Hybridization Induced Transparency in composites of metamaterials and atomic media

doi:10.1364/OE.19.023573

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Hybridization Induced Transparency in composites of metamaterials and atomic media

Peter Weis, Juan Luis Garcia-Pomar, René Beigang, and Marco Rahm »View Author Affiliations

Optics Express, Vol. 19, Issue 23, pp. 23573-23580 (2011)
http://dx.doi.org/10.1364/OE.19.023573

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– Abstract
1. Introduction
2. Analytic Model
3. Experiment and Simulation
4. Conclusion
– References and links

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Abstract

We report hybridization induced transparency (HIT) in a composite medium consisting of a metamaterial and a dielectric. We develop an analytic model that explains HIT by coherent coupling between the hybridized local fields of the metamaterial and the dielectric or an atomic system in general. In a proof-of-principle experiment, we evidence HIT in a split ring resonator metamaterial that is coupled to α-lactose monohydrate. Both, the analytic model and numerical calculations confirm and explain the experimental observations. HIT can be considered as a hybrid analogue to electromagnetically induced transparency (EIT) and plasmon-induced transparency (PIT).

1. Introduction

In the past decade, the research field of metamaterials encompassed a great variety of research topics ranging from fundamental to application-oriented research. Especially nonlinear metamaterials [1

A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, “Nonlinear properties of left-handed metamaterials,” Phys. Rev. Lett. 91, 037401 (2003). [CrossRef] [PubMed]

, 2

E. Poutrina, D. Huang, and D. R. Smith, “Analysis of nonlinear electromagnetic metamaterials,” New Journal of Physics 12, 093010 (2010). [CrossRef]

], metamaterials with gain [3

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nature Photonics 2, 351–354 (2008). [CrossRef]

, 4

M. Wegener, J. L. Garcia-Pomar, C. M. Soukoulis, N. Meinzer, M. Ruther, and S. Linden, “Toy model for plasmonic metamaterial resonances coupled to two-level system gain,” Opt. Express 16, 19785–19798 (2008). [CrossRef] [PubMed]

, 5

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010). [CrossRef] [PubMed]

], actively tunable metamaterials [6

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444, 597–600 (2006). [CrossRef] [PubMed]

, 7

H.-T. Chen, W. J. Padilla, J. M. O. Zide, S. R. Bank, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Ultrafast optical switching of terahertz metamaterials fabricated on eras/gaas nanoisland superlattices,” Opt. Express 32, 1620–1622 (2007).

, 8

O. Paul, C. Imhof, B. Lägel, S. Wolff, J. Heinrich, S. Höfling, A. Forchel, R. Zengerle, R. Beigang, and M. Rahm, “Polarization-independent active metamaterial for high-frequency terahertz modulation,” Opt. Express 17, 819–827 (2009). [CrossRef] [PubMed]

], transformation optics [9

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006). [CrossRef] [PubMed]

] and quantum metamaterials [10

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 047401 (2008). [CrossRef] [PubMed]

, 11

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the drude damping limit,” Nature Materials 8, 758–762 (2009). [CrossRef] [PubMed]

, 12

N. Liu, M. Hentschel, T. Weiss, A. P. Alivisatos, and H. Giessen, “Three-dimensional plasmon rulers,” Science 332, 1407–1410 (2011). [CrossRef] [PubMed]

, 13

A. Artar, A. A. Yanik, and H. Altug, “Multispectral Plasmon Induced Transparency in Coupled Meta-Atoms,” Nano Lett. 11, 1685–1689 (2011). [CrossRef] [PubMed]

, 14

S.-D. Liu, Z. Yang, R.-P. Liu, and X.-Y. Li, “Plasmonic-induced optical transparency in the near-infrared and visible range with double split nanoring cavity,” Opt. Express 19, 15363–15370 (2011). [CrossRef] [PubMed]

, 15

S. I. Bozhevolnyi, A. B Evlyukhin, A. Pors, M. G. Nielsen, M. Willatzen, and O. Albrektsen, “Optical transparency by detuned electrical dipoles,” New Journal of Physics 13, 023034 (2011). [CrossRef]

] lay the foundation for the development of ground-breaking photonic devices while they concurrently provide a rich nutrient medium for systematic studies of fundamental physical effects. In the latter context, metamaterials can serve as important, artificially created model systems for the investigation of novel phenomena that cannot occur in natural materials. In particular, they provide a suitable platform to study important analogies between basic physical properties that occur in the realms of different disciplines as e. g. analogue effects in classical and quantum systems [10

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 047401 (2008). [CrossRef] [PubMed]

, 11

, 12

N. Liu, M. Hentschel, T. Weiss, A. P. Alivisatos, and H. Giessen, “Three-dimensional plasmon rulers,” Science 332, 1407–1410 (2011). [CrossRef] [PubMed]

, 16

N. Liu, H. Liu, S. Zhu, and H. Giessen, “Stereometamaterials,” Nature Photonics 3, 157–162 (2009). [CrossRef]

], electromagnetic and acoustic/mechanical systems [9

, 17

S. A. Cummer and D. Schurig, “One path to acoustic cloaking,” New Journal of Physics 9, 45 (2007). [CrossRef]

], etc. In this respect, it was recently shown that metamaterials can be deliberately devised to exhibit electromagnetic properties that can be explained by the underlying concepts of electromagnetically induced transparency (EIT) in atomic systems [18

K.-J. Boller, A. Imamoglu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991). [CrossRef] [PubMed]

]. In EIT, a spectrally narrowband transmission window within a broad absorption band is established by destructive interference between the transitions of atomic quantum states [19

