Dual Toroidal Dipole Resonance Metamaterials under a ... - MDPI

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Dual Toroidal Dipole Resonance Metamaterials under a Terahertz Domain Shuang Wang 1, * , Song Wang 1 , Quan Li 1,2 , Xiaoli Zhao 1 and Jianyu Zhu 1 1

2

*

School of Electronic Engineering, Tianjin University of Technology and Education, Tianjin 300222, China; [email protected] (S.W.); [email protected] (Q.L.); [email protected] (X.Z.); [email protected] (J.Z.) National-Local Joint Engineering Laboratory of Intelligent Manufacturing Oriented Automobile Die & Mould, Tianjin University of Technology and Education, Tianjin 300222, China Correspondence: [email protected]; Tel.: +86-022-8181027

Received: 3 September 2018; Accepted: 15 October 2018; Published: 19 October 2018

Abstract: We proposed and fabricated a flexible, planar, U-shape-modified structure metamaterial (MM) that was composed of two metallic pattern layers separated by a polyimide layer, where each metallic pattern layer consists of two U-shaped split ring resonators (USRRs). The coupling effect between the two USRRs in the same metallic layer was vital to the formation of dual toroidal dipole (TD) resonances. The measured and simulated results showed that both low quality factor (Q) (~1.82) and high Q (~10.31) TD resonances were acquired synchronously at two different frequencies in the MMs by adjusting the distance between the two coplanar USRRs. With the interaction of the USRRs, the energy levels of the USRRs were split into inductance-capacitance (LC)-induced TD resonance at low frequency and dipole-induced TD resonance at high frequency. Thus, the electric multipole interaction played an important role in determining the energy level of the TD resonance. The better strength of the high frequency TD resonance can be confined to an electromagnetic field inside a smaller circular region, and thus, a higher Q was obtained. In order to investigate the TD mechanism more in depth, the power of the electric dipole, magnetic dipole, electric circular dipole, and TD were quantitatively calculated. Dual TD MMs on a freestanding substrate will have potential applications in functional terahertz devices for practical applications. Keywords: metamaterials; terahertz; toroidal dipole

1. Introduction Toroidal resonance was discovered by Zel’dovich in 1957 [1], and can enhance field confinement by concentrating a magnetic field in a small circular region. Since then, the interactions between toroidal resonance and external electromagnetic fields have become a subject of growing interest [2–14]. As the simplest resonance of a toroidal multipole, toroidal dipole (TD) resonance is created by currents flowing on the surface of a doughnut-shaped structure along its meridians, which can be visualized as a head-to-tail arrangement of magnetic dipoles along a circular path [15,16]. As the third kind of electromagnetic moment, TD resonance has unique electromagnetic characteristics, such as non-radiating mode and confined electric field mode, and their strength depends on the time derivative of the electromagnetic waves [17–19]. However, the detection of TD excitations is challenging. The TD is weakly coupled to free space, and TD can be masked by much stronger electromagnetic effects, such as electric and magnetic dipoles, and even electric quadrupoles [20–26]. Metamaterials (MMs) are broadly defined as artificial, effectively homogeneous electromagnetic structures with unusual properties not readily available in nature. MMs are of great importance to find a way to solve the problems confronted by natural materials. They are usually represented

