [PubMed]

Z. Cao, X. Xiang, C. Yang, Y. Zhang, Z. Peng, and L. Xuan, “Analysis of tunable characteristics of liquid-crystal-based hyperbolic metamaterials,” Liq. Cryst. 43(12), 1753–1759 (2016).
[Crossref]

B. Janaszek, A. Tyszka-Zawadzka, and P. Szczepański, “Tunable graphene-based hyperbolic metamaterial operating in SCLU telecom bands,” Opt. Express 24(21), 24129–24136 (2016).
[Crossref] [PubMed]

S. Prayakarao, B. Mendoza, A. Devine, C. Kyaw, R. B. van Dover, V. Liberman, and M. A. Noginov, “Tunable VO2/Au hyperbolic metamaterial,” Appl. Phys. Lett. 109(6), 061105 (2016).
[Crossref]

Y.-C. Chang, C.-H. Liu, C.-H. Liu, S. Zhang, S. R. Marder, E. E. Narimanov, Z. Zhong, and T. B. Norris, “Realization of mid-infrared graphene hyperbolic metamaterials,” Nat. Commun. 7(10568), 10568 (2016).
[Crossref] [PubMed]

2015 (6)

G. T. Paradakis and H. A. Atwater, “Field-effect induced tunability in hyperbolic metamaterials,” Phys. Rev. B 92(18), 184101 (2015).
[Crossref]

R. Ning, S. Liu, H. Zhang, B. Bian, and X. Kong, “Tunable absorption in graphene-based hyperbolic metamaterials for mid-infrared range,” Physica B 457, 144–148 (2015).
[Crossref]

R. Ning, S. Liu, H. Zhang, and Z. Jiao, “Dual-gated tunable absorption in graphene-based hyperbolic metamaterials,” AIP Adv. 5(6), 067106 (2015).
[Crossref]

L. Ferrari, C. Wu, D. Lepage, X. Zhang, and Z. Liu, “Hyperbolic metamaterials and their applications,” Prog. Quantum Electron. 40, 1–40 (2015).
[Crossref]

J. Park, J.-H. Kang, X. Liu, and M. L. Brongersma, “Electrically Tunable Epsilon-Near-Zero (ENZ) Metafilm Absorbers,” Sci. Rep. 5(1), 15754 (2015).
[Crossref] [PubMed]

N. Vasilantonakis, G. A. Wurtz, V. A. Podolskiy, and A. V. Zayats, “Refractive index sensing with hyperbolic metamaterials: strategies for biosensing and nonlinearity enhancement,” Opt. Express 23(11), 14329–14343 (2015).
[Crossref] [PubMed]

2014 (7)

S. Ishii, M. Y. Shalaginov, V. E. Babicheva, A. Boltasseva, and A. V. Kildishev, “Plasmonic waveguides cladded by hyperbolic metamaterials,” Opt. Lett. 39(16), 4663–4666 (2014).
[Crossref] [PubMed]

L. Ferrari, D. Lu, D. Lepage, and Z. Liu, “Enhanced spontaneous emission inside hyperbolic metamaterials,” Opt. Express 22(4), 4301–4306 (2014).
[Crossref] [PubMed]

C. Argyropoulos, G. D’Aguanno, and A. Alǔ, “Giant second-harmonic generation efficiency and ideal phase matching with a double ε-near-zero cross-slit metamaterial,” Phys. Rev. B 89(23), 235401 (2014).
[Crossref]

H. N. S. Krishnamoorthy, Y. Zhou, S. Ramanathan, E. Narimanov, and V. M. Menon, “Tunable hyperbolic metamaterials utilizing phase change heterostructures,” Appl. Phys. Lett. 104(12), 121101 (2014).
[Crossref]

J. S. T. Smalley, F. Vallini, B. Kanté, and Y. Fainman, “Modal amplification in active waveguides with hyperbolic dispersion at telecommunication frequencies,” Opt. Express 22(17), 21088–21105 (2014).
[Crossref] [PubMed]

R. Ning, S. Liu, H. Zhang, B. Bian, and X. Kong, “A wide-angle broadband absorber in graphene-based hyperbolic metamaterials,” Eur. Phys. J. Appl. Phys. 68(2), 20401 (2014).
[Crossref]

Y. Xiang, J. Guo, X. Dai, S. Wen, and D. Tang, “Engineered surface Bloch waves in graphene-based hyperbolic metamaterials,” Opt. Express 22(3), 3054–3062 (2014).
[Crossref] [PubMed]

2013 (6)

I. V. Iorsh, I. S. Mukhin, I. V. Shadrivov, P. A. Belov, and Y. S. Kivshar, “Hyperbolic metamaterials based on multilayer graphene structures,” Phys. Rev. B 87(7), 075416 (2013).
[Crossref]

K. V. Sreekanth, T. Biaglow, and G. Strangi, “Directional spontaneous emission enhancement in hyperbolic metamaterials,” J. Appl. Phys. 114(13), 134306 (2013).
[Crossref]

A. Andryieuski and A. V. Lavrinenko, “Graphene metamaterials based tunable terahertz absorber: effective surface conductivity approach,” Opt. Express 21(7), 9144–9155 (2013).
[Crossref] [PubMed]

M. A. Othman, C. Guclu, and F. Capolino, “Graphene-based tunable hyperbolic metamaterials and enhanced near-field absorption,” Opt. Express 21(6), 7614–7632 (2013).
[Crossref] [PubMed]

M. A. K. Othman, C. Guclu, and F. Capolino, “Graphene-dielectric composite metamaterials: evolution from elliptic to hyperbolic wavevector dispersion and the transverse epsilon-near-zero condition,” J. Nanophotonics 7(1), 073089 (2013).
[Crossref]

W. D. Newman, C. L. Cortes, and Z. Jacob, “Enhanced and directional single-photon emission in hyperbolic metamaterials,” J. Opt. Soc. Am. B 30(4), 766–775 (2013).
[Crossref]

2012 (8)

Y. He, S. He, and X. Yang, “Optical field enhancement in nanoscale slot waveguides of hyperbolic metamaterials,” Opt. Lett. 37(14), 2907–2909 (2012).
[Crossref] [PubMed]

Y. Guo, C. L. Cortes, S. Molesky, and Z. Jacob, “Broadband super-Planckian thermal emission from hyperbolic metamaterials,” Appl. Phys. Lett. 101(13), 131106 (2012).
[Crossref]

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]

Y. Guo, W. Newman, C. L. Cortes, and Z. Jacob, “Applications of Hyperbolic Metamaterial Substrates,” Adv. Optoelectron. 2012, 452502 (2012).
[Crossref]

W. Li, Z. Liu, X. Zhang, and X. Jiang, “Switchable hyperbolic metamaterials with magnetic control,” Appl. Phys. Lett. 100(16), 161108 (2012).
[Crossref]

A. Faraon, C. Santori, Z. Huang, V. M. Acosta, and R. G. Beausoleil, “Coupling of Nitrogen-Vacancy Centers to Photonic Crystal Cavities in Monocrystalline Diamond,” Phys. Rev. Lett. 109(3), 033604 (2012).
[Crossref] [PubMed]