M. Fleischhauer, A. Imamoglu, and J. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005). [CrossRef]

In 2008, Zhang et al. theoretically described plasmon-induced transparency (PIT) in a metamaterial, an effect that strongly resembles EIT in atomic systems [10

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 047401 (2008). [CrossRef] [PubMed]

]. This analogue phenomenon relies on destructive interference between a bright dipole mode and a dark quadrupole mode in artificially designed plasmonic structures that mimic the role of artificial molecules. In 2009, Liu et al. experimentally validated PIT in a plasmonic metamaterial [11

]. The main advantage of dealing with PIT in comparison to EIT is the ability to deliberately tailor the total near- and farfield electromagnetic response of the plasmonic system on a subwavelength scale. Moreover, PIT no longer requires a dressing laser. Although it is possible from the principles to prepare the quantum states of an atomic system within certain limits, this task is much more involved in comparison with the design and fabrication of plasmonic molecules. On the other hand, the maximal achievable transparency and dispersion in both systems is determined by the ratio between the resonance width of the narrowband and the broadband mode. However, in PIT this ratio is inherently limited by intrinsic metallic loss of the plasmonic molecule and thus the effect of PIT is usually less pronounced than EIT in atomic systems.

In view of these limitations, it would be desirable to combine the advantages of both worlds. Therefore, the question arises if induced transparency can also be achieved in a hybrid system composed of plasmonic structures and an ensemble of atoms. The latter could be a quantum structure or a simple dielectric with extremely narrowband absorption lines. Furthermore, the plasmonic molecules could be deliberately designed for spectrally broadband radiative dipole coupling to external fields. If the mutual interaction between the plasmonic and atomic system could be controlled such that the broadband oscillations in the plasmonic molecules interacted with the narrowband oscillations of the atomic system to interfere destructively, induced narrowband transparency within the broadband absorption line would become observable. In such a system, the EIT-like effect would be rooted in the hybridized fields of the plasmonic molecules and the atomic system. Therefore, we refer to this effect as hybridization induced transparency (HIT) throughout the text.

In this article, we describe and discuss the effect of HIT on the basis of an analytic model and substantiate the validity of the analytic description by numerical full wave simulations. Even more importantly, we evidence HIT in a composite structure consisting of split ring resonators (SRRs) and α-lactose monohydrate. In this proof-of-principle experiment, HIT is observed due to the coherent coupling of a broadband mode of the SRRs to a narrowband mode resonance of α-lactose. Although here we restrain ourselves to the hybridization of a metamaterial and an atomic/molecular system, it is important to notice that HIT is a general effect that is based on the mode hybridization of a set of oscillators. Hence, the atomic system could be represented by a wide range of solids, fluids and gaseous materials and could open new routes for the investigation of the coupling between metamaterials and ultracold gases. Moreover, the atomic system could be substituted by quantum structures [20

C. Walther, G. Scalari, M. I. Amanti, M. Beck, and J. Faist, “Microcavity laser oscillating in a circuit-based resonator,” Science 327, 1495–1497 (2010). [CrossRef] [PubMed]

, 21

X. Wu, S. K. Gray, and M. Pelton, “Quantum-dot-induced transparency in a nanoscale plasmonic resonator,” Opt. Express 18, 23633–23645 (2010). [CrossRef] [PubMed]

, 22

D. Dietze, A. Benz, G. Strasser, K. Unterrainer, and J. Darmo, “Terahertz meta-atoms coupled to a quantum well intersubband transition,” Opt. Express 19, 13700–13706 (2011). [CrossRef] [PubMed]

], mechanical oscillators [23

J. D. Teufel, D. Li, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, and R. W. Simmonds, “Circuit cavity electromechanics in the strong-coupling regime,” Nature 471, 204–208 (2011). [CrossRef] [PubMed]

], phonon excitations [24

F. Neubrech, D. Weber, D. Enders, T. Nagao, and A. Pucci, “Antenna Sensing of Surface Phonon Polaritons,” J. Phys. Chem. C 114, 7299–7301 (2010). [CrossRef]

, 25

D. J. Shelton, I. Brener, J. C. Ginn, M. B. Sinclair, D. W. Peters, K. R. Coffey, and G. D. Boreman, “Strong Coupling between Nanoscale Metamaterials and Phonons,” Nano Lett. 11, 2104–2108 (2011). [CrossRef] [PubMed]

] or waveguides [26

S. Linden, J. Kuhl, and H. Giessen, “Controlling the Interaction between Light and Gold Nanoparticles: Selective Suppression of Extinction,” Phys. Rev. Lett. 20, 4688–4691 (2001). [CrossRef]

, 27

T. Zentgraf, S. Zhang, R. F. Oulton, and X. Zhang, “Ultranarrow coupling-induced transparency bands in hybrid plasmonic systems,” Phys. Rev. B 80, 195415 (2009).

, 28

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nature Materials 9, 707–715 (2010). [CrossRef]

, 29

B. Tang, L. Dai, and C. Jiang, “Electromagnetically induced transparency in hybrid plasmonic-dielectric system,” Opt. Express 19, 628–637 (2011). [CrossRef] [PubMed]

], to name only a few examples that can be described in the regime of HIT.

