Extraordinary Optical Transmission Induced by Excitation of a Magnetic Plasmon Propagation Mode in a Diatomic Chain of Slit-hole Resonators

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1 Extraordinary Optical Transission Induced by Excitation of a Magnetic Plason Propagation Mode in a Diatoic Chain of Slit-hole Resonators H. Liu 1, *, T. Li 1, Q. J. Wang 1, Z. H. Zhu 1, S. M. Wang 1, J. Q. Li 1, S. N. Zhu 1, Y. Y. Zhu 1 and X. Zhang 1 Departent of Physics, National Laboratory of Solid State Microstructures, Nanjing University, Nanjing 193, People s Republic of China 513 Etcheverry Hall, Nanoscale Science and Engineering Center, University of California, Berkeley, California , USA Abstract In this paper, we will propose that agnetic resonance nanostructures in a etal surface could be used to realize extraordinary optical transission (EOT). Toward this goal, we designed and fabricated a one-diensional diatoic chain of slit-hole resonator (SHR). Due to the strong exchange current interaction, a type of agnetic plason (MP) propagation ode with a broad frequency bandwidth was established in this syste. Apparent EOT peaks induced by the MP ode were observed in our easured spectra at infrared frequencies. The strongest EOT peak was obtained at 1.7eV with an incident angle of. The easured dependence of EOT peaks on the incident angle coincided with the theoretical results quite well. This proposed MP propagation ode in SHR structure has good potential applications in ulti-frequency nonlinear optical processes. *Author to who correspondence should be addressed: liuhui@nju.edu.cn Website of author s group: 1

2 Surface plason polariton (SPP) results fro the coupling of electroagnetic wave and the collective electronic excitations on etal surface. It has considerably attracted the interest of researchers because of its iportant role in the extraordinary optical transission (EOT) phenoena as reported by Ebbesen in 1998 [1-3]. According to recent studies, although SPP excitation is not the only echanis responsible for EOT [4], it has undoubtedly provided one of the ost rearkable contributions in the interaction between light and etallic nanostructures. Moreover, it has very iportant applications on ulti-frequency nonlinear optical processes, such as biosensors [5], nanolasers [6], and spaser [7-8]. On the other hand, in 1999, Pendry reported that a nonagnetic etallic eleent, such as a split ring resonator (SRR), with size below the diffraction liit, exhibits strong agnetic response and behaves like an effective negative pereability aterial [9]. Analogous to the surface plason resonances in etal nanoparticles, an effective edia ade of SRRs could support agnetic plason (MP) resonance [1-11] and lead to negative refraction [1]. According to the Babinet principle, the copleentary structure of SRR (CSSRR) can also act as a good resonator in icrowave range [13]. Besides SRR and CSRR, soe new structures, such as nanorods [14], fish-nets [15], nano-sandwiches were invented to realize agnetic resonance at optical frequencies. Aside fro the negative refraction, the application of MP has also been extended to cloaking aterials [16] and polarization switches [17-18]. However, copared with SPP, which has a broad frequency bandwidth, MP is excited in a very narrow frequency range around the resonance frequency. This badly restricts MPs applications in nonlinear optical processes which usually require ulti-frequency excitations in a broad bandwidth. In our recent theoretical study [19], a new kind of MP propagation ode in a linear onatoic chain of SRRs has been proposed to transfer EM wave signal in a subwavelength waveguide. In this paper, we will experientally explore whether or not this MP propagation ode could lead to EOT. To realize this objective, we designed and fabricated a one-diensional diatoic chain of slit-hole resonator (SHR). The MP propagation ode is expected to be established in this syste with

3 the help of the strong interaction between SHRs. Contrary to traditional uncoupled SRRs or CSRRs, the excitation of this MP propagation ode s optical branch could be tuned continually in a broad frequency bandwidth by adjusting the incident angles. The related EOT peak was observed in the transitted spectru at infrared frequencies. Results show that the easured dependence of the EOT peak on the incident angle coincides with the theoretical calculations quite well. This type of broadband MP ode has good potential applications in any ulti-frequency nonlinear optical processes, such as fluorescence and Raan effects. Figure 1(a) presents our designed slit-hole resonator structure, which is based on the designing idea proposed by the reference [13]. It coprises of two parts: a nano-hole near the edge of a sei-infinite golden fil and a slit linking the hole with the edge. Its geoetry paraeters are also provided in this figure. Copared with SRR, SHR is uch easier to be fabricated and its resonance frequency can reach infrared range. To study the EM response of the proposed SHR, we perfored a set of finite-difference tie-doain (FDTD) calculations using a coercial software package, the CST Microwave Studio (Coputer Siulation Technology GbH, Darstadt, Gerany). In addition, we relied on the Drude odel to characterize the bulk etal properties. The etal perittivity in the infrared spectral range is given by ε ( ω ) = 1- ω /( ω + iωω ), where ω p is the bulk plasa frequency, and p τ ω τ is the relaxation rate. For gold, the characteristic frequencies fitted for experiental data are ω τ h ω p = 9.eV and h =.7eV []. In the nuerical calculations, a near-field dipole source excited the SHR, and a probe was used to detect the local agnetic field at the center of the nano-hole. In the siulations, we observe a well-pronounced resonance frequency at.43ev. The oscillation of both the electric and agnetic fields at this resonance frequency is given in the online aniation files [1]. The results show that the electric field is confined within the slit, while the agnetic field is concentrated inside the nano-hole. The SHR can be seen as an equivalent LC circuit, with the nano-hole working as a conductor, and the slit working as a capacitor (Fig.1 (b)). The induced resonance current in this LC circuit is also obtained in our 3

