SSpectra Analysis to Stretching of ADB Structure Metamaterial
Q. Sun, J.-Y. Tang, J.-N. Lin, M.-G. He, Z.-P. Wang
Department of Physics, University of Science and Technology of China, Hefei, Anhui, China 230026 (Dated: December 4, 2018)Asymmetric-double-bars (ADB) structure is one of the most interesting plasmonic metamaterials thathas been broadly investigated. Here we propose to manufacture ADB on top of elastic material, to getdirect control to the dimension of ADB elements. To analyze the spectra numerically, simulation bycommercial software (COMSOL) are carried out. We successfully modify the characteristic spectra andenhance Q-factor of the peak near infrared by introducing angular and amplitude parameters of the stretch-ing of substrate in the simulation. At the mean time, we significantly restrain red shift in the absorptionspectra by applying flipped-configuration and substrate etching configuration to ADB structure. Intrigu-ing quadratic functions between stretching ratio and the absorption peak wavelength are obtained whenstretching in x and y direction. For other directions, EIT lineshape appears in transmission spectra. Theseresults might contribute to future application of plasmonic metamaterial in laser controlling and sensors.
In nature, most plasmonic materials don’t have stronginteraction with the magnetic component of light. With thedevelopment of nanotechnology, plasmonic metamaterial,usually formed by metal array in nanoscale, came into sightand rapidly developed for its artificial magnetism at opticalfrequencies. With further researches, plasmonic metama-terial gives out many possible intriguing properties, suchas negative refraction index material [1–4], extraordinarytransmission [5, 6], and a lot more possibilities. Mucheffort has been made to explain this phenomenon. Thewidely accepted explanation to these features is the surfaceplasmons (SPs) theory [7]. Studies have shown that metalssuch as Au and Pt [21] are unique in that they can enhancethe magnetic field near the surface, resulting in some char-acteristic spectrum.Many possible configurations of plasmonic metamate-rial have been developed, for example split rings [8–11],has been found related with intriguing properties. Anotherimportant structure is asymmetric-double-bars(ADB)[25],which is mainly investigated in this paper. One elementof ADB matrix consists of two bars, slightly different inlength. It is one of the simplest structures in metamate-rials, resulting in relatively easy manufacture and simula-tion. ADB is also promising for realizing sharp Fano reso-nance [12–14]. A quadrupole-like dark mode with smallradiative loss is excited by a free space electromagneticwave because of asymmetry of the ADB. It consists of twodipoles with opposite phases, and Fano interference occursbetween the quadrupole mode and the dipole mode. A netdipole moment is small, which leads to weak radiative lossand high Q-factors. Therefore, ADB structure is applicablein many occasions, for example, possibility of electromag-netically induced transparency (EIT) [15–21], and modi-fication to the fluorescence spectrum of coupled QuantumDots [24].In our model, we use ADB formed by gold for high elec-trical conductance. It has been found out that alternatelyflipping the ADB structure, that is to make the adjacent el-ements to be head-to-head rather than head-to-tail, can en-hance the quality factor of the absorption spectra, accord- ing to previous work by Yuto Moritake et al. [23]. Since thedipole-dipole interaction in the non-flipped structure canbe undesirably affected from outside of the periodic struc-ture, alternately flipping can prevent this and enhance theshould-be interaction and increase the Q-factor. Anotherproblem in nanostructure fabrication is to reduce the influ-ence to the electric and magnetic field by the substrate. Thereduction of substrate influence can be achieved by usingselective and isotropic etching of the substrate as demon-strated in [22]. Substrate etching was applied to a siliconsubstrate under the gold nanostructures shown as FIG.1(a).And it was experimentally proved that it can prevent thered shift and improve the refractive index sensitivity basedon far field interference. However, the decrease in the Q-factors of the Fano resonance is observed after applyingsubstrate etching, which is due to the electric field distor-tion by a closely placed substrate. In our experiment, wecombine the alternately flipped configuration of ADB andsubstrate etching together in order to achieved the finestspectral properties of Fano resonance.The schematics of configuration is