-
Introduction of Perfect matematerial absorber 1 Introduction of
absorbing layers
An absorber is a kind of device in which all incident radiation
is absorbed. That
is to say, all wave actions such as reflection, transmission,
scattering, and other light
propagation are impossible. The most typical EM wave absorber is
so called Salisbury
screen[1] which is developed by the well know scientist W. W.
Salisbury as a basic
example of the resonant absorber. Such a device consists of two
layers, a resistive
sheet to absorb EM wave and a metal plate to reflect the wave
[1].
As reference [2] summarized, another similar absorber device is
Jaumann
absorber in which has more than one resistive sheet are placed
in front of the
mental ground plate in order to achieve a broadband response.[3]
Circuit Analog
absorber also have more than one resistive sheet to achieve
absorption at high
incidence angle[4,5] and over broad bands[6]
.
Another two type of resonant EM wave absorber are Dallenbach
layer employs
consists of a homogeneous layer in front of mental plate[2];
Crossed Grating absorber
uses a reflective metal plate with an etched shallow periodic
grid[7, 8].
2. Introduction of Metamaterial Perfect Absorbers (MPA)
Metamaterials are artificial structural materials composed of
metals and
dielectrics arranged in a periodic way. Owing to its tailored
property, e.g., permittivity
and permeability, metamaterials have been found many
applications such as
invisibility cloak [9-12], sub-wavelength imaging [13, 14],
perfect lens
[15,16] and perfect
absorber[17-39].
The most famous metamaterial perfect absorber unit cell is so
called three
layered structure, which consists of two metallic layers, one
ground plane and a varied
shaped electric ring resonator (ERR) separated by a dielectric
layer. The ERR on the
top of the dielectric layer couples strongly to uniform electric
field of the incidence
wave, but weakly to magnetic field, providing frequency
dependent electric response
(). The magnetic field of incident waves will penetrate the
space between the ERR
and back metallic ground plane, leading to a frequency dependent
magnetic response
(). One can tuned the effective () and () through adjusting the
dimension of
the ERR, back ground plane and the space gap between them. Thus
realize the perfect
impedance matching between the absorber and free space and
minimize the reflection
near to zero. Simultaneously, by varying the imaginary part of
the material
permittivity to achieve large loss and minimize the transmission
near to zero. The
resulting absorption A, is calculated A()=1-R()-T(), where R()
is the refection
and T() is the transmission, approximately equal to zero.
Generally, when electromagnetic wave incident the boundary
between metal and
-
dielectric layer and satisfy the surface electromagnetic
wave(SEWs) propagation
conditions which write as k1=k0, where k1 is the real part of
the wave vector parallel
to the surface some SEWs propagate along the surface. In optics
the surface wave are
termed surface plasmon wave because there exists an interaction
between the free
electron in the metal layer and the electromagnetic waves. These
surface waves
propagate but they are damped too and we have to determine how
they propagate and
how they are damped. The last term play the most important role
when we dealing
with absorbers.
The way that SEWs propagates can be determined from the
so-called dispersion
characteristic, the key parameter being the velocity of the
waves propagating along
the surface k=k1+ik2 and the propagate length is described as
Lp=1/2k2,[40] which
characterise the penetration intensity of the SEWs or plasmon
decays by 1/e. If k2 is
carefully selected, the SEWs be in form of loss, and Lp is
perfectly matched k1=k0, so
as to reduce the reflection and transmission and reach to nearly
unit absorption.
To analyze the absorption feature, one most important concept is
the operation
bandwidth characterized by the full wave at half maximum (FWHM),
which defined
as FWHM= 100%0
f
f, where 0f is the centre frequency of the incident wave of
the
absorption spectrum, 12 - fff , is the frequency gap when the
absorption reduce to
half of the maximum value.
3 State of the art in terms of absorbance and fractional
bandwidth,
thickness.
Since the first metamaterial(MM) perfect absorber is
demonstrated by N. I.
Landy et al[17], numerically and experimentally, which consists
of three layers,
operated at microwave, science, including the design, analysis
and experiment of
MM absorber, grow rapidly at microwave[17-26], THz[29,30],
infrared [27,28,29,31-35,38] and
visible [36,37,39]wavelength with varied structure.
In case for the absorber operated in the microwave region, the
general method is
to build split ring resonators( electric field
coupled(ELC))connected to a split-wire
the magnetic coupling required a more complicated arrangement,
and thus in order
to couple to the incident H-field, we needed flux created by
circulating charges
perpendicular to the propagation vector.. In a word, the
absorber cell mainly contents
two elements, of which one responds to the electric-field the
other responds to the
magnetic field.
