Optics Communications 295 (2013) 17–20

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Optics Communications

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journal homepage: www.elsevier.com/locate/optcom

Dielectric and Ohmic losses in perfectly absorbing metamaterials

P.V. Tuong a,b, J.W. Park a, V.D. Lam b, W.H. Jang c, S.A. Nikitov d, Y.P. Lee a,n

a Department of Physics, Quantum Photonic Science Research Center and RINS, Hanyang University, Seoul 133-791, South Koreab Institute of Material Sciences, Vietnamese Academy of Science and Technology, Hanoi, Vietnamc Electromagnetic Wave Institute, Korea Radio Promotion Association, Seoul, South Koread Institute of Radioengineering and Electronics, Russia Academy of Sciences, Moscow, Russia

a r t i c l e i n f o

Article history:

Received 21 September 2012

Received in revised form

24 December 2012

Accepted 11 January 2013Available online 31 January 2013

Keywords:

Perfect absorption

Metamaterials

Sub-wavelength structure

18/$ - see front matter & 2013 Elsevier B.V. A

x.doi.org/10.1016/j.optcom.2013.01.031

esponding author. Tel.: þ82 2 2281 5572; fax

ail address: yplee@hanyang.ac.kr (Y.P. Lee).

a b s t r a c t

We investigated two mechanisms of the heat generation to enhance the absorption peak of

metamaterials (MMs) at the normal incidence of electromagnetic radiation. The metal–dielectric–

metal sandwich-type model, in which an array of copper squares at the front and a copper plane at the

back were separated by a dielectric layer, was studied for GHz frequencies. Firstly, we studied the effect

of the thickness of copper square to obtain the absorption peak. The obtained results showed that

absorption can be enhanced to be nearly 100% at 16 GHz by increasing the sheet resistance of the

copper square. In this case, the Ohmic-loss perfect-absorption (PA) MM was devised. The PA effect was

also achieved by using the loss-tangent of dielectric layer as a dissipation factor. For this purpose, we

studied complex the dielectric constant of dielectric layer. The PA peak was demonstrated at the same

frequency. In the second case, the dielectric-loss turns out to be dominant. The comparison between TE

and TM polarizations for the PA peaks was also elucidated.

& 2013 Elsevier B.V. All rights reserved.

1. Introduction

Artificial materials, so-called metamaterials (MMs), havedemonstrated extraordinary electrodynamic properties such asnegativities of effective permittivity [1] and permeability [2]leading to negative refractive index [3,4], and applicable effectssuch as super-lenses [5], electromagnetic (EM) wave cloaking [6],sub-wavelength wireless power transfer [7,8] and perfect absor-ber (PA) [9–11]. They have attained great interest over pastdecade. In the MMs, the effective macroscopic behaviors by usingsmall inhomogeneities are yielded by exploited the plasmonicresonances from interacting with external fields of excitingEM wave. Modulating the structural designs in ‘‘meta-atoms’’ or‘‘meta-molecules’’ to manipulate the effective parameters is thepopular strategy to result in the desired phenomena. This alsocreates the variety in MMs. Thanking its advantage, the MM’seffects have been not only appeared in many geometries of theinducing resonator such as rings [2,3], bars [10,11], crosses [4],flowers [12], and so on, but also presented in most of thefrequency range of EM wave, from radio [13], micro [12], mm[10,11], THz [14], mid-IR [15], near-IR [16] to optical wave [17].

Black bodies, the ‘‘bodies’’ with high absorption properties, are ofmuch importance at present in many fields of science and technol-ogy. It was firstly realized by Landy et al. [11] in 2008 under the

ll rights reserved.

: þ82 2 2281 5573.

concept of sub-wavelength artificial materials. The perfect absorp-tion of EM wave, which mean that no radiation passes through itand none is reflected, also comes to be an attractive issue in thefield of MMs [9–11]. Exploiting the unnatural properties of MMs,the PA MMs have been gradually developed for promisingadvanced applications. For examples, PAs can be potentially usedfor bolometers [18], thermal images [19], efficiently capturing solarenergy [20], sensor devices [21], and camouflage.

