S S symmetry

Article Tunable Control of Mie Based on Hybrid VO2 and

Ju Gao 1, Kuang Zhang 1, Guohui Yang 1 , Sungtek Kahng 2 and Qun Wu 1,*

1 School of Electronic and Communication Engineering, Harbin Institute of Technology, Harbin 150001, China; [email protected] (J.G.); [email protected] (K.Z.); [email protected] (G.Y.) 2 Department of Information and Telecommunication Engineering, Incheon National University, Songdo-1-dong, Yonsu-gu, Incheon 210211, Korea; [email protected] * Correspondence: [email protected]; Tel.: +86-451-8641-3502

 Received: 3 September 2018; Accepted: 17 September 2018; Published: 20 September 2018 

Abstract: In this paper, a tunable dielectric with temperature-based vanadium dioxide (VO2) is proposed. In contrast to previous studies, both the phase of VO2 and the phase are applied to manipulate the Mie resonant modes in the dielectric cubes. By embedding VO2 in the main resonant structure, the control over Mie resonant modes in dielectric is realized. Each resonant mode is analyzed through field distribution and explains why the phase switch of VO2 could affect the absorbance spectrum. This use of tunable materials could create another new methodology for the manipulation of the Mie -based dielectric cubes and make them closer in essence to isotropic metamaterials.

Keywords: vanadium dioxide; dielectric metamaterial; absorber; Mie resonance

1. Introduction The study of electromagnetic began in the late 1800s. Over the course of a century’s research, the primary goal modern electromagnetic research has been to achieve full control of it, including amplitude control, phase control, and wave impendence control [1–5]. Dielectric composites have been proposed for many applications, and exhibit excellent absorption properties, while the electric resonant mode and magnetic resonant mode overlap with each other [6–11]. Some papers have also proposed tunable metamaterial and metasurface absorbers based on graphene [12–15] or strontium titanate [16,17] to realize tunable absorption or anomalous . -stable and continuously tunable performance could be achieved by varying the or temperature. Vanadium dioxide (VO2) has drawn a great deal of interest for its semiconductor-to-metal ◦ transition and low transition temperature (68 C) [18–20]. Another characteristic that makes VO2 a promising tunable material is that the switching time is very fast when changing from a semiconductor property to a metal property. The study of VO2 is mainly focused on two areas: the first design idea is changing the electrical length by exploiting the ultra-large change of the in VO2 between the semiconductor and the metallic states [21–23], and the second design idea is changing the transverse electric and transverse magnetic pass with different phases [24,25]. However, these two ideas are still far from achieving full control over the electromagnetic wave. In this paper, a tunable dielectric metamaterial absorber with vanadium dioxide is proposed. Unlike previous papers, which only take advantage of the metal properties of VO2 and change the electrical length of the structure, this paper makes use of both material properties to control the absorption. The basic absorber is a cross-shaped high ceramic, and VO2 is placed first in the center and then on the edge of this absorber to achieve the tunability of the absorption. The resulting

Symmetry 2018, 10, 423; doi:10.3390/sym10100423 www.mdpi.com/journal/symmetry Symmetry 2018, 10, x FOR PEER REVIEW 2 of 11 Symmetry 2018, 10, 423 2 of 12 in the center and then on the edge of this absorber to achieve the tunability of the absorption. The resulting composite material functions as a sub- metamaterial with the tunable operatingcomposite material material phase functions permitting as a sub-wavelength the realization metamaterialof an absorber. with the tunable operating material phase permitting the realization of an absorber. 2. Modeling and Design Principle 2. Modeling and Design Principle This study starts with the cross-shaped dielectric metamaterial absorption. For metamaterial or This study starts with the cross-shaped dielectric metamaterial absorption. For metamaterial or metasurface absorbers, one of the most important conditions is the exploitation of epsilon-near-zero metasurface absorbers, one of the most important conditions is the exploitation of epsilon-near-zero (ENZ) materials [26]. A cross-shaped absorber was developed from the cube absorber [27]. By (ENZ) materials [26]. A cross-shaped absorber was developed from the cube absorber [27]. By adding adding other components into the unit cell, ENZ materials can be obtained by the Mie resonances other components into the unit cell, ENZ materials can be obtained by the Mie resonances inside the inside the cross-shaped structure. cross-shaped structure. First, this study starts with the Mie resonance inside the dielectric cube. The incident wave First, this study starts with the Mie resonance inside the dielectric cube. The incident wave excites different Mie resonant modes at different . As there are different application excites different Mie resonant modes at different frequencies. As there are different application requirements, full control over the resonant modes is needed. Learning from the broadband requirements, full control over the resonant modes is needed. Learning from the broadband antenna or left-handed metamaterial design, adding some other structures into the unit cell could or left-handed metamaterial design, adding some other structures into the unit cell could manipulate manipulate the resonant modes by tuning the nearby resonances together. Based on previous the resonant modes by tuning the nearby resonances together. Based on previous experience with experience with absorbers, the cross-shaped dielectric absorber could have three absorbance peaks absorbers, the cross-shaped dielectric absorber could have three absorbance peaks corresponding corresponding to three resonant frequencies and resonant modes. At each resonant frequency, the to three resonant frequencies and resonant modes. At each resonant frequency, the incident energy incident energy is trapped in the center of the shape and both dielectric arms, on the basis of the is trapped in the center of the shape and both dielectric arms, on the basis of the electric wave. electric wave. This multi-mode resonance structure has great advantages in wave control, and also makesThis multi-mode it easier to resonance accomplish structure different has greatelectrom advantagesagnetic ingoals. wave Compared control, and to also the makes similar it easiershapes to [28,29],accomplish the differentcross-shaped electromagnetic absorber can goals. also Compared be regarded to the similaras a complementary shapes [28,29], thedielectric cross-shaped cube absorber.absorber canBased also on be regardedthe equivalent as a complementary circuit theory dielectric, the cross-shaped cube absorber. structure Based is on smaller the equivalent while keepingcircuit theory, the same the cross-shapedresonant performance. structure is Addition smaller whileally, the keeping unit thecell sameis composed resonant performance.of dielectric ceramics,Additionally, which the means unit cell low is ohmic composed loss ofand dielectric a greater ceramics, suitability which for meanshigh-temperature low ohmic and loss andhigh- a powergreater conditions. suitability forConsidering high-temperature that temperature and high- is one of conditions. the most Consideringimportant parameters that temperature in this study,is one ofit theis necessary most important to keep parameters the host unit in this ce study,ll shape it isand necessary constitutive to keep parameters the host unit stable cell while shape tuningand constitutive the temperature. parameters Therefore, stable while the cross tuning shape the temperature. is the best candidate Therefore, for the the cross study shape of isa thehybrid best candidate for the study of a hybrid VO2 and dielectric metamaterial absorber. VO2 and dielectric metamaterial absorber. ByBy replacing thethe ceramic ceramic into into the the vanadium vanadium dioxide dioxide at the at energy-concentrated the energy-concentrated positions, positions, a tunable a absorber is achieved with a different material phase of vanadium dioxide. The VO2-dielectric absorber tunable absorber is achieved with a different material phase of vanadium dioxide. The VO2- dielectricunit cell isabsorber shown inunit Figure cell 1is. shown in Figure 1.