4 siulations [1]. Due to the skin effect in the etal aterial, the current is only at the thin layer (thickness ~3n) around the nano-hole. The whole structure (SHR) could be seen as a agnetic dipole when the oscillation current is induced by an external wave at resonance frequency. We used a sei-analytic theory based on the Lagrangian foralis to describe the oscillation of this agnetic dipole. If Q is the total oscillation charge in the SHR, L is the inductor of the nano-hole, and C is the capacitance of the slit, then we can write the Largangian equation of the syste as I = LQ& Q. Fro the Euler-Lagrangian C d I I equation = dt Q&, we can then obtain the oscillation equation of SHR as Q 1 Q & + Q = LC. If we define the SHR as a single agnetic dipole, μ = Q &/S, where S is the circle area of the SHR, then μ& & + ω μ =, where ω = 1/( LC) ( ω is the resonance frequency of the SHR. Based on the above SHR, a one-diensional chain of agnetic resonator could be fored by connecting such a structure one by one. In our forer work, a onatoic chain of SRRs is proposed and the MP ode is found in such a syste [19]. However, its dispersion relation curve lies below the light line. At a given photon energy, the wave vector is not conserved when the photon is transfored into the MP ode. Such MP ode could not be excited by a far-field incident wave, and the EM energy could not be radiated out fro the chain either. We conclude, therefore, that contrary to what we expected, the MP ode in a onatoic chain could not lead to EOT. In order to satisfy the wave vector atching condition, a diatoic chain of SHR is designed and presented in Fig. (a). Here, we can see that the unit cell of this chain is coposed of two SHRs with different geoetry sizes. The bigger SHR has the sae structure as that given in Fig. 1(a), where the resonance frequency is obtained at ω =.43 1 ev. For the saller SHR, the sae siulation ethod is used and its resonance frequency is deterined at ω =.65 ev. 4

5 For the infinite diatoic chain of SHRs, the equivalent LC circuit is given in Fig. (b). The Lagrangian equation of this syste is expressed as: I = L Q& Lq + & 1 ( Q q ) ( Q q ) C 1 C. (1) Here, we define the oscillating charges in the -th unit cell as Q for the bigger SHR with an inductor L 1, and q for the saller SHR with an inductor L (=, ± 1, ±, ± 3, ). The two corresponding agnetic dipoles, U and μ, are defined as U = Q& S, μ = & s, where S and s are the areas of bigger and / q / saller SHRs, respectively. Fro the Euler-Lagrangian equations d dt I I U& U = d I I and = dt μ& μ (=, ± 1, ±, ± 3, ), we obtain the oscillation equations of the -th bigger SHR and saller SHR as: U&& + ω1 && μ + ω ( U μ μ 1) ( μ U U ) + 1 =, () = where ω = 1 1 / L1C, and ω = 1 / L C. We seek a general solution of Equation () in the for of the agnetic plason (MP) wave, U = U exp μ = μ exp ( i( ωt k d )) ( i( ωt k ( d + d / ) )), (3) where ω and k are the angular frequency and wave vector, respectively, U and μ are the initial values of the agnetic dipole oent at =, and d = 65n is the period of the chain. By substituting Equation (3) into Equation (), and then solving the Eigen equations for U and μ, the MP dispersions are attained as: 4 4 ( ω + ω ) ± ( ω + ω ) ω ω cos( kd ) ω = ±. (4) The dispersion relations are nuerically depicted as two solid black curves in Fig. 3 (a). There are two separate dispersion branches for the diatoic chain: upper branch ω ( + k ) and lower branch ω ( k ). For these two branches, the respective resonant 1 5

