Abstract

Hyperbolic materials enable numerous surprising applications that include far-field subwavelength imaging, nanolithography, and emission engineering. The wavevector of a plane wave in these media follows the surface of a hyperboloid in contrast to an ellipsoid for conventional anisotropic dielectric. The consequences of hyperbolic dispersion were first studied in the 50’s pertaining to the problems of electromagnetic wave propagation in the Earth’s ionosphere and in the stratified artificial materials of transmission lines. Recent years have brought explosive growth in optics and photonics of hyperbolic media based on metamaterials across the optical spectrum. Here we summarize earlier theories in the Clemmow’s prescription for transformation of the electromagnetic field in hyperbolic media and provide a review of recent developments in this active research area.

© 2013 OSA

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2013

S. Ishii, A. V. Kildishev, E. Narimanov, V. Shalaev, and V. P. Drachev, “Sub-wavelength interference pattern from volume plasmon polaritons in a hyperbolic medium,” Laser Photonics Rev.7(2), 265–271 (2013).
[CrossRef]

2012

J. Kim, V. P. Drachev, Z. Jacob, G. V. Naik, A. Boltasseva, E. E. Narimanov, and V. M. Shalaev, “Improving the radiative decay rate for dye molecules with hyperbolic metamaterials,” Opt. Express20(7), 8100–8116 (2012).
[CrossRef] [PubMed]

G. V. Naik, J. Liu, A. V. Kildishev, V. M. Shalaev, and A. Boltasseva, “Demonstration of Al:ZnO as a plasmonic component for near-infrared metamaterials,” Proc. Natl. Acad. Sci. U.S.A.109(23), 8834–8838 (2012), doi:.
[CrossRef] [PubMed]

L. V. Alekseyev, V. A. Podolskiy, and E. E. Narimanov, “Homogeneous Hyperbolic Systems for Terahertz and Far-Infrared Frequencies,” Adv. Optoelectron.2012, 267564 (2012).
[CrossRef]

A. S. Potemkin, A. N. Poddubny, P. A. Belov, and Y. S. Kivshar, “Green function for hyperbolic media,” Phys. Rev. A86(2), 023848 (2012).
[CrossRef]

O. Kidwai, S. V. Zhukovsky, and J. E. Sipe, “Effective-medium approach to planar multilayer hyperbolic metamaterials: Strengths and limitations,” Phys. Rev. A85(5), 053842 (2012).
[CrossRef]

H. N. Krishnamoorthy, Z. Jacob, E. Narimanov, I. Kretzschmar, and V. M. Menon, “Topological Transitions in Metamaterials,” Science336(6078), 205–209 (2012).
[CrossRef] [PubMed]

A. N. Poddubny, P. A. Belov, P. Ginzburg, A. V. Zayats, and Y. S. Kivshar, “Microscopic model of Purcell enhancement in hyperbolic metamaterials,” Phys. Rev. B86(3), 035148 (2012).
[CrossRef]

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

2011

S. I. Maslovski and M. G. Silveirinha, “Mimicking Boyer’s Casimir repulsion with a nanowire material,” Phys. Rev. A83(2), 022508 (2011).
[CrossRef]

A. P. Vinogradov, A. I. Ignatov, A. M. Merzlikin, S. A. Tretyakov, and C. R. Simovski, “Additional effective medium parameters for composite materials (excess surface currents),” Opt. Express19(7), 6699–6704 (2011).
[CrossRef] [PubMed]

G. A. Wurtz, R. Pollard, W. Hendren, G. P. Wiederrecht, D. J. Gosztola, V. A. Podolskiy, and A. V. Zayats, “Designed ultrafast optical nonlinearity in a plasmonic nanorod metamaterial enhanced by nonlocality,” Nat. Nanotechnol.6(2), 107–111 (2011).
[CrossRef] [PubMed]

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

A. N. Poddubny, P. A. Belov, and Y. S. Kivshar, “Spontaneous radiation of a finite-size dipole emitter in hyperbolic media,” Phys. Rev. A84(2), 023807 (2011).
[CrossRef]