FigureFigure 1. 1. SchematicSchematic of of absorber absorber unit unit cell. cell.

2.1.2.1. Center Center Case Case InIn the the cross-shaped dielectricdielectric metamaterialmetamaterial absorber,absorber, one one of of the the resonant resonant modes modes concentrates concentrates on onthe the incident incident energy energy around around the centerthe center of the of cross the shape.cross shape. Consequently, Consequently, in the firstin the case, first the case, effect the of effectthe material of the phasematerial on phase absorption on absorption is discussed is bydiscussed replacing by the replacing center material the center with material VO2. The with material VO2. Theproperties material used properties in this paper used are in basedthis paper on the are results based published on the results before published [7]. In this before first case, [7]. the In dielectricthis first case,arms ofthe the dielectric cross-shaped arms absorber of the cross-shaped are connected directlyabsorber with are eachconnected other without directly VO with2. The each simulated other withoutresults of VO the2. The different simulated VO2 phase results absorptions of the different are shown VO2 phase in Figure absorptions2. are shown in Figure 2.

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1.0 Semiconductor phase Metal phase

0.8

0.6

0.4 Absorbance

0.2

0.0 6 8 10 12 14 16 18 20 Frequency/GHz

(a) (b)

Figure 2. Absorbance and constitutive parameters of the dielectric metamaterial when VO2 is placed in theFigure cross-shaped 2. Absorbance center. and (a) Absorbanceconstitutive (parametersb) Constructive of the parameters. dielectric metamaterial when VO2 is placed in the cross-shaped center. (a) Absorbance (b) Constructive parameters. The constitutive parameters are calculated by the following formulas: The constitutive parameters are calculated by the following formulas: v 2 u 2 22     1 u (1 + S1(1)11) −+−SSS21 1− 1ReRe −S11 S 1Re1 −− Re SS11 µ = nZ = μ t==11Im 21ln 11− −iRe ln 11 , , (1) e f f eff nZ2 22Im ln i Re ln (1) k0d ( − ) −−−2 S21 S21 1 kdS011212111 (1 S21 ) S S S 21