Materials 2018, 11, 2036; doi:10.3390/ma11102036

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by an array of electric multipoles and magnetic multipoles. By properly designing the structure of metamolecules, the electromagnetic properties can be tailored at will to obtain any multipole radiation pattern. Hence, designing a new structure in order to enhance the TD response, as well as suppressing the electric and/or magnetic multipole resonance is a useful procedure to investigate interesting physical characteristics of TD resonances. MMs provide support to acquire further understanding of the interaction between electric multipole resonances and magnetic multipole resonances in TD resonance. In our research, we proposed a dual TD MM with a U-shaped modified structure under a terahertz regime, which exhibits low quality factor (Q) and high Q TD resonances at different frequencies simultaneously. This TD MMs had a planar structure instead of a 3D structure, which is easy to fabricate, and had a stable resonance output. Thus, it is a good method to realize the unique characteristics of TD and has potential applications at THz frequencies. We investigated the variation of dual TD resonances by changing the distance between the two coplanar U-shape split ring resonators (USRRs) and the arm width of the resonator in the metamolecule structure by looking into the surface current and magnetic-field distribution. In order to understand the mechanism of TD resonance more in depth, quantitative calculations of scattering powers for the multipoles in the metamaterial were carried out. Utilizing the characteristics of dual TD MMs in THz regime could provide various applications at THz frequencies, such as electromagnetically-induced transparency, nonreciprocal refraction, dichroism, nonlinear optical activity, plasmonic sensors, narrow-band emissions and detectors, and effective cloaking and absorbing materials [27–32]. Our work suggests that it is possible to realize any two applications of dual TD MMs in one device under a terahertz domain. It can also facilitate strategies for developing TD resonance on not only freestanding but also on flexible substrates, which can feasibly be used in many applications. 2. Sample Design and Characterization The schematic of the proposed MMs is shown in Figure 1a. The proposed structure was simplified from 3D structures to a stack of 2D planar structures, thus the fabrication was simplified. The proposed MMs was composed of two metallic pattern layers; a polyimide spacer layer (20 µm thick) and a polyimide substrate layer (5 µm thick). Each metallic pattern layer had the same metallic pattern, which consisted of two USRRs. The coplanar USRRs had 180◦ rotational symmetry about the z-axis, in order to form the time-reversal symmetry breaking and space-inversion symmetry breaking. Polyimide film was chosen as the spacer and the substrate, due to its transparency in both THz and visible regimes, thus enabling the aligned photolithography fabrication. The outer dimension of USRRs (lx × ly) was 152 µm × 80 µm and the periodicity of the metamolecule (a × b) was 168 µm × 104 µm. The arm width of the resonator (w) was 18 µm and the distance between the two coplanar USRRs (g) was 10 µm. The resonator was made up of 200-nm-thick (t) aluminum metal. All the samples were on the XY plane, and the terahertz radiation excited the samples at normal incidence with the electric field linearly polarized along the x-axis (Figure 1a). Since four USRRs were in close proximity, the nearest-neighbor mutual interactions or hybridizations between them played a dominant role in their response to external excitations [27,28]. In order to investigate the mutual electromagnetic effects between the two coplanar USRRs in the same metamolecule, the two coplanar USRRs merged to form a single enlarged double-ring USRRs, the parameter g was varied (g = 20, 0, 10, and −18 µm) and the samples were fabricated accordingly. The w (w = 12, 14, 18, and 26 µm) was varied and affected the mutual effect of the USRRs, then the samples were fabricated accordingly. The proposed MMs were fabricated using conventional photolithography and metallization processes. Firstly, the liquid polyimide of PI-5878G (HD Micro Systems TM) was spin-coated on a silicon wafer in order to form the 5 µm substrate, which was helpful to simplify the fabrication process. The thickness of the polyimide spacer could be precisely controlled by adjusting the curing temperature and the spin rate. Secondly, the first metal pattern layer was fabricated using conventional photolithography, followed by the deposition of 200 nm aluminum using vacuum coating equipment, then rinsing in acetone for several minutes. Thirdly, the polyimide spacer layer (20 µm) was fabricated

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temperature and the spin rate. Secondly, the first metal pattern layer was fabricated using followed by the deposition of 200 nm aluminum using3 ofvacuum 10 coating equipment, then rinsing in acetone for several minutes. Thirdly, the polyimide spacer layer (20 μm) was fabricated on it. Fourthly, the second metal pattern layer was fabricated using the on it. Fourthly, the second metal pattern layer was fabricated using the above-mentioned method. above-mentioned method. Finally, the patterned MMs structures on the polyimide substrate were Finally, the patterned MMs structures on the polyimide substrate were peeled off from the silicon peeled off from the silicon substrate. One of the microscope images of the sample with g = 10 μm is substrate. One of the microscope images of the sample with g = 10 µm is shown in Figure 1b. The TD shown in Figure 1b. The TD MMs were characterized by THz-time domain spectroscopy (TDS) in a MMs were characterized by THz-time domain spectroscopy (TDS) in a broadband, photoconductive broadband, photoconductive switch-based system that consisted of four parabolic mirrors in an 8-F switch-based system that consisted of four parabolic mirrors in an 8-F confocal geometry [33,34], confocal geometry [33,34], as shown in Figure 1c. This confocal geometry based on a parabolic as shown in Figure 1c. This confocal geometry based on a parabolic mirror and bare silicon reference, mirror and bare silicon reference, can highly reduce the possible dispersion. The measurements were can highly reduce the possible dispersion. The measurements were directly performed with the MMs directly performed with the MMs attached to a well-defined optical aperture at room temperature in attached to a well-defined optical aperture at room temperature in a dry air environment to eliminate a dry air environment to eliminate the absorption of terahertz waves by the water vapor present in the absorption of terahertz waves by the water vapor present in the atmosphere. the atmosphere. conventional Materials 2018, 11, 2036 photolithography,