O. Hess, J. B. Pendry, S. A. Maier, R. F. Oulton, J. M. Hamm, and K. L. Tsakmakidis, “Active nanoplasmonic metamaterials,” Nat. Mater. 11(7), 573–584 (2012).
[Crossref] [PubMed]

A. Pusch, S. Wuestner, J. M. Hamm, K. L. Tsakmakidis, and O. Hess, “Coherent amplification and noise in gain-enhanced nanoplasmonic metamaterials: a Maxwell-Bloch Langevin approach,” ACS Nano 6(3), 2420–2431 (2012).
[Crossref] [PubMed]

2011 (5)

J. T. Choy, B. J. M. Hausmann, T. M. Babinec, I. Bulu, M. Khan, P. Maletinsky, A. Yacoby, and M. Loncar, “Enhanced single-photon emission from a diamond–silver aperture,” Nat. Photonics 5(12), 738–743 (2011).
[Crossref]

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

M. A. Vincenti, D. De Ceglia, A. Ciattoni, and M. Scalora, “Singularity-driven second- and third-harmonic generation at-near-zero crossing points,” Phys. Rev. A 84(6), 063826 (2011).
[Crossref]

A. Faraon, P. E. Barclay, C. Santori, K.-M. C. Fu, and R. G. Beausoleil, “Resonant enhancement of the zero-phonon emission from a colour centre in a diamond cavity,” Nat. Photonics 5(5), 301–305 (2011).
[Crossref]

P. Peterka, I. Kasik, A. Dhar, B. Dussardier, and W. Blanc, “Theoretical modeling of fiber laser at 810 nm based on thulium-doped silica fibers with enhanced 3H4 level lifetime,” Opt. Express 19(3), 2773–2781 (2011).
[Crossref] [PubMed]

2008 (2)

R. Mroczyński, N. Kwietniewski, M. Ćwil, P. Hoffmann, R. B. Beck, and J. Jakubowski, “Improvement of electro-physical properties of ultra-thin PECVD silicon oxynitride layers by high-temperature annealing,” Vacuum 82(10), 1013–1019 (2008).
[Crossref]

J. Zhang, H. Jiang, B. Gralak, S. Enoch, G. Tayeb, and M. Lequime, “Compensation of loss to approach −1 effective index by gain in metal-dielectric stacks,” Eur. Phys. J. Appl. Phys. 46(3), 1–6 (2008).
[Crossref]

2007 (4)

L. A. Falkovsky and A. A. Varlamov, “Space-time dispersion of graphene conductivity,” Eur. Phys. J. B 56(4), 281–284 (2007).
[Crossref]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[Crossref] [PubMed]

M. G. Silveirinha and N. Engheta, “Theory of supercoupling, squeezing wave energy, and field confinement in narrow channels and tight bends using ε- near-zero metamaterials,” Phys. Rev. B 76(24), 245109 (2007).
[Crossref]

A. Alǔ, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B 75(15), 155410 (2007).
[Crossref]

1999 (1)

1965 (1)

1964 (1)

D. E. McCumber, “Einstein relations connecting broadband emission and absorption spectra,” Phys. Rev. 136(4A), A954–A957 (1964).
[Crossref]

Acosta, V. M.

A. Faraon, C. Santori, Z. Huang, V. M. Acosta, and R. G. Beausoleil, “Coupling of Nitrogen-Vacancy Centers to Photonic Crystal Cavities in Monocrystalline Diamond,” Phys. Rev. Lett. 109(3), 033604 (2012).
[Crossref] [PubMed]

Alu, A.

C. Argyropoulos, G. D’Aguanno, and A. Alǔ, “Giant second-harmonic generation efficiency and ideal phase matching with a double ε-near-zero cross-slit metamaterial,” Phys. Rev. B 89(23), 235401 (2014).
[Crossref]

A. Alǔ, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B 75(15), 155410 (2007).
[Crossref]

Andryieuski, A.

Argyropoulos, C.

C. Argyropoulos, G. D’Aguanno, and A. Alǔ, “Giant second-harmonic generation efficiency and ideal phase matching with a double ε-near-zero cross-slit metamaterial,” Phys. Rev. B 89(23), 235401 (2014).
[Crossref]

Atwater, H. A.

G. T. Paradakis and H. A. Atwater, “Field-effect induced tunability in hyperbolic metamaterials,” Phys. Rev. B 92(18), 184101 (2015).
[Crossref]

Babicheva, V. E.

Babinec, T. M.

J. T. Choy, B. J. M. Hausmann, T. M. Babinec, I. Bulu, M. Khan, P. Maletinsky, A. Yacoby, and M. Loncar, “Enhanced single-photon emission from a diamond–silver aperture,” Nat. Photonics 5(12), 738–743 (2011).
[Crossref]

Barclay, P. E.

A. Faraon, P. E. Barclay, C. Santori, K.-M. C. Fu, and R. G. Beausoleil, “Resonant enhancement of the zero-phonon emission from a colour centre in a diamond cavity,” Nat. Photonics 5(5), 301–305 (2011).
[Crossref]

Beausoleil, R. G.

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A. Faraon, C. Santori, Z. Huang, V. M. Acosta, and R. G. Beausoleil, “Coupling of Nitrogen-Vacancy Centers to Photonic Crystal Cavities in Monocrystalline Diamond,” Phys. Rev. Lett. 109(3), 033604 (2012).
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L. Ferrari, C. Wu, D. Lepage, X. Zhang, and Z. Liu, “Hyperbolic metamaterials and their applications,” Prog. Quantum Electron. 40, 1–40 (2015).
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L. Ferrari, D. Lu, D. Lepage, and Z. Liu, “Enhanced spontaneous emission inside hyperbolic metamaterials,” Opt. Express 22(4), 4301–4306 (2014).
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A. Faraon, P. E. Barclay, C. Santori, K.-M. C. Fu, and R. G. Beausoleil, “Resonant enhancement of the zero-phonon emission from a colour centre in a diamond cavity,” Nat. Photonics 5(5), 301–305 (2011).
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M. A. K. Othman, C. Guclu, and F. Capolino, “Graphene-dielectric composite metamaterials: evolution from elliptic to hyperbolic wavevector dispersion and the transverse epsilon-near-zero condition,” J. Nanophotonics 7(1), 073089 (2013).
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M. A. Othman, C. Guclu, and F. Capolino, “Graphene-based tunable hyperbolic metamaterials and enhanced near-field absorption,” Opt. Express 21(6), 7614–7632 (2013).
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Guo, Y.

Y. Guo, C. L. Cortes, S. Molesky, and Z. Jacob, “Broadband super-Planckian thermal emission from hyperbolic metamaterials,” Appl. Phys. Lett. 101(13), 131106 (2012).
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Y. Guo, W. Newman, C. L. Cortes, and Z. Jacob, “Applications of Hyperbolic Metamaterial Substrates,” Adv. Optoelectron. 2012, 452502 (2012).
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He, Y.