h  1−ReS   1−ReS i 1 Im11Re1Reln −−11 −SSiRe ln 11 k0d Im lnS21 11− i Re ln S21 11 εe f f = n/Z = .. (2) kd02121r S2 2 S ε == (1+S11) −S eff nZ/ 21 (2) (1+−SS2 )222 (1−S11) 11−S21 21 −−22 (1SS11 ) 21 Figure2a shows the different absorbance results achieved through the different VO 2 material phases. TheFigure red 2a dotted shows line the shows different the absorption absorbance of results the dielectric achieved metamaterial through the while different VO2 operates VO2 material as a metal.phases. Under The this red condition, dotted line three shows main the resonant absorption peaks of andthe twodielectric slight metamaterial resonant peaks while were VO observed.2 operates Theas main a metal. resonant Under peak this appeared condition, at 12.92 three GHz main and re thesonant resonant peaks absorption and two was slight 99.3%. resonant The other peaks two were mainobserved. resonant The peaks main appeared resonant around peak 18.04 appeared GHz andat 12.92 19.59 GHz GHz, and and the the resonant absorptions absorption were 85.2% was and 99.3%. 65.6%,The respectively. other two Eachmain of resonant these resonant peaks peaks appeared corresponds around to a18.04 resonant GHz mode, and and19.59 the GHz, underlying and the mechanismabsorptions of the were proposed 85.2% and tunable 65.6%, dielectric respectively. metamaterial Each of absorber these resonant was the peaks modification corresponds of the to a resonantresonant mode mode, and resonantand the frequencyunderlying while mechanism controlling of the the proposed material phasetunable of VOdielectric2. The othermetamaterial two slightabsorber resonant was peaks the weremodification around 7.79of the GHz resonant and 15.79 mode GHz. and resonant frequency while controlling the materialThe black phase solid of lineVO2. shows The other the absorptiontwo slight resonant of the dielectric peaks were metamaterial around 7.79 absorber GHz and while 15.79 VO GHz.2 operatesThe under black a semiconductor solid line shows phase. the Inabsorption this condition, of the thedielectric dielectric metamaterial metamaterial absorber absorber while was VO2 composedoperates of under two different a semiconductor permittivity phase. dielectric In this cubes, condition, and excited the dielectric several metamaterial orders of Mie absorber resonant was modescomposed inside theof two cubes. different Figure permittivity2 shows that dielectric the absorption cubes, and over excited the whole several frequency orders of band Mie resonant was moremodes complicated inside the when cubes. VO2 Figureoperated 2 shows under athat semiconductor the absorption phase. over There the werewhole four frequency main resonant band was peaksmore which complicated could keep when the absorption VO2 operated over 80% under at 8.11 a semiconductor GHz, 12.43 GHz, phase. 12.84 GHz,There and were 18.34 four GHz, main respectively.resonant peaks When which the VO could2 phase keep changed the absorption from metal over to 80% semiconductor, at 8.11 GHz, the12.43 first GHz, resonant 12.84 GHz, mode and was18.34 enhanced. GHz, Thisrespectively. means that When the absorbance the VO2 phase efficiency changed was improvedfrom metal to asto highsemiconductor, as 91.8% without the first a frequencyresonant shift.mode Anotherwas enhanced. resonant This enhancement means that occurredthe absorbance at 16.62 efficiency GHz. At was this improved resonant to mode, as high theas VO 91.8%2 phase without switching a frequency led to a shift. resonant Another frequency resona whichnt enhancement shifted from occurred 15.79 GHz at 16.62 to 16.61 GHz. GHz, At this andresonant the absorbance mode, efficiencythe VO2 phase was enhancedswitchingfrom led to 27.3% a resonant to 68.2%. frequency which shifted from 15.79 GHz toAt 16.61 the GHz, second and mainthe absorbance resonant efficiency frequency was of enhanced the semiconductor-phase from 27.3% to 68.2%. dielectric absorber, the resonanceAt the reached second around main 12.45resonant GHz frequency and was nearly of th combinede semiconductor-phase with the third resonance, dielectric whichabsorber, was the aroundresonance 12.84 GHz.reached Unlike around that 12.45 of the GHz metal and phase, was near the resonantly combined mode with of thisthe resonancethird resonance, split into which two.was Also around unlike 12.84 the GHz. metal Unlike phase, that by modifyingof the metal the phase, electromagnetic the resonant field mode of theof this semiconductor resonance split cubeinto at two. the center,Also unlike Mie the resonance metal phase, was excitedby modify insideing the the electromagnetic cube rather than field through of the semiconductor reflection. Therefore,cube at the the dielectric center, absorberMie resonance generated was another excited resonant inside mode the cube and shiftedrather thethan resonant through frequency. reflection. TheTherefore, resonant intensity the dielectric decreased absorber while thegenerated resonant an modeother split resonant into two mode independent and shifted modes. the resonant

Symmetry 2018, 10, x FOR PEER REVIEW 4 of 11 Symmetry 2018, 10, 423 4 of 12 frequency. The resonant intensity decreased while the resonant mode split into two independent modes. The last main resonant frequency at 18.34 GHz was enhanced from the third resonant frequency The last main resonant frequency at 18.34 GHz was enhanced from the third resonant in the metal phase. Meanwhile, the resonant intensity was also increased and shifted to a higher frequency in the metal phase. Meanwhile, the resonant intensity was also increased and shifted to a resonant mode nearby. The field distribution of the dielectric metamaterial absorber with VO in both higher resonant mode nearby. The field distribution of the dielectric metamaterial absorber2 with the metal and semiconductor phases is shown in next section. The incident electric field vector is along VO2 in both the metal and semiconductor phases is shown in next section. The incident the Y-axis. vector is along the Y-axis. Figure2b shows the effective constitutive parameters of the dielectric metamaterial while VO 2 Figure 2b shows the effective constitutive parameters of the dielectric metamaterial while VO2 operated in the metal phase. The metamaterial absorber showed either negative permittivity or a operated in the metal phase. The metamaterial absorber showed either negative permittivity or a permeability of 5 GHz to 12 GHz, so the incident wave was reflected over these frequency bands, permeability of 5 GHz to 12 GHz, so the incident wave was reflected over these frequency bands, which is also verified in Figure2a. The dashed areas in Figure2b show that the effective permittivity which is also verified in Figure 2a. The dashed areas in Figure 2b show that the effective and permeability both approximated to zero. This means the absorber operated as a double-zero permittivity and permeability both approximated to zero. This means the absorber operated as a metamaterial at these two dashed areas in Figure2b, corresponding to the best absorption performance double-zero metamaterial at these two dashed areas in Figure 2b, corresponding to the best around 12.92 GHz and 18.04 GHz, shown in Figure2a. absorption performance around 12.92 GHz and 18.04 GHz, shown in Figure 2a. 2.2. Dielectric Arm Case 2.2. Dielectric Arm Case The resonance of traditional cross-shaped dielectric metamaterial absorbers mainly focuses the The resonance of traditional cross-shaped dielectric metamaterial absorbers mainly focuses the incident energy on either the shape center or the dielectric arm. Therefore, the tunable material placed incident energy on either the shape center or the dielectric arm. Therefore, the tunable material in the dielectric arm was investigated in this part of study. The absorbance of the dielectric absorber placed in the dielectric arm was investigated in this part of study. The absorbance of the dielectric with VO2 in the dielectric arm is shown in Figure3. absorber with VO2 in the dielectric arm is shown in Figure 3.

