IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 26, NO. 2, JANUARY 15, 2014 111

Theoretical Investigation of Broadband andWide-Angle Terahertz Metamaterial AbsorberBen-Xin Wang, Ling-Ling Wang, Gui-Zhen Wang, Wei-Qing Huang, Xiao-Fei Li, and Xiang Zhai

Abstract— Broadband absorbers have attracted considerableattention due to their great prospect for practical applications.The mechanism is usually a superposition of several setsof structures with different geometrical dimensions. Herein,we numerically investigate an unconventional to existingmetamaterial-based broadband terahertz absorber based on themultilayer same-sized square plate structure. Greater than 99%absorption across a frequency range of 300 GHz with the centralfrequency ∼1.96 THz can be obtained. The FWHM of thisdevice can be up to 42% (with respect to the central frequency),which is 2.6 times greater than that of the single layer structure.Such a property is retained well at a very wide range of incidentangles. The mechanism of the broadband absorber is attributedto longitudinal coupling between layers. The results of thedesigned metamaterial absorber appear to be very promisingfor solar cell, detection, and imaging applications.

Index Terms— Bandwidth, metamaterial, perfect absorber,resonance frequencies.

I. INTRODUCTION

RECENTLY, metamaterials, with the sub-wavelength scaleunit cell, have attracted intense attention due to their

exotic properties that are unavailable in nature, such asinvisibility, superlensing and negative refraction. Split ringresonators (SRRs) [1], [2], fishnet structures [3], cut wirepairs [4] and other stereostructures [5] have been proposedfor predictions of the nature of the metamaterials spanningfrom microwaves to optical frequencies. In most applications,the absorption loss (i.e., the imaginary parts of the dielectric)of these metamaterials often degrades the performance. There-fore, the imaginary parts are given the smallest possible valueto minimize the losses. However, the absorption loss becomesuseful and can be significantly enhanced in creating perfectabsorber materials.

The first perfect metamaterial absorber, having the measuredabsorptivity of about 88%, composed of a metallic split ringand a cut wire separated by a dielectric layer was demonstratedby Landy et al. [6]. Since then, metamaterial-based absorbershave been extensively demonstrated in every relevant spectral

Manuscript received May 15, 2013; revised October 21, 2013; acceptedOctober 28, 2013. Date of publication November 7, 2013; date of currentversion December 26, 2013. This work was supported in part by the NationalNatural Science Foundation of China under Grants 11074069 and 61176116,in part by the Hunan Provincial Natural Science Foundation of China underGrant 2013FJ4043, in part by the 2013 Graduate Science and TechnologyInnovation Program of Hunan Province under Grant 521298927, and in part bythe Specialized Research Fund for the Doctoral Program of Higher Educationof China under Grant 20120161130003. (Corresponding author: L.-L. Wang.)

The authors are with the School of Physics and Microelectronic and KeyLaboratory for Micro-Nano Physics and Technology of Hunan Province,Hunan University, Changsha 410082, China (e-mail: llwang@hnu.edu.cn).

Color versions of one or more of the figures in this letter are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/LPT.2013.2289299

range including microwaves [7], [8], terahertz [12], infrared[9] and optical frequencies [10], [11]. Although they have thehigh absorptivity, these proposed absorbers are single-bandabsorption, which greatly limits their practical applications.Subsequently, some improvement works were followed tomake the absorber operate at dual-band [12] and triple-band[13] absorptions. Unfortunately, these efforts have commonshortcomings of narrow absorption bandwidth. In pragmaticapplications, it is desirable to have perfect absorption overbroader spectral bands.

Currently used such narrowband metamaterial absorber asbuilding blocks for broadband metamaterial absorber appearsstraightforward: combining several such narrowband resonantfrequencies together and packing them closely through varyingthe geometric parameters of different component in the unitcell, broadband resonance metamaterials can be obtained.Following this design strategy, broadband metamaterialabsorbers have been widely demonstrated from the microwaveregion to the optical region [7], [8], [14]–[18]. For example,Luo et al. [7], Liu et al. [8] and Ding et al. [15] achieved thebandwidth broadening based on multi-squared metallic patchesin microwave frequencies. Ye et al. [11] and Grant et al. [14]demonstrated wideband absorbers by stacking metal-dielectriclayers with different sized metallic crosses in terahertz region.Cui et al. [16], [17] and Cheng et al. [18] obtained broadbandperfect absorber by using multiplexed plasmonic metallicnanostructures in infrared region.