(a)

(b)

(c)

Figure 1. (a) Schematic of the proposed MMs (metamaterials) metamolecule. (b) Microscope image of the fabricated with g of = 10 (c)THz-TDS system. Figure 1.sample (a) Schematic theµm. proposed MMs (metamaterials) metamolecule. (b) Microscope image of

the fabricated sample with g = 10 μm. (c)THz-TDS system.

3. Results and Discussion

3. Results Discussion Figure 2a,band show the measured transmission spectra of the proposed MMs samples with different values of Figure g. Two2a,b resonances were observed in all samples: the of lowthe frequency (LF) resonance show the measured transmission spectra proposed MMs samplesat with around 0.35 THz, and the high frequency (HF) resonance at around 0.75 THz. As shown in Figure 2a, (LF) different values of g. Two resonances were observed in all samples: the low frequency the LF resonance frequency first decreased then increased as a function of g, that is, the LF resonance resonance at around 0.35 THz, and the high frequency (HF) resonance at around 0.75 THz. As shown frequency shifted lower frequency as the g increased from − 18 µm to 0 µm,aswhile the LFof resonance in Figure 2a, to thea LF resonance frequency first decreased then increased a function g, that is, the frequency shifted to a higher frequency as the g further increased to 20 µm. The variation thewhile LF resonance frequency shifted to a lower frequency as the g increased from −18 μm to 0 of μm, HF resonance frequency showed the same tendency as the LF resonance frequency, as shown in The the LF resonance frequency shifted to a higher frequency as the g further increased to 20 μm. Figure 2b. TheofQthe factor was defined as the ratio of resonance frequencyastothe the width atfrequency, half variation HF resonance frequency showed the same tendency LFfull resonance maximum. When g = 10 µm, two excitations with the highest Q factor were obtained, and the two as shown in Figure 2b. The Q factor was defined as the ratio of resonance frequency to the full width excitations were both confirmed as TD resonances, which will be introduced in detail later. For the at half maximum. When g = 10 μm, two excitations with the highest Q factor were obtained, and the HF TD at were 0.76 THz, Q (~10.31) was almost sixwhich times will stronger than that in of detail the LFlater. TD For tworesonance excitations both the confirmed as TD resonances, be introduced resonance at 0.32 THz (~1.82). the HF TD resonance at 0.76 THz, the Q (~10.31) was almost six times stronger than that of the LF TD The parameters w also affected the electromagnetic characteristics of the proposed MMs, resonance at 0.32of THz (~1.82). which are illustrated in Appendix A. The LF resonance frequency shifted to a higher frequency as the w increased from 12 to 26 µm due to the inductive coupling between the two metallic layers. However, the w had almost no effect on the HF resonance frequency.


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The parameters of w also affected the electromagnetic characteristics of the proposed MMs, which are illustrated in Appendix A. The LF resonance frequency shifted to a higher frequency as the w2018, increased Materials 11, 2036 from 12 to 26 μm due to the inductive coupling between the two metallic 4layers. of 10 However, the w had almost no effect on the HF resonance frequency. For the purpose of understanding the TD characteristics, numerical simulations were For the purpose of understanding the TD characteristics, numerical simulations were performed performed the in time domain by using the commercially available software CST Microwave Studio. the in time domain by using the commercially available software CST Microwave Studio. The aluminum metal was described by the Drude model, where the angular frequency dependent The aluminum metal was described by the Drude model, where the angular frequency dependent permittivity is given by ε(ω) = ε − [ω /ω(ω iΓ)], with the plasma frequency ω set as permittivity is given by ε(ω) = ε∞ − [ω 2p /ω(ω + iΓ)], with the plasma frequency ωp set as −1 and the damping rate 124.34 × 1012 rads−1 [35], and the dielectric constant of the rads− 22.43××10 101515 rads 1 and the damping rate 124.34 × 1012 rads−1 [35], and the dielectric constant 22.43 polyimide is ε = 0.02i) As illustrated in 2,Figure 2, the experimental and of the polyimide is ε =3.1 3.1 × × (1 (1 + 0.02i) [36].[36]. As illustrated in Figure the experimental and simulated simulated results were in good agreement except for some acceptable variations, which could be due results were in good agreement except for some acceptable variations, which could be due to the to the deviation in the thickness of the polyimide arising the fabrication deviation in the thickness of the polyimide arising from thefrom fabrication process. process.