Hess, O.

O. Hess, J. B. Pendry, S. A. Maier, R. F. Oulton, J. M. Hamm, and K. L. Tsakmakidis, “Active nanoplasmonic metamaterials,” Nat. Mater. 11(7), 573–584 (2012).
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R. Mroczyński, N. Kwietniewski, M. Ćwil, P. Hoffmann, R. B. Beck, and J. Jakubowski, “Improvement of electro-physical properties of ultra-thin PECVD silicon oxynitride layers by high-temperature annealing,” Vacuum 82(10), 1013–1019 (2008).
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A. Faraon, C. Santori, Z. Huang, V. M. Acosta, and R. G. Beausoleil, “Coupling of Nitrogen-Vacancy Centers to Photonic Crystal Cavities in Monocrystalline Diamond,” Phys. Rev. Lett. 109(3), 033604 (2012).
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I. V. Iorsh, I. S. Mukhin, I. V. Shadrivov, P. A. Belov, and Y. S. Kivshar, “Hyperbolic metamaterials based on multilayer graphene structures,” Phys. Rev. B 87(7), 075416 (2013).
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Ishii, S.

Jackson, S. D.

Jacob, Z.

W. D. Newman, C. L. Cortes, and Z. Jacob, “Enhanced and directional single-photon emission in hyperbolic metamaterials,” J. Opt. Soc. Am. B 30(4), 766–775 (2013).
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Y. Guo, C. L. Cortes, S. Molesky, and Z. Jacob, “Broadband super-Planckian thermal emission from hyperbolic metamaterials,” Appl. Phys. Lett. 101(13), 131106 (2012).
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Z. Jacob, I. I. Smolyaninov, and E. E. Narimanov, “Broadband Purcell effect: Radiative decay engineering with metamaterials,” Appl. Phys. Lett. 100(18), 181105 (2012).
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Y. Guo, W. Newman, C. L. Cortes, and Z. Jacob, “Applications of Hyperbolic Metamaterial Substrates,” Adv. Optoelectron. 2012, 452502 (2012).
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R. Mroczyński, N. Kwietniewski, M. Ćwil, P. Hoffmann, R. B. Beck, and J. Jakubowski, “Improvement of electro-physical properties of ultra-thin PECVD silicon oxynitride layers by high-temperature annealing,” Vacuum 82(10), 1013–1019 (2008).
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Jiang, H.

J. Zhang, H. Jiang, B. Gralak, S. Enoch, G. Tayeb, and M. Lequime, “Compensation of loss to approach −1 effective index by gain in metal-dielectric stacks,” Eur. Phys. J. Appl. Phys. 46(3), 1–6 (2008).
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W. Li, Z. Liu, X. Zhang, and X. Jiang, “Switchable hyperbolic metamaterials with magnetic control,” Appl. Phys. Lett. 100(16), 161108 (2012).
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R. Ning, S. Liu, H. Zhang, and Z. Jiao, “Dual-gated tunable absorption in graphene-based hyperbolic metamaterials,” AIP Adv. 5(6), 067106 (2015).
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M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
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J. Park, J.-H. Kang, X. Liu, and M. L. Brongersma, “Electrically Tunable Epsilon-Near-Zero (ENZ) Metafilm Absorbers,” Sci. Rep. 5(1), 15754 (2015).
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Kasik, I.

Khan, M.

J. T. Choy, B. J. M. Hausmann, T. M. Babinec, I. Bulu, M. Khan, P. Maletinsky, A. Yacoby, and M. Loncar, “Enhanced single-photon emission from a diamond–silver aperture,” Nat. Photonics 5(12), 738–743 (2011).
[Crossref]

Kildishev, A. V.

Kim, Y. L.

R. Chandrasekar, Z. Wang, X. Meng, A. Lagutchev, Y. L. Kim, A. Wei, A. Boltasseva, and V. M. Shalaev, “Lasing action with gold nanorod hyperbolic metamaterials,” in Conference on Lasers and Electro-Optics CLEO: Applications and Technology (2016), paper JTh4A.4.
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Kivshar, Y. S.

I. V. Iorsh, I. S. Mukhin, I. V. Shadrivov, P. A. Belov, and Y. S. Kivshar, “Hyperbolic metamaterials based on multilayer graphene structures,” Phys. Rev. B 87(7), 075416 (2013).
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R. Ning, S. Liu, H. Zhang, B. Bian, and X. Kong, “Tunable absorption in graphene-based hyperbolic metamaterials for mid-infrared range,” Physica B 457, 144–148 (2015).
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R. Ning, S. Liu, H. Zhang, B. Bian, and X. Kong, “A wide-angle broadband absorber in graphene-based hyperbolic metamaterials,” Eur. Phys. J. Appl. Phys. 68(2), 20401 (2014).
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Krishnamoorthy, H. N. S.

H. N. S. Krishnamoorthy, Y. Zhou, S. Ramanathan, E. Narimanov, and V. M. Menon, “Tunable hyperbolic metamaterials utilizing phase change heterostructures,” Appl. Phys. Lett. 104(12), 121101 (2014).
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R. Mroczyński, N. Kwietniewski, M. Ćwil, P. Hoffmann, R. B. Beck, and J. Jakubowski, “Improvement of electro-physical properties of ultra-thin PECVD silicon oxynitride layers by high-temperature annealing,” Vacuum 82(10), 1013–1019 (2008).
[Crossref]

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S. Prayakarao, B. Mendoza, A. Devine, C. Kyaw, R. B. van Dover, V. Liberman, and M. A. Noginov, “Tunable VO2/Au hyperbolic metamaterial,” Appl. Phys. Lett. 109(6), 061105 (2016).
[Crossref]

Lagutchev, A.

R. Chandrasekar, Z. Wang, X. Meng, A. Lagutchev, Y. L. Kim, A. Wei, A. Boltasseva, and V. M. Shalaev, “Lasing action with gold nanorod hyperbolic metamaterials,” in Conference on Lasers and Electro-Optics CLEO: Applications and Technology (2016), paper JTh4A.4.
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Lee, H.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[Crossref] [PubMed]

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L. Ferrari, C. Wu, D. Lepage, X. Zhang, and Z. Liu, “Hyperbolic metamaterials and their applications,” Prog. Quantum Electron. 40, 1–40 (2015).
[Crossref]

L. Ferrari, D. Lu, D. Lepage, and Z. Liu, “Enhanced spontaneous emission inside hyperbolic metamaterials,” Opt. Express 22(4), 4301–4306 (2014).
[Crossref] [PubMed]

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J. Zhang, H. Jiang, B. Gralak, S. Enoch, G. Tayeb, and M. Lequime, “Compensation of loss to approach −1 effective index by gain in metal-dielectric stacks,” Eur. Phys. J. Appl. Phys. 46(3), 1–6 (2008).
[Crossref]

Li, W.

W. Li, Z. Liu, X. Zhang, and X. Jiang, “Switchable hyperbolic metamaterials with magnetic control,” Appl. Phys. Lett. 100(16), 161108 (2012).
[Crossref]

Liberman, V.