shown as FIG.1(b).The unit cell of the ADB is composed of two gold bars ofwhich the size is l1 =280 nm, l2 =200 nm, and width w =100nm, gap between two bars w =100 nm, height h =50 nm. Theperiodic lengths in x,y directions are both 500 nm, and fouralternately-flipped ADB units are placed symmetrically infour quadrants of square. Substrate etching is also appliedin our design, which is estimated to be 25 nm during sim-ulation. In experiment, we suggest coating another 5 nmTi between gold bar and the silicon dioxide to improve theadhesive strength, which is not shown in this figure.Previous fabrication of ADB metamaterial was alwaysconducted on silicon dioxide, because of its high trans-parency to all colors of light, endurance to laser and stablechemistry property. Yet silicon dioxide retains the possibil-ity of being elastic to change the period and the distance,which means that one piece of sample corresponds to onespectra. In order to improve the flexibility of the experi-ment, the substrate will have to meet the requirement men-tioned above, and have the controllable flexibility. Piezo- a r X i v : . [ phy s i c s . a pp - ph ] D ec (a) (b)(c) (d) FIG. 1. (Color online) (a) Substrate etching diagram, and theconnection is omitted in simulation; (b) Demonstration of sim-ulation model – ADB structure on surface of silicon dioxide orplastic; (c) Absorption spectra of same ADB structure on differ- ent substrate, silicon dioxide, PET and PEEK (d) Silicon dioxideabsorption spectra of alternately flipped+substrate etched, nonflipped+etched, and flipped+unetched, respectively. electric material and thermal expansion material share theflexibility but the degree of relative deformation of the for-mer is too small and the direction of expansion of the lat-ter can hardly be controlled. Thus, we try to achieve thisgoal by mechanically manipulating suitable elastic plas-tic. According to the description above, we think thatPolyethylene Terephthalate (PET) and Polyether Ether Ke-tone (PEEK) are both worth expecting candidates. How-ever, it might require more stringent conditions to EBL pro-cess, which will not be discussed any further in this paper.Here we present our simulation result based on the finiteelement method (FEM) by commercial software COM-SOL. As is shown in FIG.1 (c), we perform spectra analysisof the designed ADB structure on different substrates, in-cluding silicon dioxide, PET and PEEK. There are threeabsorption peaks for silicon dioxide. We observe the spa-tial magnetic field around ADB and find the interaction be-tween dark mode and bright mode similar with each other.Four peaks for PET and PEEK are observed, and it lookslike the two peaks on the right derive from the right oneof silicon dioxide spectra. Considering the difference onreflective index molecular structure, it’s not surprising tosee the difference. And it is possible to make use of thesetwo peaks for higher Q-factor. To clarify, we name theright peak on the silicon dioxide absorption spectra to be
R peak . What’s important is, we observe the similar reac-tion of two-peaks (from PET and PEEK) compared with
Rpeak in the stretching process, including the separation ofpeaks, which means the one-peak becomes two-peak, andthe two-peak becomes four-peak. We will come to this partsoon. Hereby, we will take more look into to the
R peak onsilicon dioxide spectra.As shown in FIG.1 (d), we also run simulation to prove (a) (b)(c)
FIG. 2. (Color online) (a) Simulation result of absorption spectrawith different
Ratio in y and (b) x axis on silicon dioxide; (c)wavelength and the Q-factor of
R peak relative to
Ratio , and thefitting result of peak to
Ratio using quadratic function. The fittingresidual norm of peak y is 1.0465, for peak x is 2.3805. the reasonability of alternately flipped configuration andsubstrate etching. Yellow line refers to alternately flippedconfiguration with substrate etching, and red line and blueline refer to alternately flipped configuration without sub-strate etching and non-flipped configuration with substrateetching, respectively. It is observed from the spectra thatflipping unit cells would create a sharper peak and sub-strate etching would eliminate red shift. Alternately flippedconfiguration with substrate etching, which combined bothadvantages, would have a sharper peak than non-flippedconfiguration with substrate etching and much weaker redshift compare with alternately flipped configuration with-out substrate etching.In order to characterize the stretch, we set two param-eters in the model. θ means angle between the stretchingdirection and x axis, and Ratio means the rate of increasein the specific direction. First of all we can see the spectramodification when θ = π/ or 0, that is y and x direction,as is shown in FIG.2 (a) and (b), which means in y and xaxis, respectively. Different lines represents different Ra-tio . And we can see the