Then multiple of such units are arranged orderly onto a
substrate. For modifying
and optimizing the absorption properties, such as the absorption
ratio and the location
of the absorption peak, the respond to polarized wave and
incident wave with
arbitrary angular, firstly one have to carefully choose material
for fabricating the
-
absorber unit, and then the shape (ring or quadrate) with proper
structure parameters
such as length, height and the gap between these two elements,
and the last work is
how to compile this elements.
Fig. 3.1 shows the absorber unit cell with a ring shape and a
quadrate shape.
Experimentally can achieve an absorption of 88% which have a
little error compared
to the simulation results, and the authors explained that due to
fabrication errors.
Ref. [20] demonstrated a perfect absorber using non-magnetic
metamaterials,
which functions as a black body and be able to effectively
absorb incident waves
from all directions. The unit cell used here consists of an
I-shaped unit and an ELC
resonator illustrated in Fig.3.2. Based on this unit cells, the
mainly difference from the
other metamaterial absorber is that this absorber is formed by
orderly compiling these
I-shaped unit and ELC resonators into a ring disc, thus all the
incoming wave with all
direction and be effectively trapped and consequently spirally
travels inside the disc
as shown in Fig.3.2.
Fig. 3.1 Electric resonator, magnetic resonator, unit cell
and results of a metamaterial perfect absorber.[17]
Fig. 3.2 Unit cell and the electric field distribution at
resonance frequency 18GHz[20]
-
Aside from the mainstream idea of arraying those absorber units
into a two
dimension plate, Ref.[18] demonstrated an 3-dimension absorber
based on a cubic
with three absorber units on each surface, of which the unit
cell is formed by
combining an electric resonators with a magnetic resonator, but
not the split-wire mentioned
above. The unit cell and result are show in Fig.3.3.
Comparing with the absorbers operating in microwave band, the
typical unit cells
used for constructing the infrared absorbers are with a cross
shaped geometries [29,
30] and the detail structures are show as Fig. 3.4. As a
development from this type of
cells, Ref[31] Fig. 3.4 shows a H shaped nanoresonator, based on
which a narrow
band, polarization-independent absorptivity of >90% over a
wide 50 angular range
centered at mid-infrared wavelengths of 3.3 and 3.9 m was
achieved.
The other method for realizing IR absorb is by generating
surface plasma using a
so called Plasmonic metamaterials (MMs). Generally, a narrow
band absorber(NBA)
is fabricated by sandwiching an array of plasmonic
strips[28]/patches[27] by a thin
dielectric spacer from a ground plate, show in Fig.3.5 and the
absorb ratio at the peak
can be up to nearly 100%. For expanding the absorb band, one can
combining several
Fig. 3.3 unit cell of 3-diemention and the absorption
spectrum[18]
Fig. 3.4 simulation structure of cross unit cell and
low-magnification field emission scanning
electron microscope image and the experimental and simulation
absorption results [29, 30,31]
-
NBAs with their absorption peaks being close to each other[28].
Apart from the
approach based on plasmonic material used above, Kamil Boratay
Alici and etc.
demonstrated a polarization independent absorber utilizing both
electrical and
magnetic impedance matching at the near-infrared regime, the
half absorption width
of which is as large as 893nm, and when the incidence angles is
up to 60 respecting
to the surface of the plane, the absorption still remains more
than 70% .
As another wave band, visible wavelength has attracted much
attention in recent
years. Similar to the mechanism exploited in infrared absorbers,
the Plasmonic
material is also widely used for realizing visible light absorb.
Developing from grating
configuration, Koray Aydin and etc. proposed a visible light
absorber consisting of a
metalinsulatormetal stack with a nanostructured top silver film
composed of
crossed trapezoidal arrays, whose absorption ranges from
400nm~700nm, covering
the entire visible spectrum. On the other hand, Peng Zhu and L.
Jay Guo also realized
an absorber with the same absorption range and an average
absorption of more than
80% by designing the dispersion and geometry of a Cu/Si3N4/Cu
stack[36]. Show as
Fig. 3.6(left).
Additionally, a perfect black absorber operating in visible
regime was also
demonstrated by using the Plasmonic material, but different from
the stripe and cross
structure used in the above approaches, the
nanocomposite-SiO2-Gold film-Glass
substrate multi-layers structure designed in this work is
relatively simple and cost
effectively.[39] Show as Fig.3.6(right).