6 anners of the -th unit cell are quite different. Our siulations [1] show that for the lower branch, ω (k ), U and μ oscillate in the sae phase (see Fig.3 (b)), whereas for the upper branch, ω (k + ), they oscillate in the anti-phase (see Fig.3 (c)). Using the analogy of the diatoic odel of crystal lattice wave [], we can refer to the upper curve ω (k + ) as optical branch and the lower curve ω (k ) as acoustic branch. Copared with the onatoic chain [19], which possesses only the acoustic dispersion branch, the optical branch is a kind of MP ode found in the diatoic chain. In Fig. 3 (a), the light line in the free space is given as a blue dotted straight line ( ω = ck ). It is quite exciting to see that the upper optical branch intersects with the light line, and that the ajor part of this curve lies on the left side of the intersection point. For an oblique incident plane wave, the resonant excitation of the MP odes could be achieved under the wave vector atching condition: k = k sinθ, (5) where θ is the incident angle as denoted in Fig. (a). Cobining Equations (4) and (5), the dependence of resonance excitation frequency on the incident angle could be solved nuerically, and is shown as a white line in Fig. 4(b). For a perpendicular incident wave ( θ = ), the MP ode is excited at the frequency 1.11eV. At the crossing point of the optical branch curve and the blue line in Fig. 3 (a), the MP ode is excited by a plane wave propagating along the etal surface ( θ = 9 ), with the corresponding frequency at.94ev. Thus, the excitation frequency range of the MP ode is.94 ~ 1.11eV with a bandwidth.186ev Based on the above theoretical odel, we expected that the optical branch of the MP ode could lead to EOT when excited by the incident plane wave. To achieve this experientally, a one-diensional chain of SHRs on a silver fil was fabricated with the focused-ion-bea (FIB) syste (Strata FIB 1, FEI copany, 3keV Ga ions). The saple picture is shown in Fig. (c), along with its structure paraeters. The saple is set on a rotation table, and as can be seen, a polarized light is directed 6

7 to the saple with its e-field in the y direction. The transitted waves are collected by an optical-spectru analyzer (ANDO AQ-6315A), and the easured transission efficiency noralized to the area of the holes are shown in Fig. 4(a) under different incident angles. As expected, the EOT peaks are evidently observed around the resonance frequency of the optical MP ode, when the incident angle is in the range of 6 θ 4. In contrast, there is no obvious peak to be found in the transission curve for the sall incident angles ( θ < 6 ). This is because MPs EOT is fored via the coupling to the h-field coponent of light. In order to excited strong agnetic resonance, agnetic flux ust pass through the nano-hole, and the noral coponent of the h-field ust not be equal to zero ( H ). When the incident angle θ is less z than 6, ost of the h-field of the incident wave would be parallel to the etal fil and, therefore, would not be able to pass through the nano-hole. There is not enough energy coupling into the MP ode. Hence, it is hard to find obvious EOT peaks in our easureent. In order to induce ore agnetic flux to pass through the nanohole, we increased the incident angle. Consequently, ore EM energy was absorbed into the MP odes and then radiated out fro the backside of the saple. The corresponding EOT peaks becae stronger and were then easured in the transitted wave (Fig. 4(a)). Afterwards, we attained the strongest EOT peak at around θ =. When the incident angle was further increased, the EOT peak declined and becae too weak to be observed when θ > 4. This is because if the incident angle θ is increased, the projected area ( S ' ) of the fabricated region ( S ) in the incident direction will be decreased ( S ' = S cosθ ). Less EM energy could be coupled into SHRs and attributed to the EOT peak. Thus, no evident EOT peak could be easured in the range θ > 4. For the incident angle 8 < θ < 3, the noralized transission efficiency could exceed unity (see Fig.4 (a)), proving that the excitation of the optical MP ode leads to extraordinary transission. The angle dependence of the EOT peak obtained in this experient is quite different fro that of the SPP ode. 7

8 The excitation of SPP is through the coupling to the e-field coponent of light and the EOT peak could be attained with the perpendicular incident wave ( θ = ). In order to obtain the coparison between these easured experient results and the theoretical results, the transission curves under different incident angles were cobined into a -D contour ap (Fig. 4(b)). In this ap, the transitted intensity is denoted as the brightness of each point. Fro the figure, it could be seen that the bright part of the ap atches the theoretical white line quite well. This confirs that the easured EOTs are obtained fro the excitation of the optical MP odes in the diatoic chain of SHRs. Actually, the bandwidth of the optical branch can be enlarged if we increase the coupling interaction between eleents by changing the length of the slit. In our experients, we fabricated another saple with the slit length equals 5n (saller than 7n for the old saple). Other structure paraeters are kept the sae value as Fig. (a). The bandwidth obtained is about.1ev, which is larger than the bandwidth of the old saple. The above EOT based on 1-D diatoic SHR chain could be also realized in -D SHR structures [1]. The detailed discussion will be provided in another paper. Fro the above experiental results, we can see that the MP propagation ode in our syste can be excited in a broad frequency bandwidth. Actually, the dispersion curves in Fig. 3 are divided into two parts by the blue light line. The part above the blue line is the bright MP ode, which can couple to the far-zone optical field. Aside fro the EOT reported in this paper, the bright MP ode could also be used to produce efficient nanolasers, which has recently aroused intense interest [6]. Meanwhile, the rest part below the blue line corresponds to the dark MP ode, which cannot be excited by the far-field wave and whose energy does not radiate outwards. Without radiation loss, the dark MP ode can be greatly aplified by the stiulated eission fro an active ediu (e.g., quantu dots and the like) siilarly as SPASER achieved in dark SPP ode [7-8]. This could provide a good nanoscale optical source for nuerous potential applications in nonlinear optical processes, such as single-olecule detection and florescence iaging. In suary, we proposed and studied a agnetic plason propagation ode 8