2. Analytic Model

The analytic model is based on a density matrix formalism and the solution of Maxwell-Bloch equations as described in detail in [4

]. In a very simplified approach, we can describe the plasmonic and the atomic system as 2-level oscillators. This is illustrated in the level diagram of Fig.1. In this picture, the density matrix ρ₁₂ of the plasmonic system and ρ̃₁₃ of the atomic system obey the coupled differential equations

{\dot{ρ}}_{12} = - i (Δ_{12} - i γ_{12}) ρ_{12} + i \frac{μ_{12}}{\bar{h}} E_{L}

(1)

{\dot{\tilde{ρ}}}_{13} = - i ({\tilde{Δ}}_{13} - i {\tilde{γ}}_{13}) {\tilde{ρ}}_{13} + i \frac{{\tilde{μ}}_{13}}{\bar{h}} {\tilde{E}}_{L}

(2)

Hereby, Δ₁₂ = ω₁₂ – ω and Δ̃₁₃ = ω̃₁₃ – ω denote the detuning between the resonance frequencies ω₁₂, ω̃₁₃ and the excitation frequency ω, μ₁₂ and μ̃₁₃ are the transition dipole moments, γ₁₂ and γ̃₁₃ are the damping constants and E_L = E_ext + κP̃₁₃ and Ẽ_L = E_ext + κP₁₂ are the local electric fields that are induced by the external electric field E_ext and the mutually excited polarizations P and P̃. The parameter κ describes the coupling strength between the plasmonic and atomic oscillators. The macroscopic polarizations can be calculated by

P_{12} = N μ_{12} ρ_{12}

(3)

{\tilde{P}}_{13} = \tilde{N} {\tilde{μ}}_{13} {\tilde{ρ}}_{13}

(4)

N and Ñ describe the number densities of plasmonic and atomic oscillators. From the solutions of Eqs. (1)–(4) and by homogenizing the composed system by a simplified Maxwell-Garnett approach, we obtain for the complex susceptibility χ of the composed system:

χ = \frac{1}{2 ɛ_{0}} (\frac{{\tilde{P}}_{13}}{E_{ext}} + \frac{P_{12}}{E_{ext}})

(5)

For simplification of the following discussion, it is justified to assume that ω₁₂ ≈ ω̃₁₃, which means that the resonance frequencies of the transitions |1〉 → |2〉 and |1〉 → |3〉 are approximately equal. From the steady-state solutions of (1) and (2) we obtain by applying (5) for the imaginary part of the susceptibility χ″ at frequency ω₁₂ ≈ ω̃¹³ for Δ₁₂ = Δ̃₁₃ = 0:

χ^{″} = \frac{1}{2 ɛ_{0} \bar{h}} (\frac{1}{A_{12}^{- 1}} + \frac{1}{\frac{1}{{\bar{h}}^{2}} κ^{2} {\tilde{A}}_{13}} + \frac{1}{{\tilde{A}}_{13}^{- 1} + \frac{1}{{\bar{h}}^{2}} κ^{2} A_{12}})

(6)

with

A_{12} = \frac{N μ_{12}^{2}}{γ_{12}}

and

{\tilde{A}}_{13} = \frac{\tilde{N} {\tilde{μ}}_{13}^{2}}{{\tilde{γ}}_{13}}

. By inspection of (6) we observe that, for a given A₁₂, the imaginary part of the susceptibility χ″ and thus the absorption is reduced to a minimum (I) if Ã₁₃ is maximized and (II) if the coupling constant κ is maximized. In the first case, Ã₁₃ can be maximized by exploiting a spectrally narrowband resonance (γ̃₁₃ small) in the atomic system that overlaps with the broadband resonance of the metamaterial. Fig. 2 shows the real and imaginary part of the susceptibility and the transmission of a hybrid system for two different ratios γ̃₁₃/γ₁₂ (Figs. 2(a),(b)) and coupling factors (Figs. 2(c),(d)) which confirm the discussed behavior.

Fig. 1 Level scheme of a hybrid system composed of a plasmonic metamaterial and an atomic medium. The two resonators have similar resonance frequencies ω₁₂ ≈ ω₁₃ (further properties as described in the text) and couple via the local electric fields represented by the coupling strength κ.

Fig. 2 Real part (solid line) and imaginary part (dashed line) of the susceptibility (left column) and transmission (right column) of a hybrid system for several ratios γ̃₁₃/γ₁₂ (upper row) and coupling strengths κ (lower row).

3. Experiment and Simulation

In order to verify our model, we investigated HIT in the coherent coupling between a narrowband absorption resonance of α-lactose monohydrate and the broadband resonance of an array of SRRs in a proof-of-principle experiment. α-lactose exhibits a spectrally narrowband, strong resonance at a frequency of 0.53 THz [30

D. Allis, A. Fedor, T. Korter, J. Bjarnason, and E. Brown, “Assignment of the lowest-lying THz absorption signatures in biotin and lactose monohydrate by solid-state density functional theory,” Chemical Physics Letters 440, 203–209 (2007). [CrossRef]

, 31

E. Brown, J. Bjarnson, A. Fedor, and T. Korter, “On the strong and narrow absorption signature in lactose at 0.53 THz,” Appl. Phys. Lett. 90, 061908 (2007). [CrossRef]

, 32

A. Roggenbuck, H. Schmitz, A. Deninger, I. C. Mayorga, J. Hemberger, R. Güsten, and M. Grüninger, “Coherent broadband continuous-wave terahertz spectroscopy on solid-state samples,” New Journal of Physics 12, 043017 (2010). [CrossRef]

]. The metamaterial structure was composed of a single layer of square-shaped gold SRRs on top of a 27 μm thick benzocyclobutene (BCB) substrate. The SRRs had a thickness of 200 nm, a side length of 58 μm and the split gap was 7 μm. The unit cells were arrayed with a periodicity of 75 μm. For studying the coupling between the SRR metamaterial and an atomic system, we coated the SRRs with a 50 μm thick layer of α-lactose. To obtain a thin lactose film we diluted α-lactose powder in a saturated aqueous solution and deposited it on top of the metamaterial. To accelerate the crystallization process, we heated the sample to a temperature of 90° C, thus minimizing mutarotation of lactose from the α to the β anomeric form [33