However, current designed broadband absorbers suffer frommany disadvantages such as sensitivity to the polarizationof the incident wave or narrow accepted angles [7], [8],[16]–[18], which greatly hampers their practical applications.Most importantly, the present the broadband light absorberdesign neglects the case of stacking the metal-dielectric layerswith same structural dimensions. Little attention being paid tothe stacked metal-dielectric layers with same structural dimen-sions is possibly due to the fact that its absorptivity rise sharplywith additional layers and is asymptotic to unity [6], [19]. Par-ticularly, the mechanism of overlapping multi-frequencies isno longer valid to explain the stacked of the same-sized metal-lic plates and there only a resonance absorption peak when thesame-sized metallic structures are stacked [6], [15]–[17], [19].This feature giving the illusion that the characteristicabsorption resonance of the bandwidth cannot be widened bystacking metal-dielectric layers with the same sizes.

Herein, we report the novel discoveries that the opticalresponses of the stacking same-sized square plates showa broadband, polarization-insensitive and wide-angle perfectabsorption. The FWHM of the device is greatly improvedto 42%, which is 2.6 times greater than that of the single

1041-1135 © 2013 IEEE

112 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 26, NO. 2, JANUARY 15, 2014

Fig. 1. Cross section (a) and top view (b) of the designed absorber;(c) Simulated absorption spectra of the single layer, double layers and thedesigned absorber.

layer structure. Besides, the absorber works very well in awide angle range from 0 to 50°. The mechanism for thebroadband absorption is attributed to longitudinal couplingbetween layers. Such a simple device may provide a desirableabsorption method and operation to select frequency band inthe THz regime and thus lead to most practical applications.

II. STRUCTURE AND DESIGN

A unit cell of the compact metamaterial absorber structureis illustrated in Figs. 1(a) and (b), which consists of analternating stack of same-sized square plates and dielectriclayers on the top of a metal board. The repeat period isP = Px = Py = 85 μm, and the length of square plate isl = lx = ly = 40 μm. The thicknesses of each dielectricslab (polyimide) are set to t1 = 7 μm, t2 = 2 μm andt3 = 1 μm, and then the thickness of the metal (Au)is 2 μm with a frequency independent conductivity ofσ = 4.09 × 107 S/m. The dielectric constant of the poly-imide [12] is 2.4 + 0.005i . Our results are obtained throughfinite-difference time-domain (FDTD) simulations, where theperiodic structures are illuminated by a normally incidentplane wave with the electric field parallel to the x-axis (seeFig. 1(b)). Perfectly matched layers (PML) are applied alongthe z direction and periodic boundary conditions in the x and ydirections.

III. SIMULATION RESULTS AND DISCUSSION

Fig. 1(c) shows the calculated absorption spectra of thedesigned 3-layer absorber structure. It is obvious that a veryhigh (greater than 99%) and flat-top absorption is obtainedover a frequency range of 300 GHz with the central frequencyaround 1.96 THz. The absorption spectra consists of three

Fig. 2. The magnetic field (H y (a1-c1) and |H y| (a2-c2)) distributions forthe designed structure at the resonance frequencies f1 (a1, a2), f2 (b1, b2)and f3 (c1, c2). The white rectangle frames at a1-c1 and a2-c2 are Au layers.(a3-c3) Schematic illustration of the resonance hybridization in the designedbroadband absorber.

