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asymmetric plasmonic waveguide system and its application in nanosensor
Optics Communications 370 (2016) 203–208
Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Evolution of Fano resonance based on symmetric/asymmetric plasmonic waveguide system and its application in nanosensor Yunyun Zhang a,b, Shilei Li a,b, Xinyuan Zhang a,b, Yuanyuan Chen a,b, Lulu Wang a,b, Yong Zhang a,b, Li Yu a,b,n a b
State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876, China School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China
art ic l e i nf o
a b s t r a c t
Article history: Received 3 December 2015 Received in revised form 28 February 2016 Accepted 1 March 2016 Available online 15 March 2016
We proposed a plasmonic nanosensor based on Fano resonance in the symmetric and asymmetric plasmonic waveguide system, which comprises with a rectangular cavity and two slot cavities with the metal-dielectric-metal waveguide. Simulation results show that by symmetric/asymmetry rectangular cavity and regulating the rectangular cavity coupling with slot cavities, different waveguide modes can be excited. Due to the interaction of the waveguide mode, the transmission spectra possess single, double or multiple sharp asymmetrical profiles. Because of the different origins, these Fano resonances exhibit different dependence on the parameters of the structure and can be easily tuned. These characteristics offer flexibility to design the device. This nanosensor yields a sensitivity of ∼800 nm/RIU and a figure of merit of about ∼1.35 104, which can find widely applications in the plasmonic nano-sensing area. & 2016 Elsevier B.V. All rights reserved.
Keywords: Surface plasmon polaritons Plasmonic waveguide Fano resonance Sensor
1. Introduction Surface plasmon polaritons(SPPs) are regarded as the most promising candidates for the realization of highly integrated optical circuits, due to their capability to overcome the diffraction limit of light [1]. Recently, some novel physical features enabling the miniaturization of optical devices have been investigated in various plasmonic nanostructures, such as waveguide [2–4], metamaterials [5]. Among all the nanostructures, the metal-dielectric-metal (MDM) waveguide based on SPPs has deep subwavelength field confinements and low bend loss, and thus, it has important applications in highly integrated photonic circuits [6– 10]. Based on the MDM waveguide, a large number of devices, such as splitters [11–13], filters [14–17], sensors [2,18,19], and demultiplexers [13,20,21] have been designed and demonstrated in theory and experiment. As a fundamental resonant effect, the Fano resonance, originates from the interference effect between a localized state and a continuum band in quantum or classical systems [22,23]. Recently, many plasmonic structures have been designed to achieve the Fano resonance. Usually, using asymmetric plasmonic structure is a common way to obtain the Fano n Corresponding author at: State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876, China. E-mail address: [email protected] (L. Yu).
http://dx.doi.org/10.1016/j.optcom.2016.03.001 0030-4018/& 2016 Elsevier B.V. All rights reserved.
resonance such as the symmetry-breaking T-shape double slit [24], the broken symmetry in disk cavities or the ring [25,26], asymmetric stub pair in Metal- dielectric -metal (MDM) waveguide [27,28]. Besides, the Fano resonance also be achieved in the symmetric plasmonic structures, including cavity–cavity interference [2–4], nanoslits in a metallic membrane [29], waveguidecoupled resonators [30]. Different from the Lorentzian resonance, the Fano resonance exhibits a typical sharp and asymmetric line profile [20], which has great important applications in demultiplexing [21], plasmonic switch [22], and so on. The specific feature of Fano resonance promises applications in sensors [19], such as Lu et al. designed a dual resonator structure to achieve a plasmonic nanosensor [4], Chen et al. designed a stub and groove resonator to achieve a refractive index sensor [18]. Therefore, combining the Fano resonance with MDM plasmonic structures would create the possibility of achieving ultracompact functional optical components for use in highly integrated optics [31]. In this paper, a MDM-waveguide structure is proposed to realize the Fano resonances in the symmetric or asymmetric plasmonic structure. In our proposed symmetric plasmonic structure, two identical slot-cavity resonators are placed close to the ends of the rectangular cavity, which symmetrically locate at both sides of a MDM bus waveguide. Simulation results show that the two sharp and asymmetric transmission profiles are formed with interaction of the narrow discrete spectrum and a broad continuous spectrum caused by the slot cavities and the rectangular cavity,
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respectively. The asymmetrical line shape and the resonant wavelength can be easily tuned by changing the geometrical parameters of the structure. Meanwhile, we extend this plasmonic structure by asymmetric rectangular cavity or the regulating rectangular cavity coupling with the slot cavities for the more investigations. Simulation results show that a new sharp asymmetrical line shape appears and can be easily tuned. The proposed structure can serve as an excellent plasmonic sensor with a sensitivity of ∼800 nm/RIU and a figure of merit of about 1.35 104, which can find widely applications in the plasmonic nano-sensing area.