R. Lefort, V. Caron, J.-F. Willart, and M. Descamps, “Mutarotational kinetics and glass transition of lactose,” Solid State Comm. 140, 329–334 (2006). [CrossRef]

We measured the transmission spectrum of the SRR-lactose sample by terahertz (THz) time domain spectroscopy. The polarization vector of the THz electric field was oriented along the gap of the SRRs in order to excite the magnetic SRR resonance at normal incidence by electromagnetic cross coupling. The amplitude transmission spectrum is shown in Fig. 3(a). Globally, the spectrum of α-lactose displays three distinct transmission minima. The minima at 0.53 THz, 1.2 THz and 1.37 THz are related to absorption lines of α-lactose. The composed metamaterial/lactose system reveals four transmission minima whereof the minima at 1.2 THz and 1.37 THz purely originate from α-lactose and the minimum at 1.6 THz corresponds to the Mie resonance of the SRRs [34

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95, 203901 (2005). [CrossRef] [PubMed]

]. The broadband transmission minimum around 0.53 THz stems from the magnetic SRR resonance. Taking a closer look at the minimum in Fig.3(b), we observe that the broadband absorption is superimposed by a spectrally narrowband transmission window within the broadband SRR resonance at a frequency of 0.53 THz. This frequency is similar to the resonance frequency of the narrowband absorption of α-lactose. The induced transparency traces back to the coherent, destructively interferent coupling between the broadband SRR resonance oscillations and the narrowband, absorptive transition in α-lactose. In this respect, the SRR metamaterial and the α-lactose interact via the hybridized local electric fields.

Fig. 3 (a) Measured transmission spectrum of α-lactose (red) and observation of HIT in a metamaterial/α-lactose system (blue), (b) zoomed excerpt of the transmission spectrum around the HIT frequency range. The green dotted line represents the transmission spectrum of the metamaterial only. For a better comparison it was shifted to match the resonance frequency of the lactose covered system. (c) and (d) comparison between the experimental data and the numerical and analytic calculations.

To substantiate this explanation, we further investigated the interaction process between the SRR metamaterial and α-lactose by 3D full wave simulations based on a Finite Integration Technique in the frequency domain (CST Microwave Studio). In the model, the gold SRRs were described as lossy metal. The permittivity of the BCB was 2.67 with a loss tangent tanδ = 0.1. The geometric dimensions of the SRRs were identical to the experimental values. We described the permittivity of the narrowband absorption resonance of α-lactose by a Lorentz-model

ɛ = ɛ_{b} + \frac{{\tilde{b}}_{13}}{{\tilde{ω}}_{13}^{2} - i {\tilde{γ}}_{13} ω - ω^{2}}

(7)

Hereby, ɛ_b denotes the off-resonance background permittivity of lactose, ω̃₁₃ is the resonance frequency of the transition, γ̃₁₃ is the damping factor and b̃₁₃ is the oscillator strength per s². We obtained a value of ɛ_b = 3.01 and a resonance frequency ω̃₁₃ = 2π · 0.53 THz from spectroscopic measurements of α-lactose on a BCB substrate. From the spectral width of the absorption line of α-lactose we deduced a damping factor of the resonance γ̃₁₃ = 1.59 · 10¹¹s⁻¹, whereas we employed the lactose density dependent oscillator strength per s² as a free parameter to fit the simulation results to the experimental data. From this optimization we obtained a value b̃₁₃ = 2.24 · 10²³s⁻².

The calculated transmission spectrum is shown by the dashed line in Fig. 3(c). The transmission spectrum is in good agreement with the experimentally observed transmission and the HIT effect can be well reproduced by the numerical calculations. The simulation results indicate coherent coupling between the SRR resonance and the lactose resonance and evidence the effect of HIT.

To further corroborate the physical interpretation of HIT, we employed the analytic model to determine the transmission spectrum. For this purpose, we calculated the imaginary part of the susceptibility of Eq. 5 by solving the coupled differential equations (1) and (2). For the model, we used the SRR and lactose resonance frequencies and the damping factors from the experimental data while we retrieved the dipole moments and the number densities from numerical calculations. We optimized the coupling factor κ to fit the analytic transmission spectrum to the experimental data. As can be seen from Fig. 3(d), the analytic model accurately describes the transmission spectrum of the composite metamaterial/lactose system. Since the model is based on coherent coupling of the hybridized local fields of a metamaterial and an atomic system, the good agreement with the experimental measurements and the numerical simulations provides a convincing proof of HIT. Although only demonstrated for a specific proof-of-principle experiment, HIT is a general effect that describes coherent coupling in hybrid structures composed of plasmonic and atomic oscillators. Since – in principle – the optical properties of the plasmonic system and the atomic system can be designed almost independently, HIT provides an enormous freedom for the deliberate design of optical systems with tailored dispersion.

Recently a similar experiment has been reported by Hutchison et al., who discovered a narrow transmission window in a hole array structure away from its resonance frequency when covered by a J-aggregate at the absorption frequency of the dye [35

J. A. Hutchison, D. M. O’Carroll, T. Schwartz, C. Genet, and T. W. Ebbesen, “Absorption-Induced Transparency,” Angewandte Chemie 50, 2085–2089 (2011). [CrossRef] [PubMed]

]. They traced this observation back to interactions between the localized surface plasmons and the molecular absorption and called this effect Absorption-Induced Transparency. This experiment can be interpreted in the light of the analytical model presented in this paper, where we demonstrated that the induced transparency originates from coherent interactions between the hybridized fields of two or more oscillating systems that can be different in nature (mechanical, electromagnetic, acoustic, etc.) rather than from pure absorption of one of the oscillating systems. For this reason, we conclude that the term hybridization induced transparency adequately describes the underlying physical mechanism of a great variety of considered systems involving induced transparency phenomena.