S. Prayakarao, B. Mendoza, A. Devine, C. Kyaw, R. B. van Dover, V. Liberman, and M. A. Noginov, “Tunable VO2/Au hyperbolic metamaterial,” Appl. Phys. Lett. 109(6), 061105 (2016).
[Crossref]

Liu, C.-H.

Y.-C. Chang, C.-H. Liu, C.-H. Liu, S. Zhang, S. R. Marder, E. E. Narimanov, Z. Zhong, and T. B. Norris, “Realization of mid-infrared graphene hyperbolic metamaterials,” Nat. Commun. 7(10568), 10568 (2016).
[Crossref] [PubMed]

Y.-C. Chang, C.-H. Liu, C.-H. Liu, S. Zhang, S. R. Marder, E. E. Narimanov, Z. Zhong, and T. B. Norris, “Realization of mid-infrared graphene hyperbolic metamaterials,” Nat. Commun. 7(10568), 10568 (2016).
[Crossref] [PubMed]

Liu, M.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

Liu, S.

R. Ning, S. Liu, H. Zhang, B. Bian, and X. Kong, “Tunable absorption in graphene-based hyperbolic metamaterials for mid-infrared range,” Physica B 457, 144–148 (2015).
[Crossref]

R. Ning, S. Liu, H. Zhang, and Z. Jiao, “Dual-gated tunable absorption in graphene-based hyperbolic metamaterials,” AIP Adv. 5(6), 067106 (2015).
[Crossref]

R. Ning, S. Liu, H. Zhang, B. Bian, and X. Kong, “A wide-angle broadband absorber in graphene-based hyperbolic metamaterials,” Eur. Phys. J. Appl. Phys. 68(2), 20401 (2014).
[Crossref]

Liu, X.

J. Park, J.-H. Kang, X. Liu, and M. L. Brongersma, “Electrically Tunable Epsilon-Near-Zero (ENZ) Metafilm Absorbers,” Sci. Rep. 5(1), 15754 (2015).
[Crossref] [PubMed]

Liu, Z.

L. Ferrari, C. Wu, D. Lepage, X. Zhang, and Z. Liu, “Hyperbolic metamaterials and their applications,” Prog. Quantum Electron. 40, 1–40 (2015).
[Crossref]

L. Ferrari, D. Lu, D. Lepage, and Z. Liu, “Enhanced spontaneous emission inside hyperbolic metamaterials,” Opt. Express 22(4), 4301–4306 (2014).
[Crossref] [PubMed]

W. Li, Z. Liu, X. Zhang, and X. Jiang, “Switchable hyperbolic metamaterials with magnetic control,” Appl. Phys. Lett. 100(16), 161108 (2012).
[Crossref]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[Crossref] [PubMed]

Loncar, M.

J. T. Choy, B. J. M. Hausmann, T. M. Babinec, I. Bulu, M. Khan, P. Maletinsky, A. Yacoby, and M. Loncar, “Enhanced single-photon emission from a diamond–silver aperture,” Nat. Photonics 5(12), 738–743 (2011).
[Crossref]

Lu, D.

Maier, S. A.

O. Hess, J. B. Pendry, S. A. Maier, R. F. Oulton, J. M. Hamm, and K. L. Tsakmakidis, “Active nanoplasmonic metamaterials,” Nat. Mater. 11(7), 573–584 (2012).
[Crossref] [PubMed]

Maletinsky, P.

J. T. Choy, B. J. M. Hausmann, T. M. Babinec, I. Bulu, M. Khan, P. Maletinsky, A. Yacoby, and M. Loncar, “Enhanced single-photon emission from a diamond–silver aperture,” Nat. Photonics 5(12), 738–743 (2011).
[Crossref]

Malitson, I. H.

Marder, S. R.

Y.-C. Chang, C.-H. Liu, C.-H. Liu, S. Zhang, S. R. Marder, E. E. Narimanov, Z. Zhong, and T. B. Norris, “Realization of mid-infrared graphene hyperbolic metamaterials,” Nat. Commun. 7(10568), 10568 (2016).
[Crossref] [PubMed]

Marini, A.

A. Marini and F. J. de Abajo, “Self-organization of frozen light in near-zero-index media with cubic nonlinearity,” Sci. Rep. 6(1), 20088 (2016).
[Crossref] [PubMed]

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D. E. McCumber, “Einstein relations connecting broadband emission and absorption spectra,” Phys. Rev. 136(4A), A954–A957 (1964).
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S. Prayakarao, B. Mendoza, A. Devine, C. Kyaw, R. B. van Dover, V. Liberman, and M. A. Noginov, “Tunable VO2/Au hyperbolic metamaterial,” Appl. Phys. Lett. 109(6), 061105 (2016).
[Crossref]

Meng, X.

R. Chandrasekar, Z. Wang, X. Meng, A. Lagutchev, Y. L. Kim, A. Wei, A. Boltasseva, and V. M. Shalaev, “Lasing action with gold nanorod hyperbolic metamaterials,” in Conference on Lasers and Electro-Optics CLEO: Applications and Technology (2016), paper JTh4A.4.
[Crossref]

Menon, V. M.

H. N. S. Krishnamoorthy, Y. Zhou, S. Ramanathan, E. Narimanov, and V. M. Menon, “Tunable hyperbolic metamaterials utilizing phase change heterostructures,” Appl. Phys. Lett. 104(12), 121101 (2014).
[Crossref]

Molesky, S.

Y. Guo, C. L. Cortes, S. Molesky, and Z. Jacob, “Broadband super-Planckian thermal emission from hyperbolic metamaterials,” Appl. Phys. Lett. 101(13), 131106 (2012).
[Crossref]

Mroczynski, R.

R. Mroczyński, N. Kwietniewski, M. Ćwil, P. Hoffmann, R. B. Beck, and J. Jakubowski, “Improvement of electro-physical properties of ultra-thin PECVD silicon oxynitride layers by high-temperature annealing,” Vacuum 82(10), 1013–1019 (2008).
[Crossref]

Mukhin, I. S.

I. V. Iorsh, I. S. Mukhin, I. V. Shadrivov, P. A. Belov, and Y. S. Kivshar, “Hyperbolic metamaterials based on multilayer graphene structures,” Phys. Rev. B 87(7), 075416 (2013).
[Crossref]

Narimanov, E.

H. N. S. Krishnamoorthy, Y. Zhou, S. Ramanathan, E. Narimanov, and V. M. Menon, “Tunable hyperbolic metamaterials utilizing phase change heterostructures,” Appl. Phys. Lett. 104(12), 121101 (2014).
[Crossref]

Narimanov, E. E.

Y.-C. Chang, C.-H. Liu, C.-H. Liu, S. Zhang, S. R. Marder, E. E. Narimanov, Z. Zhong, and T. B. Norris, “Realization of mid-infrared graphene hyperbolic metamaterials,” Nat. Commun. 7(10568), 10568 (2016).
[Crossref] [PubMed]

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]

Newman, W.