(a) (b)

FigureFigure 3. 3.Absorbance Absorbance and and constitutive constitutive parameter parameter of of the the dielectric dielectric metamaterial metamaterial when when VO VO2 2is is in in the the cross-shapedcross-shaped arm. arm. (a ()a Absorbance) Absorbance (b ()b Constitutive) Constitutive parameters. parameters.

TheThe black black solid solid line line in in Figure Figure3 represents3 represents the the absorbance absorbance of of the the dielectric dielectric absorber absorber when when VO VO2 2 operatesoperates as as a a semiconductor semiconductor in in the the dielectric dielectric arm. arm. There There were were four four main main resonant resonant frequencies frequencies in in this this case,case, with with four four main main resonant resonant frequency frequency bands bands around around 6.71 6.71 GHz, GHz, 12.89 12.89 GHz, GHz, 15.41 GHz,15.41 andGHz, 17.83 and GHz. 17.83 TheGHz. best The absorbance best absorbance efficiency efficiency was 99.97% was when 99.97% the absorberwhen the operated absorber at operated 17.83 GHz. at The17.83 electric GHz. and The magneticelectric and field magnetic distributions field atdistributions these four main at these resonant four main frequencies resonant are frequencies shown in next are section. shown in next section.The red dotted line in Figure3 shows the absorbance when the temperature was above 68 ◦C and VO2 operatedThe red asdotted a metal. line Comparingin Figure 3 shows the absorption the absorbance to when when VO2 theis a temperature semiconductor, was the above material 68 °C phaseand VO switch2 operated suppressed as athe metal. resonance Comparing to around the 6.71absorption GHz and to 12.89when GHz. VO2This is a issemiconductor, because the main the resonantmaterial part phase is theswitch semiconductor suppressed platethe resonance in the dielectric to around arm, 6.71 which GHz means and 12.89 that GHz. these This two resonantis because modesthe main are resonant evanescent part after is the the se materialmiconductor phase plate switches. in the There dielectric were arm, two mainwhich resonant means that peaks these of thetwo redresonant dotted linemodes around are evanescent 14.88 GHz andafter 17.88 the GHz.material The phase absorbance switches. at these There two were frequencies two main was resonant 86.4% andpeaks 99.1%, of respectively.the red dotted line around 14.88 GHz and 17.88 GHz. The absorbance at these two frequenciesFigure3b was shows 86.4% the and effective 99.1%, constitutive respectively. parameters when VO 2 operated as a metal phase in the dielectricFigure arms. 3b Similarshows tothe the effective first case, constitutive the metamaterial parameters absorber when showed VO2 operated double-zero as a characteristicsmetal phase in atthe the dielectric resonant frequencies.arms. Similar It is to therefore the first important case, the to excitemetamaterial a double-zero absorber electromagnetic showed double-zero response incharacteristics the design of aat metamaterial the resonant absorber. frequencies. The double-zero It is therefore areas inimportant Figure3b areto shownexcite ina shaded.double-zero electromagnetic response in the design of a metamaterial absorber. The double-zero areas in Figure 3b are shown in shaded.

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3. Tunable Mechanism Illustration through Field Distribution 3. Tunable Mechanism Illustration through Field Distribution Tunable performance was achieved through material phase switching. By demonstrating the Tunable performance was achieved through material phase switching. By demonstrating the electric and magnetic field distributions over resonant frequencies, the physical mechanism inside the electric and distributions over resonant frequencies, the physical mechanism inside VO2-dielectric metamaterial absorber is illustrated. the VO2-dielectric metamaterial absorber is illustrated. 3.1. Center Case 3.1. Center Case Figure4 shows the field distribution at each resonant frequency while the temperature is above ◦ Figure 4 shows the field distribution at each resonant frequency while the temperature is 68 C and VO2 operates as a metal phase. Figure4a,b shows that most of the incident wave was above 68 °C and VO2 operates as a metal phase. Figure 4a,b shows that most of the incident wave concentrated in the dielectric arm along the X-axis. The incident electric field is along the Y-axis, and was concentrated in the dielectric arm along the X-axis. The incident electric field is along the Y- at a resonant frequency of 12.92 GHz the incident electric wave was converted to form a circular field axis, and at a resonant frequency of 12.92 GHz the incident electric wave was converted to form a distribution, resulting in a magnetic field enhancement in the dielectric arm which can also be verified circular field distribution, resulting in a magnetic field enhancement in the dielectric arm which can in Figure4b. This resonant mode can therefore be regarded as a magnetic dipole, and this is a magnetic also be verified in Figure 4b. This resonant mode can therefore be regarded as a magnetic dipole, resonant mode. and this is a magnetic resonant mode.

(a) (b)

(c) (d)

(e) (f)

Figure 4. Field distributions at different frequencies while VO2 operates as a metal in the center. (a) Figure 4. Field distributions at different frequencies while VO2 operates as a metal in the center. Electric(a) Electric field field distribution distribution at 12.92 at 12.92 GHz; GHz; (b) ( bMagnetic) Magnetic field field distribution distribution at at 12.92 12.92 GHz; GHz; (c (c) )Electric Electric field field distributiondistribution at 18.04 GHz; (d)) MagneticMagnetic fieldfield distributiondistribution at at 18.04 18.04 GHz; GHz; ( e()e Electric) Electric field field distribution distribution at at19.6 19.6 GHz; GHz; (f )(f Magnetic) Magnetic field field distribution distribution at at 19.6 19.6 GHz. GHz.