4. Conclusion

In conclusion, we showed that hybridization induced transparency (HIT) can occur in a composite consisting of a metamaterial and an atomic medium. HIT is the hybrid analogue of electromagnetically induced transparency (EIT) and plasmon-induced transparency (PIT) in a mixed plasmonic/atomic structure. We explained HIT based on an analytic model that describes the coherent coupling between the oscillations of plasmonic and atomic oscillators. In a proof-of-principle experiment, we evidenced HIT in a hybrid structure composed of a split ring resonator metamaterial and α-lactose monohydrate. The results were substantiated by numerical full wave simulations. HIT is a general effect that can be exploited for tailoring the dispersion of optical systems that consist of a mixture of plasmonic and atomic elements at will.

Acknowledgments

We thank the Nano+Bio Center at the University of Kaiserslautern for their support in the sample fabrication and Jens Klier from the Fraunhofer Institute IPM in Freiburg for valuable discussions concerning measurement techniques. J.L. G-P. acknowledges financial support from Consolider nanolight ( CSD2007-00046) and the Spanish Ministry of Education by ”Programa Nacional de Movilidad de Recursos Humanos del Plan Nacional de I-D+i 2008–2011”.

References and links

1.	A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, “Nonlinear properties of left-handed metamaterials,” Phys. Rev. Lett. 91, 037401 (2003). [CrossRef] [PubMed]
2.	E. Poutrina, D. Huang, and D. R. Smith, “Analysis of nonlinear electromagnetic metamaterials,” New Journal of Physics 12, 093010 (2010). [CrossRef]
3.	N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nature Photonics 2, 351–354 (2008). [CrossRef]
4.	M. Wegener, J. L. Garcia-Pomar, C. M. Soukoulis, N. Meinzer, M. Ruther, and S. Linden, “Toy model for plasmonic metamaterial resonances coupled to two-level system gain,” Opt. Express 16, 19785–19798 (2008). [CrossRef] [PubMed]
5.	S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010). [CrossRef] [PubMed]
6.	H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444, 597–600 (2006). [CrossRef] [PubMed]
7.	H.-T. Chen, W. J. Padilla, J. M. O. Zide, S. R. Bank, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Ultrafast optical switching of terahertz metamaterials fabricated on eras/gaas nanoisland superlattices,” Opt. Express 32, 1620–1622 (2007).
8.	O. Paul, C. Imhof, B. Lägel, S. Wolff, J. Heinrich, S. Höfling, A. Forchel, R. Zengerle, R. Beigang, and M. Rahm, “Polarization-independent active metamaterial for high-frequency terahertz modulation,” Opt. Express 17, 819–827 (2009). [CrossRef] [PubMed]
9.	D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006). [CrossRef] [PubMed]
10.	S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 047401 (2008). [CrossRef] [PubMed]
11.	N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the drude damping limit,” Nature Materials 8, 758–762 (2009). [CrossRef] [PubMed]
12.	N. Liu, M. Hentschel, T. Weiss, A. P. Alivisatos, and H. Giessen, “Three-dimensional plasmon rulers,” Science 332, 1407–1410 (2011). [CrossRef] [PubMed]
13.	A. Artar, A. A. Yanik, and H. Altug, “Multispectral Plasmon Induced Transparency in Coupled Meta-Atoms,” Nano Lett. 11, 1685–1689 (2011). [CrossRef] [PubMed]
14.	S.-D. Liu, Z. Yang, R.-P. Liu, and X.-Y. Li, “Plasmonic-induced optical transparency in the near-infrared and visible range with double split nanoring cavity,” Opt. Express 19, 15363–15370 (2011). [CrossRef] [PubMed]
15.	S. I. Bozhevolnyi, A. B Evlyukhin, A. Pors, M. G. Nielsen, M. Willatzen, and O. Albrektsen, “Optical transparency by detuned electrical dipoles,” New Journal of Physics 13, 023034 (2011). [CrossRef]
16.	N. Liu, H. Liu, S. Zhu, and H. Giessen, “Stereometamaterials,” Nature Photonics 3, 157–162 (2009). [CrossRef]
17.	S. A. Cummer and D. Schurig, “One path to acoustic cloaking,” New Journal of Physics 9, 45 (2007). [CrossRef]
18.	K.-J. Boller, A. Imamoglu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991). [CrossRef] [PubMed]
19.	M. Fleischhauer, A. Imamoglu, and J. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005). [CrossRef]
20.	C. Walther, G. Scalari, M. I. Amanti, M. Beck, and J. Faist, “Microcavity laser oscillating in a circuit-based resonator,” Science 327, 1495–1497 (2010). [CrossRef] [PubMed]
21.	X. Wu, S. K. Gray, and M. Pelton, “Quantum-dot-induced transparency in a nanoscale plasmonic resonator,” Opt. Express 18, 23633–23645 (2010). [CrossRef] [PubMed]
22.	D. Dietze, A. Benz, G. Strasser, K. Unterrainer, and J. Darmo, “Terahertz meta-atoms coupled to a quantum well intersubband transition,” Opt. Express 19, 13700–13706 (2011). [CrossRef] [PubMed]
23.	J. D. Teufel, D. Li, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, and R. W. Simmonds, “Circuit cavity electromechanics in the strong-coupling regime,” Nature 471, 204–208 (2011). [CrossRef] [PubMed]
24.	F. Neubrech, D. Weber, D. Enders, T. Nagao, and A. Pucci, “Antenna Sensing of Surface Phonon Polaritons,” J. Phys. Chem. C 114, 7299–7301 (2010). [CrossRef]
25.	D. J. Shelton, I. Brener, J. C. Ginn, M. B. Sinclair, D. W. Peters, K. R. Coffey, and G. D. Boreman, “Strong Coupling between Nanoscale Metamaterials and Phonons,” Nano Lett. 11, 2104–2108 (2011). [CrossRef] [PubMed]
26.	S. Linden, J. Kuhl, and H. Giessen, “Controlling the Interaction between Light and Gold Nanoparticles: Selective Suppression of Extinction,” Phys. Rev. Lett. 20, 4688–4691 (2001). [CrossRef]
27.	T. Zentgraf, S. Zhang, R. F. Oulton, and X. Zhang, “Ultranarrow coupling-induced transparency bands in hybrid plasmonic systems,” Phys. Rev. B 80, 195415 (2009).
28.	B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nature Materials 9, 707–715 (2010). [CrossRef]
29.	B. Tang, L. Dai, and C. Jiang, “Electromagnetically induced transparency in hybrid plasmonic-dielectric system,” Opt. Express 19, 628–637 (2011). [CrossRef] [PubMed]
30.	D. Allis, A. Fedor, T. Korter, J. Bjarnason, and E. Brown, “Assignment of the lowest-lying THz absorption signatures in biotin and lactose monohydrate by solid-state density functional theory,” Chemical Physics Letters 440, 203–209 (2007). [CrossRef]
31.	E. Brown, J. Bjarnson, A. Fedor, and T. Korter, “On the strong and narrow absorption signature in lactose at 0.53 THz,” Appl. Phys. Lett. 90, 061908 (2007). [CrossRef]
32.	A. Roggenbuck, H. Schmitz, A. Deninger, I. C. Mayorga, J. Hemberger, R. Güsten, and M. Grüninger, “Coherent broadband continuous-wave terahertz spectroscopy on solid-state samples,” New Journal of Physics 12, 043017 (2010). [CrossRef]
33.	R. Lefort, V. Caron, J.-F. Willart, and M. Descamps, “Mutarotational kinetics and glass transition of lactose,” Solid State Comm. 140, 329–334 (2006). [CrossRef]
34.	C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95, 203901 (2005). [CrossRef] [PubMed]
35.	J. A. Hutchison, D. M. O’Carroll, T. Schwartz, C. Genet, and T. W. Ebbesen, “Absorption-Induced Transparency,” Angewandte Chemie 50, 2085–2089 (2011). [CrossRef] [PubMed]

