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Mie resonance-based dielectric metamaterials

Mie resonance-based dielectric metamaterials Increasing attention on metamaterials has been paid due to their exciting physical behaviors and potential applications. While most of such artificial material structures developed so far are based on metallic resonant structures, Mie resonances of dielectric particles open a simpler and more versatile route for construction of isotropic metamaterials with higher operating frequencies. Here, we review the recent progresses of Mie resonance-based metamaterials by providing a description of the underlying mechanisms to realize negative permeability, negative permittivity and double negative media. We address some potential novel applications. Qian Zhao1,2, Ji Zhou1,*, Fuli Zhang3, Didier Lippens3 1 State Key Lab of New Ceramics and Fine Processing, Department of Materials Science and Engineering, Tsinghua University, Beijing, PRC 2 State Key Lab of Tribology, Department of Precision Instruments and Mechanology, Tsinghua University, Beijing, PRC 3 Institut d’Electronique de Micro-électronique et de Nanotechnologie, UMR CNRS 8520, University of Lille 1, Villeneuve d’Ascq Cedex, France *E-mail: [email protected]

Metamaterials are artificial electromagnetic media structured on

opening the effective parameter space, so that new functionalities

a scale much shorter than their operating wavelength. Under this

in the light scattering can be envisaged.

condition they can be considered as homogeneous media whose

values of the effective permittivity and permeability was also

than periodic effects as it is the case for photonic crystal or more

recognized as one of the major goals of this research area. Great

generally electromagnetic band gap material. Their basic cells

progress in electromagnetic metamaterials has been achieved for

are generally constituted of resonant inclusions which yield a π

these unique physical properties and novel potential applications,

phaseshift in the material response above the resonant frequency.

such as negative refraction2, 3, perfect lens4, 5 and cloaking6-8 have

As a consequence, their effective permittivity and permeability

been shown. They have been experimentally demonstrated in a

can be negative either in separate or overlapping frequency

frequency range from the radio frequencies9 to millimeter waves10,

bands, a unique and distinct property that is not observed in

infrared wavelengths11-13, and visible optics14. Up to date, most

naturally occurring

materials1

. For the latter condition they can

be considered as double negative or negative index media hence

60

Also recently, the achievement of near-zero or less than unity

electromagnetic properties rely mainly on the basic cell rather

DECEMBER 2009 | VOLUME 12 | NUMBER 12

of metamaterials are constructed with the use of sub-wavelength resonant metallic elements. For instance, the first left-handed

ISSN:1369 7021 © Elsevier Ltd 2009

Mie resonance-based dielectric metamaterials

(a)

(b)

(c)

(d)

REVIEW

Fig. 1 Electric and magnetic field distribution in a dielectric cube with the magnetic field polarized along the z axis and electric field polarized along the y axis. (a) Electric field in the plane z=0 near the first Mie resonance. (b) Magnetic field in the plane y=0 near the first Mie resonance. (c) Electric field in the plane z=0 near the second Mie resonance. (d) Magnetic field in the plane y=0 near the second Mie resonance. (Reprinted with permission from37. © 2008 American Physical Society.)

metamaterials (LHMs) with simultaneously negative permittivity and

Mie resonance of particles

permeability have been fabricated by means of metallic split ring

From the viewpoint of scattering theory, all scattering objects can

resonators (SRRs) and wires15, 16, for tailoring the magnetic and electric

be represented by effective electric and/or magnetic polarizability

responses, respectively. Other metallic elements, such as Ω-shaped

densities. Light scattering by small (relative to the incident light

structures17, 18, U-shaped structures19, staplelike structures20, paired

wavelength) spherical particles is a fundamental topic in classical

rods21, dendritic22 and fishnet structures23, are also successfully used

electrodynamics35, and is based upon the exact Mie solution of the

to fabricate LHMs.

diffraction problem36. The scattered field of a single isolated dielectric

Usually, the metallic constitutive elements have conductive loss and

sphere with radius r0 and relative refractive index n can be decomposed

anisotropic electromagnetic responses. Several authors have suggested

into a multipole series with the 2m-pole term of the scattered electric

methods24-26 to construct isotropic metamaterials by combining

field proportional to

metallic SRRs and wires. However it is difficult to fabricate the bulk arrays of complex geometry with submicron or nanoscale sizes in

am =

order to generate a negative permeability effect at infrared and optical frequencies27. Recently, another route based on the interaction