SPP-associated dual left-handed bands and field enhancement in metal-dielectric-metal metamaterial perforated by asymmetric cross hole arrays

SPP-associated dual left-handed bands and field enhancement in metal-dielectric-metal metamaterial perforated by asymmetric cross hole arrays P. Ding 1,2, E. J. Liang 1,*, W. Q. Hu 1, Q. Zhou 1, L. Zhang 1, Y. X. Yuan 1, and Q. Z. Xue 3 1 School of Physical Science & Engineering and Key Laboratory of Materials Physics of Ministry of Education of China, Zhengzhou University, Zhengzhou 450052, China 2 Department of Mathematics & Physics, Zhengzhou Institute of Aeronautical Industry Management, Zhengzhou 450015, China 3 Institute of electronics, Chinese Academy of Sciences, Beijing 100080, China * Corresponding author: ejliang@zzu.edu.cn Abstract: Dual-band left-handed transmissions in the near infrared frequencies through the metal-dielectric-metal metamaterial perforated with an array of asymmetric cross holes are demonstrated. It is shown that the left-handed bands originate from the SPP-associated magnetic response excited by different polarized light and their frequencies can be tuned by the arm s length or width of the cross-gaps. The structures are further optimized at 1.064 µm laser light excitation for elucidating the mechanism and possible application in surface enhanced Raman spectroscopy in sandwiched architectures. This study provides valuable information for the design of compact optical devices with dual left-handed bands in a single structure and may also pave the way toward stable and reproducible substrate design for surface enhanced Raman spectroscopy. 2009 Optical Society of America OCIS codes: (160.3918) Materials : Metamaterials; (240.6680) Surface Plasmons; (240.6695) Surface-enhanced Raman scattering References and links 1. T. W. Ebbesen, H. J. Lezec, H. Ghaemi, T. Thio, and P. A. Wolf, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998). 2. A. G. Brolo, E. Arctander, R. Gordon, B. Leathem, and K. L. Kavanagh, "Nanohole-enhanced Raman scattering," Nano Lett. 4, 2015-2018 (2004). 3. H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, "Beaming light from a subwavelength aperture," Science 297, 820-822 (2002). 4. C. Genet and T. W. Ebbesen, "Light in tiny holes," Nature 445, 39-46 (2007). 5. V. M. Shalaev, "Optical negative-index metamaterials," Nature Photonics 1, 41-48 (2006) 6. C. M. Soukoulis, J. Zhou, T. Koschny, M. Kafesaki, and E.N. Economou, "The science of negative index materials," J. Phys.: Condens. Matter 20, 304217/1-7 (2008). 7. A. Mary, Sergio G. Rodrigo, F. J. Garcia-Vidal, and L. Martin-Moreno, "Theory of negative-refractiveindex response of double-fishnet structures," Phys. Rev. Lett. 101, 103902/1-4 (2008). 8. T. Li, H. Liu, F. M. Wang, J. Q. Li, Y. Y. Zhu, and S. N. Zhu, "Surface-plasmon-induced optical magnetic response in perforated trilayer metamaterial," Phys. Rev. E 76, 016606/1-5 (2007). 9. U. K. Chettiar, A. V. Kildishev, H. Yuan, W. Cai, S. Xiao, V. P. Drachev, and V. M. Shalaev, "Dual-band negative index metamaterial: double negative at 813 nm and single negative at 772 nm," Opt. Lett. 32, 1671-1673 (2007). 10. D. Kwon, D. H. Werner, A. V. Kildishev, and V. M. Shalaev, "Near-infrared metamaterials with dual-band negative-index characteristics," Opt. Express 15, 1647-1652 (2007). 11. Y. Wang, H. Chen, S. Dong, and E. Wang, "Surface enhanced Raman scattering of p-aminothiophenol selfassembled monolayers in sandwich structure fabricated on glass," J. Chem. Phys. 124, 074709/1-8 (2006). (C) 2009 OSA 16 February 2009 / Vol. 17, No. 4 / OPTICS EXPRESS 2198

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polarization of the incident light. Besides, the possibility of the same structure for special applications of SERS at 1.06 µm laser wavelength excitation is explored. It is found that the electric fields associated with the plasmon modes can be localized and enhanced not only in the holes areas, but also in the partial region between two metal layers. This design has a strong benefit for a compact and broadband optical device and may hold for potential application in surface-enhanced spectroscopy and sensing. 