2. Symmetric rectangular cavity coupling with the slot cavities Fig. 1(a) shows the two-dimensional geometry of the symmetric plasmonic structure composed of a MDM waveguide and two identical slot-cavity resonators, which is placed close to the ends of the rectangular cavity. The width and height of the rectangular cavity are denoted as W, H (H1þ H2 þW1) and △H¼ H1 H2, respectively. Meanwhile, the coupling distances from the rectangular cavity to the slot cavities are g. W1 and L are the width and length of the slot cavities, and the width of the MDM waveguide is also W1. Here, the value W1 ¼50 nm and g ¼10 nm are fixed throughout this paper. The white and blue parts denote air ( εair ¼1.0) and Ag ( εm ), respectively. In order to investigate the optical responses of the proposed structure, its transmission spectra are numerically calculated by using the finite element method (FEM) of COMSOL Multiphysics. The transmittance of SPPs is defined as the quotient between the SPP power flows (obtained by integrating the Poynting vector over the channel cross-section) of the observing port with structures (rectangular cavity and slot-cavity resonators) and without structures [11,18,19,24]. The permittivity of Ag is characterized by the Drude model:
εm (ω) = ε∞ − ω p2/[ω (ω + iγ )]
(1)
Here, ε∞ is the dielectric constant at the infinite frequency and
ωp and γ stand for the bulk plasma frequencies and the electron collision, respectively. ω is the angular frequency of incident light. The parameters for silver can be set as ε∞=3.7,ωp=9.1eV and γ = 0. 018eV [32]. The parameters of the proposed structure are set as: L¼ 550 nm, H ¼345 nm, △H¼ 0 and W1 ¼225 nm and the calculated transmission spectra are displayed in Fig. 1(b). It is found that the transmission spectrum in the plasmonic waveguide system exhibits two sharp and asymmetric resonant peaks, which are typical Fano-like profiles [2,11,18]. This is quite different from the symmetric Lorentzian transmission line shape. Here, we called the left peak of the Fano resonance of FR1, correspondingly, the right peak of the Fano resonance is FR2, for description conveniently. Clearly, the two Fano peaks drop sharply from the peak to the dip in the spectra. In order to understand the underlying physics of the resonant peaks in the transmission spectra, the field distributions of Hz 2 at λ ¼706 nm and λ ¼869 nm, corresponding to the FR1 and FR2, are displayed in Fig. 1(c)–(d), respectively. Because the input light is set to be transverse magnetic (TM) plane wave, the resonant modes can be classified using TMmn [25], m, n are integers and indicate the x-directional and y-directional resonant orders, respectively. Obviously, at λ ¼706 nm, the system shows a relatively complicated interference phenomenon with TM10 mode in the rectangular cavity and TM30 mode in the two identical slot cavities, as can be seen in Fig. 1(c). On the other hand, at λ ¼ 869 nm, almost all the energy confined in the slot cavities with TM20 mode, indicating a relatively simple interference phenomenon, as can be seen in Fig. 1(d). Here, we can make a simple inference that FR1 is influenced both by the slot cavities and the rectangular cavity, while FR2 mainly affected by the slot cavities. As we know, in a plasmonic resonator, the accumulated phased shift per round trip for the SPPs is ϕ = 4πneff S /λ + 2φ [15,34]. Constructive interference should occur whenϕ = 2Nπ , and thus the resonant wavelength is determined by
λ=
2neff S (N − φ/π )
(2)
where neff denotes the effective index of the SPPs, which can be obtained by solving the eigenfunction in the MDM waveguide [35].
Fig. 1. (a) Schematic configuration and geometric parameters of the plasmonic waveguide system. (b) Transmission spectra of the plasmonic waveguide system: the parameters are set as L ¼ 550 nm, △H¼0 and W1 ¼225 nm. (c and d) The Hz 2 field distributions at the resonance wavelength λ ¼706 nm and λ ¼869 nm.
Y. Zhang et al. / Optics Communications 370 (2016) 203–208
φ is the phase shift brought by the SPP reflection off the metal wall in the resonator, S presents the effective length of the resonator, and N denotes resonance orders in the slot cavity or the rectangular cavity. Based on Eq. (2), we can obtain that the dependence of the variation of the resonant wavelength on the resonator length S is
2neff dλ = dS N − φ /π
(3)
Note that the geometric length of the plasmonic resonator is only on the order of an optical wavelength, so different waveguide modes can be reflected back and forth off the metal walls in the plasmonic resonators, constructing a FP resonator. Because of the quite different field distributions and propagation characteristics of these waveguide modes, these different resonances will emerge in the plasmonic resonators. At λ ¼706 nm, the system shows a complicated interference phenomenon among TM10 mode in the rectangular cavity and TM30 modes in the two identical slot cavities, which gives rise to the FR1. Besides, TM20 modes are excited in the two identical slot cavities at λ ¼869 nm, indicating the interference phenomenon which gives rise to the FR2 only affected by the length of the slot cavities. Based on Eqs. (2) and (3), we can infer FR1 is proportional to width of the rectangular cavity or length of the slot cavities. Analogously, the resonant wavelength keeps almost unchanged with increasing width of the rectangular cavity and is proportional to length of the slot cavities for the FR2. To test our inference, the FEM is used to investigate the properties of the proposed structure. First, we calculate the transmission spectra for different W with L¼ 550 nm, as shown in Fig. 2(a)–
Fig. 2. (a)–(e) Transmission spectra for different W with L ¼ 550 nm, H¼345 nm and △H¼0.
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(e). For the FR2, the effective cavity length S is W, it is hardly influenced the resonance wavelength when L is fixed, here Δλ /ΔW ≈ 0, as shown in the black symbol line in Fig. 2(a)–(e). Besides, from the field distribution at the resonance wavelength in Fig. 1(d), we also know that a large power flow is confined in the two identical slot cavities. The mutual coupling of the two identical slot cavities is the origin of FR2. Therefore, the resonant wavelength is determined by the fixed values of L. For the FR1, it originates from the interference between the TM10 mode in the rectangular cavity with TM30 mode in the two identical slot cavities and its mechanism is relatively complex, we only analyze qualitatively. According to the theory of standing wave [35], the wavelength is proportional to the effective length S, Δλ ∝ ΔS . It shows a phenomenon of redshift and is consistent with the red symbol line in Fig. 2(a)–(e). Meanwhile, we can also infer the extent redshift will become bigger when we change width of the rectangular cavity comparing to the changing length of the slot cavity for the FR1. It is because the rectangular cavity plays a dominant role comparing to the slot cavity for the FR1 and a large power flow is trapped in the rectangular cavity, as shown in Fig. 1(c)–(d). Here, Δλ /ΔS ≈ 1.1 when the width of the rectangular resonator increases. Therefore, the resonant wavelength can be easily manipulated by adjusting the width of the rectangular cavity but without influence on the other peak. This character may offer excellent flexibility to the design the sensors. Successively, the transmission spectra is investigated by changing length of the slot cavities, and the results are displayed in Fig. 3(a)–(e). Herein, the parameters are set with a fixed W¼225 nm, and an alterable L. For the FR1, we only analyze
Fig. 3. (a)–(e) Transmission spectra for different L with W ¼225 nm, H¼ 345 nm and △H¼0. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
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Fig. 4. (a) Transmission spectra for different refractive index. (b) The calculated FOM at different wavelength, the parameters are set as L ¼550 nm, △H¼ 0, H¼345 nm and W1 ¼225 nm.