J. Sun, J. Zhou, B. Li, and F. Kang, “Indefinite permittivity and negative refraction in natural material: graphite,” Appl. Phys. Lett.98(10), 101901 (2011).
[CrossRef]

G. Li, J. Li, and K. W. Cheah, “Subwavelength focusing using a hyperbolic medium with a single slit,” Appl. Opt.50(31), G27–G30 (2011).
[CrossRef] [PubMed]

A. Chebykin, A. Orlov, A. Vozianova, S. Maslovski, Y. Kivshar, and P. Belov, “Nonlocal effective medium model for multilayered metal-dielectric metamaterials,” Phys. Rev. B84(11), 115438 (2011).
[CrossRef]

2010

2009

Y. Xiong, Z. Liu, and X. Zhang, “A simple design of flat hyperlens for lithography and imaging with half-pitch resolution down to 20 nm,” Appl. Phys. Lett.94(20), 203108 (2009).
[CrossRef]

S. Thongrattanasiri and V. A. Podolskiy, “Hypergratings: nanophotonics in planar anisotropic metamaterials,” Opt. Lett.34(7), 890–892 (2009).
[CrossRef] [PubMed]

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Deep-subwavelength focusing and steering of light in an aperiodic metallic waveguide array,” Phys. Rev. Lett.103(3), 033902 (2009).
[CrossRef] [PubMed]

R. J. Pollard, A. Murphy, W. R. Hendren, P. R. Evans, R. Atkinson, G. A. Wurtz, A. V. Zayats, and V. A. Podolskiy, “Optical nonlocalities and additional waves in epsilon-near-zero metamaterials,” Phys. Rev. Lett.102(12), 127405 (2009).
[CrossRef] [PubMed]

2008

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science321(5891), 930 (2008).
[CrossRef] [PubMed]

W. Wang, H. Xing, L. Fang, Y. Liu, J. Ma, L. Lin, C. Wang, and X. Luo, “Far-field imaging device: planar hyperlens with magnification using multi-layer metamaterial,” Opt. Express16(25), 21142–21148 (2008).
[CrossRef] [PubMed]

Y. Xiong, Z. Liu, and X. Zhang, “Projecting deep-subwavelength patterns from diffraction-limited masks using metal-dielectric multilayers,” Appl. Phys. Lett.93(11), 111116 (2008).
[CrossRef]

R. M. Bakker, V. P. Drachev, Z. Liu, H. K. Yuan, R. H. Pedersen, A. Boltasseva, J. Chen, J. Irudayaraj, A. V. Kildishev, and V. M. Shalaev, “Nanoantenna array-induced fluorescence enhancement and reduced lifetimes,” New J. Phys.10(12), 125022 (2008).
[CrossRef]

2007

W. Cai, U. Chettiar, A. Kildishev, and V. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics1(4), 224–227 (2007).
[CrossRef]

J. B. Khurgin, G. Sun, and R. A. Soref, “Enhancement of luminescence efficiency using surface plasmon polaritons: figures of merit,” J. Opt. Soc. Am. B24(8), 1968–1980 (2007).
[CrossRef]

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater.6(12), 946–950 (2007).
[CrossRef] [PubMed]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science315(5819), 1686 (2007).
[CrossRef] [PubMed]

I. I. Smolyaninov, Y. J. Hung, and C. C. Davis, “Magnifying superlens in the visible frequency range,” Science315(5819), 1699–1701 (2007).
[CrossRef] [PubMed]

2006

Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical hyperlens: far-field imaging beyond the diffraction limit,” Opt. Express14(18), 8247–8256 (2006).
[CrossRef] [PubMed]

A. Salandrino and N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystals: theory and simulations,” Phys. Rev. B74(7), 075103 (2006).
[CrossRef]

A. Govyadinov and V. Podolskiy, “Metamaterial photonic funnels for subdiffraction light compression and propagation,” Phys. Rev. B73(15), 155108 (2006).
[CrossRef]

M. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using ε-near-zero materials,” Phys. Rev. Lett.97(15), 157403 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

L. V. Alekseyev and E. Narimanov, “Slow light and 3D imaging with non-magnetic negative index systems,” Opt. Express14(23), 11184–11193 (2006).
[CrossRef] [PubMed]