Figure 2. Experimental (a,b) and simulated (c,d) amplitude transmission spectra for samples with Figure values 2. Experimental amplitude different of g, when(a,b) the Eand fieldsimulated is parallel(c,d) to the x-axis. transmission spectra for samples with different values of g, when the E field is parallel to the x-axis.

In order to explore the variation of the LF TD resonance with different g (g = −18, 0, 10, and 20 µm), In order to explore the variation theXZ LFplane TD resonance with different g (gwere = −18,investigated, 0, 10, and 20 the surface currents and magnetic field (onofthe at Y = 0) induced in the MMs μm), the surface currents and magnetic field (on the XZ plane at Y = 0) induced in the MMsstrip were as shown in Figure 3. At g = −18 µm, the current density was concentrated upon the vertical metal as shown in Figure 3. the At ginduced = −18 μm, the current concentrated uponon the ininvestigated, the center of the metamolecule, and magnetic dipoledensity formed was around the metal strip vertical strip in the the of metamolecule, thethe induced magnetic dipole formed the basis ofmetal the right hand rule.center As theofvalue g increased toand 10 µm, two coplanar USRRs departed around metal on the basisformed of the right rule. the which value of g increased to 10 μm, the from each the other. Thestrip induced current a loophand along the As USRR, is the inductive-capacitive tworesonance, coplanar USRRs each other. The induced currentinformed a loop along the USRR, (LC) then thedeparted magneticfrom dipole type excitation was induced the metallic resonator [37,38]. which is theUSRR inductive-capacitive (LC)magnetic resonance, thentype the excitation magnetic pointing dipole type excitation was Two coplanar resonators had their dipole in the upward or induced in the metallic resonator to [37,38]. Two coplanar resonators had their magnetic downward direction, perpendicular the MM surface. TheUSRR neighboring resonators were flipped dipole over excitation pointing the upward ortheir downward direction, to the MM surface. intype a different manner in oneindirection, hence magnetic moment perpendicular pointed in the opposite direction The the neighboring resonators were overThe in aTD different manner in due one to direction, their along z-axis according to the rightflipped hand rule. resonance formed the nearhence coupling magnetic pointed in the direction along z-axis according thevertical right hand rule. between themoment horizontal USRRs andopposite the hybridization effect the of trapped modes into the USRRs. TD in resonance formed due to the near coupling horizontaland USRRs and the AsThe shown Figure 3e–g, the induced magnetic field was between arrangedthe head-to-tail, the obvious hybridization effect offield trapped modes in which the vertical USRRs. As shown inof Figure 3e–g, the [12,15]. induced vortex of the magnetic was observed, are typical characteristics TD resonance Thus, LF TD resonance was induced by LC resonance. However, when the g further increased to 20 µm, the current density focused on the horizontal strips of the metamolecule. The mutual effect


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magnetic field was arranged head-to-tail, and the obvious vortex of the magnetic field was observed, Materials 2018, 11, 2036 5 of 10 which are typical characteristics of TD resonance [12,15]. Thus, LF TD resonance was induced by LC resonance. However, when the g further increased to 20 μm, the current density focused on the between the two of coplanar USRRs was The too weak to effect form the TD resonance, and TD USRRs resonance horizontal strips the metamolecule. mutual between the two coplanar waswas too hardly observed, as shown in Figure 3h. weak to form the TD resonance, and TD resonance was hardly observed, as shown in Figure 3h.