OCIS Codes
(160.4760) Materials : Optical properties
(220.4000) Optical design and fabrication : Microstructure fabrication
(270.1670) Quantum optics : Coherent optical effects
(160.3918) Materials : Metamaterials
(230.4555) Optical devices : Coupled resonators
(300.6495) Spectroscopy : Spectroscopy, teraherz

ToC Category:
Metamaterials

Citation
Peter Weis, Juan Luis Garcia-Pomar, René Beigang, and Marco Rahm, "Hybridization Induced Transparency in composites of metamaterials and atomic media," Opt. Express 19, 23573-23580 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-23-23573

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References

A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, “Nonlinear properties of left-handed metamaterials,” Phys. Rev. Lett.91, 037401 (2003). [CrossRef] [PubMed]
E. Poutrina, D. Huang, and D. R. Smith, “Analysis of nonlinear electromagnetic metamaterials,” New Journal of Physics12, 093010 (2010). [CrossRef]
N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nature Photonics2, 351–354 (2008). [CrossRef]
M. Wegener, J. L. Garcia-Pomar, C. M. Soukoulis, N. Meinzer, M. Ruther, and S. Linden, “Toy model for plasmonic metamaterial resonances coupled to two-level system gain,” Opt. Express16, 19785–19798 (2008). [CrossRef] [PubMed]
S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature466, 735–738 (2010). [CrossRef] [PubMed]
H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature444, 597–600 (2006). [CrossRef] [PubMed]
H.-T. Chen, W. J. Padilla, J. M. O. Zide, S. R. Bank, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Ultrafast optical switching of terahertz metamaterials fabricated on eras/gaas nanoisland superlattices,” Opt. Express32, 1620–1622 (2007).
O. Paul, C. Imhof, B. Lägel, S. Wolff, J. Heinrich, S. Höfling, A. Forchel, R. Zengerle, R. Beigang, and M. Rahm, “Polarization-independent active metamaterial for high-frequency terahertz modulation,” Opt. Express17, 819–827 (2009). [CrossRef] [PubMed]
D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science314, 977–980 (2006). [CrossRef] [PubMed]
S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett.101, 047401 (2008). [CrossRef] [PubMed]
N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the drude damping limit,” Nature Materials8, 758–762 (2009). [CrossRef] [PubMed]
N. Liu, M. Hentschel, T. Weiss, A. P. Alivisatos, and H. Giessen, “Three-dimensional plasmon rulers,” Science332, 1407–1410 (2011). [CrossRef] [PubMed]
A. Artar, A. A. Yanik, and H. Altug, “Multispectral Plasmon Induced Transparency in Coupled Meta-Atoms,” Nano Lett.11, 1685–1689 (2011). [CrossRef] [PubMed]
S.-D. Liu, Z. Yang, R.-P. Liu, and X.-Y. Li, “Plasmonic-induced optical transparency in the near-infrared and visible range with double split nanoring cavity,” Opt. Express19, 15363–15370 (2011). [CrossRef] [PubMed]
S. I. Bozhevolnyi, A. B Evlyukhin, A. Pors, M. G. Nielsen, M. Willatzen, and O. Albrektsen, “Optical transparency by detuned electrical dipoles,” New Journal of Physics13, 023034 (2011). [CrossRef]
N. Liu, H. Liu, S. Zhu, and H. Giessen, “Stereometamaterials,” Nature Photonics3, 157–162 (2009). [CrossRef]
S. A. Cummer and D. Schurig, “One path to acoustic cloaking,” New Journal of Physics9, 45 (2007). [CrossRef]
K.-J. Boller, A. Imamoglu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett.66, 2593–2596 (1991). [CrossRef] [PubMed]
M. Fleischhauer, A. Imamoglu, and J. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys.77, 633–673 (2005). [CrossRef]