In conclusion, the absorbers operating at microwave regime
mainly constructed
by orderly arraying a great deal of unit cells that generally
formed by electric
resonators with cut wire or magnetic field resonators and, each
of the unit cell with
certain structure parameters could provide an absorption peak.
Different from the
Fig. 3.5 Geometry of the sample and measured and simulated
absorbance spectra [27,28]
-
mechanism utilized in the microwave absorbers, plasmonic
materials are intensively
used for realizing a broadband absorption in infrared and
visible regime. Additionally,
the absorption properties (bandwidth, absorptivity, location of
the absorption peak or
band) greatly depend on the fixed material of the matematerial
and the structure of the
unit cells. Considering that the effective permittivity e(x) and
permeability l(x) of the
metamaterial can be independently changed by modifying the
geometry of its unit cell,
it is possible to realize an efficient absorption in different
frequency bands with
perfect absorption ability by designing unit cells with an
optimized structure using a
material with perfect electro-magnetic properties respecting to
a target operating wave
band[25].
Generally, a single SRR type absorber exhibits one corresponding
absorption
peak. So its reasonably to suppose that multi-absorption peaks
can be achieved by
combining multi-SSR units with different resonance peaks
together.
Based on the former mechanism mentioned above, a three
absorption bands
absorber were realized by adjacently placed multiple unit cells,
which comprises an
electric ring resonator and a pair of crossed wires imprinted on
the opposite faces of a
dielectric substrate, with different resonant resonances
together. As shown in Figure
3.7, three types of resonances were placed together as a unit
and the corresponding
resonances are shown in Figure.3.7(left). [23]
Fig. 3.6 Geometry of the sample and measured and simulated
absorbance spectra [36,39]
-
Beside the proposal for achieving multi-peaks absorption,
Jingping Zhou and
etc.[26] have proposed a metamatrerial absorber based on a
cross-circular-loop
resonator, of which the absorption effect can be easily altered
form single-band to
dual-band by adjusting the positions of the shorted stubs inside
the loop. Show as Fig.
3.7(right).
When it comes to the absorption bandwidth of the absorber, one
can also extend
it by overlapping multi-SRRs with multiple absorption peaks, but
the frequency peak
differences among each SSR should not be big. Ref. [24] shows an
absorber
constructed by overlapping multiple ELC and SRR layers show as
Fig. 3.8(above). A
maximum absorption of 99.9% at 2.4 GHz with a relative broad
half maximum
bandwidth (700MHz) was achieved, which was contributed by the
different
resonances provided by multiple elements. Additionally, the
resistors embedded in the
metamaterial structure effectively lower the Q factor.
Based on the interference theory that is also used in Ref. [29],
a metamaterial
absorber with a multilayered SRRs structure was numerically
demonstrated to be with
an ultra broad band absorption of 60Hz, ranging from 0Hz to 70Hz
with a bandwidth
Fig. 3.7unit cell of multy-band metamaterial
absorber and the simulation results[23]
Fig.3.8 broad band absorption structure and results[24,29]
-
of absorptance >90%, which is originated from the destructive
interference of the
reflection wave based on the anti-reflection formed by the SRR
and substrate together,
but not the intrinsic electromagnetic resonance loss. Show as
Fig. 3.8(below)In
contrast to the perfect absorber realized by exploiting the
coherent effect of among
SRRs, herein the resonance was mainly used for providing an
optimal refractive
index for forming the destructive interference, rather than for
realizing an effective
absorber by itself with its insufficient loss[21].
Similar to the method of combining multi-absorber units with
single absorption
peak for realizing multiband absorption, a microwave[25] and
infrared[32]
rization-independent absorption with an width band and an
absorption of nearly 7GHz
and more than 90%, respectively, was realized by an pyramids
structure formed by
periodically overlapping 20 metal-dielectric quadrangular
frustum layers. Show as Fig.
3.9, in the left is operated at microwave, in the right one is
operated at infrared wave.
4 Optimization of PMA
Although lots of works about PMA explored the very affirmative
results of high
absorbance with broad band spectrum, it is a perpetual issue to
optimize the PMA. For
one thing to reach to unit absorption under the condition of
perfect impendence
matched determined by the thickness and loss tan of the
absorber. One the other hand,
in order to achieve broad band absorbance through designing
multiresonance in planar
and stack structure[23-26,29,30,32] or useing broadband periodic
structure like
grating[27,28,36].