Y. Guo, W. Newman, C. L. Cortes, and Z. Jacob, “Applications of Hyperbolic Metamaterial Substrates,” Adv. Optoelectron. 2012, 452502 (2012).
[Crossref]

Newman, W. D.

Ning, R.

R. Ning, S. Liu, H. Zhang, B. Bian, and X. Kong, “Tunable absorption in graphene-based hyperbolic metamaterials for mid-infrared range,” Physica B 457, 144–148 (2015).
[Crossref]

R. Ning, S. Liu, H. Zhang, and Z. Jiao, “Dual-gated tunable absorption in graphene-based hyperbolic metamaterials,” AIP Adv. 5(6), 067106 (2015).
[Crossref]

R. Ning, S. Liu, H. Zhang, B. Bian, and X. Kong, “A wide-angle broadband absorber in graphene-based hyperbolic metamaterials,” Eur. Phys. J. Appl. Phys. 68(2), 20401 (2014).
[Crossref]

Noginov, M. A.

S. Prayakarao, B. Mendoza, A. Devine, C. Kyaw, R. B. van Dover, V. Liberman, and M. A. Noginov, “Tunable VO2/Au hyperbolic metamaterial,” Appl. Phys. Lett. 109(6), 061105 (2016).
[Crossref]

Norris, T. B.

Y.-C. Chang, C.-H. Liu, C.-H. Liu, S. Zhang, S. R. Marder, E. E. Narimanov, Z. Zhong, and T. B. Norris, “Realization of mid-infrared graphene hyperbolic metamaterials,” Nat. Commun. 7(10568), 10568 (2016).
[Crossref] [PubMed]

Othman, M. A.

Othman, M. A. K.

M. A. K. Othman, C. Guclu, and F. Capolino, “Graphene-dielectric composite metamaterials: evolution from elliptic to hyperbolic wavevector dispersion and the transverse epsilon-near-zero condition,” J. Nanophotonics 7(1), 073089 (2013).
[Crossref]

Oulton, R. F.

O. Hess, J. B. Pendry, S. A. Maier, R. F. Oulton, J. M. Hamm, and K. L. Tsakmakidis, “Active nanoplasmonic metamaterials,” Nat. Mater. 11(7), 573–584 (2012).
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G. T. Paradakis and H. A. Atwater, “Field-effect induced tunability in hyperbolic metamaterials,” Phys. Rev. B 92(18), 184101 (2015).
[Crossref]

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J. Park, J.-H. Kang, X. Liu, and M. L. Brongersma, “Electrically Tunable Epsilon-Near-Zero (ENZ) Metafilm Absorbers,” Sci. Rep. 5(1), 15754 (2015).
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O. Hess, J. B. Pendry, S. A. Maier, R. F. Oulton, J. M. Hamm, and K. L. Tsakmakidis, “Active nanoplasmonic metamaterials,” Nat. Mater. 11(7), 573–584 (2012).
[Crossref] [PubMed]

Peng, Z.

Z. Cao, X. Xiang, C. Yang, Y. Zhang, Z. Peng, and L. Xuan, “Analysis of tunable characteristics of liquid-crystal-based hyperbolic metamaterials,” Liq. Cryst. 43(12), 1753–1759 (2016).
[Crossref]

Peterka, P.

Podolskiy, V. A.

Prayakarao, S.

S. Prayakarao, B. Mendoza, A. Devine, C. Kyaw, R. B. van Dover, V. Liberman, and M. A. Noginov, “Tunable VO2/Au hyperbolic metamaterial,” Appl. Phys. Lett. 109(6), 061105 (2016).
[Crossref]

Pusch, A.

A. Pusch, S. Wuestner, J. M. Hamm, K. L. Tsakmakidis, and O. Hess, “Coherent amplification and noise in gain-enhanced nanoplasmonic metamaterials: a Maxwell-Bloch Langevin approach,” ACS Nano 6(3), 2420–2431 (2012).
[Crossref] [PubMed]

Ramanathan, S.

H. N. S. Krishnamoorthy, Y. Zhou, S. Ramanathan, E. Narimanov, and V. M. Menon, “Tunable hyperbolic metamaterials utilizing phase change heterostructures,” Appl. Phys. Lett. 104(12), 121101 (2014).
[Crossref]

Salandrino, A.

A. Alǔ, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B 75(15), 155410 (2007).
[Crossref]

Santori, C.

A. Faraon, C. Santori, Z. Huang, V. M. Acosta, and R. G. Beausoleil, “Coupling of Nitrogen-Vacancy Centers to Photonic Crystal Cavities in Monocrystalline Diamond,” Phys. Rev. Lett. 109(3), 033604 (2012).
[Crossref] [PubMed]

A. Faraon, P. E. Barclay, C. Santori, K.-M. C. Fu, and R. G. Beausoleil, “Resonant enhancement of the zero-phonon emission from a colour centre in a diamond cavity,” Nat. Photonics 5(5), 301–305 (2011).
[Crossref]

Scalora, M.

M. A. Vincenti, D. De Ceglia, A. Ciattoni, and M. Scalora, “Singularity-driven second- and third-harmonic generation at-near-zero crossing points,” Phys. Rev. A 84(6), 063826 (2011).
[Crossref]

Shadrivov, I. V.

I. V. Iorsh, I. S. Mukhin, I. V. Shadrivov, P. A. Belov, and Y. S. Kivshar, “Hyperbolic metamaterials based on multilayer graphene structures,” Phys. Rev. B 87(7), 075416 (2013).
[Crossref]

Shalaev, V. M.

R. Chandrasekar, Z. Wang, X. Meng, A. Lagutchev, Y. L. Kim, A. Wei, A. Boltasseva, and V. M. Shalaev, “Lasing action with gold nanorod hyperbolic metamaterials,” in Conference on Lasers and Electro-Optics CLEO: Applications and Technology (2016), paper JTh4A.4.
[Crossref]

Shalaginov, M. Y.

Silveirinha, M. G.

M. G. Silveirinha and N. Engheta, “Theory of supercoupling, squeezing wave energy, and field confinement in narrow channels and tight bends using ε- near-zero metamaterials,” Phys. Rev. B 76(24), 245109 (2007).
[Crossref]

A. Alǔ, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B 75(15), 155410 (2007).
[Crossref]

Smalley, J. S. T.

Smolyaninov, I. I.

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]

Sreekanth, K. V.

K. V. Sreekanth, T. Biaglow, and G. Strangi, “Directional spontaneous emission enhancement in hyperbolic metamaterials,” J. Appl. Phys. 114(13), 134306 (2013).
[Crossref]

Strangi, G.

K. V. Sreekanth, T. Biaglow, and G. Strangi, “Directional spontaneous emission enhancement in hyperbolic metamaterials,” J. Appl. Phys. 114(13), 134306 (2013).
[Crossref]

Su, H.

H. Wang, H. Zhao, H. Su, G. Hu, and J. Zhang, “Active tuning of epsilon-near-zero point of hyperbolic metamaterial at visible and near-infrared regimes,” Appl. Phys. Express 9(9), 092201 (2016).
[Crossref]

Sun, C.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[Crossref] [PubMed]

Szczepanski, P.