Figure 3. 3. Simulated Simulated surface magnetic field (on the the XZ XZ plane plane at at Y Y == 00 (e–h) (e–h) of of Figure surface currents currents (a–d) (a–d) and and magnetic field (on resonator at low frequency resonances. resonator at low frequency resonances.

To further further analyze analyze the the TD TD resonance resonance in in the the MMs, MMs, we we carried carried out out aa quantitative quantitative calculation calculation To various multipoles by using the multipole scattering theory regarding the the scattering scatteringpowers powersof of various multipoles by using the multipole scattering according to the volume current density distribution (for the calculation method see Appendix B) theory according to the volume current density distribution (for the calculation method [11,12,24]. FourB)USRRs corresponded to a mixture of magnetic multipoles, and see Appendix [11,12,24]. Four USRRs corresponded to a multipoles, mixture ofelectric magnetic multipoles, toroidalmultipoles, multipoles.and In order to simplify theIn analysis, higher the multipoles ignored. At THz electric toroidal multipoles. order toall simplify analysis,were all higher multipoles normal incidence, the normal electricincidence, dipole vector was along thevector x-axis,was thealong magnetic dipolethe vector (Mz) were ignored. At THz the electric dipole the x-axis, magnetic was parallel the z-axis, the TD to vector (Ty) was to the y-axis, the electric circularand dipole dipole vectorto(Mz) was parallel the z-axis, theparallel TD vector (Ty) was and parallel to the y-axis, the (Gy) was along the z-axis. Figure 4 illustrates the calculated scattering powers of Ty, Px, Mz, and Gy, electric circular dipole (Gy) was along the z-axis. Figure 4 illustrates the calculated scattering powers when g = Mz, 10 μm. shown Figure 4a,As Tyshown was much stronger than any other multipoles, of Ty, Px, andAs Gy, whenin g= 10 µm. in Figure 4a, Ty was much stronger than and any made other the strongest contribution to a resonant dip atto0.32 THz. We the investigated relationship multipoles, and made the strongest contribution a resonant dipfurther at 0.32 investigated THz. We further between Ty and g by plotting scattering of powers Ty as aoffunction of g inofFigure 5. The the relationship between Ty and gthe by plotting thepowers scattering Ty as a function g in Figure 5. relationship between the the scattering powers of Ty andand g isg nontrivial: when g increased from −18 to The relationship between scattering powers of Ty is nontrivial: when g increased from −18 1010 μm, the strength ofofthe to µm, the strength theLF LFTD TDresonance resonancewas wasenhanced. enhanced.When Whenggfurther furtherincreased increased to to g == 20 20 μm, µm, the strength strength of of the the LF LF TD TD resonance resonance was was suppressed. suppressed. When g = = 10 µm, μm, the LF TD resonance had the strongest Ty. Ty.The Thecalculated calculatedresults resultscoincided coincidedwith withthe thenumerical numericalsimulation simulationresults results shown Figure strongest shown inin Figure 3. 3. In our research, the HF resonance was also demonstrated as TD resonance. In order to investigate In our research, HF resonance was also demonstrated as currents TD resonance. In order to the mechanism of the TDthe resonance more in depth, the simulated surface and magnetic field at investigate thewere mechanism of the TD resonance depth, the flow simulated surface and HF resonances discussed. As shown in Figuremore 6a–d,inthe currents opposite alongcurrents the strips in the same USRR, which is the typical dipole resonance of split ring resonators [37,38]. Focusing on the


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magnetic field at HF resonances were discussed. As shown in Figure 6a–d, the currents flow Materials 2018,along 11, 2036 ofring 10 magnetic field at resonances wereUSRR, discussed. Asis shown in Figure the currents opposite theHF strips in the same which the typical dipole6a–d, resonance of split6 flow