C. Walther, G. Scalari, M. I. Amanti, M. Beck, and J. Faist, “Microcavity laser oscillating in a circuit-based resonator,” Science327, 1495–1497 (2010). [CrossRef] [PubMed]
X. Wu, S. K. Gray, and M. Pelton, “Quantum-dot-induced transparency in a nanoscale plasmonic resonator,” Opt. Express18, 23633–23645 (2010). [CrossRef] [PubMed]
D. Dietze, A. Benz, G. Strasser, K. Unterrainer, and J. Darmo, “Terahertz meta-atoms coupled to a quantum well intersubband transition,” Opt. Express19, 13700–13706 (2011). [CrossRef] [PubMed]
J. D. Teufel, D. Li, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, and R. W. Simmonds, “Circuit cavity electromechanics in the strong-coupling regime,” Nature471, 204–208 (2011). [CrossRef] [PubMed]
F. Neubrech, D. Weber, D. Enders, T. Nagao, and A. Pucci, “Antenna Sensing of Surface Phonon Polaritons,” J. Phys. Chem. C114, 7299–7301 (2010). [CrossRef]
D. J. Shelton, I. Brener, J. C. Ginn, M. B. Sinclair, D. W. Peters, K. R. Coffey, and G. D. Boreman, “Strong Coupling between Nanoscale Metamaterials and Phonons,” Nano Lett.11, 2104–2108 (2011). [CrossRef] [PubMed]
S. Linden, J. Kuhl, and H. Giessen, “Controlling the Interaction between Light and Gold Nanoparticles: Selective Suppression of Extinction,” Phys. Rev. Lett.20, 4688–4691 (2001). [CrossRef]
T. Zentgraf, S. Zhang, R. F. Oulton, and X. Zhang, “Ultranarrow coupling-induced transparency bands in hybrid plasmonic systems,” Phys. Rev. B80, 195415 (2009).
B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nature Materials9, 707–715 (2010). [CrossRef]
B. Tang, L. Dai, and C. Jiang, “Electromagnetically induced transparency in hybrid plasmonic-dielectric system,” Opt. Express19, 628–637 (2011). [CrossRef] [PubMed]
D. Allis, A. Fedor, T. Korter, J. Bjarnason, and E. Brown, “Assignment of the lowest-lying THz absorption signatures in biotin and lactose monohydrate by solid-state density functional theory,” Chemical Physics Letters440, 203–209 (2007). [CrossRef]
E. Brown, J. Bjarnson, A. Fedor, and T. Korter, “On the strong and narrow absorption signature in lactose at 0.53 THz,” Appl. Phys. Lett.90, 061908 (2007). [CrossRef]
A. Roggenbuck, H. Schmitz, A. Deninger, I. C. Mayorga, J. Hemberger, R. Güsten, and M. Grüninger, “Coherent broadband continuous-wave terahertz spectroscopy on solid-state samples,” New Journal of Physics12, 043017 (2010). [CrossRef]
R. Lefort, V. Caron, J.-F. Willart, and M. Descamps, “Mutarotational kinetics and glass transition of lactose,” Solid State Comm.140, 329–334 (2006). [CrossRef]
C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett.95, 203901 (2005). [CrossRef] [PubMed]
J. A. Hutchison, D. M. O’Carroll, T. Schwartz, C. Genet, and T. W. Ebbesen, “Absorption-Induced Transparency,” Angewandte Chemie50, 2085–2089 (2011). [CrossRef] [PubMed]

Angewandte Chemie

J. A. Hutchison, D. M. O’Carroll, T. Schwartz, C. Genet, and T. W. Ebbesen, “Absorption-Induced Transparency,” Angewandte Chemie50, 2085–2089 (2011). [CrossRef] [PubMed]

Appl. Phys. Lett.

E. Brown, J. Bjarnson, A. Fedor, and T. Korter, “On the strong and narrow absorption signature in lactose at 0.53 THz,” Appl. Phys. Lett.90, 061908 (2007). [CrossRef]

Chemical Physics Letters

D. Allis, A. Fedor, T. Korter, J. Bjarnason, and E. Brown, “Assignment of the lowest-lying THz absorption signatures in biotin and lactose monohydrate by solid-state density functional theory,” Chemical Physics Letters440, 203–209 (2007). [CrossRef]

J. Phys. Chem. C

F. Neubrech, D. Weber, D. Enders, T. Nagao, and A. Pucci, “Antenna Sensing of Surface Phonon Polaritons,” J. Phys. Chem. C114, 7299–7301 (2010). [CrossRef]

Nano Lett.