Additionally, operation flexible is another significant element,
including
polarization independence, broad incidence angle, and selected
waveband. There are
three kinds of method to realize polarization independence by
appealing to repeat of
unit cells[20,41,42]; by utilizing an asymmetric unit cell[26];
by using chiral
metamaterials[43].
5 Conclusion and prospects
As conclusion, we have experimentally design a perfect
electromagnetic
absorber using BST cube with high permittivity. The experiment
results show great
agreement with the simulation we have done before, and the
absorptive very close to
100% with FWHM around 4% at Mie resonance frequency. It is
notably that the
Fig. 3.9 pyramid structure for broad band absorber and
results[25,32]
-
absorption characters are significantly influenced by the
lattice period, space gap and
loss tangent. In other word, we can optimize the BST absorber
through adjusting the
geometry and BST local properties.
6 References
[1] W. W. Salisbury, US Patent 1952 2599944.
[2] Claire M. Watts, Xianliang Liu, and Willie J. Padilla,
Metamaterial
Electromagnetic Wave Absorber, Adv. Mater, 24 2012.
[3] E. Kott, J. F. Shaeffer, M. T. Tuley, Radar Cross Section.
2004.
[4] Benedikt A. Munk, Life Fellow, IEEE, Peter Munk, and
Jonothan Poryor, On
Designing Jaumann and Circuit Analog Absorbers(CA Absorbers) for
Oblique
Angle of Incidence, IEEE, 55(1):186-193, 2007.
[5] S. A. Tretyalov, and S. I. Maslovski, Thin Absorbing
Structure for all Incidence
angles Based on the use of a High-Impedance surface. Opt Technol
Lett
38:175-178, 2003.
[6] W Tang, and Z Shen, Simple design of thin and wideband
circuit analogue
absorber, ELECTRONICS LETTERS, 43(12), 2007.
[7] D. Maystre, A new general integral theory for dielectric
coated gratings, J. Opt.
Soc. Am., 68(4), 1978.
[8] Evgeny Popov, Stefan Enoch, and Nicolas Bonod, Absorption of
light by
extremely shallow metallic gratings: metamaterial behavior,
OPTICS EXPRESS,
17(8), 2009.
[9] Schurig, D., 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, Vol. 314, 977-980, 2006.
[10] Liu, R., C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D.
R. Smith, Broadband
ground-plane cloak, Science, Vol. 323, 366-369, 2009.
[11] Davy P. Gaillot, Chafles Cro enne, and Didier Lippens, An
all-dielectric route for
terahertz cloaking, Opt. Express, Vol. 16(6), 3986-3992,
2008.
[12] Olivier Vanbsien, Nathalie Fabre, Xavier Mlique, and Didier
Lippens,
Photonic-crystal based cloaking device at optical wavelength,
Appl.Optics, Vol.
47(10), 1358-1362, (2008)
[13] Zhao, J., Y. Feng, B. Zhu, and T. Jiang, Sub-wavelength
image manipulating
through compensated anisotropic metamaterial prisms, Opt.
Express, Vol. 16,
18057-18066, 2008.
[14] Maxence Hofman, Didier Lippens, and Olivier Vanbsien, Image
reconstruction
49(30), 5806-5813, 2010.
[15] Pendry, J. B., Negative refraction makes a perfect lens,
Phys.Rev. Lett., Vol. 85,
3966-3969, 2000.
[16] Maxence Hofman, Nathalie Fabre, Xavier Mlique, Didier
Lippens, Olivier
-
Vanbsien, Defect assisted subwavelength resolution in -V
semiconductor
photonic crystal flat lenses with n=-1, Opt. Commun, Vol.
283(6), 1169-1173,
2010.
[17] N. I. Landy, S. Sajuyigbe, J. J.Mock, D. R. Smith and W. J.
Padilla, Perfect
Metamaterial Absorber, Phys.Rev. Lett., Vol. 100,
207402-1-207402-4, 2008.
[18] J. F. Wang, S. B. Qu, Z. T. Fu, H. Ma, Y. M. Yang and X.
Wu, Three dimension
metamaterial microwave absorbers composed of coplanar magnetic
and electric
resonators, Progress In Electromagnetics Research Letter, Vol.
7, 15-24, 2009.
[19] ZHU Bo, WANG Zheng-Bin, YU Zhen-Zhong, ZHANG Qi, ZHAO
Jun-Ming,
FENG Yi-Jun and JIANG Tian, Planar Metamaterial Microwave
Absorber for all
Wave Polarization, CHIN. PHYS. LETT., Vol. 26(11), 114102,
2009.