B. Wood, J. Pendry, and D. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B74(11), 115116 (2006).
[CrossRef]

S. Feng and J. M. Elson, “Diffraction-suppressed high-resolution imaging through metallodielectric nanofilms,” Opt. Express14(1), 216–221 (2006).
[CrossRef] [PubMed]

P. A. Belov and Y. Hao, “Subwavelength imaging at optical frequencies using a transmission device formed by a periodic layered metal-dielectric structure operating in the canalization regime,” Phys. Rev. B73(11), 113110 (2006).
[CrossRef]

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Y. Zhang, B. Fluegel, and A. Mascarenhas, “Total negative refraction in real crystals for ballistic electrons and light,” Phys. Rev. Lett.91(15), 157404 (2003).
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S. Ishii, A. V. Kildishev, E. Narimanov, V. Shalaev, and V. P. Drachev, “Sub-wavelength interference pattern from volume plasmon polaritons in a hyperbolic medium,” Laser Photonics Rev.7(2), 265–271 (2013).
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R. M. Bakker, V. P. Drachev, Z. Liu, H. K. Yuan, R. H. Pedersen, A. Boltasseva, J. Chen, J. Irudayaraj, A. V. Kildishev, and V. M. Shalaev, “Nanoantenna array-induced fluorescence enhancement and reduced lifetimes,” New J. Phys.10(12), 125022 (2008).
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Kivshar, Y.

A. Chebykin, A. Orlov, A. Vozianova, S. Maslovski, Y. Kivshar, and P. Belov, “Nonlocal effective medium model for multilayered metal-dielectric metamaterials,” Phys. Rev. B84(11), 115438 (2011).
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A. N. Poddubny, P. A. Belov, P. Ginzburg, A. V. Zayats, and Y. S. Kivshar, “Microscopic model of Purcell enhancement in hyperbolic metamaterials,” Phys. Rev. B86(3), 035148 (2012).
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A. S. Potemkin, A. N. Poddubny, P. A. Belov, and Y. S. Kivshar, “Green function for hyperbolic media,” Phys. Rev. A86(2), 023848 (2012).
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A. N. Poddubny, P. A. Belov, and Y. S. Kivshar, “Spontaneous radiation of a finite-size dipole emitter in hyperbolic media,” Phys. Rev. A84(2), 023807 (2011).
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H. Kogelnik, “On electromagnetic radiation in magneto-ionic media,” J. Res. Nat. Bur. Stand. D.64D, 515 (1960).

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V. Agranovich and V. Kravtsov, “Notes on crystal optics of superlattices,” Solid State Commun.55(1), 85–90 (1985).
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K. G. Balmain, A. A. E. Luttgen, and P. C. Kremer, “Resonance cone formation, reflection, refraction, and focusing in a planar anisotropic metamaterial,” IEEE Antennas Wirel. Propag. Lett.1(1), 146–149 (2002).
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H. H. Kuehl, “Electromagnetic radiation from an electric dipole in a cold anisotropic plasma,” Plasma Phys. Fluids5(9), 1095 (1962).
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J. Sun, J. Zhou, B. Li, and F. Kang, “Indefinite permittivity and negative refraction in natural material: graphite,” Appl. Phys. Lett.98(10), 101901 (2011).
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Li, H.

Li, J.

Lin, L.

Liu, J.

G. V. Naik, J. Liu, A. V. Kildishev, V. M. Shalaev, and A. Boltasseva, “Demonstration of Al:ZnO as a plasmonic component for near-infrared metamaterials,” Proc. Natl. Acad. Sci. U.S.A.109(23), 8834–8838 (2012), doi:.
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Figures (7)

Fig. 1
Fig. 1

Typical vector diagram and dispersion relations in uniaxial media. (a) Plane-wave vectors. (b), Isofrequency cross-sections for a negative elliptic media, ε< ε z . c, d Isofrequency curves for different types of ideal, lossless hyperbolic media: dielectric, ε z <0,ε>0 (c), metallic, ε z >0,ε<0 , (d). (e), (f) Isofrequency curves for different types of non-ideal, absorbing hyperbolic media: dielectric type, with ε x,y = 0.57+ι0.13 , ε z =4.22+ι2.03 (e); metallic type, with ε x,y =2.78+ι0.13 , ε z =6.31+i0.09 (f).