resonance frequencies, located at the frequencies of 1.84 THz( f1), 1.98 THz ( f2) and 2.06 THz ( f3) with the absorptivitiesof 99.72%, 99.93%, 99.72%, respectively. The absorptivity,A is obtained by A = 1-T-R, where T and R are thetransmissivity and reflectivity, respectively. The T is very closeto zero as the thickness of the metal board is much larger thanits skin depth, and then the A is calculated by A = 1-R. TheA may achieve perfect absorption when the R is close to zero.For comparison, the absorption of the single layer and doublelayers absorbers is also presented in Fig. 1(c). The thicknessof the dielectric slab is 5 μm for the single layer structure,and the thicknesses of the dielectric layers are set to t1 =7 μm and t2 = 2 μm for the double layers absorber. Theperiod and the length of the plate are the same in all cases.As shown in Fig. 1(c), there is an absorption peak for thesingle layer absorber, which is derived from a strong magneticresonance [6]–[8], while two closely positioned resonanceswith absorption up to 98% can be obtained in the doublelayers absorber. The resonance bandwidth of the designed3-layer absorber structure is 2.6 and 1.4 times larger thanthose of the single layer and double layers absorber structures,respectively.

To reveal the physical origin of the broadband and flat-top metamaterial absorber, we give the calculated magneticfield (Hy and |Hy|) distributions corresponding to three absorp-tion maximums ( f1, f2 and f3) in Fig. 2. Different fielddistributions are observed for the resonances at 1.84 THz,1.98 THz and 2.06 THz. For the resonance at 1.84 THz, twopositive magnetic resonances (a strong and a weak) can be

WANG et al.: BROADBAND AND WIDE-ANGLE TERAHERTZ METAMATERIAL ABSORBER 113

observed in Fig. 2(a1). Similarly, at 1.98 THz (Fig. 2(b1))and 2.06 THz (Figs. 2(c1)), three magnetic resonances (twopositive and a negative) can be observed, respectively. Theirmain difference lies in the intensity of the field of the dielectriclayer (see Figs. 2(b2) and (c2)), and in particular the first andthird layers. Actually, the magnetic resonance is associatedwith the excitation of a circuit current loop, and thus thedistribution of the charges is mainly accumulated at the endof the square plates [11], [20]. Figs. 2(a3)-(c3) show theschematic illustration of the hybridized charge distributionscorresponding to three absorption maximums, respectively. Asshown in Fig. 2(a3), the positive and negative charges arealternatively distributed as “+”, “−”, “+”, “−” along thez direction in the left side of the metal layer from bottomto top layer or vice versa in the right side of the metal layer.The charges distribution of mode f2 is different from the caseof the f1, and it changed to “−”, “+”, “+”, “−”, “+”, “−”in the left side of the metal layer. The frequency difference ofthe two modes ( f1 and f2) can be understood as follows: forthe mode f2, the charges at the end of the third layer metalplate repel each other (Fig. 2(b3)), while the charges at theend of the same metal plate attract each other (Fig. 2(a3))for the mode f1 [21], [22]. The repulsion and attraction ofthe charges inside the third metal plate result in an increasedand decreased restoring force, respectively. Consequently, theresonance frequency f1 is less than that of f2.

It can be seen from Figs. 2(b3) and (c3) that the distributionof the charges of the mode f2 is the same as that of themode f3. However, the intensity of the charges of the modef2 at the end of the third metal layer and metal board islarger than that of the mode f3 because the intensity of thefield of the mode f2 at the third dielectric layer is stronger.Actually, the charges at the ends of the third metal layerand metal board attract each other (Figs. 2(b3) and (c3)).As the distribution of the charges is increased, the restoringforce will reduce, leading to the decrease of the resonancefrequency. Thus, the resonance frequency of f2 is less thanthat of f3. Although the intensity of the accumulated chargesof the mode f2 at first layer is slightly less than that of themode f3, the influence of the restoring force is neglectedas the larger interlayer distance t1. Obviously, the near-fieldinteraction of these square plates determines the broadbandand flat-top metamaterial absorption. The designed perfectabsorber has a wide application prospect in the detection ofexplosives, stealth, band-stop filters and solar cells and can beeasily fabricated using electron-beam lithography or focusedion-beam milling.