[20] Qiang Cheng, Tie Jun Cui, Wei Xiang Jiang and Ben Geng Cai,
An
omnidirectional electromagnetic absorber made of metamaterials,
New Journal
of Physics, Vol. 12, 063006, 2010.
[21] Jingbo Sun, Lingyun Liu, Guoyan Dong and Ji Zhou, An
estremely broad band
metamaterial absorber based on destructive interference, Opt.
Express, Vol.
19(22), 21155-21162, 2011.
[22] H.-M. Lee and H.-S. Lee, A Metamaterial Based Microwave
Absorber Composed
of Coplanar Electric-field-coup- led Resonation and Wire Array,
Progress In
Electromagnetics Research Letter, Vol. 34, 111-121, 2013.
[23] Theofana M. Kollatou, Alexandros I. Dimitriadis and
Christos S. Antonopoulos,
Utra-Thin, Polarization-Insensitive, Microwave Metamaterial
Absorbers for
EMC Applications, conference, 2012.
[24] S. Gu, J. P. Barrett, T. H. Hand, B-I. Popa and S. A.
Cummer, A broadband
low-reflection metamaterial absorber, Applied Physics, Vol. 108,
064913, 2010.
[25] Fei Ding, Yanxia Cui, Xiaochen Ge, Feng Zhang, Yi Jin and
Sailing He,
Ultra-broadband Microwave Metamaterial Absorber, Appl. Phys.
Lett. Vol. 100,
103506, 2012.
[26] Jingping Zhong, Yongjun Huang, Guangjun Wen, Haibin Sun,
Ping Wang and
Oghenemuero Gordon, Single-/Dual-band metamaterial absorber
based on
cross-circular-loop resonator with shorted stubs, Appl Phys A,
Voi. 108, 329-335,
2012.
[27] Jiaming Hao, Jing Wang, Xianliang Liu, Willie J. Padilla,
Lei Zhou et al., High
performance optical absorber based on a plasmonic metamaterial,
Appl. Phys.
Lett., Vol. 96, 251104, 2010.
[28] Chihhui Wu and Gennaady Shvets, Design of metamaterial
surfaces with
broadband absorber, Opt. Lett., Vol. 37(3), 308-310, 2012.
[29] Zhi Hao Jiang, Seokho, Fatima Toor, Douglas H. Werner and
Theresa S. Mayer,
Conformal Dual- Band Near-Perfectly Absorbing Mid- Infrared
Metamaterial
Coating, Nano. Lett. Vol. 5(6), 4641-4647, 2011.
-
[30] Hou-Tong Chen, Interference theory of metamaterial perfect
absorbers,
[31] Xiao-Yu Peng, Bing Wang, Shumin Lai, Dao Hua Zhang and
Jing-Hua Teng,
Ultrathin multi-band planar metamaterial absorber based on
standing wave
resonances, Opt. Express, Vol. 20(25), 27756-27765, 2012.
[32] Yanxia Cui, Kin Hung Fung, Jun Xu, Hyungjin Ma, Yi Jin,
Sailing He and
Nicholas X. Fang, Uitra-broadband Light Absorption by a sawtooth
Anisotropic
Meramaterial Slab,
[33] James Grant, Yong Ma, Shimul Saha, Ata Khalid and David R.
S. Cumming,
Polarization insensitive, broadband terahertz metamaterial
absorber, Opt. Lett.,
Vol. 36(17), 3476-3478, 2011.
[34] Joungyong Lee, Young Joong Yoon and Sungjoon Lim,
Ultra-thin Polarization
Independent Absorber Using Hexagonal Interdigital Metamaterial,
ETRI, Vol.
34(1), 2012.
[35] Lijun Meng, Ding Zhao, Qiang Li and Min Qiu,
Polarization-sensitive perfect
absorber at mear-infrared wavelengths, Opt. Express, Vol.
21(S1), 2012.
[36] Peng Zhu and L. Jay Guo, High performance broadband
absorber in the visible
band by engineered dispersion and geometry of a
meta-dielectric-metal stack,
Appl. Phys. Lett., Vol. 101, 241116, 2012.
[37] Koray Aydin, Vivian E. Ferry, Ryan M. Briggs and Harry A.
Atwater, Broadband
polarization-indenpendt resonant light absorption using
ultrathin plasmonic super
absorbers, Nat. Comm., Vol. 2, 517, 2011.