Tang, D.

Tayeb, G.

J. Zhang, H. Jiang, B. Gralak, S. Enoch, G. Tayeb, and M. Lequime, “Compensation of loss to approach −1 effective index by gain in metal-dielectric stacks,” Eur. Phys. J. Appl. Phys. 46(3), 1–6 (2008).
[Crossref]

Tsakmakidis, K. L.

A. Pusch, S. Wuestner, J. M. Hamm, K. L. Tsakmakidis, and O. Hess, “Coherent amplification and noise in gain-enhanced nanoplasmonic metamaterials: a Maxwell-Bloch Langevin approach,” ACS Nano 6(3), 2420–2431 (2012).
[Crossref] [PubMed]

O. Hess, J. B. Pendry, S. A. Maier, R. F. Oulton, J. M. Hamm, and K. L. Tsakmakidis, “Active nanoplasmonic metamaterials,” Nat. Mater. 11(7), 573–584 (2012).
[Crossref] [PubMed]

Tyszka-Zawadzka, A.

Ulin-Avila, E.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

Vallini, F.

van Dover, R. B.

S. Prayakarao, B. Mendoza, A. Devine, C. Kyaw, R. B. van Dover, V. Liberman, and M. A. Noginov, “Tunable VO2/Au hyperbolic metamaterial,” Appl. Phys. Lett. 109(6), 061105 (2016).
[Crossref]

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L. A. Falkovsky and A. A. Varlamov, “Space-time dispersion of graphene conductivity,” Eur. Phys. J. B 56(4), 281–284 (2007).
[Crossref]

Vasilantonakis, N.

Vincenti, M. A.

M. A. Vincenti, D. De Ceglia, A. Ciattoni, and M. Scalora, “Singularity-driven second- and third-harmonic generation at-near-zero crossing points,” Phys. Rev. A 84(6), 063826 (2011).
[Crossref]

Wang, F.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

Wang, H.

H. Wang, H. Zhao, H. Su, G. Hu, and J. Zhang, “Active tuning of epsilon-near-zero point of hyperbolic metamaterial at visible and near-infrared regimes,” Appl. Phys. Express 9(9), 092201 (2016).
[Crossref]

Wang, Z.

R. Chandrasekar, Z. Wang, X. Meng, A. Lagutchev, Y. L. Kim, A. Wei, A. Boltasseva, and V. M. Shalaev, “Lasing action with gold nanorod hyperbolic metamaterials,” in Conference on Lasers and Electro-Optics CLEO: Applications and Technology (2016), paper JTh4A.4.
[Crossref]

Wei, A.

R. Chandrasekar, Z. Wang, X. Meng, A. Lagutchev, Y. L. Kim, A. Wei, A. Boltasseva, and V. M. Shalaev, “Lasing action with gold nanorod hyperbolic metamaterials,” in Conference on Lasers and Electro-Optics CLEO: Applications and Technology (2016), paper JTh4A.4.
[Crossref]

Wen, S.

Wu, C.

L. Ferrari, C. Wu, D. Lepage, X. Zhang, and Z. Liu, “Hyperbolic metamaterials and their applications,” Prog. Quantum Electron. 40, 1–40 (2015).
[Crossref]

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A. Pusch, S. Wuestner, J. M. Hamm, K. L. Tsakmakidis, and O. Hess, “Coherent amplification and noise in gain-enhanced nanoplasmonic metamaterials: a Maxwell-Bloch Langevin approach,” ACS Nano 6(3), 2420–2431 (2012).
[Crossref] [PubMed]

Wurtz, G. A.

Xiang, X.

Z. Cao, X. Xiang, C. Yang, Y. Zhang, Z. Peng, and L. Xuan, “Analysis of tunable characteristics of liquid-crystal-based hyperbolic metamaterials,” Liq. Cryst. 43(12), 1753–1759 (2016).
[Crossref]

Xiang, Y.

Xiong, Y.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[Crossref] [PubMed]

Xuan, L.

Z. Cao, X. Xiang, C. Yang, Y. Zhang, Z. Peng, and L. Xuan, “Analysis of tunable characteristics of liquid-crystal-based hyperbolic metamaterials,” Liq. Cryst. 43(12), 1753–1759 (2016).
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J. T. Choy, B. J. M. Hausmann, T. M. Babinec, I. Bulu, M. Khan, P. Maletinsky, A. Yacoby, and M. Loncar, “Enhanced single-photon emission from a diamond–silver aperture,” Nat. Photonics 5(12), 738–743 (2011).
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Yang, C.

Z. Cao, X. Xiang, C. Yang, Y. Zhang, Z. Peng, and L. Xuan, “Analysis of tunable characteristics of liquid-crystal-based hyperbolic metamaterials,” Liq. Cryst. 43(12), 1753–1759 (2016).
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Yang, X.

Yin, X.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

Zayats, A. V.

Zentgraf, T.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

Zhang, H.

R. Ning, S. Liu, H. Zhang, and Z. Jiao, “Dual-gated tunable absorption in graphene-based hyperbolic metamaterials,” AIP Adv. 5(6), 067106 (2015).
[Crossref]

R. Ning, S. Liu, H. Zhang, B. Bian, and X. Kong, “Tunable absorption in graphene-based hyperbolic metamaterials for mid-infrared range,” Physica B 457, 144–148 (2015).
[Crossref]

R. Ning, S. Liu, H. Zhang, B. Bian, and X. Kong, “A wide-angle broadband absorber in graphene-based hyperbolic metamaterials,” Eur. Phys. J. Appl. Phys. 68(2), 20401 (2014).
[Crossref]

Zhang, J.

H. Wang, H. Zhao, H. Su, G. Hu, and J. Zhang, “Active tuning of epsilon-near-zero point of hyperbolic metamaterial at visible and near-infrared regimes,” Appl. Phys. Express 9(9), 092201 (2016).
[Crossref]

J. Zhang, H. Jiang, B. Gralak, S. Enoch, G. Tayeb, and M. Lequime, “Compensation of loss to approach −1 effective index by gain in metal-dielectric stacks,” Eur. Phys. J. Appl. Phys. 46(3), 1–6 (2008).
[Crossref]

Zhang, S.

Y.-C. Chang, C.-H. Liu, C.-H. Liu, S. Zhang, S. R. Marder, E. E. Narimanov, Z. Zhong, and T. B. Norris, “Realization of mid-infrared graphene hyperbolic metamaterials,” Nat. Commun. 7(10568), 10568 (2016).
[Crossref] [PubMed]

Zhang, X.

L. Ferrari, C. Wu, D. Lepage, X. Zhang, and Z. Liu, “Hyperbolic metamaterials and their applications,” Prog. Quantum Electron. 40, 1–40 (2015).
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W. Li, Z. Liu, X. Zhang, and X. Jiang, “Switchable hyperbolic metamaterials with magnetic control,” Appl. Phys. Lett. 100(16), 161108 (2012).
[Crossref]

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[Crossref] [PubMed]

Zhang, Y.