In order to exploit the perfect absorption for the devices, it isimportant to study the heat generation to enhance the absorptionpeak of MMs. The mechanism of PA MMs could be understood,based on the effective material parameters. In this case, thecomplex parameters are functions of frequency of exciting EMwave: effective relative permittivity, eðoÞ ¼ e0ðoÞþe00ðoÞ, andeffective relative permeability, mðoÞ ¼ m0ðoÞþm00ðoÞ: At the reso-nance frequency, the real parts of relative permittivity and/orpermeability are adjusted to achieve of impedance matching withfree space [22] by customizing the component parameters andthe material. Simultaneously, the imaginary parts, e00ðoÞ andm00ðoÞ, are also manipulated to developed high dissipation factorinside the MM medium. In other words, the surface plasmas areformed in the sub-wavelength structure to reveal the PA peaksand the heat generations [23]. The impedance matching conditionis obtained by utilizing the plasmonic resonance of couplingbetween the metallic parts in a unit cell. At the resonantfrequency, the total energy of source wave provides the metallicplasma and for good optical materials they are transferred orreflected. Hence, the material should be chosen and designed

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P.V. Tuong et al. / Optics Communications 295 (2013) 17–2018

to induce the appropriate losses to satisfy the second conditionfor the PA applications. The losses in MMs could be the Ohmic-loss by the resistance of metallic components [24] and/or thedielectric-loss by the substrate layer between the metals [25].Essentially, if the MM satisfies both conditions, such resonancescan trap light energy efficiently and provide sufficient time todissipate it by the dielectric and/or Ohmic losses; that is, the lightis absorbed and, consequently, converted into dissipated heat.However, it is not easy to yield a PA peak, since the adjustmentsof relevant physical parameters and of component materialsguarantee both conditions. Therefore, the achievement is stillthe challenging issue in the MM researches.

In our paper, by controlling parameters of MM unit cell, the PApeaks were obtained in two ways with different loss factors.Firstly, a conventional model of absorbing MMs was designed tooperate at GHz, where the failure of perfect absorption wasexamined. Secondly, in order to develop an Ohmic-loss PA MM,we optimized the thickness of metal layer to be in the order ofnm. The sheet resistance was responsible for the perfect absorp-tion and the heat generation. Thirdly, the dielectric componentwas studied to realize the impedance matching with free spaceand the suitable losses. The loss-tangent of dielectric layer wasadjusted to enhance the PA peak so that a dielectric-loss PA MMwas obtained. Finally, the comparison for TE and TM polarizationsof the PA peaks for both strategies were demonstrated.

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Fig. 1. (a) Model of PA MM and (b) Absorption and effective surface impedance

spectra indicate the failure to achieve the PA.

2. Results and Discussion

The simulations were performed by using a finite-integration-technique package of CST Microwave Studio 2010. The sandwich-type model includes periodic conductor squares at the font andconductor plane at the back separated by a dielectric substrate.The design of PA MM unit cell is depicted in Fig. 1(a). Thegeometrical parameters were set to be a¼6.0, l¼4.0, andt¼0.4 mm. The metal layers were copper with an electric con-ductivity of 5.96�107 S/m and a thickness of 36 mm. Thesubstrate was FR-4 with a dielectric constant of 4.2þ0.018i. Thedimension was chosen to expectedly observe a resonance in arange of 12–22 GHz. The longest lattice constant is smaller thanthe center wavelength of the operating range of EM wave.

According to the designed structure, the EM wave only reflectsand absorbs when contacting to MM. Therefore, the absorptioncan be calculated by using S parameter of reflection: AðoÞ ¼1�RðoÞ ¼ 1�½S11ðoÞ�2 [11]. Firstly, absorption and the effectivesurface impedance, for the aforementioned unit cell parameters,are showed in Fig. 1(b). An absorption peak of 63.62% is demon-strated at a resonance frequency of 15.7 GHz. This presents thatthe conditions of PA peak, impedance matching with free spaceand appropriate dissipation factors, are not satisfied. According tothe surface impedance results, we can judge for the failure ofperfect absorption. The effective surface impedance reaches to91 O while the free space one is Z0 � 376:730 O. At least, the firstPA condition is not met. Hence, the responding absorptionspectrum is imperfect.

We studied the mechanism of heat generation in the MM. Theenergy of incidence wave is dissipated by loss factors which aredeveloped by the dielectric and the conductor. In order to yield thePA peak in the GHz regime, two methods are employed by utilizingdifferent dissipations based on the dielectric and the metalliccomponents. The dielectric-loss or the Ohmic-loss is adjusted toobtain the PA peaks in which the respective loss is dominant.