[38] Kamil Boratay Alici, Adil Burak Turhan, Costas M. Soukoulis
and Ekmel Ozbay,
Optically thin composite resonant absorber at the near-infrared
band: a
polarization independent and spectrally broadband configuration,
Opt. Express,
Vol. 19(15), 14260-14267, 2011.
[39] M. K. Hedayati, M. Javaherirahim, B. Mozooni, R. Abdelaziz,
A. Tavassolizdeh
eh., Design of a perfect Black Absorber at Visible Frequencies
Using Plasmonic
Metamaterials, Advanced Material, Vol. 23, 5410-5414, 2011.
[40] H.Raether, Suface plasons on smooth and rough surface and
on grating, Springer
Tracts in Modern Physics 111, Springer-Verlag, New York
1988.
[41] D. R. Smith, J. Gollub, J. J. Mock, W. J. Padilla, D.
Schurig, Calculation and
measurement of bianisotropy in a split ring resonator
metamaterial, J. Appl. Phys.
100, 024507, 2006.
[42] D. R. Smith, D. Schurig, J. J. Mock, Characterization of a
planar artificial
magnetic metamaterial surface, Phys. Rev. E, 74, 036604,
2006.
[43] B. Wang, T. Koschny, C. M. Soukoulis, Wide-angle and
polarization-independent
chiral metalaterial absorber, Phys. Rev. B, 80, 033108,
2009.
[44] J. B. Pendry, A. J. Holden, D. J. Ribbins and W. J.
Stewart, IEEE Trans.
Microwave Theory Tech, Vol. 47, 2075, 1999.
[45] J. B. Pendry, A. J. Holden, W. J. Stewart and I. Youngs,
Extremely Low
-
Frequency Plasmons in Metallic Mesostructures, Phys. Rev. Lett.
Vol. 76, 4773,
1996.
[46] Hongjie Zhao, Ji Zhou, Lei Kang and Qian Zhao, Tunable
two-dimensional
left-handed material consisting of ferrite rods and metallic
wires, Opt. Exp. Vol.
17(16), 13373-13380, 2009.
[47] Liang Peng, Lixin Ran, Hongsheng Chen, Haifei Zhang, Jin Au
Kong and
Tomasz M. Grzegorczyk, Experimental Observation of Left-Handed
Behavior in
an Array of Standard Dielectric Resonators, Phy. Rev. Lett. Vol.
98, 157403,
2007.
[48] Fuli Zhang, Davy P. Gaillot, Charles Croenne, Eric
Leurette, XavierMlique and
Didier Lippens, Low-loss left-handed metamaterials at millimeter
waves, Appl.
Phys. Lett, Vol. 93, 083104, 2008.
[49] N. Setter, D. Damjanovic, L. Eng, G. Fox, S. Gevorgian, S.
Hong, A. Kingon, H.
Kohlstedt, N. Y. Park, G. B. Stephenson, I. Stolitchnov, A. K.
Taganstev, D. V.
Taylor, T. Yamada, and S. Streiffer, J. Appl. Phys. Vol. 100,
051606, 2006.
[50] Gregory Houzet, Ludovic Burgnies, Gabriel Velu, Jean-Claude
Carru and Didier
Lippens, Dispersion and loss of ferroelectric Ba0.5 Sr0.5TiO3
thin films up to
110 GHz, Appl. Phys. Lett. Vol. 93, 053507, 2008.
[51] Qian Zhao, Lei Kang, B. Du, H. Zhao, Q. Xie, X. Huang, B.
Li, J. Zhou and L.Li,
Experimental Demonstration of Isotropic Negative Permeability in
a
Three-Dimensional Dielectric Composite, Phy. Rev. Lett. Vol.
101, 027402,
2008.
[52] Fuli Zhang, Qian Zhao, Lei Kang, Ji Zhou, and Didier
Lippens, Experimental
verification of isotropic and polarization properties of high
permittivity- based
metamaterial, Phys Rev. B, Vol. 80, 195119, 2009.
[53] Qian Zhao, Ji Zhou, Fuli Zhang and Didier Lippens, Mie
resonance-based
dielectric metamaterials, Materialstoday, Vol. 12, 2009.
[54] Zhao Q, Du B, Kang L, Zhao, H, Xie Q, Li B, Zhang X, Zhou
J, Li L and Meng
Y, Appl. Phys. Lett, Vol. 92, 051106, 2008.