IV. GEOMETRICAL EFFECTS ON THE

RESONANCE FREQUENCIES

The size of the square plate is critical to obtain the broad-band and flat-top near-perfect absorption because the changesin the length l of these plates can significantly influence thenear-field interaction and consequently tune the property ofthe resonance. Fig. 3(a) shows the influence of the size ofthe plates on the resonance frequencies and absorptivities.It shows that the absorption bandwidth especially greater

Fig. 3. (a) Dependence of the absorption spectra on the length l of thesquare metallic plates; (b) Absorption spectra of the designed structureswith different incident angles; (c) Absorption spectra for different dielectricmaterial properties. (d) Dependence of the absorption spectra on the numberof the stacked layers.

than 90% absorption bandwidth gradually decreases with theincrease of the length of the plates. Besides, owing to thehigh degree symmetry of the resonance structure, the designedabsorber is insensitive to the polarization of the incident light.In practical applications, however, electromagnetic wave isusually incident onto absorber with an oblique incident angle.Fig. 3(b) shows the dependence of the absorption spectra ofthe proposed structure with the incident angles. It shows thatthe broadband perfect absorption (greater than 90%) does notlimit to normal incidence but can be extended at least to 50°.Thus, the designed metamaterial absorber operates quite wellover a larger range of angles of incident.

We next investigate the origin of the loss to understandthe contributions of each part of the metamaterial absorber.Fig. 3(c) shows the absorption spectra of the absorber undertwo different loss conditions (loss-free and lossy) of thedielectric layer. As observed from the absorption spectra, theresonance frequencies of loss-free and lossy of the dielectricare not maintaining the same frequencies, such an absorptionmechanism has not been reported in single-band, dual-bandand even triple-band absorbers [6], [12], [13].

To broaden the resonance bandwidth of the metamaterialabsorber in the stacking the same-sized metal-dielectric layerpatterns, we design and optimize the 4- and 5-layer structures,respectively. The optimal thicknesses of the dielectric slab areset to t1 = 4 μm, t2 = 2 μm, t3 = 1 μm, t4 = 1 μm andt1 = 3 μm, t2 = 2 μm, t3 = 2 μm, t4 = 1 μm, t5 = 1 μm(from top layer to bottom layer) for the 4- and 5-layer stackedstructures, respectively, while the length of the square plates land the repeat period P are the same as those used in Fig. 1(b).The simulated absorption spectra is presented in Fig. 3(d). Itcan be seen from Fig. 3(d) that the absorption spectra of the4-layer structure has three frequencies at 1.78, 2.01, 2.20 THzwith the absorptivities of 99.96%, 95.86% and 99.03%,respectively. The calculated result shows that the FWHMabsorption bandwidth of the 4-layer structure can reach

114 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 26, NO. 2, JANUARY 15, 2014

0.94 THz, which covers the 1.55-2.49 THz range, and theFWHM of this device is about 48.7%. Moreover, for the5-layer structure, there are four absorption peaks at frequencies1.74, 1.96, 2.13 and 2.70 THz with the absorptivities of96.22%, 97.84%, 97.72% and 70.25%, respectively. TheFWHM absorption bandwidth of the device can be broadenedto 1.54 THz, from 1.44 to 2.98 THz, with the relative FWHMabsorption bandwidth of 69.7%.

V. CONCLUSION

In conclusion, we demonstrate an unconventional to existingmetamaterial-based broadband terahertz absorber formed bythree alternating layers of same-sized square patterned metallicplates and dielectric layers, and a metallic ground plane at thebottom. An extremely high absorption (greater than 99%) ina continuous range of frequencies with a bandwidth of about300 GHz can be obtained. Importantly, the designed absorberhas an absorption bandwidth 2.6 times that of the singlelayer absorber structure, which is different from previousreports that the absorption cannot broaden the resonance byincreasing the number of metallic layers with same structuraldimensions [6], [15]–[17], [19]. Besides, the response achieveda minimum absorption of 90% for incident angles up to 50°.The mechanism for the broadband absorption originates fromlongitudinal coupling between layers. A further broadening ofthe absorption bandwidth is also possible by increasing thenumber of stacked layers (for example, the FWHM of thedevice can be greatly improved to 69.7% when the numberof the stacking layers is 5.), and the concept could be readilyextended to other frequency regimes for a host of applicationssuch as detection, imaging and solar cell.

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