2. Structures and simulation method Figures 1(a)-1(c) show the Ag/MgF 2 /Ag sandwich structure with an array of orthogonally crossed symmetric rectangular holes. The geometrical parameters are defined as shown in Figs. 1(b) and 1(c). The thicknesses of sliver and MgF 2 layers are fixed at t=40 nm and s=60 nm in our simulating. The periodicity in the x-y plane is P=600 nm and light propagates along the z direction. An array of asymmetric cross holes is obtained by varying one of the arms length (configuration A) or width (configuration B) as shown in the inset of Figs. 3(a) and 3(b). Fig. 1. (a) Scheme of symmetric cross hole arrays with two unit cells denoted; (b) Top view and (c) side view of the unit cell of type-i. The simulations were performed using full-wave finite element solver (Ansoft HFSS). A theoretical model at normal-to-plane incidence is developed based on an artificial waveguide with two ideal magnetic conductor and two ideal electric conductor planes as the transverse boundaries, which is equivalent to an infinite layer medium illuminated by a normal incident plane wave [14]. In such a way, the transmission problem of an infinite lateral structure with periodic holes in an open space is reduced to a waveguide with the transversal unit cell inside [15]. The transmission and reflection properties are obtained by evaluating the waveguide s S parameters. The effective electromagnetic parameters are retrieved following the method in [16, 17]. The property of the metal is treated as a dispersive medium following the Drude dispersion model with the plasma frequency ω pl =1.37 10 16 s -1 and the scattering frequency γ=8.5 10 13 s -1 for sliver [18]. The refractive index of MgF 2 is taken as 1.38 [18]. In our numerical investigations, the structure is embedded in an effective homogeneous medium with a refractive index of n=1.05 because good agreement between experimental and theoretical results can be achieved with n=1.05 and using a vacuum in simulating would slightly blue shift all resonance frequencies with respect to the experimental values for regular fishnet metamaterials in infrared frequencies [18]. The normal-incidence complex field transmittance and reflectance are computed straightforward for a slab of metamaterial of thickness d (here d=t+2s). 3. Results and discussion 3.1 Polarization-controlled dual left-handed propagation Due to the identical transmission behavior at normal incidence with the polarization along x- axis (X-polarization) and y-axis (Y-polarization), the array of symmetric cross holes is actually a planar polarization-independent metamaterial [19]. The figure of merit (FOM) defined as the ratio of -n 1 /n 2 is often taken as a measure of the quality of the negative refraction, where n 1 and n 2 are the real and imaginary parts of index, respectively. A higher FOM indicates a lower loss in transmission. As shown in Fig. 2, a broad double-negative (C) 2009 OSA 16 February 2009 / Vol. 17, No. 4 / OPTICS EXPRESS 2200

passband (highlighted shadow area) with a maximum FOM of 3.4 at a wavelength of 1.51 µm can be achieved for the symmetric cross hole arrays with geometrical parameters of L 1 =L 2 =480 nm and W 1 =W 2 =100 nm. Fig. 2. FOM and index versus incident wavelength for the symmetric cross hole arrays (L 1=L 2=480 nm and W 1=W 2=100 nm). The double-negative (or left-handed) passband is highlighted by yellow shadow with the maximum FOM marked out by vertical dashed line. Fig. 3. (a) Left-handed passband as a function of the geometry parameter L 2 for configuration A (W 1=W 2=100 nm, L 1=480 nm and L 2< L 1); (b) Left-handed passband as a function of W 2 for configuration B (L 1=L 2=480 nm, W 1=100 nm and W 2>W 1). Here, black and red spots correspond to the wavelength at which maximum FOM obtained with respect to various L 2 or W 2 for both polarizations, and the error bars are used to show the wavelength range of lefthanded band. The insets display the value of maximum FOM versus the geometry parameter L 2 and W 2. (C) 2009 OSA 16 February 2009 / Vol. 17, No. 4 / OPTICS EXPRESS 2201

When the plane wave propagates through asymmetric cross hole arrays, different transmission performances are expected for X- or Y-polarization due to the different response originated from the asymmetric geometry. In order to see the effect of the asymmetry on the LH performance, we calculated the variation of the two LH band positions as well as the corresponding FOMs for configuration A and B with altering one of the arm s length (L 2 ) or width (W 2 ) in the crosses, respectively. With increasing the asymmetry of the crosses, the LH band splits into higher and lower frequency branches for both configurations and both branches are shown to have LH behavior. Figure 3(a) shows that the peak frequency of the LH passband excited by Y-polarized light shifts markedly and continuously to blue which is inversely proportional to the arm length, while that excited by X-polarized light remains almost unchanged with decreasing one of the arm s length (L 2 ). It should be mentioned that there is an overlapping region of the two LH bands for smaller asymmetry (L 2 400 nm) and they are completely