qualitatively because of its complex mechanism. It is observed that its resonant wavelength is linearly redshifted with increasing length L with the slope of Δλ /ΔS ≈ 0.44 . The value is about 2/5 comparing to changing the width in the rectangular cavity and agrees well with the above inference. Increasing ΔL , the resonance wavelength of FR2 has a redshift with a slope Δλ /ΔS ≈ 1.36, as shown in the red symbol line in Fig. 3(a)–(e). In this case, a large power flow is confined in the two identical slot cavities. We have S ¼L, N ¼3 (resonance order in the slot cavity) neff = 1.4 and simulations show that φ equals about π . Thus, Eq. (3) becomes dλ dS
= 2 × 1.4/3 − φ /π ≈ 1.4 , agreeing well with the slope of the red symbol line in Fig. 3(a)–(e). By utilizing the asymmetric Fano transmission spectrum, we study the performance of our structure as a plasmonic nanosensor, and the results are displayed in Fig. 4(a) and (b). Moreover, the sensitivity and the FOM as the key parameter are widely used to evaluate the performance of the double Fano resonance. The resonant wavelength has a red shift when increasing the refractive index. The sensitivity of a sensor (nm/RIU) is usually defined as the shift in the resonance wavelength per unit variations of the refractive index [5,33]. The sensitivity of the proposed structure is about 800 nm/RIU, which is excellent compared with that of the plasmonic sensors reports [30]. To better evaluate the performance of the plasmonic sensor, the figure of merit ( FOM) is studied, which defined as FOM = ∆T /T ∆n [11,18,19], where T denotes the transmittance in the proposed structure. Fig. 4(b) depicts the calculated FOM. The maximum value of FOM is as high as
1.01 104 at λ ¼ 894 nm, which is due to the sharp asymmetric Fano line-shape with ultra-low transmittance at this wavelength. The FOM is much higher than that of the plasmonic sensors [2,27,30].
3. Asymmetric rectangular cavity coupling with the slot cavity According to the above characteristics of the plasmonic system based on rectangular cavity coupling with the slot cavity, the proposed Fano structure in Fig. 1(a) is flexible and can be easily extended to a multiple Fano resonances system by asymmetric rectangular cavity coupling with the slot cavites. Herein, the parameters are set with a fixed △H¼ 45 nm, H2 ¼125 nm, L¼550 nm and W1 ¼ 225 nm. In order to investigate the optical responses of the proposed structure, its transmission spectra are numerically calculated using the finite element method. It is found that a new sharp and asymmetric response line-shape emerges comparing to the symmetric rectangular cavity coupling with the slot cavities, as shown in Fig. 5(a). Meanwhile, a little platform appears at about 691 nm, which is caused by the symmetrybreaking of the MDM waveguide plasmonic structure. Fig. 5 (b) shows the field distributions of Hz 2 at the resonance peak of 783 nm, we know that a strong field distribution is confined in the rectangular cavity and two identical slot cavities. The FR3, which is caused by the structure symmetry breaking, originates from the interference of the TM01 mode in the rectangular cavity with TM20
Fig. 5. (a) Transmission spectra of the plasmonic waveguide system: the red, black line represents the transmission spectra of the asymmetric rectangular cavity and symmetric rectangular coupling with the slot cavites, respectively. The parameters are set as L ¼ 550 nm, △H¼45, H2¼ 125 nm and W1¼ 225 nm. (b) The Hz 2 field distributions with and without the groove at the resonance wavelength λ¼ 783 nm. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Y. Zhang et al. / Optics Communications 370 (2016) 203–208
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calculated FOM. The maximum value of FOM is as high as 1.35 104 at λ ¼791 nm, which is due to the sharp asymmetric Fano line-shape with ultra-low transmittance at this wavelength. Here, FOM is much higher than that of the plasmonic sensors [2,27,30].
4. By regulating symmetric rectangular cavity coupling with the slot cavities
Fig. 6. Dependence of the resonant wavelengths on the difference △H with fixed H2¼ 125 nm, L ¼550 nm and W1¼ 225 nm. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
mode in the two identical slot cavities. Furthermore, the FEM is used to investigate the more properties of the proposed structure. Here, we calculate the dependence of the resonant wavelengths on the difference △H with fixed H2¼ 125 nm, L ¼550 nm and W1 ¼225 nm, as shown in Fig. 6. Due to the resonance wavelength of FR1 and FR2 keeps almost unchanged, as shown in Fig. 5(a). Therefore, they have the analogous characteristics when we change the parameter of the plasmonic system based on the above investigations, here not be discussed. Here, we focus on the FR3 and analyze it qualitatively base on its complex mechanism. From Fig. 5(b), it is found that there exists one node for the distribution along the y-axis direction in the rectangular cavity, yielding a symmetric waveguide mode in the plasmonic resonator. Here, the effective length is H. According to the theory of standing wave [35], the wavelength is proportional to the effective length, namely Δλ ∝ ΔH . That is with the increasing effective length, the resonance wavelength is increasing linearly, which denotes redshift and is consistent with the blue symbol line in Fig. 6. Successively, we investigate the application as the sensor based on the proposed plasmonic structure, as shown in Fig. 7(a) and (b). The resonant wavelength has a red shift when increasing the refractive index. Here, the sensor still has the good sensitivity, about 800 nm/RIU, which is excellent compared with the previous plasmonic sensors reports [30]. Besides, FOM as an important parameter of the sensor is also investigated. Fig. 7(b) depicts the
For the schematic configuration of Fig. 1(a), we investigate the proposed plasmonic system for the possible application. Since in the process of production, it is difficult to get sharp angle of the rectangular cavity and slot cavities. In contrast, circular bead is more accessible. Based on the Fig. 1(a), we use a circular bead replace right angle of the rectangular cavity and slot cavities and keep the same parameters with Fig. 1(b), as shown the inserted schematic configuration in Fig. 8(a). It is found that the transmission spectrum in the plasmonic waveguide system exhibits a sharp and asymmetric response line-shape, which is different from the double Fano profile, as shown in Fig. 8(a). Here, we can infer that the broad resonance mode in the circular bead of the rectangular cavity is not excited, only the narrow resonance mode in the circular bead of the slot cavities is excited. To further understand the underlying physics of the resonant peaks in the transmission spectra, the field distributions of Hz 2 at λ ¼846 nm is displayed in Fig. 8(b). We find that a strong field distribution is confined in the circular bead of two identical slot cavities. Due to the characteristics of the circular bead of the rectangular cavity, angular resonance in the rectangular is vanished comparing to the Fig. 1(c). In this case, SPPs will propagate into the rectangular cavity and then be captured into the slot cavity. The interference of a narrow discrete spectrum in the slot cavities and a broad continuous spectrum in the rectangular cavity, gives rise to the Fano profile. Based on the above investigations and analyses, we can obtain single, double and multiple Fano profile by the different plasmonic system. Due to different origins, these Fano profile can be easily tuned.