The thickness of copper squares was reduced to be in nm, utilizingthe sheet resistance as major dissipation. Fig. 2(a) presents thevariation of absorption spectrum according to the thickness ofperiodic squares. The absorption turns out to be 82.25% at 16 GHz

as expected for a thickness of 50 nm. The perfect absorption isachieved when the thickness is 10 nm. For this thickness, the sheetresistance of equivalent circuit is Rs¼1.7 O/sq. Most of the energy ofEM wave is dissipated by the thin squares on the MM surface. Indeed,the energy loss is clarified by the distribution of power loss at 16 GHzin Fig. 2(b). This represent that the PA peak is achieved by heatgeneration in the squares. In other words, the Ohmic-loss plays adominant role for the PA. In addition, it is noted that the perfectimpedance matching is also satisfied in this case. The effective surfaceimpedance is matched with Z0 of free space at the PA peak frequency[the blue solid spectrum and right label of Fig. 2(a)].The structurewith 10 nm-thick squares is appropriate to cover both conditions ofthe PA MM.

The dielectric-loss PA is obtained by investisgating the quanlity ofinsulation layer in the MM. The original dimensional parameters arekept. The optimum loss-tangent of dielectric substrate is sough forthe PA peak at the resonance frequency. In Fig. 3(a), the absorptionspectra are shown according to the loss-tangent from 0 (loss free orperfect dielectric) to 0.09. At a loss-tangent of 0.09, the perfectabsorption is achieved. Fig. 3(b) gives us the distribution of powerloss at the PA frequency. This clarifies that most of the energy of EMwave is dissipated by the imperfection of dielectric substrate. Similarto the Ohmic-loss PA, it is noted that the role of loss-tangentadjustment is not only heat generation to satisfy the high losscondition, but also control of the effective parameters to realize theimpedance matching with free space. The blue solid spectrum andright label of Fig. 3(a) illustrate the effective surface impedance isclose to the free space impedance (Z0 ¼ 376:730 O).

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Fig. 2. Ohmic-loss PA: (a) Absorption spectra responding to the reductions in thickness of periodic squares, and the effective surface impedance in case of perfect

absorption and (b) Distribution of power loss at the resonance frequency: yz-cutting planes and isosurface contour. (For interpretation of the references to color in this

figure, the reader is referred to the web version of this article.)

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Fig. 3. Dielectric-loss PA. (a) Absorption spectra responding to the increase in loss-tangent of the insulator layer, and the effective surface impedance in case of perfect

absorption and (b) Distribution of power loss at resonance frequency: yz-cutting planes and isosurface contour. (For interpretation of the references to color in this figure,

the reader is referred to the web version of this article.)

Fig. 4. Compared spectra between TE and TM polarizations for the (a) Ohmic-loss and (b) dielectric-loss PA peaks. The insets are respective induced fields (Ez) in the

xy-cutting plane.

P.V. Tuong et al. / Optics Communications 295 (2013) 17–20 19

We discuss further about the mechanism and the method forthe perfect absorption, based on the plasmonic resonance in sub-wavelength MMs. Two conditions have to be simultaneouslysatisfied to observe the peak of PA. The employed resonance canbe responded by electric or magnetic fields of exciting EM wave.Because of the difference in the operation of induced current fortwo kinds of perfect absorption, the dielectric-loss PA couldbe presented only by utilizing the magnetic resonance whichinduces anti-parallel current, producing dielectric capacitors.Both magnetic and electric resonances can be employed for the

PA MM. Hence, in the above case, it is seen that the plasmonresonance is excited by external magnetic field.

Finally, the PA spectra for the cases of Ohmic-loss (Fig. 4(a))and dielectric-loss (Fig. 4(b)) are examined for both TE and TMpolarizations of incident radiation. It is shown that the polariza-tion mode of EM wave does not affect the absorption spectra. Inother words, the perfect absorption can be achieved in twostrategies of absorption for both modes of polarization. Theresults can be explained by the symmetry of the unit cell in thexy plane. In the insets of Fig. 4, we presented the induced electric

P.V. Tuong et al. / Optics Communications 295 (2013) 17–2020

field Ez of each polarization to clarify the results. It is concludedthat, for aforementioned MM structure, TE or TM mode of EMincidence gives similar influence in enhancing the absorptionpeak by two mechanisms of the heat generation.

3. Conclusions

MM was designed, simulated, and investigated to characterizethe mechanism of perfect absorption in the GHz range of EMwave. By controlling the unit cell of MM, the perfect absorptionwas achieved with different loss factor. By making the dielectric-loss dominant, a dielectric-loss PA was devised. On the otherhand, the Ohmic-loss PA was obtained with enhancing themetallic resistance for absorbing EM wave. The PA peaks of theMM are independent of the polarization mode of radiation. Ourstudies contributed to the explanation on the kinds and themechanisms of perfect absorption, the highly applicableeffect in MM.

Acknowledgments

This research was supported by ICT Standardization programof Korea Communications Commission, by the NRF Grant fundedby the MEST, Korea (No. 2012 – K1A2B2A09033424), and by MESTand PAL, Korea.

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