opposite along the Focusing strips in on thethe same USRR, dipole resonance of flowing split ring resonators [37,38]. strips in thewhich centerisofthe thetypical metamolecule, the currents in resonators [37,38]. Focusing on the strips in the center the metamolecule, the currents flowing in the adjacent vertical metal strips were anti-phase, andof the magnetic dipole was formed oppositely. strips in the center of the metamolecule, the currents flowing in the adjacent vertical metal strips were the vertical metal dipoles strips were and thearound magnetic wasin formed oppositely. Theadjacent head-to-tail magnetic wereanti-phase, tightly confined the dipole metal bar a smaller circular anti-phase, and the magnetic dipole was formed oppositely. The head-to-tail magnetic dipoles were The head-to-tail dipoles were current tightly confined around the metal barUSRRs in a smaller circulara region. A strongmagnetic antiparallel surface distribution in neighboring pronounced tightly confined around the metal bar in a smaller circular region. A strong antiparallel surface current region. A stronger strong antiparallel currentThus, distribution neighboring USRRs a relatively coupling in surface TD resonance. it could in be confirmed that the HFpronounced TD resonance distribution in neighboring USRRs pronounced a relatively stronger coupling in TD resonance. Thus, relatively stronger coupling in TD resonance. Thus,TD it could be confirmed that themetamolecule HF TD resonance was induced by dipole resonance. The smaller around the edge of the was it could be confirmed that the HF TD resonance was induced by dipole resonance. The smaller TD was induced dipole The TD around edgein of the metamolecule was observed to beby due to the resonance. margin effect of smaller the metamolecule. Asthe shown Figure 4b, the contribution around the edge of the metamolecule was observed to be due to the margin effect of the metamolecule. observed to be due to the margin effect ofwhile the metamolecule. As shown resonance in Figure 4b,atthe contribution of the Mz was strongly suppressed, Ty had the strongest 0.76 THz. The As shown in Figure 4b, the contribution of the Mz was strongly suppressed, while Ty had the strongest of the Mz was strongly whileofTyTyhad strongest resonance 0.76 THz.as The relationship between the suppressed, scattering power andthe g around 0.76 THz wasatthe same the resonance at 0.76 THz. The relationship between the scattering power of Ty and g around 0.76 THz relationship power of and asg shown aroundin0.76 THz5. was theg same as the relationship between between the the scattering Ty and g around 0.32TyTHz, Figure When = 10 μm, the was the same as the relationship between the Ty and g around 0.32 THz, as shown in Figure 5. relationship between thewas Ty the andstrongest g around asresonance. shown in Figure 5. When g = 10 μm, the scattering powers of Ty for0.32 the THz, HF TD When g = 10 µm, the scattering powers of Ty was the strongest for the HF TD resonance. scattering powers of Ty was the strongest for the HF TD resonance.

(a) (a)

(b) (b)

Figure 4. Decomposed scattering powers corresponding to different multipole moments (g = 10 μm). Figure 4. Decomposed scattering powers corresponding to different multipole moments (g = 10 µm). Figure 4. Decomposed scattering powers corresponding to different multipole moments (g = 10 μm). (a) around LF resonance (b) around HF resonance. (a) around LF resonance (b) around HF resonance. (a) around LF resonance (b) around HF resonance.

Figure 5. Scattering power of Ty as a function of g.

Figure 5. Scattering power of Ty as a function of g. Figure 5. Scattering power of Ty as a function of g.

