Arbitrary Super Surface Modes Bounded by Multilayered Metametal

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1 Micromachines, 3, 45-54; oi:.339/mi345 Article OPEN ACCESS micromachines ISSN 7-666X Arbitrary Super Surface Moes Boune by Multilayere Metametal Ruoxi Yang, Xiaoyue Huang an Zhaolin Lu, * Microsystems Engineering, Kate Gleason College of Engineering, Rochester Institute of Technology, Rochester, NY 463, USA; rxy4@rit.eu Department of Physics, Michigan Technological University, Houghton, MI 4993, USA; xiahuang@mtu.eu * Author to whom corresponence shoul be aresse; zhaolin.lu@rit.eu; Tel.: ; Fax: Receive: 3 December ; in revise form: 5 January / Accepte: 7 January / Publishe: February Abstract: The ispersion of the funamental super moe confine along the bounary between a multilayer metal-insulator (MMI stack an a ielectric coating is theoretically analyze an compare to the ispersion of surface waves on a single metal-insulator (MI bounary. Base on the classical Kretschmann setup, the MMI system is experimentally teste as an anisotropic material to exhibit plasmonic behavior an a caniate of metametal to engineer the preset surface plasmon frequency of conventional metals for optical sensing applications. The conitions to obtain artificial surface plasmon frequency are thoroughly stuie, an the tuning of surface plasmon frequency is verifie by electromagnetic moeling an experiments. The esign rules rawn in this paper woul bring important insights into applications such as optical lithography, nano-sensing an imaging. Keywors: surface waves; metal-insulator multilayer; effective surface plasmon frequency. Introuction The multilayer metal-insulator (MMI stack system (also terme as metal-ielectric composite or MDC has been wiely use as an optically-anisotropic composite [ 3], utilize for imaging [4 8], optical lithography [9] an subwavelength sensing/etecting []. One of the most attractive features of this stratifie meium is its ability to engineer the ispersion of engage electromagnetic waves, an

2 Micromachines, 3 46 to tune the frequency range where interesting optical phenomena coul occur. As a funamental form of D perioic structure, the optical property of MMI stack has been extensively stuie [4 9] an both rigorous formalism an approximation approach have been evelope. Base on a rigorous transfer-matrix metho (TMM [], the transmittance an reflectance of any incient beams at any layer can be accurately obtaine. The effective meium theory (EMT [3,4], on the contrary, has been applie to approximate the macroscopic behavior of the MMI system as a uniform anisotropic material, an offers more control than TMM towars a eman-oriente esign proceure, while important corrections relate to non-local effect [7,8] has been mae. As a promising approach towars eep subwavelength optics, plasmonics have attracte great research interests for optical sensing an imaging in recent years. However, plasmonic materials are generally scarce in variety plus the working frequency is limite because of the preset plasma frequency of each plasmonic metal. This problem is worse off in optical frequency, as almost no substitutions (mostly ope semiconuctor compouns can be chosen to replace the overwhelmingly use metals such as aluminum (for DUV, silver an gol (for visible an NIR ue to high loss. It woul therefore be significant for optical sensing or imaging applications to explore stratifie meium as a plasmonic material or metametal an unerstan how its plasmonic features coul be controlle, so as to broaen the frequency winow for imaging or sensing applications [,]. As one of the most important prototype for plasmonic sensing, Kretschmann configuration can accurately pick off the surface wave s resonant point at metal-ielectric half-plane by exciting the funamental TM surface moe on the bounary [,6]. In this paper, we investigate this surface moe thoroughly an manage to highlight the backgroun (host material as an important factor, which is rarely notice in prior art. Specifically, we outline explicit esign rules for shifting surface plasmon frequency to not only lower [], but also higher, for optical sensing. We have then experimentally verifie the tuning of surface plasmon frequency in optical frequency base on Kretschmann setup. The conclusions woul bring important insights into plasmonic applications from optical lithography to nano-sensing an imaging.. Theoretical Analysis an its Comparison with Finite-Difference Time-Domain (FDTD Moeling Starting from the anisotropy of MMI structure, the effective permittivity tensor is obtaine as [4] ε+ ηε η εx = εz =, = ( +, + η ε + η ε ε ( y where η is the filling ratio of the layer thickness efine by η = /, an the axes are setup in Figure (a. In the following erivation, we treat ε as the insulator an ε as the metal. Regare as a single anisotropic meium, it can be place next to the semi-space of a ielectric material (ε an form a bounary as host of surface waves. Assuming a funamental TM-polarize surface wave (super moe propagating along this bounary an applying proper bounary conitions, the MMI-insulator bounary supports a propagation surface moe with the ispersion relation obtaine as ω ε ε ε ε ηε ε ε ηε β = = c ( / / (. ( x y ω ( + ( + ε εxεy c ε ε+ η ε ε+ ηε ( To ensure this wave is confine to the bounary, an aitional conition is applie as ε x <, or