9 with a broad frequency bandwidth. The optical branch of this MP ode was excited by an oblique incident wave, the occurrence of which led to an extraordinary transission of infrared light in our experients. The easured dependence of EOT peaks on the incident angle coincided with the theoretical results quite well. Both the bright and dark odes could be obtained in this syste. Their nuerous prospective applications in nonlinear optical processes are worthy to be explored in the future. This work is supported by the National Natural Science Foundation of China (No.1649, No and No ), and by the National Key Projects for Basic Researches of China (No.9CB9351, No.6CB9184 and No. 4CB6193). References [1] T. W. Ebbesen, H. J. Lezec et al., Nature 391, 667 (1998) [] C. Genet and T. W. Ebbesen, Nature 445, 39 (7) [3] H. T. Liu and P. Lalanne, Nature 45, 78 (8) [4] F. J. Garcia de Abajo, Rev. Mod. Phys. 79, 167 (7) [5] K. Kneipp et al., Che. Rev. 99, 957 (1999) [6] M. T. Hill et al., Nature Photonics 1, 589 (7) [7] D. J. Bergan et al., Phys. Rev. Lett. 9, 74 (3) [8] N. I. Zheludev et al., Nature Photonics,, 351 (8) [9] J. B. Pendry et al., IEEE Trans. Microwave Theory Tech. 47, 75 (1999). [1] T. J. Yen, W. J. Padilla et al., Science 33, 1494 (4). [11] S. Linden, C. Enkrich et al., Science 36, 1351 (4). [1] R. A. Shelby, D. R. Sith and S. Schultz, Science 9, 77 (1). [13] F. Falcone et al., Phys. Rev. Lett. 93, (4). [14] V. M. Shalaev, W. Cai et al., Opt. Lett. 3, 3356 (5). [15] S. Zhang, W. Fan et al., Phys. Rev. Lett. 95, (5). [16] D. Schurig, J. J. Mock et al., Science 314, 977 (6). [17] H. Liu, D. A. Genov et al., Phys. Rev. B 76, 7311 (7) [18] T. Q. Li, H. Liu, T. Li et al., Appl. Phys. Lett. 9, (8). 9

10 [19] H. Liu, D. A. Genov et al., Phys. Rev. Lett. 97, 439 (6). [] M. A. Ordal et al., Appl. Opt., 199 (1983). [1] EPAPS Docuent No. E-PRBMDO for aniation files of agnetic resonance odes in slit-hole resonator structures. For ore inforation on EPAPS, see [] C. Kittel, Introduction to Solid State Physics (John Wiley & Sons, Inc., 5). 1

Fig.1 (a) Structure of a single SHR; (b) Equivalent LC circuit

Fig.3 (a) Dispersion curves for the MP odes in the diatoic

11 Fig.1 (a) Structure of a single SHR; (b) Equivalent LC circuit of the single SHR. Fig. (a) Structure of a diatoic chain of SHRs; (b) Equivalent LC circuit of the chain; (c) FIB iage of the fabricated saple. Fig.3 (a) Dispersion curves for the MP odes in the diatoic chain of SHRs; the local current distributions are calculated for the (b) optical and (c) acoustic odes. 11

12 (a) (b) sin θ = k / k Fig.4 (a) Measured transission efficiency noralized to the area of the holes under different incident angles; (b) Measured transission ap and the calculated angular dependence curve of the optical MP ode. 1

Electric and magnetic excitation of coherent magnetic plasmon waves in a one-dimensional meta-chain

Electric and magnetic excitation of coherent magnetic plasmon waves in a one-dimensional meta-chain C. Zhu 1, H. Liu 1,*, S. M. Wang 1, T. Li 1, J. X. Cao 1, Y. J. Zheng 1, L. Li 1, Y. Wang 1, S. N. Zhu