5. Conclusion In summary, a MDM-waveguide structure is proposed to realize the single or the multiple Fano resonances in the symmetric and asymmetric plasmonic structure. In our proposed plasmonic
Fig. 7. (a) Transmission spectra for different refractive index and (b) the calculated FOM at different wavelength, the parameters are set as L ¼ 550 nm, △H ¼45 nm, H ¼ 345 nm and W1¼ 225 nm.
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Fig. 8. (a) Schematic configuration and transmission spectra of the plasmonic waveguide system, (b) the Hz resonance wavelength λ ¼ 846 nm.
system, simulation results show that symmetric/asymmetry rectangular cavity or the regulating rectangular cavity couple with slot cavities and different waveguide modes can be excited. Due to the interaction of the waveguide mode, the transmission spectra possess single, double or multiple sharp asymmetrical profiles. Because of the different origins, these Fano resonances exhibit different dependence on the parameters of the structure and can be easily tuned. These characteristics offer flexibility to design the device. This nanosensor yields a sensitivity of ∼800 nm/RIU and a figure of merit of about ∼1.35 104, which can find widely applications in the plasmonic nano-sensing area.
Acknowledgments This work was supported by the National Natural Science Foundation of China under Grant nos. 11374041, 11374042, 11404030 and 11574035 and the BUPT Excellent Ph.D. Students Foundation under Grant Nos. CX201324 and Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Tele-communications), PR China
References [1] [2] [3] [4] [5] [6] [7] [8] [9]
W.L. Barnes, A. Dereux, T.W. Ebbesen, Nature 424 (2003) 824. H. Lu, X.M. Liu, D. Mao, G.X. Wang, Opt. Lett. 37 (2012) 3780. K.H. Wen, Y.H. Hu, L. Chen, J.Y. Zhou, L. Lei, Z. Meng, Plasmon 10 (2015) 27. H. Lu, X.M. Liu, D. Mao, G.X. Wang, Opt. Lett. 36 (2011) 3233. N. Liu, M. Mesch, T. Weiss, M. Hentschel, H. Giessen, Nano Lett. 10 (2010) 2342. T. Xu, Y.K. Wu, X. Luo, L.J. Guo, Nat. Commun. 1 (2010) 118. G. Veronis, S. Fan, Appl. Phys. Lett. 87 (2005) 131102. E.N. Economou, Veronis, S. Fan, Phys. Rev. 182 (1969) 539. K.H. Wen, Y.H. Hu, L. Chen, J.Y. Zhou, M. He, L. Lei, Z.M. Meng, IEEE Photonics J.
2
field distributions with and without the groove at the
7 (2015) 1. [10] K.H. Wen, L.S. Yan, W. Pan, B. Luo, Z. Guo, Y.H. Guo, X.G. Luo, J. Light. Technol. 32 (2014) 1701. [11] Z. Chen, W.H. Wang, N.L. Cui, L. Yu, G.Y. Duan, F.Y. Zhao, J.H. Xiao, Plasmonics 10 (2015) 721. [12] J.J. Chen, Z. Li, M. Lei, X.L. Fu, J.H. Xiao, Q.H. Gong, Plasmonics 7 (2012) 441. [13] Y. Kou, F.X. Chen, Opt. Express 19 (2011) 6042. [14] J. Tao, X.G. Huang, X. Lin, J. Chen, Q. Zhang, X. Jin, J. Orthop. Allied Sci. 27 (2010) 323. [15] J. Tao, X.G. Huang, X. Lin, Q. Zhang, X. Jin, Opt. Express 17 (2009) 13989. [16] Q. Zhang, X.G. Huang, X.S. Lin, J. Tao, X.P. Jin, Opt. Express 17 (2009) 7549. [17] X.S. Lin, X.G. Huang, Opt. Lett. 33 (2008) 2874. [18] Z. Chen, L. Yu, L.L. Wang, G.Y. Duan, F.Y. Zhao, J.H. Xiao, IEEE Photonics Technol. Lett. 27 (2015) 1695. [19] Z. Chen, L.N. Cui, X.K. Song, L. Yu, J.H. Xiao, Opt. Commun. 340 (2015) 1. [20] J.J. Chen, Z. Li, J. Li, Q.H. Gong, Opt. Express 19 (2011) 9976. [21] H. Lu, X.M. Liu, Y.K. Gong, D. Mao, L.R. Wang, Opt. Express 19 (2011) 12885. [22] U. Fan, Phys. Rev. 124 (1866) 1961. [23] A.E. Miroshnichenko, S. Flach, Y.S. Kivshar, Rev. Mod. Phys. 82 (2009) 2257. [24] J.J. Chen, Z. Li, Y.J. Zou, Z.L. Deng, J.H. Xiao, Q.H. Gong, Plasmonics 8 (2013) 1627. [25] J.B. Lassiter, H. Sobhani, J.A. Fan, J. Kundu, F. Capasso, P. Nordlander, Nano Lett. 10 (2010) 3184. [26] F. Hao, Y. Sonnefraud, P.V. Dorpe, S.A. Maier, N. Halas, P. Nordlander, Nano Lett. 8 (2008) 3983. [27] J.W. Qi, Z.Q. Chen, J. Chen, Y.D. Li, W. Qiang, J.J. Xu, Q. Sun, Opt. Express 22 (2014) 14688. [28] Z. Chen, J.J. Chen, L. Yu, J.H. Xiao, Plasmonics 10 (2015) 131. [29] S. Collin, G. Vincent, R. Haïdar, N. Bardou, S. Rommeluère, J. Pelouard, Phys. Rev. Lett. 104 (2010) 358. [30] Z.Q. Chen, J.W. Qi, J. Chen, Y.D. Li, Z.Q. Hao, W.Q. Lu, J.J. Xu, Q. Sun, Chin. Phys. Lett. 30 (2013) 057301. [31] N. L, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, H. Giessen, Nat. Mater. 8 (2009) 758. [32] Z. Han, S.I. Bozhevolnyi, Opt. Express 19 (2011) 3251. [33] J. Becker, A. Trügler, A. Jakab, U. Hohenester, C. Sönnichsen, Plasmonics 5 (2010) 161. [34] F.F. Hu, H.X. Yi, Z.P. Zhou, Opt. Lett. 36 (2011) 1500. [35] J.A. Dionne, L.A. Sweatlock, H.A. Atwater, A. Polman, Phys. Rev. B 73 (2006) 035407.
Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Evolution of Fano resonance based on symmetric/asymmetric plasmonic waveguide system and its application in nanosensor Yunyun Zhang a,b, Shilei Li a,b, Xinyuan Zhang a,b, Yuanyuan Chen a,b, Lulu Wang a,b, Yong Zhang a,b, Li Yu a,b,n a b
State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876, China School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China
art ic l e i nf o
a b s t r a c t
Article history: Received 3 December 2015 Received in revised form 28 February 2016 Accepted 1 March 2016 Available online 15 March 2016
We proposed a plasmonic nanosensor based on Fano resonance in the symmetric and asymmetric plasmonic waveguide system, which comprises with a rectangular cavity and two slot cavities with the metal-dielectric-metal waveguide. Simulation results show that by symmetric/asymmetry rectangular cavity and regulating the rectangular cavity coupling with slot cavities, different waveguide modes can be excited. Due to the interaction of the waveguide mode, the transmission spectra possess single, double or multiple sharp asymmetrical profiles. Because of the different origins, these Fano resonances exhibit different dependence on the parameters of the structure and can be easily tuned. These characteristics offer flexibility to design the device. This nanosensor yields a sensitivity of ∼800 nm/RIU and a figure of merit of about ∼1.35 104, which can find widely applications in the plasmonic nano-sensing area. & 2016 Elsevier B.V. All rights reserved.
Keywords: Surface plasmon polaritons Plasmonic waveguide Fano resonance Sensor
1. Introduction Surface plasmon polaritons(SPPs) are regarded as the most promising candidates for the realization of highly integrated optical circuits, due to their capability to overcome the diffraction limit of light [1]. Recently, some novel physical features enabling the miniaturization of optical devices have been investigated in various plasmonic nanostructures, such as waveguide [2–4], metamaterials [5]. Among all the nanostructures, the metal-dielectric-metal (MDM) waveguide based on SPPs has deep subwavelength field confinements and low bend loss, and thus, it has important applications in highly integrated photonic circuits [6– 10]. Based on the MDM waveguide, a large number of devices, such as splitters [11–13], filters [14–17], sensors [2,18,19], and demultiplexers [13,20,21] have been designed and demonstrated in theory and experiment. As a fundamental resonant effect, the Fano resonance, originates from the interference effect between a localized state and a continuum band in quantum or classical systems [22,23]. Recently, many plasmonic structures have been designed to achieve the Fano resonance. Usually, using asymmetric plasmonic structure is a common way to obtain the Fano n Corresponding author at: State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876, China. E-mail address: [email protected] (L. Yu).
http://dx.doi.org/10.1016/j.optcom.2016.03.001 0030-4018/& 2016 Elsevier B.V. All rights reserved.
resonance such as the symmetry-breaking T-shape double slit [24], the broken symmetry in disk cavities or the ring [25,26], asymmetric stub pair in Metal- dielectric -metal (MDM) waveguide [27,28]. Besides, the Fano resonance also be achieved in the symmetric plasmonic structures, including cavity–cavity interference [2–4], nanoslits in a metallic membrane [29], waveguidecoupled resonators [30]. Different from the Lorentzian resonance, the Fano resonance exhibits a typical sharp and asymmetric line profile [20], which has great important applications in demultiplexing [21], plasmonic switch [22], and so on. The specific feature of Fano resonance promises applications in sensors [19], such as Lu et al. designed a dual resonator structure to achieve a plasmonic nanosensor [4], Chen et al. designed a stub and groove resonator to achieve a refractive index sensor [18]. Therefore, combining the Fano resonance with MDM plasmonic structures would create the possibility of achieving ultracompact functional optical components for use in highly integrated optics [31]. In this paper, a MDM-waveguide structure is proposed to realize the Fano resonances in the symmetric or asymmetric plasmonic structure. In our proposed symmetric plasmonic structure, two identical slot-cavity resonators are placed close to the ends of the rectangular cavity, which symmetrically locate at both sides of a MDM bus waveguide. Simulation results show that the two sharp and asymmetric transmission profiles are formed with interaction of the narrow discrete spectrum and a broad continuous spectrum caused by the slot cavities and the rectangular cavity,
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respectively. The asymmetrical line shape and the resonant wavelength can be easily tuned by changing the geometrical parameters of the structure. Meanwhile, we extend this plasmonic structure by asymmetric rectangular cavity or the regulating rectangular cavity coupling with the slot cavities for the more investigations. Simulation results show that a new sharp asymmetrical line shape appears and can be easily tuned. The proposed structure can serve as an excellent plasmonic sensor with a sensitivity of ∼800 nm/RIU and a figure of merit of about 1.35 104, which can find widely applications in the plasmonic nano-sensing area.