3 Micromachines, 3 47 η ε >. ε (3 When η approaches infinite as the MMI graually becomes a uniform metal layer, Equation ( can be simplifie to ω εε β =, c ε + ε (4 which is exactly the well-known ispersion relation for a metal-insulator (MI bounary. When ω approaches zero, the ispersion curve overlaps with ω β = ε, c (5 which is the lightline of the ielectric coating. Figure. (a The multilayer metal-insulator (MMI scheme an efinitions of parameters; (b The q vs. p curve use to analyze ifferent conitions for tuning effective surface plasmon frequency with a semi-space ielectrics ε. z y x q (-ε - /ε η =. η =.3 η =.5 η =.7 η =.9 η =. η =. η = 3. η = 4. η = 5. ε > ε < η = p (ε /ε (a (b The similarity of the ispersion between MMI-insulator an MI-insulator structure reveale in Equations (4 an (5 gives a possibility to evelop a concept of effective surface plasmon frequency (ESPF, especially when MMI is place insie (or neighbore to a ielectric semi-space to act just like a uniform metal (metametal. Firstly, we try to erive the value of the ESPF of MMI structure. Similar to the case of MI-insulator, the surface plasmon resonance (SPR happens at the pole of the β-ω relation escribe in Equation (. The poles of Equation ( can be analytically obtaine after solving a quaratic equation of ε. The solution can be expresse by ε, ε an the filling ratio η, as ε ε ± ( ε ε + 4η εε ε =, (6 ηε while the positive root shoul be iscare base on the preconitions ε x < applie in the relate section of Equation (3. Base on Equation (, at least one of the two materials in the multilayere

4 Micromachines, 3 48 meium nees to have negative permittivity to make ε x <. The negative root from Equation 6 gives the largest ielectric constant the metametal coul reach at ε ε ( ε ε + 4η εε ε ( =. (7 ηε To stuy the plasmonic property of the metametal, it is convenient to start from the Drue moel of the filling metal /, when ω p is the plasmonic frequency of the filling metal. Here a characteristic frequency for the metametal can be efine as equal to ESPF (, which yiels /. This is analogy to the efinition of surface plasmon frequency efine by /, in while ε escribes the ielectric half space. It woul be interesting to stuy the relation between / an then, as for the latter, there are many parameters that can be controlle even if the same metal is use in the system. Base on the efinition above, the relation between an can be easily appreciate by the ratio of ε ( an ε. For simplicity, we introuce a new term p = ε /ε, an another term q for the ratio of ε ( an ε. From Equation (7, the factor q can be expresse by p an η as 4 ( p p η p p ε q =. ε ηp (8 Figure (b shows how q varies with ifferent η an p. Again, the factor q is a irect inication of the relation between an since ε ( ωp / ωsp q ε ω / ω ' p sp. (9 The observation inicates that the ratio q oes change with both p an η as expecte. More importantly, q can change from less than unity to larger than unity. From Equation (9, it is clear that can also be shifte higher or lower than with ifferent values of p an η. The limitation shown in Equation (3 as another upper cut-off frequency an this value can be smaller than ESPF when η is smaller than, which shoul also be taken into account while exploiting the tunability of MMI system. When p is larger than (which means the insulator use in MMI has higher inex than the backgroun material, q is usually larger than. From Equation (9, the ESPF will usually be smaller than the conventional surface plasma frequency for all possible filling ratio η. This can usually be unerstoo as a result of smaller electron ensity because of the existence of ielectric filling. Note that when p =, the ESPF remains the same to conventional surface plasma frequency regarless of the filling ratio η. On the other han, the ESPF can be shifte higher an even close to when η is small an p <, which means the tuning of surface plasma frequency can theoretically overcome the upper cut-off frequency for any funamental TM moe supporte on a single MI bounary. This case (p < highlights an especially interesting property of MMI stack, as the iluting of electron ensity by mixing metals with ielectrics oes not sufficiently lea to a ecrease surface plasmon frequency. When a low-inex filling material has applie its relaxation on the electron oscillation of a pure metal to form a MMI stack, a high-inex coating (or substrate ε will not be able to ecrease the free electron oscillation own to /, as the uner-relaxe MMI has