R peak tends to be continuously red (a)(b)
FIG. 3. (Color online) (a) when θ is set to π/ , and scan Ratio ,then a small peak in the absorption spectra grows; (b) the cor-responding transmission spectra, and an EIT lineshape appearsbecause of the emergence of a metastable state. shifting, and FWHM increasing, as
Ratio grows. We canconsider the enlargement of space between the two bars islike that of an optical cavity. By pulling the two bars awayfrom each other, the resonance wavelength is to red shift.Here the effect of head-to-head structure is also weakened,thus the red shift isn’t suppressed.To describe the red shift and change in FWHM, we findpeaks shown in FIG.2 (a) and (b) and plot them with
Ra-tio , which is shown in FIG.2 (c). Y-axis on the left refersto
R peak wavelength, on the right is the Q-factor, and Q = λ peak ∆ λ , where ∆ λ is FWHM. Monotone increasingis observed. Then we use the quadratic function to fit thecurve of the peak to ratio, as is also shown in figure FIG.2.In order to explain that, we can regards ADB structure asan optical cavity, and the eigen-wavelength should be pro-portional to cavity length as a result. And we can see thatwhen Ratio is from 0 to 0.2, linear distribution is obvi-ous; yet other factors will introduce higher order terms, asthe quadratic function we use to fit indicates second-orderterm. These nonlinear terms come from various causes, forexample, the impact caused by flipped structure should de-crease in a quadratic way as
Ratio goes up, and if the dou- (a) (b) (a) (b)
FIG. 4. (Color online) (a) The spatial distribution of Hz when
Ra-tio =0, the corresponding wavelength is 1065 nm, Hz is in unit ofA/m, which is not shown in figure, and strong resonance appears;(b) The spatial distribution of Hz when
Ratio =0.1, θ = π/ , thedisruption of structure symmetry and Hz distribution symmetryis observed. ble bars get too close or too far-away, it will also introducenonlinear term. The second-order approximation can workfine when Ratio is smaller than 0.3, which is most likely tohappen in future applications.We also study on different angles, for example θ = π/ ,and interesting modification is discovered. If we set theparameter θ = π/ , and scan Ratio , an EIT lineshape ap-pears, as in FIG.3 (b). When
Ratio is small, a small peakin the absorption spectra, near
R peak , begins to grow with
Ratio . As
Ratio becomes big enough ( ≈ . ), the littlepeak becomes as big as R peak . And if we see FIG.3 (a),the transmission spectra, the characteristic lineshape of EITis shown. We may consider the small peak help gener-ate a metastable state near the fano resonance peak, andthe small peak comes from the disruption of symmetry be-tween two bars. ADB structure in our design have an axisof symmetry. And stretching in an angle like π/ breaksthis sysmmetry, and introduce a bias of the bright modein spatial distribution, which has influence on the couplingbetween the bright mode and the dark mode. According toFIG.4, the spatial distribution of Hz have changed. More-over, the peaks continues to red shift with the growing of Ratio , which is estimated before. If we set
Ratio constant,and scan θ , it will introduce more nonlinear effects, whichmakes the analysis less applicable. However, when Ratio is 0.1 and nonlinear effects are unnoticeable in this particu-lar region, it seems that the transmission has give out somehints for future investigation. And in other region, nonlin-ear effects are strong, which makes the scanning of θ lessuseful. But when θ is close to π/ or 0, the difference inspectra is ignorable, which means it’s not to sensitive todirection error in future application.In conclusion, plasmonic metamaterial is becomingmore and more important in scientific investigation for itspotential in improving quality factor of sensors and quan-tum dots and so on. Adjusting the plasmonic metamate-rial in ADB structure with one piece is tempting, whichmight bring great effect to this industry. We run simulationon silicon dioxide and set two important parameters, Ratio
FIG. 5. (Color online) The transmission spectra when
Ratio =0.1,and θ is scanned. This peace is trivial since the strong nonlineareffects would appear in other region. and θ , to represent the stretching on the substrate. When θ equals to π/ or 0, the R peak wavelength is the functionof