2. Symmetric rectangular cavity coupling with the slot cavities Fig. 1(a) shows the two-dimensional geometry of the symmetric plasmonic structure composed of a MDM waveguide and two identical slot-cavity resonators, which is placed close to the ends of the rectangular cavity. The width and height of the rectangular cavity are denoted as W, H (H1þ H2 þW1) and △H¼ H1 H2, respectively. Meanwhile, the coupling distances from the rectangular cavity to the slot cavities are g. W1 and L are the width and length of the slot cavities, and the width of the MDM waveguide is also W1. Here, the value W1 ¼50 nm and g ¼10 nm are fixed throughout this paper. The white and blue parts denote air ( εair ¼1.0) and Ag ( εm ), respectively. In order to investigate the optical responses of the proposed structure, its transmission spectra are numerically calculated by using the finite element method (FEM) of COMSOL Multiphysics. The transmittance of SPPs is defined as the quotient between the SPP power flows (obtained by integrating the Poynting vector over the channel cross-section) of the observing port with structures (rectangular cavity and slot-cavity resonators) and without structures [11,18,19,24]. The permittivity of Ag is characterized by the Drude model:
εm (ω) = ε∞ − ω p2/[ω (ω + iγ )]
(1)
Here, ε∞ is the dielectric constant at the infinite frequency and
ωp and γ stand for the bulk plasma frequencies and the electron collision, respectively. ω is the angular frequency of incident light. The parameters for silver can be set as ε∞=3.7,ωp=9.1eV and γ = 0. 018eV [32]. The parameters of the proposed structure are set as: L¼ 550 nm, H ¼345 nm, △H¼ 0 and W1 ¼225 nm and the calculated transmission spectra are displayed in Fig. 1(b). It is found that the transmission spectrum in the plasmonic waveguide system exhibits two sharp and asymmetric resonant peaks, which are typical Fano-like profiles [2,11,18]. This is quite different from the symmetric Lorentzian transmission line shape. Here, we called the left peak of the Fano resonance of FR1, correspondingly, the right peak of the Fano resonance is FR2, for description conveniently. Clearly, the two Fano peaks drop sharply from the peak to the dip in the spectra. In order to understand the underlying physics of the resonant peaks in the transmission spectra, the field distributions of Hz 2 at λ ¼706 nm and λ ¼869 nm, corresponding to the FR1 and FR2, are displayed in Fig. 1(c)–(d), respectively. Because the input light is set to be transverse magnetic (TM) plane wave, the resonant modes can be classified using TMmn [25], m, n are integers and indicate the x-directional and y-directional resonant orders, respectively. Obviously, at λ ¼706 nm, the system shows a relatively complicated interference phenomenon with TM10 mode in the rectangular cavity and TM30 mode in the two identical slot cavities, as can be seen in Fig. 1(c). On the other hand, at λ ¼ 869 nm, almost all the energy confined in the slot cavities with TM20 mode, indicating a relatively simple interference phenomenon, as can be seen in Fig. 1(d). Here, we can make a simple inference that FR1 is influenced both by the slot cavities and the rectangular cavity, while FR2 mainly affected by the slot cavities. As we know, in a plasmonic resonator, the accumulated phased shift per round trip for the SPPs is ϕ = 4πneff S /λ + 2φ [15,34]. Constructive interference should occur whenϕ = 2Nπ , and thus the resonant wavelength is determined by
λ=
2neff S (N − φ/π )
(2)
where neff denotes the effective index of the SPPs, which can be obtained by solving the eigenfunction in the MDM waveguide [35].
Fig. 1. (a) Schematic configuration and geometric parameters of the plasmonic waveguide system. (b) Transmission spectra of the plasmonic waveguide system: the parameters are set as L ¼ 550 nm, △H¼0 and W1 ¼225 nm. (c and d) The Hz 2 field distributions at the resonance wavelength λ ¼706 nm and λ ¼869 nm.
Y. Zhang et al. / Optics Communications 370 (2016) 203–208
φ is the phase shift brought by the SPP reflection off the metal wall in the resonator, S presents the effective length of the resonator, and N denotes resonance orders in the slot cavity or the rectangular cavity. Based on Eq. (2), we can obtain that the dependence of the variation of the resonant wavelength on the resonator length S is
2neff dλ = dS N − φ /π
(3)
Note that the geometric length of the plasmonic resonator is only on the order of an optical wavelength, so different waveguide modes can be reflected back and forth off the metal walls in the plasmonic resonators, constructing a FP resonator. Because of the quite different field distributions and propagation characteristics of these waveguide modes, these different resonances will emerge in the plasmonic resonators. At λ ¼706 nm, the system shows a complicated interference phenomenon among TM10 mode in the rectangular cavity and TM30 modes in the two identical slot cavities, which gives rise to the FR1. Besides, TM20 modes are excited in the two identical slot cavities at λ ¼869 nm, indicating the interference phenomenon which gives rise to the FR2 only affected by the length of the slot cavities. Based on Eqs. (2) and (3), we can infer FR1 is proportional to width of the rectangular cavity or length of the slot cavities. Analogously, the resonant wavelength keeps almost unchanged with increasing width of the rectangular cavity and is proportional to length of the slot cavities for the FR2. To test our inference, the FEM is used to investigate the properties of the proposed structure. First, we calculate the transmission spectra for different W with L¼ 550 nm, as shown in Fig. 2(a)–
Fig. 2. (a)–(e) Transmission spectra for different W with L ¼ 550 nm, H¼345 nm and △H¼0.
205
(e). For the FR2, the effective cavity length S is W, it is hardly influenced the resonance wavelength when L is fixed, here Δλ /ΔW ≈ 0, as shown in the black symbol line in Fig. 2(a)–(e). Besides, from the field distribution at the resonance wavelength in Fig. 1(d), we also know that a large power flow is confined in the two identical slot cavities. The mutual coupling of the two identical slot cavities is the origin of FR2. Therefore, the resonant wavelength is determined by the fixed values of L. For the FR1, it originates from the interference between the TM10 mode in the rectangular cavity with TM30 mode in the two identical slot cavities and its mechanism is relatively complex, we only analyze qualitatively. According to the theory of standing wave [35], the wavelength is proportional to the effective length S, Δλ ∝ ΔS . It shows a phenomenon of redshift and is consistent with the red symbol line in Fig. 2(a)–(e). Meanwhile, we can also infer the extent redshift will become bigger when we change width of the rectangular cavity comparing to the changing length of the slot cavity for the FR1. It is because the rectangular cavity plays a dominant role comparing to the slot cavity for the FR1 and a large power flow is trapped in the rectangular cavity, as shown in Fig. 1(c)–(d). Here, Δλ /ΔS ≈ 1.1 when the width of the rectangular resonator increases. Therefore, the resonant wavelength can be easily manipulated by adjusting the width of the rectangular cavity but without influence on the other peak. This character may offer excellent flexibility to the design the sensors. Successively, the transmission spectra is investigated by changing length of the slot cavities, and the results are displayed in Fig. 3(a)–(e). Herein, the parameters are set with a fixed W¼225 nm, and an alterable L. For the FR1, we only analyze
Fig. 3. (a)–(e) Transmission spectra for different L with W ¼225 nm, H¼ 345 nm and △H¼0. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
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Fig. 4. (a) Transmission spectra for different refractive index. (b) The calculated FOM at different wavelength, the parameters are set as L ¼550 nm, △H¼ 0, H¼345 nm and W1 ¼225 nm.