5 Micromachines, 3 49 somehow average or compensate for the relaxation taking place along the substrate bounary. This observation introuces new perspectives into spoof plasmonics, as an essential supplement to the conventional concept such as effective free electron ensity. To verify the existence of this super resonance moe an better explain the tuning of effective surface plasmon frequency (ESPF, we introuce a specific case for an ientical substrate material uner uniform gol an two types of MMIs. In Figure, both MMI structures (an the uniform gol as reference use the same substrate with ε =.5 (which can be regare as a polymer-base photoresist. We then apply gol-sio (ε =. for SiO at 633 nm an gol-al O 3 (ε = 3.5 for Al O 3 at 633 nm multilayer stacks respectively to this substrate. It is obvious that the filling insulators have been chosen to make sure the ratio p = ε insulator /ε can be less than unity for one case, an larger than unity for the other. Using the Equation ( an the moe matching conition, we preicte the shifts of ESPF an SPR angle towars ifferent irections (prism n p =.6. In Figure (a, the ESPF (upper cut-off for the TM ban is below an above the preset surface plasmon frequency for gol-sio an gol-al O 3 case respectively. Figure. (a The analytical ispersion curves calculate by effective meium theory. The upper cut-off frequencies are treate as the effective surface plasmon frequencies (ESPFs for two MMI cases. Near 633 nm, the shift of wave vectors are shown in the inset for uniform gol (blue, gol-al O 3 MMI (green an gol-sio MMI (re; (b FDTD simulation for the shift of surface plasmon resonance (SPR angles base on uniform gol (blue, gol-al O 3 MMI (green an gol-sio MMI (re. All three curves are on top of the same ε =.5 substrate. The small arrows mark the calculate angles base on moe matching. Normalize Frequency ( ω p Au on ε =.5 Au-Alumina on ε =.5 Au-Silica on ε = Reflection Au on ε =.5 Au-Silica on ε =.5 Au-Alumina on ε = Normalize k x ( ω p /c (a Incient Angle (egree (b The FDTD moeling of these 3 structures uner a Kretschmann setup is shown in Figure (b. MMI stacks are efine as nm gol (ε =.84 + j.4 plus nm insulator for 5 cycles, an the shifts of SPR angle apparently go to opposite irections for ifferent p value, verifying the theoretical calculations above. The simulate angles match well with the analytical results marke by small arrows (Figure (b. The insets of Figure (a also imply that uner the light source of the same