Z. Cao, X. Xiang, C. Yang, Y. Zhang, Z. Peng, and L. Xuan, “Analysis of tunable characteristics of liquid-crystal-based hyperbolic metamaterials,” Liq. Cryst. 43(12), 1753–1759 (2016).
[Crossref]

Zhao, H.

H. Wang, H. Zhao, H. Su, G. Hu, and J. Zhang, “Active tuning of epsilon-near-zero point of hyperbolic metamaterial at visible and near-infrared regimes,” Appl. Phys. Express 9(9), 092201 (2016).
[Crossref]

Zhong, Z.

Y.-C. Chang, C.-H. Liu, C.-H. Liu, S. Zhang, S. R. Marder, E. E. Narimanov, Z. Zhong, and T. B. Norris, “Realization of mid-infrared graphene hyperbolic metamaterials,” Nat. Commun. 7(10568), 10568 (2016).
[Crossref] [PubMed]

Zhou, Y.

H. N. S. Krishnamoorthy, Y. Zhou, S. Ramanathan, E. Narimanov, and V. M. Menon, “Tunable hyperbolic metamaterials utilizing phase change heterostructures,” Appl. Phys. Lett. 104(12), 121101 (2014).
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ACS Nano (1)

A. Pusch, S. Wuestner, J. M. Hamm, K. L. Tsakmakidis, and O. Hess, “Coherent amplification and noise in gain-enhanced nanoplasmonic metamaterials: a Maxwell-Bloch Langevin approach,” ACS Nano 6(3), 2420–2431 (2012).
[Crossref] [PubMed]

Adv. Optoelectron. (1)

Y. Guo, W. Newman, C. L. Cortes, and Z. Jacob, “Applications of Hyperbolic Metamaterial Substrates,” Adv. Optoelectron. 2012, 452502 (2012).
[Crossref]

AIP Adv. (1)

R. Ning, S. Liu, H. Zhang, and Z. Jiao, “Dual-gated tunable absorption in graphene-based hyperbolic metamaterials,” AIP Adv. 5(6), 067106 (2015).
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Appl. Phys. Express (1)

H. Wang, H. Zhao, H. Su, G. Hu, and J. Zhang, “Active tuning of epsilon-near-zero point of hyperbolic metamaterial at visible and near-infrared regimes,” Appl. Phys. Express 9(9), 092201 (2016).
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Appl. Phys. Lett. (5)

Y. Guo, C. L. Cortes, S. Molesky, and Z. Jacob, “Broadband super-Planckian thermal emission from hyperbolic metamaterials,” Appl. Phys. Lett. 101(13), 131106 (2012).
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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]

S. Prayakarao, B. Mendoza, A. Devine, C. Kyaw, R. B. van Dover, V. Liberman, and M. A. Noginov, “Tunable VO2/Au hyperbolic metamaterial,” Appl. Phys. Lett. 109(6), 061105 (2016).
[Crossref]

H. N. S. Krishnamoorthy, Y. Zhou, S. Ramanathan, E. Narimanov, and V. M. Menon, “Tunable hyperbolic metamaterials utilizing phase change heterostructures,” Appl. Phys. Lett. 104(12), 121101 (2014).
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W. Li, Z. Liu, X. Zhang, and X. Jiang, “Switchable hyperbolic metamaterials with magnetic control,” Appl. Phys. Lett. 100(16), 161108 (2012).
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Eur. Phys. J. Appl. Phys. (2)

R. Ning, S. Liu, H. Zhang, B. Bian, and X. Kong, “A wide-angle broadband absorber in graphene-based hyperbolic metamaterials,” Eur. Phys. J. Appl. Phys. 68(2), 20401 (2014).
[Crossref]

J. Zhang, H. Jiang, B. Gralak, S. Enoch, G. Tayeb, and M. Lequime, “Compensation of loss to approach −1 effective index by gain in metal-dielectric stacks,” Eur. Phys. J. Appl. Phys. 46(3), 1–6 (2008).
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Eur. Phys. J. B (1)

L. A. Falkovsky and A. A. Varlamov, “Space-time dispersion of graphene conductivity,” Eur. Phys. J. B 56(4), 281–284 (2007).
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J. Appl. Phys. (1)

K. V. Sreekanth, T. Biaglow, and G. Strangi, “Directional spontaneous emission enhancement in hyperbolic metamaterials,” J. Appl. Phys. 114(13), 134306 (2013).
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J. Lightwave Technol. (1)

J. Nanophotonics (1)

M. A. K. Othman, C. Guclu, and F. Capolino, “Graphene-dielectric composite metamaterials: evolution from elliptic to hyperbolic wavevector dispersion and the transverse epsilon-near-zero condition,” J. Nanophotonics 7(1), 073089 (2013).
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J. Opt. Soc. Am. (1)

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

Liq. Cryst. (1)

Z. Cao, X. Xiang, C. Yang, Y. Zhang, Z. Peng, and L. Xuan, “Analysis of tunable characteristics of liquid-crystal-based hyperbolic metamaterials,” Liq. Cryst. 43(12), 1753–1759 (2016).
[Crossref]

Nat. Commun. (1)

Y.-C. Chang, C.-H. Liu, C.-H. Liu, S. Zhang, S. R. Marder, E. E. Narimanov, Z. Zhong, and T. B. Norris, “Realization of mid-infrared graphene hyperbolic metamaterials,” Nat. Commun. 7(10568), 10568 (2016).
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Nat. Mater. (1)

O. Hess, J. B. Pendry, S. A. Maier, R. F. Oulton, J. M. Hamm, and K. L. Tsakmakidis, “Active nanoplasmonic metamaterials,” Nat. Mater. 11(7), 573–584 (2012).
[Crossref] [PubMed]

Nat. Photonics (2)

J. T. Choy, B. J. M. Hausmann, T. M. Babinec, I. Bulu, M. Khan, P. Maletinsky, A. Yacoby, and M. Loncar, “Enhanced single-photon emission from a diamond–silver aperture,” Nat. Photonics 5(12), 738–743 (2011).
[Crossref]

A. Faraon, P. E. Barclay, C. Santori, K.-M. C. Fu, and R. G. Beausoleil, “Resonant enhancement of the zero-phonon emission from a colour centre in a diamond cavity,” Nat. Photonics 5(5), 301–305 (2011).
[Crossref]

Nature (1)

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
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Opt. Express (8)