separated for lager asymmetry (L 2 <400 nm). The FOMs for X-polarized and Y-polarized light are respectively 3.5 at the wavelength of 1.5 µm and 3.3 at 1.4 µm for L 2 =400 nm and L 1 =480 nm. However, when one of the arms width W 2 increases gradually from 100 nm to 250 nm with fixed arms length (L 1 =L 2 =480 nm) and another arm s width (W 1 =100 nm), both LH passbands shift obviously to blue but with different slopes, leading to a smaller separation of them, as shown in Fig. 3(b). A comparison of Figs. 3(a) and 3(b) shows that altering one of the arms lengths is more effective than changing the width in separating the two double negative bands. Fig. 4. (a)-(b) Magnitude distributions of the electric fields for configuration A (L 2=400 nm) on the middle plane between two electrically conducting plates for both polarizations; (c) Comparison of the effective refractive indexes obtained from the retrieval procedures with increasing number of stacked layers along the propagation direction (lines) with those obtained from the wedge-shaped model (scatters) for configuration A at X-polarized light incidence. The normalized scale bar is the same for both field maps. The coexistence of dual LH bands is further verified by Snell s law using a twodimensional wedge with an inclined angle of 13.1 as shown in Fig. 4. The wedge-shaped model constructed by stacking a staircase pattern of one-unit cell step along the z-axis and 8 unit cells along the x-axis (or y-axis) is positioned between two conducting plates with the absorber boundary conditions at the side faces. Figures 4(a) and 4(b) show the typical electric field patterns of negative refraction for configuration A (L 2 =400 nm) with X- and Y-polarized light, respectively. Compared to the resonance frequency of the retrieved effective index, a slight blue-shift of the LH band frequency (~0.04 µm) is observed through the wedge-shaped (C) 2009 OSA 16 February 2009 / Vol. 17, No. 4 / OPTICS EXPRESS 2202

model. In order to see the origin of the blue shift, we calculated the effective refractive indexes with increasing number of stacking layers along the propagation direction from the retrieval procedures (lines in Fig. 4(c)) and those with the wedge-shaped model at tree different frequencies (scatters in Fig. 4(c)) for configuration A at X-polarized light incidence. It is shown that similar values of effective refractive indexes are obtained at the same frequencies by both methods and the resonance frequency shifts to blue with increasing the number of stacking layers. This suggests that the shift is caused by the coupling effect of stacking multiple fishnet functional layers [15], namely by the interaction of unit cells along the EM wave propagation direction. In order to get insight into the dependence of the negative-index passbands on both the geometry and the polarization, the surface charge oscillations (surface plasmons) excited by different polarized light are investigated. For more intuitive display, the distributions of induced surface current are employed to schematically represent the charge oscillations which are shown in Fig. 5. Figure 5 displays the current distributions for the top and bottom metal layer surface adjacent to the dielectric spacer just above the magnetic resonant frequency for Y-polarized light excitation, respectively. The charge distributions in the asymmetric cross aperture arrays have identical character with that in rectangular-hole fishnet metamaterial [20]. It can be seen that the induced surface currents flow oppositely in the square and the neck regions in either surface and also reversely in the two surfaces. Similar charge oscillations in x-direction are obtained for X-polarized light excitation. This means that both LH bands result from the out-of-phase charge oscillating in the neighboring metal layers and therefore they are assigned to anti-symmetric modes. The currents are formed by the out-of phase charge oscillating driven by the incident electric fields and the magnetic resonances responsible for the negative permeability are caused by the anti-parallel currents in the top and bottom layers [21]. Fig. 5. Surface currents distributions for configuration A (L 2=400 nm) at the frequency just above the magnetic resonance. Here, 1st and 2nd are the top and bottom metal-layer surfaces adjacent the MgF 2 spacer. The incident light is Y-polarized. The dependence of both LH bands on the asymmetry (Fig. 3) can be understood by the magnetic response of the charge oscillating to the geometric size changes of the length or the width of the arms which affect the inductance (L) as well as the capacitance (C) of the sandwich structure. The magnetic resonant frequency may be written as [20] 2 1 1 1 1 ω m = = ( + ), (1) LC C Ls Ln where L s and L n are respectively the inductances of the slabs and the necks. According to the definition of these quantities for regular fishnet metamaterials in [20], we rewrite the expression of capacitance and inductance for our proposed structure based on the geometrical parameters defined in Fig. 1, i.e. (C) 2009 OSA 16 February 2009 / Vol. 17, No. 4 / OPTICS EXPRESS 2203