6 Micromachines, 3 5 frequency, MMI stack can host a surface wave with a ifferent wave vector as well as the moe size, which can be useful for optical lithography [9]. Although in the theoretical analysis above we have limite the iscussion to real propagation constant, we fin that the general conclusion can still be applie even to visible spectrum when the ohmic loss from metal is moerate. 3. Numerical an Experimental Demonstration To verify the tuning of surface plasma frequency, we have moele a Kretschmann prism-coupling process (Figure 3 for 633-nm light engaging a uniform gol film an an MMI gol-alumina stack (both cases have 5-nm total thickness of metal using FDTD Solutions of Lumerical []. Previous effort [6] has successfully emonstrate the existence of complex moes supporte by MMI systems, while here we focus on the link between the tunability of surface waves an the p parameter. Here we try to launch incient beams from a ielectric prism (n p =.6 to excite the surface waves when the plasmons are neighbore to silicon ioxie (n =.45 or silicon nitrie (n =.. The ielectric constants of gol (ε =.84 + j.4 an alumina (n =.776 are fitte ata from [] an [] respectively. Accoring to momentum matching conition for SPR, the incient angle can be calculate theoretically as nprismk sin θsp( ω = ksp( ω. ( Figure 3. Experimental setup for stuying multilayer metal-insulator stacks an the cross-sectional view of the fabricate multilayer sample (SEM. Each iniviual layer is nm an there are layers (5 pairs in total. Multilayer Prism Multilayer PECVD Substrate PECVD Substrate Silicon Wafer nm Note that for Kretschmann setup an the calculation from Equation (, the moe of greatest interest here is the confine funamental TM moe. Although MMI coul support more complex moes [,6 8], the analysis in last section is sufficient to preict the sharpest resonance point of boune SPP waves uner this conition. As the original surface plasmon frequencies are shifte lower (silicon ioxie substrate, Figure 4(a an higher (silicon nitrie substrate, Figure 4(b, the k-vectors are shifte larger an smaller accoringly. The variation of the incient angle for minimum reflection can then be use to observe the tuning of surface plasmon frequency. Base on Equation, we have theoretically calculate the resonant angle shift from 38 to 4 for silicon oxie substrate, an from 73 to 64 for silicon nitrie substrate. The Figure 4(a,b show the FDTD simulate reflection (left axis versus incient angle, in which the tuning from uniform metal (soli re to MMI (ashe blue is clearly visible. Here the gol single layer has a total thickness of 5 nm, an the gol-alumina stack

7 Micromachines, 3 5 consists of 5 cycles of -nm gol plus -nm alumina for a total gol thickness of 5 nm. The multilayer region is meshe by nm gri. The excitation angles shift from 38 to 4 for tuning own (silicon ioxie substrate, Figure 4(a, an 7 to 6 for tuning up (silicon nitrie substrate, Figure 4(b, which match well with the theoretical preictions performe above. Measure reflecte power from a Kretschmann setup with a ZnSe (n =.6 hemispherical prism are collecte by an optical power meter from multiple samples illuminate by a collimate TM-polarize He-Ne laser beam (Figure 3, left. The SiO an Si 3 N 4 substrates are eposite via plasma-enhance chemical vapor eposition (PECVD, while the gol single-layer an gol-alumina multilayer are eposite via e-beam evaporation (Figure 3, right. The thickness of eposition is kept ientical to the simulations performe above. The re crosses an the blue triangles in Figure 4 (right axis enote the results of gol single layer an gol-alumina multilayer respectively. The observe SPR angles shift from 39 to 4 for silicon ioxie substrate, an 68 to 65 for silicon nitrie substrate. The shift irection of SPR agrees with the major conclusion regaring the refractive inex relation between the substrate an the filling ielectric film. The iscrepancy between the exact observe SPR angle an the calculation might be cause by fabrication isorer an the variation of ielectric constants compare to fitte ata, but the isagreement of the effective inexes of super moes between the measure an calculate values are all below.5% level. Figure 4. Numerical an experimental results of reflection vs. effective inex for (a increase ESPF with SiO substrate an (b ecrease ESPF with Si 3 N 4 substrate. Re an blue lines escribe the simulation results for single-layer an multilayer respectively. Re crosses an blue triangles enote the measure results. (a (b