M. A. Othman, C. Guclu, and F. Capolino, “Graphene-based tunable hyperbolic metamaterials and enhanced near-field absorption,” Opt. Express 21(6), 7614–7632 (2013).
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A. Andryieuski and A. V. Lavrinenko, “Graphene metamaterials based tunable terahertz absorber: effective surface conductivity approach,” Opt. Express 21(7), 9144–9155 (2013).
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J. S. T. Smalley, F. Vallini, B. Kanté, and Y. Fainman, “Modal amplification in active waveguides with hyperbolic dispersion at telecommunication frequencies,” Opt. Express 22(17), 21088–21105 (2014).
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N. Vasilantonakis, G. A. Wurtz, V. A. Podolskiy, and A. V. Zayats, “Refractive index sensing with hyperbolic metamaterials: strategies for biosensing and nonlinearity enhancement,” Opt. Express 23(11), 14329–14343 (2015).
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L. Ferrari, D. Lu, D. Lepage, and Z. Liu, “Enhanced spontaneous emission inside hyperbolic metamaterials,” Opt. Express 22(4), 4301–4306 (2014).
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P. Peterka, I. Kasik, A. Dhar, B. Dussardier, and W. Blanc, “Theoretical modeling of fiber laser at 810 nm based on thulium-doped silica fibers with enhanced 3H4 level lifetime,” Opt. Express 19(3), 2773–2781 (2011).
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B. Janaszek, A. Tyszka-Zawadzka, and P. Szczepański, “Tunable graphene-based hyperbolic metamaterial operating in SCLU telecom bands,” Opt. Express 24(21), 24129–24136 (2016).
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Y. Xiang, J. Guo, X. Dai, S. Wen, and D. Tang, “Engineered surface Bloch waves in graphene-based hyperbolic metamaterials,” Opt. Express 22(3), 3054–3062 (2014).
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Opt. Lett. (2)

Phys. Rev. (1)

D. E. McCumber, “Einstein relations connecting broadband emission and absorption spectra,” Phys. Rev. 136(4A), A954–A957 (1964).
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Phys. Rev. A (1)

M. A. Vincenti, D. De Ceglia, A. Ciattoni, and M. Scalora, “Singularity-driven second- and third-harmonic generation at-near-zero crossing points,” Phys. Rev. A 84(6), 063826 (2011).
[Crossref]

Phys. Rev. B (5)

C. Argyropoulos, G. D’Aguanno, and A. Alǔ, “Giant second-harmonic generation efficiency and ideal phase matching with a double ε-near-zero cross-slit metamaterial,” Phys. Rev. B 89(23), 235401 (2014).
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M. G. Silveirinha and N. Engheta, “Theory of supercoupling, squeezing wave energy, and field confinement in narrow channels and tight bends using ε- near-zero metamaterials,” Phys. Rev. B 76(24), 245109 (2007).
[Crossref]

A. Alǔ, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B 75(15), 155410 (2007).
[Crossref]

G. T. Paradakis and H. A. Atwater, “Field-effect induced tunability in hyperbolic metamaterials,” Phys. Rev. B 92(18), 184101 (2015).
[Crossref]

I. V. Iorsh, I. S. Mukhin, I. V. Shadrivov, P. A. Belov, and Y. S. Kivshar, “Hyperbolic metamaterials based on multilayer graphene structures,” Phys. Rev. B 87(7), 075416 (2013).
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Phys. Rev. Lett. (1)

A. Faraon, C. Santori, Z. Huang, V. M. Acosta, and R. G. Beausoleil, “Coupling of Nitrogen-Vacancy Centers to Photonic Crystal Cavities in Monocrystalline Diamond,” Phys. Rev. Lett. 109(3), 033604 (2012).
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Physica B (1)

R. Ning, S. Liu, H. Zhang, B. Bian, and X. Kong, “Tunable absorption in graphene-based hyperbolic metamaterials for mid-infrared range,” Physica B 457, 144–148 (2015).
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Prog. Quantum Electron. (1)

L. Ferrari, C. Wu, D. Lepage, X. Zhang, and Z. Liu, “Hyperbolic metamaterials and their applications,” Prog. Quantum Electron. 40, 1–40 (2015).
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Figures (5)

Fig. 1
Fig. 1 Scheme of considered structure.
Fig. 2
Fig. 2 Real part of effective permittivity tensor components ε|| (red curve) and ε (blue curve) plotted vs. wavelength for biasing voltage Vg = 0 V, where λ 0 (1,3) and λ 0 (2) denote the resonance wavelengths of ε and ε||, respectively.
Fig. 3
Fig. 3 Spectral dependencies of effective gain/absorption (g, g|| / α, α||) corresponding to resonance wavelengths λ 0 (1) for different values of biasing voltage as well as gain/absorption (g/α) of constituent material: (a) g (left axis; blue curves) for Vg = 0,3,8 mV and g (right axis; solid green curve); (b) g|| (left axis; red curves) for Vg = 0,3,8 mV and g (right axis; solid green curve); (c) α (left axis; blue curves) for Vg = 11,13,15 mV and α (right axis; dashed green curve); (d) α|| (left axis; red curves) for Vg = 11,13,15 mV and α (right axis; dashed green curve).
Fig. 4
Fig. 4 Spectral dependencies of effective gain/absorption (g, g|| / α, α||) corresponding to resonance wavelengths λ 0 (2) for different values of biasing voltage as well as gain/absorption (g/α) of constituent material: (a) g (left axis; blue curves) for Vg = 0.55,0.75,0.9 V and g (right axis; solid green curve); (b) g|| (left axis; red curves) for Vg = 0.55,0.75,0.9 V and g (right axis; solid green curve); (c) α (left axis; blue curves) for Vg = 1.1,1.2,1.4 V and α (right axis; dashed green curve); (d) α|| (left axis; red curves) for Vg = 1.1,1.2,1.4 V and α (right axis; dashed green curve).
Fig. 5
Fig. 5 Spectral dependencies of effective absorption (α, α||) corresponding to resonance wavelengths λ 0 (3) for different values of biasing voltage as well as absorption (α) of constituent material: (c) α (left axis; blue curves) for Vg = 0,0.5,1 mV and α (right axis; dashed green curve); (d) α|| (left axis; red curves) for Vg = 0,0.5,1 mV and α (right axis; dashed green curve).

Equations (12)

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ε graph =1j σ(ω, μ c ) ω ε o t graph ,
σ(ω, μ c )= j4π q 2 k B T h 2 (ωj2τ) [ μ c k B T +2ln( e μ / k B T +1 ) ]+ j4π q 2 ( ωj2τ ) h 2 0 f D (ξ) f D (ξ) ( ωj2τ ) 2 16( πξ h ) dξ,
| μ c |= υ F π| a 0 ( V g V dirac ) | ,
Re( ε g/ab (λ))1+ a 1 λ 2 λ 2 l 1 2 + a 2 λ 2 λ 2 l 2 2 + a 3 λ 2 λ 2 l 3 2
g(λ)=N σ em (λ),
α(λ)=N σ abs (λ),
σ em/abs (λ)= k=1 4 α k exp( 2 ( λ λ k Δ λ k ) 2 ) .
Im( ε g/ab )=g(λ)λ Re( ε g/ab ) .
ε || = t graph ε graph + t g/ab ε g/ab t graph + t g/ab ,
ε = ε graph ε g/ab ( t graph + t g/ab ) t graph ε g/ab + t g/ab ε graph ,
g ||, ( λ )= Im[ ε ||, ( λ ) ]λ Re[ | ε ||, ( λ ) | ]
α ||, ( λ )= Im[ ε ||, ( λ ) ]λ Re[ | ε ||, ( λ ) | ] , .

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