Fig. 2
Fig. 2

Volume plasmon-polariton. a) Angular dependence of the permittivity for extraordinary wave, imaginary (brown) and real (blue) parts. Critical angle between wave vector and optic axis φ c =57°; b) Angle between Poynting vector and optic axis θ( φ ), θ c =33°; c) magnetic field angular dependence localized at the critical angle (calculated at 650 nm from the source) [24]. Figures reproduced with permission from ©2013 Wiley-VCH

Fig. 3
Fig. 3

Radiation from elementary 2D sources and permittivity spectra. a-d, Radiation from a 2D electric dipole in (a) vacuum; (b) lossy dielectric HMMat 340 nm with ε x,y = 0.57+ι0.13 , ε z =4.22+ι2.03 ,(the dispersion curve of Fig. 1(e)); (c) ENZ materialat 359.4 nm with ε x,y =0.005+ι0.123 , ε z =2.82+ι43.3 ; and (d) lossy metallic HMMat 465 nm with ε x,y =2.78+ι0.13 , ε z =6.31+i0.09 ,(the dispersion curve of Fig. 1(f)); (e) spectra of the xy and (f) z components of the permittivity [24]. Figures reproduced with permission from ©2013 Wiley-VCH

Fig. 4
Fig. 4

Imaging (a) [15] and nanolithography (b), (c) [24] with hyperbolic metamaterials. Figures reproduced with permissions: (a) Ref [15] from ©2007 AAAS and (b),(c) Ref [24]. from ©2013 Wiley-VCH.

Fig. 5
Fig. 5

Wire (a), (b) [28] and layered (c) [25] HMM samples for life time engineering. Figures reproduced with permissions: (a),(b) Ref [28]. from ©2010 OSA and (c) Ref [25]. from ©2012 OSA.

Fig. 6
Fig. 6

Effect of nonlocality on extinction in nanowire medium: at high absorption (a) metamaterial exhibits the extinction spectrum consistent with predictions of effective medium theory, at smaller losses (b), interference of two TM-polarized beams becomes evident in transmission [29]. Figures reproduced with permission from ©2009 APS.

Fig. 7
Fig. 7

Natural hyperbolic media. a, Negative refraction in graphite [31]; b, c, Components of the principal dielectric tensor of calcite (b) [81] and monocrystalline Bismuth (c) [32]. Figure 7(a) reproduced with permission from Appl. Phys. Lett. 98, 101901 (2011) Copyright 2011 American Institute of Physics.

Tables (1)

Tables Icon

Table 1 Radiative, nonradiative decay rates, apparent quantum yield, and fluorescence and absorption enhancements in layered HMM are shown in the table for four samples, each at 89 and 21 nm dielectric spacer [25]. Table reproduced with permission from ©2012 OSA.

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

E( r )=[ n ] E 0 ( [ n ]r ),H( r )= ε ε z H 0 ([ n ]r),
E( r )= E 0 ( nr ),H( r )=n H 0 (nr).
kD=0, μ 0 kH=0,k×E= μ 0 cH,k×E= μ 0 cH,and k×H=cD
k x 2 + k y 2 + k z 2 ε =1,and k x 2 + k y 2 ε z + k z 2 ε =1.
1 ε( φ ) =  sin 2 ( φ ) ε e + cos 2 ( φ ) ε o ,
tanθ= ε o ε e tanφ.
Q= Γ r τ,  τ= ( Γ r + κ nr ) 1 = Γ 1 .
ε o = ε ¯ o ( 1 ιkab 4d μ d ε m μ m ε d ε ¯ o μ ¯ o ), ε ¯ o =( b ε m +a ε d a+b ),
μ o = μ ¯ o ( 1+ ιkab 4d μ d ε m μ m ε d ε ¯ o μ ¯ o ), μ ¯ o =( b μ m +a μ d a+b ),
ε e = ε ˜ e , ε ˜ e 1 = a/ ε d +b/ ε m a+b .

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