D. J. Shelton, I. Brener, J. C. Ginn, M. B. Sinclair, D. W. Peters, K. R. Coffey, and G. D. Boreman, “Strong Coupling between Nanoscale Metamaterials and Phonons,” Nano Lett.11, 2104–2108 (2011). [CrossRef] [PubMed]
A. Artar, A. A. Yanik, and H. Altug, “Multispectral Plasmon Induced Transparency in Coupled Meta-Atoms,” Nano Lett.11, 1685–1689 (2011). [CrossRef] [PubMed]

Nature

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature466, 735–738 (2010). [CrossRef] [PubMed]
H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature444, 597–600 (2006). [CrossRef] [PubMed]
J. D. Teufel, D. Li, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, and R. W. Simmonds, “Circuit cavity electromechanics in the strong-coupling regime,” Nature471, 204–208 (2011). [CrossRef] [PubMed]

Nature Materials

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nature Materials9, 707–715 (2010). [CrossRef]
N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the drude damping limit,” Nature Materials8, 758–762 (2009). [CrossRef] [PubMed]

Nature Photonics

N. Liu, H. Liu, S. Zhu, and H. Giessen, “Stereometamaterials,” Nature Photonics3, 157–162 (2009). [CrossRef]
N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nature Photonics2, 351–354 (2008). [CrossRef]

New Journal of Physics

E. Poutrina, D. Huang, and D. R. Smith, “Analysis of nonlinear electromagnetic metamaterials,” New Journal of Physics12, 093010 (2010). [CrossRef]
S. A. Cummer and D. Schurig, “One path to acoustic cloaking,” New Journal of Physics9, 45 (2007). [CrossRef]
A. Roggenbuck, H. Schmitz, A. Deninger, I. C. Mayorga, J. Hemberger, R. Güsten, and M. Grüninger, “Coherent broadband continuous-wave terahertz spectroscopy on solid-state samples,” New Journal of Physics12, 043017 (2010). [CrossRef]
S. I. Bozhevolnyi, A. B Evlyukhin, A. Pors, M. G. Nielsen, M. Willatzen, and O. Albrektsen, “Optical transparency by detuned electrical dipoles,” New Journal of Physics13, 023034 (2011). [CrossRef]

Opt. Express

X. Wu, S. K. Gray, and M. Pelton, “Quantum-dot-induced transparency in a nanoscale plasmonic resonator,” Opt. Express18, 23633–23645 (2010). [CrossRef] [PubMed]
D. Dietze, A. Benz, G. Strasser, K. Unterrainer, and J. Darmo, “Terahertz meta-atoms coupled to a quantum well intersubband transition,” Opt. Express19, 13700–13706 (2011). [CrossRef] [PubMed]
B. Tang, L. Dai, and C. Jiang, “Electromagnetically induced transparency in hybrid plasmonic-dielectric system,” Opt. Express19, 628–637 (2011). [CrossRef] [PubMed]
S.-D. Liu, Z. Yang, R.-P. Liu, and X.-Y. Li, “Plasmonic-induced optical transparency in the near-infrared and visible range with double split nanoring cavity,” Opt. Express19, 15363–15370 (2011). [CrossRef] [PubMed]
M. Wegener, J. L. Garcia-Pomar, C. M. Soukoulis, N. Meinzer, M. Ruther, and S. Linden, “Toy model for plasmonic metamaterial resonances coupled to two-level system gain,” Opt. Express16, 19785–19798 (2008). [CrossRef] [PubMed]
H.-T. Chen, W. J. Padilla, J. M. O. Zide, S. R. Bank, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Ultrafast optical switching of terahertz metamaterials fabricated on eras/gaas nanoisland superlattices,” Opt. Express32, 1620–1622 (2007).
O. Paul, C. Imhof, B. Lägel, S. Wolff, J. Heinrich, S. Höfling, A. Forchel, R. Zengerle, R. Beigang, and M. Rahm, “Polarization-independent active metamaterial for high-frequency terahertz modulation,” Opt. Express17, 819–827 (2009). [CrossRef] [PubMed]

Phys. Rev. B

T. Zentgraf, S. Zhang, R. F. Oulton, and X. Zhang, “Ultranarrow coupling-induced transparency bands in hybrid plasmonic systems,” Phys. Rev. B80, 195415 (2009).

Phys. Rev. Lett.

S. Linden, J. Kuhl, and H. Giessen, “Controlling the Interaction between Light and Gold Nanoparticles: Selective Suppression of Extinction,” Phys. Rev. Lett.20, 4688–4691 (2001). [CrossRef]
S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett.101, 047401 (2008). [CrossRef] [PubMed]
C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett.95, 203901 (2005). [CrossRef] [PubMed]
A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, “Nonlinear properties of left-handed metamaterials,” Phys. Rev. Lett.91, 037401 (2003). [CrossRef] [PubMed]
K.-J. Boller, A. Imamoglu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett.66, 2593–2596 (1991). [CrossRef] [PubMed]

Rev. Mod. Phys.

M. Fleischhauer, A. Imamoglu, and J. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys.77, 633–673 (2005). [CrossRef]

Science

C. Walther, G. Scalari, M. I. Amanti, M. Beck, and J. Faist, “Microcavity laser oscillating in a circuit-based resonator,” Science327, 1495–1497 (2010). [CrossRef] [PubMed]
N. Liu, M. Hentschel, T. Weiss, A. P. Alivisatos, and H. Giessen, “Three-dimensional plasmon rulers,” Science332, 1407–1410 (2011). [CrossRef] [PubMed]
D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science314, 977–980 (2006). [CrossRef] [PubMed]

Solid State Comm.

R. Lefort, V. Caron, J.-F. Willart, and M. Descamps, “Mutarotational kinetics and glass transition of lactose,” Solid State Comm.140, 329–334 (2006). [CrossRef]

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Abstract

1. Introduction

2. Analytic Model

3. Experiment and Simulation

4. Conclusion

Acknowledgments

References and links

References

Angewandte Chemie

Appl. Phys. Lett.

Chemical Physics Letters

J. Phys. Chem. C

Nano Lett.

Nature

Nature Materials

Nature Photonics

New Journal of Physics

Opt. Express

Phys. Rev. B

Phys. Rev. Lett.

Rev. Mod. Phys.

Science

Solid State Comm.

Cited By

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