qualitatively because of its complex mechanism. It is observed that its resonant wavelength is linearly redshifted with increasing length L with the slope of Δλ /ΔS ≈ 0.44 . The value is about 2/5 comparing to changing the width in the rectangular cavity and agrees well with the above inference. Increasing ΔL , the resonance wavelength of FR2 has a redshift with a slope Δλ /ΔS ≈ 1.36, as shown in the red symbol line in Fig. 3(a)–(e). In this case, a large power flow is confined in the two identical slot cavities. We have S ¼L, N ¼3 (resonance order in the slot cavity) neff = 1.4 and simulations show that φ equals about π . Thus, Eq. (3) becomes dλ dS
= 2 × 1.4/3 − φ /π ≈ 1.4 , agreeing well with the slope of the red symbol line in Fig. 3(a)–(e). By utilizing the asymmetric Fano transmission spectrum, we study the performance of our structure as a plasmonic nanosensor, and the results are displayed in Fig. 4(a) and (b). Moreover, the sensitivity and the FOM as the key parameter are widely used to evaluate the performance of the double Fano resonance. The resonant wavelength has a red shift when increasing the refractive index. The sensitivity of a sensor (nm/RIU) is usually defined as the shift in the resonance wavelength per unit variations of the refractive index [5,33]. The sensitivity of the proposed structure is about 800 nm/RIU, which is excellent compared with that of the plasmonic sensors reports [30]. To better evaluate the performance of the plasmonic sensor, the figure of merit ( FOM) is studied, which defined as FOM = ∆T /T ∆n [11,18,19], where T denotes the transmittance in the proposed structure. Fig. 4(b) depicts the calculated FOM. The maximum value of FOM is as high as
1.01 104 at λ ¼ 894 nm, which is due to the sharp asymmetric Fano line-shape with ultra-low transmittance at this wavelength. The FOM is much higher than that of the plasmonic sensors [2,27,30].
3. Asymmetric rectangular cavity coupling with the slot cavity According to the above characteristics of the plasmonic system based on rectangular cavity coupling with the slot cavity, the proposed Fano structure in Fig. 1(a) is flexible and can be easily extended to a multiple Fano resonances system by asymmetric rectangular cavity coupling with the slot cavites. Herein, the parameters are set with a fixed △H¼ 45 nm, H2 ¼125 nm, L¼550 nm and W1 ¼ 225 nm. In order to investigate the optical responses of the proposed structure, its transmission spectra are numerically calculated using the finite element method. It is found that a new sharp and asymmetric response line-shape emerges comparing to the symmetric rectangular cavity coupling with the slot cavities, as shown in Fig. 5(a). Meanwhile, a little platform appears at about 691 nm, which is caused by the symmetrybreaking of the MDM waveguide plasmonic structure. Fig. 5 (b) shows the field distributions of Hz 2 at the resonance peak of 783 nm, we know that a strong field distribution is confined in the rectangular cavity and two identical slot cavities. The FR3, which is caused by the structure symmetry breaking, originates from the interference of the TM01 mode in the rectangular cavity with TM20
Fig. 5. (a) Transmission spectra of the plasmonic waveguide system: the red, black line represents the transmission spectra of the asymmetric rectangular cavity and symmetric rectangular coupling with the slot cavites, respectively. The parameters are set as L ¼ 550 nm, △H¼45, H2¼ 125 nm and W1¼ 225 nm. (b) The Hz 2 field distributions with and without the groove at the resonance wavelength λ¼ 783 nm. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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calculated FOM. The maximum value of FOM is as high as 1.35 104 at λ ¼791 nm, which is due to the sharp asymmetric Fano line-shape with ultra-low transmittance at this wavelength. Here, FOM is much higher than that of the plasmonic sensors [2,27,30].
4. By regulating symmetric rectangular cavity coupling with the slot cavities
Fig. 6. Dependence of the resonant wavelengths on the difference △H with fixed H2¼ 125 nm, L ¼550 nm and W1¼ 225 nm. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
mode in the two identical slot cavities. Furthermore, the FEM is used to investigate the more properties of the proposed structure. Here, we calculate the dependence of the resonant wavelengths on the difference △H with fixed H2¼ 125 nm, L ¼550 nm and W1 ¼225 nm, as shown in Fig. 6. Due to the resonance wavelength of FR1 and FR2 keeps almost unchanged, as shown in Fig. 5(a). Therefore, they have the analogous characteristics when we change the parameter of the plasmonic system based on the above investigations, here not be discussed. Here, we focus on the FR3 and analyze it qualitatively base on its complex mechanism. From Fig. 5(b), it is found that there exists one node for the distribution along the y-axis direction in the rectangular cavity, yielding a symmetric waveguide mode in the plasmonic resonator. Here, the effective length is H. According to the theory of standing wave [35], the wavelength is proportional to the effective length, namely Δλ ∝ ΔH . That is with the increasing effective length, the resonance wavelength is increasing linearly, which denotes redshift and is consistent with the blue symbol line in Fig. 6. Successively, we investigate the application as the sensor based on the proposed plasmonic structure, as shown in Fig. 7(a) and (b). The resonant wavelength has a red shift when increasing the refractive index. Here, the sensor still has the good sensitivity, about 800 nm/RIU, which is excellent compared with the previous plasmonic sensors reports [30]. Besides, FOM as an important parameter of the sensor is also investigated. Fig. 7(b) depicts the
For the schematic configuration of Fig. 1(a), we investigate the proposed plasmonic system for the possible application. Since in the process of production, it is difficult to get sharp angle of the rectangular cavity and slot cavities. In contrast, circular bead is more accessible. Based on the Fig. 1(a), we use a circular bead replace right angle of the rectangular cavity and slot cavities and keep the same parameters with Fig. 1(b), as shown the inserted schematic configuration in Fig. 8(a). It is found that the transmission spectrum in the plasmonic waveguide system exhibits a sharp and asymmetric response line-shape, which is different from the double Fano profile, as shown in Fig. 8(a). Here, we can infer that the broad resonance mode in the circular bead of the rectangular cavity is not excited, only the narrow resonance mode in the circular bead of the slot cavities is excited. To further understand the underlying physics of the resonant peaks in the transmission spectra, the field distributions of Hz 2 at λ ¼846 nm is displayed in Fig. 8(b). We find that a strong field distribution is confined in the circular bead of two identical slot cavities. Due to the characteristics of the circular bead of the rectangular cavity, angular resonance in the rectangular is vanished comparing to the Fig. 1(c). In this case, SPPs will propagate into the rectangular cavity and then be captured into the slot cavity. The interference of a narrow discrete spectrum in the slot cavities and a broad continuous spectrum in the rectangular cavity, gives rise to the Fano profile. Based on the above investigations and analyses, we can obtain single, double and multiple Fano profile by the different plasmonic system. Due to different origins, these Fano profile can be easily tuned.