InIn Figure Figure 44c,d,c,d, thethe resonantresonant frequencyfrequency increasedincreased toto 18.0418.04 GHz.GHz. At this frequency, thethe incidentincident magneticmagnetic field field was was converted converted to to form form a acircularly circularly field field distribution distribution in inthe the dielectric dielectric arm arm along along the theY- axis,Y-axis, resulting resulting in inthe the enhancement enhancement of of the the electric electric field. field. The The dielectric dielectric absorber absorber can can therefore therefore be be regardedregarded as anan electricelectric dipole dipole at at this this resonant resonant frequency, frequency, and and this this resonant resonant mode mode is an electricis an electric mode. mode.The incident The incident energy energy was contained was contained in the dielectricin the dielectric arm and arm reduced and reduced to a lower to a energylower energy level. level. TheThe higher higher Mie Mie resonance resonance mode mode in the in thedielectric dielectric absorber absorber can be can observed be observed in Figure in Figure4e,f. These4e,f. twoThese figures two figuresshow the show electric the electric and magnetic and magnetic field di fieldstribution distribution at 19.6 atGHz. 19.6 In GHz. this resonant In this resonant mode, bothmode, the both electric the electric and magnetic and magnetic field were field circularly were circularly distributed, distributed, so this so absorption this absorption peak peakresulted resulted in a quadrupole-likein a quadrupole-like resonant. resonant. However, However, the absorption the absorption at this at frequency this frequency was not was over not over80% 80%because because this frequencythis frequency corresponds corresponds to a tohigher a higher resonant resonant mode mode in inthe the dielectric dielectric absorber, absorber, and and the the resonant resonant intensityintensity was was not not that that strong. strong. It It is is not not difficult difficult to to see see that that all all these these resonant resonant modes modes were were excited excited in in the dielectric arm along the X-axis or Y-axis instead of at the center of the cross shape. This can be explained by the phase of VO2. When VO2 operates as a metal, it prevents the

Symmetry 2018, 10, 423 6 of 12 the dielectric arm along the X-axis or Y-axis instead of at the center of the cross shape. This can be explained by the phase of VO2. When VO2 operates as a metal, it prevents the electromagnetic field from forming normal Mie resonance modes. In this case, all the resonance concentrated in the center is suppressed and the resonance within the dielectric arm is enhanced. From this point of view, the basic mechanism of the tunable dielectric VO2 metamaterial absorber lies in the suppression and enhancement of Mie resonant modes in the high-permittivity dielectric cubes. Figure5 shows the electric and magnetic field distributions with VO 2 operating as a semiconductor at the center of the dielectric absorber. Figure5a,b,g,h correspond to the field distributions at 8.11 GHz and 16.6 GHz, respectively. Neither of these resonant frequencies were strong enough when VO2 operated as a metal (the two slight resonant modes at 7.79 GHz and 15.79 GHz). The metal phase VO2 prevented the field distribution from the center of the cross shape, so all the resonances were excited in the dielectric arm. As the temperature decreased, VO2 turned into a semiconductor. The phase transformation allowed the electromagnetic field to excite in the cross-shaped center and enhanced its resonance. This greatly increased the absorption across these frequency bands. Both resonances at 8.11 GHz and 16.6 GHz generated a strong resonant and higher resonant mode in the center of the cross shape. There were also 0.32 GHz and 0.81 GHz frequency shifts towards a higher-frequency band accompanying the VO2 phase switching. The first resonant frequency was 12.92 GHz when the VO2 phase was a metal. This resonant mode split into two resonant modes when the VO2 phase switched from metal to semiconductor. The field distribution of these two resonant modes can be seen in Figure5c–f. Comparing Figure5c,e to Figure4a, it is clear that the electric field distribution did not change very much. The field remained concentrated in the dielectric arm along the X-axis while VO2 switched phase. We can therefore conclude that these two resonant frequencies in the semiconductor VO2 phase split from the resonant frequency at 12.92 GHz when VO2 was in the metal phase. Additionally, comparing Figure5d,f to Figure4b, the material phase had a great impact on the magnetic field distribution in the center of the cross shape. The magnetic field distribution at 12.43 GHz and 12.84 GHz was formed by the reflection of the metal and the incident wave. Additionally, the field distribution in the center was anisotropic along the Z-axis when affected by the dielectric arm resonant. This is why the magnetic field presented several circles at these two resonant frequencies. The initial resonance also split into two resonant modes, and the resonant intensity as well as the absorbance were decreased at these two frequencies. The field distribution shown in Figure5i,j was at the same resonant mode as the one shown in Figure4d,e but with different VO 2 material phases. The electric field in the dielectric arm remained firm to keep this resonant mode an electric mode while changing the VO2 phase from metal to semiconductor, but generated another resonant in the cross-shaped center at the same time. As also displayed with frequencies 12.43 GHz and 12.84 GHz, this resonant mode was formed by the incident wave, the reflection from the ground plane, and the influence from the dielectric arm. The absorption increased at this frequency because another resonant was excited at the cross-shaped center. This ensured that the resonant was strong enough to keep the absorbance efficiency. Symmetry 2018, 10, x FOR PEER REVIEW 6 of 11 from forming normal Mie resonance modes. In this case, all the resonance concentrated in the center is suppressed and the resonance within the dielectric arm is enhanced. From this point of view, the basic mechanism of the tunable dielectric VO2 metamaterial absorber lies in the suppression and enhancement of Mie resonant modes in the high-permittivity dielectric cubes. Figure 5 shows the electric and magnetic field distributions with VO2 operating as a semiconductor at the center of the dielectric absorber. Figure 5a,b,g,h correspond to the field distributions at 8.11 GHz and 16.6 GHz, respectively. Neither of these resonant frequencies were strong enough when VO2 operated as a metal (the two slight resonant modes at 7.79 GHz and 15.79 GHz). The metal phase VO2 prevented the field distribution from the center of the cross shape, so all the resonances were excited in the dielectric arm. As the temperature decreased, VO2 turned into a semiconductor. The phase transformation allowed the electromagnetic field to excite in the cross- shaped center and enhanced its resonance. This greatly increased the absorption across these frequency bands. Both resonances at 8.11 GHz and 16.6 GHz generated a strong resonant and higher resonant mode in the center of the cross shape. There were also 0.32 GHz and 0.81 GHz Symmetry 2018, 10, 423 7 of 12 frequency shifts towards a higher-frequency band accompanying the VO2 phase switching.