and ( 1)( 2 ) C ~ P W P W, t (2) ( P W1(2) ) t Ls ~, P W (3) W1(2) t Ln ~ P L 1(2) for X-polarized (Y-polarized) light excitation. For configuration A (i.e.w 1 =W 2 and L 1 >L 2 ) with X-polarized light excitation, the reduction of L 2 has little influence on the slabs capacitance and inductances and consequently the resonant frequency remains nearly unchanged, whereas when Y-polarized light is applied, considerable reduction in the necks inductance and consequently evident increase in the resonant frequency occurs. For configuration B (i.e. L 1 =L 2 and W 1 <W 2 ), the increasing of W 2 leads to an obvious reduction of the slabs capacitance, and hence an increasing in magnetic resonant frequency with either X- or Y-polarized light excitation. However, the increase in W 2 has different effect on the inductances of L s and L n with X- and Y-polarized light excitations. With X-polarized light, L s increases with W 2 while L n does not; whereas with Y-polarized light, L n increases much rapider than L s decreases with increasing W 2. As a result, increasing the width W 2 causes the magnetic resonant frequencies shift to blue for both X- and Y-polarized light but with different slopes. This also explains why the configuration A is more effective than configuration B in separating the two polarization dependent LH bands. Equations (2)-(3) describe the dependence of the capacitance and inductance on the scaling of the cross arms. The effective impedance of the metal film depends also on the scaling of the cross arms. The impedance (Z) with the scaling of the cross arms is obtained from the retrieval procedure (not shown here) and 1 Z 1 follows a similar trends as those of the FOMs (see the insets of Figs. 3(a) and 3(b)). This can be understood by the fact that a higher FOM implies a better impedance match ( Z= µ ε 1 ) to free space. 3.2 SPP-associated magnetic modes for localized field enhancement The dual LH band nature of the asymmetric cross hole arrays may find applications where jump frequency or double frequencies are needed. However, for spectroscopic applications such as SERS, electromagnetic resonances in double frequency ranges are preferred, one for excitation and another for scattered light. For the enhancement of the scattered Raman light, same polarization is not required due to the depolarization effect of the molecules. The field felt by the molecules is important and maximum enhancement occurs when both the incident laser light and the scattered Raman signals are near resonances with the plasmon energies. For this purpose, we optimized the array of asymmetric cross holes so that the predicted higher frequency magnetic mode is located at around 1064 nm, available Nd:YAG laser wavelength used for SERS [22]. In Fig. 6, we present the calculated transmission spectra of the optimized structure for both polarizations with geometrical parameters of P=440 nm, t=30 nm, s=40 nm, W 1 =W 2 =90 nm, L 1 =360 nm and L 2 =220 nm. The two major transmission peaks located at around 0.74 µm and 1.12 µm (E1 mode) for X- and Y-polarization corresponding to the SPP modes associated with EOT [23] with a normal positive refractive index. The two transmission dips (indicated as M1) at longer wavelength regions are the LH bands originated from the above mentioned magnetic resonances. For comparison, the transmission spectrum of a sliver monolayer (the thickness of 60 nm) with the identical asymmetric cross aperture arrays is also provided in Fig. 6. Obviously, only the SPP mode corresponding to EOT appears for monolayer structure. The excitation of SPP-associated magnetic modes (M1) are ascribed to the plasmon hybridization or coupling between the two metal layers [24, 25]. 2(1) (4) (C) 2009 OSA 16 February 2009 / Vol. 17, No. 4 / OPTICS EXPRESS 2204