5. Conclusion In summary, a MDM-waveguide structure is proposed to realize the single or the multiple Fano resonances in the symmetric and asymmetric plasmonic structure. In our proposed plasmonic
Fig. 7. (a) Transmission spectra for different refractive index and (b) the calculated FOM at different wavelength, the parameters are set as L ¼ 550 nm, △H ¼45 nm, H ¼ 345 nm and W1¼ 225 nm.
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Fig. 8. (a) Schematic configuration and transmission spectra of the plasmonic waveguide system, (b) the Hz resonance wavelength λ ¼ 846 nm.
system, simulation results show that symmetric/asymmetry rectangular cavity or the regulating rectangular cavity couple with slot cavities and different waveguide modes can be excited. Due to the interaction of the waveguide mode, the transmission spectra possess single, double or multiple sharp asymmetrical profiles. Because of the different origins, these Fano resonances exhibit different dependence on the parameters of the structure and can be easily tuned. These characteristics offer flexibility to design the device. This nanosensor yields a sensitivity of ∼800 nm/RIU and a figure of merit of about ∼1.35 104, which can find widely applications in the plasmonic nano-sensing area.
Acknowledgments This work was supported by the National Natural Science Foundation of China under Grant nos. 11374041, 11374042, 11404030 and 11574035 and the BUPT Excellent Ph.D. Students Foundation under Grant Nos. CX201324 and Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Tele-communications), PR China
References [1] [2] [3] [4] [5] [6] [7] [8] [9]
W.L. Barnes, A. Dereux, T.W. Ebbesen, Nature 424 (2003) 824. H. Lu, X.M. Liu, D. Mao, G.X. Wang, Opt. Lett. 37 (2012) 3780. K.H. Wen, Y.H. Hu, L. Chen, J.Y. Zhou, L. Lei, Z. Meng, Plasmon 10 (2015) 27. H. Lu, X.M. Liu, D. Mao, G.X. Wang, Opt. Lett. 36 (2011) 3233. N. Liu, M. Mesch, T. Weiss, M. Hentschel, H. Giessen, Nano Lett. 10 (2010) 2342. T. Xu, Y.K. Wu, X. Luo, L.J. Guo, Nat. Commun. 1 (2010) 118. G. Veronis, S. Fan, Appl. Phys. Lett. 87 (2005) 131102. E.N. Economou, Veronis, S. Fan, Phys. Rev. 182 (1969) 539. K.H. Wen, Y.H. Hu, L. Chen, J.Y. Zhou, M. He, L. Lei, Z.M. Meng, IEEE Photonics J.
2
field distributions with and without the groove at the
7 (2015) 1. [10] K.H. Wen, L.S. Yan, W. Pan, B. Luo, Z. Guo, Y.H. Guo, X.G. Luo, J. Light. Technol. 32 (2014) 1701. [11] Z. Chen, W.H. Wang, N.L. Cui, L. Yu, G.Y. Duan, F.Y. Zhao, J.H. Xiao, Plasmonics 10 (2015) 721. [12] J.J. Chen, Z. Li, M. Lei, X.L. Fu, J.H. Xiao, Q.H. Gong, Plasmonics 7 (2012) 441. [13] Y. Kou, F.X. Chen, Opt. Express 19 (2011) 6042. [14] J. Tao, X.G. Huang, X. Lin, J. Chen, Q. Zhang, X. Jin, J. Orthop. Allied Sci. 27 (2010) 323. [15] J. Tao, X.G. Huang, X. Lin, Q. Zhang, X. Jin, Opt. Express 17 (2009) 13989. [16] Q. Zhang, X.G. Huang, X.S. Lin, J. Tao, X.P. Jin, Opt. Express 17 (2009) 7549. [17] X.S. Lin, X.G. Huang, Opt. Lett. 33 (2008) 2874. [18] Z. Chen, L. Yu, L.L. Wang, G.Y. Duan, F.Y. Zhao, J.H. Xiao, IEEE Photonics Technol. Lett. 27 (2015) 1695. [19] Z. Chen, L.N. Cui, X.K. Song, L. Yu, J.H. Xiao, Opt. Commun. 340 (2015) 1. [20] J.J. Chen, Z. Li, J. Li, Q.H. Gong, Opt. Express 19 (2011) 9976. [21] H. Lu, X.M. Liu, Y.K. Gong, D. Mao, L.R. Wang, Opt. Express 19 (2011) 12885. [22] U. Fan, Phys. Rev. 124 (1866) 1961. [23] A.E. Miroshnichenko, S. Flach, Y.S. Kivshar, Rev. Mod. Phys. 82 (2009) 2257. [24] J.J. Chen, Z. Li, Y.J. Zou, Z.L. Deng, J.H. Xiao, Q.H. Gong, Plasmonics 8 (2013) 1627. [25] J.B. Lassiter, H. Sobhani, J.A. Fan, J. Kundu, F. Capasso, P. Nordlander, Nano Lett. 10 (2010) 3184. [26] F. Hao, Y. Sonnefraud, P.V. Dorpe, S.A. Maier, N. Halas, P. Nordlander, Nano Lett. 8 (2008) 3983. [27] J.W. Qi, Z.Q. Chen, J. Chen, Y.D. Li, W. Qiang, J.J. Xu, Q. Sun, Opt. Express 22 (2014) 14688. [28] Z. Chen, J.J. Chen, L. Yu, J.H. Xiao, Plasmonics 10 (2015) 131. [29] S. Collin, G. Vincent, R. Haïdar, N. Bardou, S. Rommeluère, J. Pelouard, Phys. Rev. Lett. 104 (2010) 358. [30] Z.Q. Chen, J.W. Qi, J. Chen, Y.D. Li, Z.Q. Hao, W.Q. Lu, J.J. Xu, Q. Sun, Chin. Phys. Lett. 30 (2013) 057301. [31] N. L, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, H. Giessen, Nat. Mater. 8 (2009) 758. [32] Z. Han, S.I. Bozhevolnyi, Opt. Express 19 (2011) 3251. [33] J. Becker, A. Trügler, A. Jakab, U. Hohenester, C. Sönnichsen, Plasmonics 5 (2010) 161. [34] F.F. Hu, H.X. Yi, Z.P. Zhou, Opt. Lett. 36 (2011) 1500. [35] J.A. Dionne, L.A. Sweatlock, H.A. Atwater, A. Polman, Phys. Rev. B 73 (2006) 035407.