(a) (b)

(c) (d)

(e) (f)

Symmetry 2018, 10, x FOR PEER REVIEW 7 of 11 (g) (h)

(i) (j)

Figure 5. Field distributions at different frequencies when VO2 operates as a semiconductor in the Figure 5. Field distributions at different frequencies when VO2 operates as a semiconductor in the center.center. (a(a)) Electric Electric field field distribution distribution at 8.11at 8.11 GHz; GHz; (b) Magnetic(b) Magnetic field distributionfield distribution at 8.11 at GHz; 8.11 (c )GHz; Electric (c) fieldElectric distribution field distribution at 12.43 GHz; at 12.43 (d) MagneticGHz; (d) fieldMagnetic distribution field distribution at 12.43 GHz; at (12.43e) Electric GHz; field (e) Electric distribution field atdistribution 12.84 GHz; at ( f12.84) Magnetic GHz; ( fieldf) Magnetic distribution field atdistribution 12.84 GHz; at ( g12.84) Electric GHz; field (g) Electric distribution field atdistribution 16.6 GHz; (ath) 16.6 Magnetic GHz; field(h) Magnetic distribution field at 16.6distribution GHz; (i) at Electric 16.6 GHz; field distribution(i) Electric field at 18.34 distribution GHz; (j) Magneticat 18.34 GHz; field distribution(j) Magnetic atfield 18.34 distribution GHz. at 18.34 GHz.

The first resonant frequency was 12.92 GHz when the VO2 phase was a metal. This resonant mode split into two resonant modes when the VO2 phase switched from metal to semiconductor. The field distribution of these two resonant modes can be seen in Figure 5c–f. Comparing Figure 5c,e to Figure 4a, it is clear that the electric field distribution did not change very much. The field remained concentrated in the dielectric arm along the X-axis while VO2 switched phase. We can therefore conclude that these two resonant frequencies in the semiconductor VO2 phase split from the resonant frequency at 12.92 GHz when VO2 was in the metal phase. Additionally, comparing Figure 5d,f to Figure 4b, the material phase had a great impact on the magnetic field distribution in the center of the cross shape. The magnetic field distribution at 12.43 GHz and 12.84 GHz was formed by the reflection of the metal ground plane and the incident wave. Additionally, the field distribution in the center was anisotropic along the Z-axis when affected by the dielectric arm resonant. This is why the magnetic field presented several circles at these two resonant frequencies. The initial resonance also split into two resonant modes, and the resonant intensity as well as the absorbance were decreased at these two frequencies. The field distribution shown in Figure 5i,j was at the same resonant mode as the one shown in Figure 4d,e but with different VO2 material phases. The electric field in the dielectric arm remained firm to keep this resonant mode an electric mode while changing the VO2 phase from metal to semiconductor, but generated another resonant in the cross-shaped center at the same time. As also displayed with frequencies 12.43 GHz and 12.84 GHz, this resonant mode was formed by the incident wave, the reflection from the ground plane, and the influence from the dielectric arm. The absorption increased at this frequency because another resonant was excited at the cross-shaped center. This ensured that the resonant was strong enough to keep the absorbance efficiency.

3.2. Dielectric Arm Case Figure 6 shows the electric and magnetic field distribution at different frequencies. Figure 6a,b respectively show the electric and magnetic field distributions at 6.71 GHz. The excited electric field formed a circular distribution in the dielectric arm along the X-axis. In Figure 6b, it is clearly shown that most of the incident wave was concentrated in the semiconductor VO2 plate. In Figure 6a, the electric distribution showed a higher resonant intensity in the dielectric cube near the ground plane than in the part near air. Thereby, most incident energy was transformed into a lower energy level in the bottom of VO2 at this resonant mode. Just as when the resonant was at 6.71 GHz, the resonant at 12.89 GHz was also gathering the incident energy in the semiconductor VO2 plate, as shown in Figure 6c,d. The difference is that the absorption occurred in the whole VO2 plate at 12.89 GHz instead of only around the bottom.

Symmetry 2018, 10, 423 8 of 12

3.2. Dielectric Arm Case Figure6 shows the electric and magnetic field distribution at different frequencies. Figure6a,b respectively show the electric and magnetic field distributions at 6.71 GHz. The excited electric field formed a circular distribution in the dielectric arm along the X-axis. In Figure6b, it is clearly shown that most of the incident wave was concentrated in the semiconductor VO2 plate. In Figure6a, the electric distribution showed a higher resonant intensity in the dielectric cube near the ground plane than in the part near air. Thereby, most incident energy was transformed into a lower energy level in the bottom of VO2 at this resonant mode. Just as when the resonant was at 6.71 GHz, the resonant at 12.89 GHz was also gathering the incident energy in the semiconductor VO2 plate, as shown in Figure6c,d. The difference is that the absorption occurred in the whole VO 2 plate at 12.89 GHz instead of only around the bottom. Symmetry 2018, 10, x FOR PEER REVIEW 8 of 11

(a)

(b)

(c) (d)

(e) (f)

(g) (h)

