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 μm 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

metal–insulator–metal 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 it’s 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.

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