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The magnetic magnetic dipole dipole resonance resonance of of aa single single USRRs USRRs was was split split into into two two discrete discrete resonances resonances that that The originate from the hybridization of magnetic resonance in the stacked USRRs. The hybridization originate from the hybridization of magnetic resonance in the stacked USRRs. The hybridization effect was wasmainly mainlyattributed attributedtotomutual mutual inductive and capacitive coupling between USRRs, effect inductive and capacitive coupling between the the USRRs, and and the the two resonances were far from the original magnetic mode of USRRs due to extreme overlap and two resonances were far from the original magnetic mode of USRRs due to extreme overlap and close proximity. proximity. In In previous previous works, works, the theenergy energylevel level of of the thedegenerated degenerated resonance resonance modes modes was was split split close into toroidal toroidal and and magnetic magnetic resonances, resonances, and and the the energy energy level level was was determined determined by by the the electric electric dipole dipole into interaction [24–26]. In our work, the energy level of the degenerated resonance modes was split into interaction [24–26]. In our work, the energy level of the degenerated resonance modes was split LC-induced TD resonance and dipole-induced TD resonance at two different frequencies when g≤ into LC-induced TD resonance and dipole-induced TD resonance at two different frequencies when TheThe energy level of of thethe dipole resonance in the the g10≤μm. 10 µm. energy level dipole resonancewas wasmuch muchhigher higherthan thanthe the LC LC resonance resonance in typical split ring resonators. The electric multipole interaction played an important role in typical split ring resonators. The electric multipole interaction played an important role in determining determining theofenergy level ofmodes. the resonant modes. The strength on the of time derivative of the energy level the resonant The strength depends on the depends time derivative electromagnetic electromagnetic waves, hence the interaction energy of the TD resonances also increased with the waves, hence the interaction energy of the TD resonances also increased with the shift from lower shift fromfrequencies. lower to higher frequencies. Compared with the LF the HF TD resonance to higher Compared with the LF TD resonance, theTD HFresonance, TD resonance showed a larger showed a larger field confinement per unit volume, attributed to the tightly confined time varying field confinement per unit volume, attributed to the tightly confined time varying magnetic field in a magnetic field in a smaller circular region. The coupling between the four USRRs was enhanced, and smaller circular region. The coupling between the four USRRs was enhanced, and the TD was weakly the TD was weakly coupled free space, thereduced, radiative losses reduced, thus the Q coupled to the free space, and to thethe radiative lossesand were thus the were Q factor was dramatically factor was dramatically enhanced. In our research, dual TD excitations were experimentally enhanced. In our research, dual TD excitations were experimentally demonstrated at the LF and HF demonstrated at the LF andby HFproper frequencies simultaneously by proper theTD g value. The frequencies simultaneously adjustment of the g value. The Q adjustment factor of theofHF resonance Q factor of the HF TD resonance was much higher than that of the LF TD resonance in the proposed was much higher than that of the LF TD resonance in the proposed MMs. The nature of the high Q MMs. in The of the was highhelpful Q factor the efficient TD response wasMMs helpful to make efficient resonant factor thenature TD response to in make resonant devices. MMs devices.

. Figure 6. Simulated surface currents (a–d) and magnetic field (on XZ plane at Y = 0 (e–h)) of resonator Figure 6. Simulated surface currents (a–d) and magnetic field (on XZ plane at Y = 0 (e–h)) of at high frequency resonances. resonator at high frequency resonances.


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4. Conclusions Materials 2018, 11, 2036

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We experimentally demonstrated planar freestanding dual TD MMs with normal incident light. The structure of the metamolecule was designed precisely in order to obtain time-reversal symmetry 4. Conclusions breaking and space-inversion symmetry breaking, which is vital to the formation of TD resonance. ByWe adjusting the g value, both low planar Q and freestanding high Q TD resonances were obtained experimentally demonstrated dual TD MMs with normalsimultaneously incident light. at two different frequencies in the MMs. With the interaction of the USRRs, the energy levels of the The structure of the metamolecule was designed precisely in order to obtain time-reversal symmetry USRRsand were split into two symmetry resonances,breaking, corresponding to vital the LC-induced TD resonance at the LF breaking space-inversion which is to the formation of TD resonance. frequency and dipole-induced TD resonance at the HF frequency, respectively. In HF TD resonance, By adjusting the g value, both low Q and high Q TD resonances were obtained simultaneously at two the head-to-tail magnetic dipoleWith wasthe confined to a small which ledof tothe increased different frequencies in the MMs. interaction of the circular USRRs, region, the energy levels USRRs Q. The Q of thetwo HFresonances, TD resonance was found to tothe be LC-induced much higherTD than that of the LFLF TD resonance. were split into corresponding resonance at the frequency andThe dual TD MMs on the freestanding substrate could have enormous potential applications in terahertz dipole-induced TD resonance at the HF frequency, respectively. In HF TD resonance, the head-to-tail functional metadevices. magnetic dipole was confined to a small circular region, which led to increased Q. The Q of the HF TD resonance was found to Conceptualization, be much higher than of the LF TD resonance. S.W. The (Shuang dual TDWang MMs);on the Author Contributions: S.W.that (Shuang Wang); methodology, software, S.W. (Songsubstrate Wang), J.Z. andhave X.Z.;enormous validation,potential S.W. (Song Wang), J.Z. X.Z.; formal analysis, S.W. (Song freestanding could applications in and terahertz functional metadevices. Wang); investigation, S.W. (Song Wang); resources, S.W. (Song Wang); data curation, X.Z.; writing—original Author Conceptualization, S.W.and (Shuang methodology, (Shuang Wang ); software, draftContributions: preparation, S.W. (Shuang Wang) Q.L.; Wang); writing—review andS.W. editing, S.W. (Shuang Wang); S.W. (Song Wang),X.Z.; J.Z. and X.Z.; validation, S.W. (Song Wang), J.Z. administration, and X.Z.; formalS.W. analysis, S.W.Wang) (Song Wang); visualization, supervision, S.W. (Shuang Wang); project (Shuang and Q.L.; investigation, S.W. (Song Wang); resources, S.W. (Song Wang); data curation, X.Z.; writing—original draft funding acquisition, S.W. (Shuang Wang) and Q.L. preparation, S.W. (Shuang Wang) and Q.L.; writing—review and editing, S.W. (Shuang Wang); visualization, X.Z.; supervision, project administration, (Shuang Wang)Foundation and Q.L.; funding acquisition, S.W. Funding: S.W. This(Shuang researchWang); was funded by the NationalS.W. Natural Science of China (grant numbers (Shuang Wang) and Q.L. 61505146 and 61705167), the Scientific Research Foundation for the Returned Overseas Chinese Scholars, Funding: This wasoffunded theTalent National NaturalProjects, Science Foundation of China numbers Ministry of research Education Chinaby and Planning (grant numbers 48),(grant and the Tianjin61505146 City High andSchool 61705167), the Scientific Research Foundation for the Returned Overseas Chinese Scholars, Ministry of Science and Technology Fund Planning Project (Grant number JWK1608). Education of China and Talent Planning Projects, (grant numbers 48), and the Tianjin City High School Science andConflicts Technology Fund Planning Project (Grantno number of Interest: The authors declare conflictJWK1608). of interest. Conflicts of Interest: The authors declare no conflict of interest.