Figure 6. Field distributions at different frequencies when VO2 operated as a semiconductor in the Figure 6. Field distributions at different frequencies when VO2 operated as a semiconductor in the dielectricdielectric arms.arms. (a()a) Electric Electric field field distribution distribution at 6.71at 6.71 GHz; GHz; (b) Magnetic(b) Magnetic field field distribution distribution at 6.71 at GHz; 6.71 (GHz;c) Electric (c) Electric field distribution field distribution at 12.89 GHz;at 12.89 (d) MagneticGHz; (d) fieldMagnetic distribution field distribution at 12.89 GHz; at (e12.89) Electric GHz; field (e) distributionElectric field at distribution 15.41 GHz; at (f) 15.41 Magnetic GHz; field (f) Magnetic distribution field at distribution 15.41 GHz; ( gat) 15.41 Electric GHz; field (g distribution) Electric field at 17.83distribution GHz; (h at) Magnetic17.83 GHz; field (h) distributionMagnetic field at 17.83 distribution GHz. at 17.83 GHz. Figure 6e,f show the electric and magnetic field distributions at 15.41 GHz. In this resonant Figure6e,f show the electric and magnetic field distributions at 15.41 GHz. In this resonant mode, the incident energy was no longer completely concentrated in the semiconductor VO2 plate. mode, the incident energy was no longer completely concentrated in the semiconductor VO2 plate. The cross-shaped center and the distance between the center and the plate also played important The cross-shaped center and the distance between the center and the plate also played important roles in the absorption. The VO2 phase did have an impact on this resonant mode, but this impact roles in the absorption. The VO2 phase did have an impact on this resonant mode, but this impact was not as strong as in the first two resonant modes. In the last resonant mode at 17.83 GHz, all of was not as strong as in the first two resonant modes. In the last resonant mode at 17.83 GHz, all of the incident wave vector was converted and formed a circle in the cross-shaped center, as shown in Figure 6g,h. This resonant mode is completely independent from the dielectric arm, so the phase of VO2 had little effect. Figure 7 shows the electric and magnetic field distributions of a dielectric metamaterial absorber with VO2 in the cross-shaped arm at the two main resonant frequencies of 14.88 GHz and 17.88 GHz. At a frequency of 14.88 GHz, the field distribution was composed of two parts: one in the cross-shaped center, and the other around the VO2 plate. This resonant was therefore affected by the VO2 phase. This can also be confirmed from the absorbance efficiency line. When VO2 transformed from a semiconductor into a metal, the resonant mode around 15.41 GHz decreased to 14.88 GHz, and the absorbance efficiency was increased from 82.3% to 86.4%. In Figure 7c,d the field distribution was fully concentrated in the cross-shaped center, and there was no effect when the VO2 phase switched. This result can also be confirmed by the absorbance efficiency line.

Symmetry 2018, 10, 423 9 of 12 the incident wave vector was converted and formed a circle in the cross-shaped center, as shown in Figure6g,h. This resonant mode is completely independent from the dielectric arm, so the phase of VO2 had little effect. Figure7 shows the electric and magnetic field distributions of a dielectric metamaterial absorber with VO2 in the cross-shaped arm at the two main resonant frequencies of 14.88 GHz and 17.88 GHz. At a frequency of 14.88 GHz, the field distribution was composed of two parts: one in the cross-shaped center, and the other around the VO2 plate. This resonant was therefore affected by the VO2 phase. This can also be confirmed from the absorbance efficiency line. When VO2 transformed from a semiconductor into a metal, the resonant mode around 15.41 GHz decreased to 14.88 GHz, and the absorbance efficiency was increased from 82.3% to 86.4%. In Figure7c,d the field distribution was fully concentrated in the cross-shaped center, and there was no effect when the VO2 phase switched.

SymmetryThis result 2018 can, 10, x also FOR be PEER confirmed REVIEW by the absorbance efficiency line. 9 of 11

(a) (b)

(c) (d)

FigureFigure 7. FieldField distributions distributions at at different different frequencies when when VO VO22 operatedoperated as as a a metal metal in in the the dielectric arms.arms. ( a) ElectricElectric fieldfield distribution distribution at at 14.88 14.88 GHz; GHz; (b) Magnetic(b) Magnetic field field distribution distribution at 14.88 at GHz;14.88 ( cGHz;) Electric (c) Electricfield distribution field distribu at 17.88tion at GHz; 17.88 (d GHz;) Magnetic (d) Magnetic field distribution field distribution at 17.88 at GHz. 17.88 GHz.

FigureFigure 88 shows the the absorption absorption results results of of the the structure structure tuned tuned by byvarying varying temperatures. temperatures. VO2 ◦ operatesVO2 operates as a assemiconductor a semiconductor when when the thetemperatur temperaturee is lower is lower than than 68 68 °CC and and presents presents different different dielectricdielectric permittivity permittivity with with different different temperatures. temperatures. The The VO VO22 materialmaterial properties properties used used in in this this paper paper ◦ werewere adopted from Wu work group [[20].20]. When the temperature is above 68 °C,C, VO 22 presentspresents as as a a ◦ metal.metal. The The material propertyproperty ofof VOVO22changes changes gradually gradually when when the the temperature temperature increases increases towards towards 68 68C. °C.The The effect effect that materialthat material property property has on absorptionhas on absorption can therefore can betherefore observed be by observed equally dividingby equally the dividingtemperature the temperature into three curves into three before curves it reaches before 68 it◦ C.reaches This method68 °C. This guarantees method aguarantees clear explanation a clear explanationwhile keeping while the figurekeeping distinguishable. the figure distinguis Therefore,hable. the tunableTherefore, performance the tunable was performance observed at 20 was◦C, observed40 ◦C, 60 at◦C, 20 and °C, above40 °C, 6860◦ °C,C. and above 68 °C.