8 Micromachines, 3 5 The results shown in Figure 4 not only verify the analytical basis of last section for optical sensing base on SPR, but also suggest possibilities of using MMI stack to achieve manageable moe size an wier frequency range for plasmonics applications. Specifically, as the surface plasma frequency is tune own, the ispersion curve flattens faster in MMI case an therefore at the same frequency of incient light, the propagation constant is increase an smaller wavelength of surface waves can be create which is impossible using uniform metal. On the other han, by tuning up the ESPF it is possible to broaen the frequency range of surface waves. As an example, in Figure 4(a,b, we use the esign rules mentione above to illustrate how the increase ESPF allows super surface moes at frequency beyon the conventional surface plasmon frequency. In this moeling we use normalize frequency an length unit. We set the backgroun material as ε =.5, an the MMI system consists of pairs of thin layers (ε =.5 an ε =.8 for a filling ratio η = 3. If a Drue metal is use here, the working frequency will locate at approximate.6, larger than the conventional cutoff of /.53. For uniform metal at this frequency, there will be no surface waves supporte at the bounary (Figure 5(a. With the tuning of ESPF from MMI, however, the working frequency can now excee.58. Here we use COMSOL [] to simulate the propagation of the super surface moe (Figure 5(b, showing the subwavelength confinement of the engineere super surface moe boune an propagate along. Note that in this simulation, the thickness of each repeate unit is.4 λ ( =.3 λ, η = / = 3, an the EMT theory coul well approximate the behavior of the super surface moe. The mesh-size is small enough to resolve the finest layer. Figure 5. H fiel istribution for: (a No propagation of boune surface moes above surface plasmon frequency; (b Boune surface wave with subwavelength moe profile beyon the conventional cutoff frequency efine in (a; (c Boune surface wave propagate on a single metal-insulator interface; ( Boune surface wave on a MMI-insulator bounary with shorter wavelength an manageable moe size compare to (c... ε =.5.. ε = Y ( λ Y ( λ -. ε = X ( λ.. -. ε = -.8 (a ε =.5 ε =.5, η = 3 =.3 λ X ( λ - - Y ( λ Y ( λ -. ε = X ( λ.. -. (c ε = ε = -.6 ε = 3., η = 3 =.5 λ X ( λ - - (b (

9 Micromachines, 3 53 Figure 5(c, gives another pair of illustration for moe size engineering with multilayer stack. Here the backgroun material is ε =., an the MMI system consists of 35 pairs of thin layers (ε = 3. an ε =.6 for a filling ratio η = 3. Accoring to the esign rule, a low-inex coating will ecrease the ESPF as well as the wavelength of the super surface wave. The metal-insulator bounary shown in Figure 5(c supports the funamental TM surface wave for a wavelength of.6 λ, as can also be calculate from Equation 4. When the uniform metal is replace by metametal, the ispersion curve will ben faster away from lightline (Figure (b. Therefore, a larger wave vector plus a ecrease wavelength (.6 λ is expecte. Accoring to the ispersion relation, this tren will also shrink the length of the exponential tail in the ielectric sie, as can be clearly seen comparing the H fiel istribution in the ε =. region of Figure 5(c,. We have also observe the variation of wavelength relative to the thickness of each repeate unit, as have been mentione in [5,7,8], which inicates the limit of EMT an a general preference of using thin layers to match EMT s preiction given by Equation (. 4. Summary We have theoretically an experimentally investigate the MMI stack as a plasmonic metametal an stuie its capability of supporting surface waves an engineering surface plasmon frequency. The analysis proposes a concept of effective surface plasma frequency that can be effectively controlle, an provies new insight into using MMI stacks to accomplish eep subwavelength imaging an artificial ispersion of electromagnetic waves. The outline esign rules woul empower researchers to excite confine surface waves more freely from a limite pool of plasmonic materials for optical lithography an subwavelength imaging, an to envision an emonstrate novel etecting/sensing scheme. Acknowlegments This material is base upon work supporte in part by the US Army uner Awar No. W9NF---53 an the National Science Founation uner Awar No. ECCS Acknowlegement is mae to the Donors of the American Chemical Society Petroleum Research Fun for partial support of this research. References. Smith, D.R.; Schurig, D. Electromagnetic wave propagation in meia with inefinite permittivity an permeability tensors. Phys. Rev. Lett. 3, 9, Shi, Z.; Pirea, G.; Liapis, A.C.; Nelson, M.A.; Novotny, L.; Boy, R.W. Surface-plasmon polaritons on metal-ielectric nanocomposite films. Opt. Lett. 9, 34, Beruete, M.; Navarro-Cía, M.; Sorolla, M. Strong lateral isplacement in polarization anisotropic extraorinary transmission metamaterial. New J. Phys.,, Nielsen, R.; Thoreson, M.; Chen, W.; Kristensen, A.; Hvam, J.; Shalaev, V.; Boltasseva, A. Towar superlensing with metal ielectric composites an multilayers. Appl. Phys. B: Lasers Opt.,, 93.

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