Appendix A Appendix A Figure A1a,b shows the measured and simulated transmittance of MMs samples with different A1a,b shows theLF measured and simulated transmittance of MMs samples different w. 12 w.Figure The frequency of the TD resonance shifted to a higher frequency as the wwith increased from Theμm frequency of The the LF TDshift resonance shifted to a higher frequency as thecoupling w increased from 12 to to 26 μm. blue in toroidal resonance indicates a weaker between theµm USRRs. 26 As µm.the The blueof shift in toroidal a weaker coupling the USRRs. However, As the value w increased toresonance 26 μm, theindicates interaction between the twobetween USRRs weakened. value increased to 26 µm,onthe interaction between the two weakened. the by w had theof wwhad little influence the HF TD resonance. The LFUSRRs TD frequency canHowever, be adjusted the w, little influence onalmost the HFno TD resonance. TheTD LF frequency. TD frequency can be adjusted by the w, while having while having effect on the HF almost no effect on the HF TD frequency.

Figure A1.A1. Experimental (a) (a) andand simulated (b) (b) amplitude transmission spectra for for samples with Figure Experimental simulated amplitude transmission spectra samples with different value of w, the the E field is parallel to x-axis. different value of when w, when E field is parallel to x-axis.

Appendix B B Appendix Dynamic toroidal multipoles constitute an an independent family of elementary electromagnetic Dynamic toroidal multipoles constitute independent family of elementary electromagnetic sources. The lowest order toroidal flowing on sources. The lowest order toroidalmultipole, multipole,the thetoroidal toroidaldipole, dipole,corresponds corresponds to to currents currents flowing on the the surface surface of the torus, along its meridians. The moment of the electric dipole, magnetic dipole, of the torus, along its meridians. The moment of the electric dipole, magnetic dipole, electric circular dipole, and toroidal dipole directed along the axis of torus is given by the following equation [11,12,24]:

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1 iω

jd3 r R 1 Magnetic dipole: M = 2c (r × j ) d3 r R Electric circular dipole: G = 12 (r × p)d3 r R 1 Toroidal dipole: T = 10c (r × j)r − 2r2 j d3 r Electric dipole: P =

R

where r is the coordinate vector with its origin placed at the center of torus, c is the speed of light, and j is the current density. The simulated current density (j) was obtained via CST Microwave Studio simulations, which are used to calculate the strength of toroidal dipole by means of MATLAB programs. References 1. 2.

3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20.

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