Figure8a shows the absorption when VO 2 was placed in the cross-shaped center. When VO2 operated as a semiconductor phase, the absorption frequency was decreased when the temperature increased. Temperature affected the first resonance the most. The first resonant frequency shifted to the left by 1.48 GHz when the temperature increased from 20 to 60 ◦C. When the temperature was low, some of the resonances in the dielectric absorber were not excited because of the low dielectric permittivity. With increased temperature, the dielectric absorber also excited new resonant modes. As the temperature continued to increase, VO2 changed its material phase into metal and suppressed the resonance within. Figure8b shows that the same performance could also be observed when VO 2 was placed in the dielectric arm. The resonance around 7.44 GHz was excited at 60 ◦C when the dielectric permittivity was high enough, and was subsequently suppressed once the temperature rose

(a) (b)

Figure 8. Tunable absorption with different temperatures: (a) Center case; (b) Dielectric arm case.

Figure 8a shows the absorption when VO2 was placed in the cross-shaped center. When VO2 operated as a semiconductor phase, the absorption frequency was decreased when the temperature increased. Temperature affected the first resonance the most. The first resonant frequency shifted to the left by 1.48 GHz when the temperature increased from 20 to 60 °C. When the temperature was low, some of the resonances in the dielectric absorber were not excited because of the low dielectric permittivity. With increased temperature, the dielectric absorber also excited new resonant modes. As the temperature continued to increase, VO2 changed its material phase into metal and suppressed the resonance within. Figure 8b shows that the same performance could also be observed when VO2 was placed in the dielectric arm. The resonance around 7.44 GHz was excited at 60 °C when the dielectric permittivity was high enough, and was subsequently suppressed once

Symmetry 2018, 10, x FOR PEER REVIEW 9 of 11

(a) (b)

(c) (d)

Figure 7. Field distributions at different frequencies when VO2 operated as a metal in the dielectric arms. (a) Electric field distribution at 14.88 GHz; (b) Magnetic field distribution at 14.88 GHz; (c) Electric field distribution at 17.88 GHz; (d) Magnetic field distribution at 17.88 GHz.

Figure 8 shows the absorption results of the structure tuned by varying temperatures. VO2 operates as a semiconductor when the temperature is lower than 68 °C and presents different dielectric permittivity with different temperatures. The VO2 material properties used in this paper were adopted from Wu work group [20]. When the temperature is above 68 °C, VO2 presents as a metal. The material property of VO2 changes gradually when the temperature increases towards 68 Symmetry 2018, 10, 423 10 of 12 °C. The effect that material property has on absorption can therefore be observed by equally dividing the temperature into three curves before it reaches 68 °C. This method guarantees a clear explanationabove 68 ◦C. while As the keeping resonances the werefigure all distinguis excited inhable. the higher Therefore, frequency the band,tunable continuous performance frequency was observedabsorption at was20 °C, achieved 40 °C, 60 when °C, and the temperatureabove 68 °C. increased from 20 to 68 ◦C.

(a) (b)

FigureFigure 8. 8. TunableTunable absorption absorption with with different different temperatures: temperatures: (a (a) )Center Center case; case; (b (b) )Dielectric Dielectric arm arm case. case.

FigureDielectric 8a shows metamaterial the absorption absorbers when based VO on2 was Mie placed resonance in the have cross-shaped a wide range center. ofapplications, When VO2 operatedsuch as as telecommunications, a semiconductor phase, nanoelectronics, the absorption antennas, frequency and was automotives decreased when [30–32 the], temperature all of which increased.require multiple Temperature operating affected bands. the first The resonance hybrid VO the2 most.and dielectric The first resonant metamaterial frequency can easily shifted tune to thethe left operating by 1.48 bandGHz when stably the and temperature with high efficiency.increased from By tuning20 to 60 the °C. VO When2 material the temperature phase, the was Mie low,resonance some of manipulation the resonances method in the proposed dielectric here abso canrber be were an excellent not excited candidate because for of absorption the low dielectric control in permittivity.these applications. With increased temperature, the dielectric absorber also excited new resonant modes. As the temperature continued to increase, VO2 changed its material phase into metal and suppressed4. Conclusions the resonance within. Figure 8b shows that the same performance could also be observedIn this when paper, VO a2 tunablewas placed dielectric in the metamaterial dielectric arm. absorber The resonance with temperature-based around 7.44 GHz VO 2wasis proposed excited atand 60 simulated.°C when the By dielectric combining permittivity VO2 with was traditional high enough, dielectric and cubes, was subsequently multiple control suppressed methods once can be applied in the Mie resonances, including the suppression and enhancement of the Mie resonance intensity, as well as the offsetting and splitting of the resonant frequency, and also the combination of different frequencies nearby. The metal phase of VO2 has a strong inhibitory effect on the dielectric resonance at its location. These regulation methods over dielectric metamaterials proposed in this paper can be used not only in absorber design, but also in any other Mie resonant-based dielectric metamaterial. In this study, the Mie resonance manipulation method based on VO2 phase change did not realize wideband absorption due to the isolation of resonant modes. This tuning method could be applied in tandem with equivalent circuit model theory in future studies to overcome the resonant modes isolation in the dielectric materials.

Author Contributions: Conceptualization, K.Z. and Q.W.; methodology, J.G.; software, J.G.; investigation, J.G.; writing–original draft preparation, J.G.; writing–review and editing, K.Z., G.Y., S.K. and Q.W. Funding: This research was funded by the National Natural Science Foundation of China [No. 61371044 and 61571155]. Acknowledgments: The authors would like to thank the anonymous reviewers and editors for their helpful and constructive suggestions that improved this paper. Conflicts of Interest: The authors declare no conflict of interest. Symmetry 2018, 10, 423 11 of 12

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