Fig. 6. Calculated transmission spectra of the Ag/MgF 2/Ag sandwich structure with an array of asymmetric cross aperture for both polarizations (the black or red line with solid scatters), in which the fundamental modes M1 and E1 are marked. The geometrical parameters defined here are: P=440 nm, t=30 nm, s=40 nm, W 1=W 2=90 nm, L 1=360 nm and L 2=220 nm. The transmission spectra of a single sliver layer (the thickness of 60 nm) with the identical asymmetric cross apertures are also provided for comparisons (gray scatters). Fig. 7. Both the calculated E-field distribution map in x-y plane (z=0) and the corresponding E- field enhancement of the asymmetric cross hole arrays for E1 and M1 modes (indicated in Fig. 6). (a)-(c) X-polarization; (d)-(f)y-polarization. In (b)-(c) and (e)-(f), E is the actual polarization dependent local electric field and E 0 is the incident field. The first scale bar is given for (a) and (d), and the second scale bar is for (b)-(c) and (e)-(f). (C) 2009 OSA 16 February 2009 / Vol. 17, No. 4 / OPTICS EXPRESS 2205

Figures 7(a) and 7(d) show the electric field ( E ) distributions in the x-y plane (z=0) lying in the center of the MgF 2 spacer for both E1 and M1 modes for X- and Y-polarization, respectively. The effect of polarization of the exciting radiation on the distribution of the localized electric field is clearly demonstrated. As shown by the E maps in the x-y plane, the maximum electric fields are localized at the corners of the square plate region when excited with either of the SPP-associated magnetic response modes (M1), whereas those are confined within the holes when excited with either of the E1 modes for both X- and Y-polarized light excitations. The electromagnetic field enhancement factor defined as E E, where E and E 0 0 are respectively the local field felt by the spacer or molecules residing in the spacer and the incident field, is calculated and shown in Figs. 7(b)-7(c) and 7(e)-7(f) for X- and Y- polarization, respectively. Largest enhancements are found for excitations with the two SPPassociated magnetic modes (M1) which are approximately 12 for X-polarization and 9 for Y- polarization. Given that the Raman enhancement factor is approximately proportional to the fourth power of the electromagnetic field enhancement [26], we expect a Raman enhancement factor of ~10 4 in these electromagnetic field hotspots. In the field of SERS, there are still many problems remain unclear or unsolved. One of the unsolved problems is the stability and reproducibility resulted from the same problem encountered by substrates [27]. Another is that large enhancements are generally not observed with excitations at the plasmon resonance wavelength of the nano-particles and the reason has not been clarified. Our result that larger enhancement occur in the spacer area around the SPPassociated magnetic resonance frequencies may provide valuable information for clarifying some puzzles in SERS, as well as explain the enhancement mechanism of SERS in metalmolecule-metal sandwich architectures by the self-assembly of Ag (Au) nanoparticles (NPs)- analytes-ag NPs or Au NPs-analytes-smooth Au substrate [11-13]. Besides, since the sandwich structure with the array of orthogonally crossed asymmetric rectangular holes are designed based on metamaterial concept, they are stable and reproducible architectures and hence hold promising for SERS applications. 4. Conclusions The metal-dielectric-metal sandwich structures with an array of asymmetric cross holes penetrating through the multiple layers are designed as the dual-band left-handed metamaterial in infrared regime. By investigating the dependence of the left-handed passbands on the asymmetric cross configuration for both orthonormal polarizations, it is found that either a broad or dual separated NIR bands with negative-index transmission can be realized in a single structure, which can be well explained by the effective LC circuit description of the fishnet metamaterials. The polarization-dependent dual-band LH transmissions are verified by both the retrieved effective media parameters and the wedge-shaped mode. Furthermore, we have analyzed the SPP-associated magnetic resonant modes in the proposed structures and explored the corresponding electric field distributions. It is found that the maximum field enhancement factor of 12 is achieved within the dielectric layer between two metal plates when the magnetic modes are excited, and consequently an enhancement factor of ~10 4 for SERS is expected. The design may provide significant step toward compact optical device with dual polarization-dependent LH bands in a single structure and the sandwich architecture may also have potential for applications in surface-enhanced spectroscopy and sensing. Acknowledgments This work was supported by the Aeronautical Science Foundation of China (No. 2008ZF55006) and the Natural Science Foundation of the Education Department of Henan Province of China (No. 2008A140012). (C) 2009 OSA 16 February 2009 / Vol. 17, No. 4 / OPTICS EXPRESS 2206