Abstract

In this paper, an asymmetric plasmonic structure composed of two MIM (metal-insulator-metal) waveguides and two rectangular cavities is reported, which can support triple Fano resonances originating from three different mechanisms. And the multimode interference coupled mode theory (MICMT) including coupling phases is proposed based on single mode coupled mode theory (CMT), which is used for describing and explaining the multiple Fano resonance phenomenon in coupled plasmonic resonator systems. Just because the triple Fano resonances originate from three different mechanisms, each Fano resonance can be tuned independently or semi-independently by changing the parameters of the two rectangular cavities. Such, a narrow ‘M’ type of double Lorentzian-like line-shape transmission windows with the position and the full width at half maximum (FWHM) can be tuned freely is constructed by changing the parameters of the two cavities appropriately, which can find widely applications in sensors, nonlinear and slow-light devices.

© 2016 Optical Society of America

1. Introduction

Fano resonance has emerged as an important area in the field of plasmonics over the recent past, because surface plasmon polaritons (SPPs) can overcome the diffraction limit and confine light in deep sub-wavelength dimensions [1]. Many plasmonic structures have been designed to realize the Fano resonance [2–5]. J. Wang et al. [6] reported a planar plasmonic structure to obtain double Fano resonances originated from interplay of electric and magnetic plasmon modes. D. Wang [7] realized tuning multiple Fano and plasmon resonances in plasmonic-photonic nanostructures. In our previous work [8], the multiple Fano resonances with high figure of merit(FOM) is also achieved in coupled plasmonic resonator system. Due to the advantage for enhanced bio-chemical sensing, spectroscopy, and multicolor nonlinear processes, the multiple Fano resonances become more important and have gained much attention [9–13]. Among all the nanostructures, the MIM waveguide structures have attracted many researchers attention because these structures exhibiting more suitable for the highly integrated optical circuits due to their deep-sub-wavelength confinement of light [14, 15]. And based on the MIM waveguides, a large number of devices, such as splitters [12, 16], sensors [17, 19], optical switches [20], nonlinear [21] and slow-light devices [22–24]. Thus, investigations of the response line-shapes and the physical mechanism in the coupled-resonator systems are of importance for designing complex functional plasmonic devices as well as for improving their performances [25]. For many applications, the tunability of the Fano resonances is very important. However, because the multiple Fano resonances are caused by the collective behavior of the total plasmonic systems, it is difficult to get an independent and precise tailoring of the multiple Fano resonances.

In this paper, independently or semi-independently tunable triple Fano resonances are realized in asymmetric coupled plasmonic resonator system, and the multimode interference coupled mode theory (MICMT) including coupling phases is proposed based on single mode coupled mode theory (CMT). MICMT is used for describing and explaining the multiple Fano resonances phenomenon in coupled plasmonic resonator systems. Firstly, an asymmetric plasmonic structure composed of a rectangular cavity and two MIM (metal-insulator-metal) waveguides is investigated. The double Fano resonances produced by this structure originate from the interference between different resonant modes according to MICMT, one is induced by the interference between the symmetric modes, and another originates from the interference between the symmetric and anti-symmetric modes. Another rectangular cavity is added to this structure, so as to form a new coupled plasmonic resonator system including new resonant modes, which can support triple Fano resonances originating from three different mechanisms. The third Fano resonance originates from the interference between the resonant modes of the added and original rectangular cavities. Because the triple Fano resonances originate from three different mechanisms, each Fano resonance can be tuned independently or semi-independently by changing the height and length of the two rectangular cavities. And during the tuning process, the FOMs (figure of merit) of the three Fano resonances remain keep large values, all larger than 725. Based on the large FOM and independent tunability of the triple Fano resonances, our tunable triple Fano resonances plasmonic structure can be used in highly integrated plasmonic devices with excellent performance, such as splitters, filters, bio-chemical sensors and optical switches.

2. Structures descriptions

The coupled plasmonic resonator system in Fig. 1(b) is the aim of our research, before which is investigated the coupled plasmonic resonator system in Fig. 1(a) needed to be investigated first. The structure in Fig. 1(a) is composed of two MIM waveguides (S1 and S2) and a rectangular cavity (A). The height and length of rectangular cavity A are H and LA respectively, and the waveguides S1 and S2 with the widths are both D1 are symmetric about rectangular cavity A. The change of the relative positions between the axis of the MIM waveguide and the rectangular cavity in y direction ΔH=H2H1, as shown in Fig. 1(a), is used to describe the symmetry-breaking. Another small rectangular cavity B is added to the structure shown in Fig. 1(a), thereby forming a new coupled plasmonic resonator system shown in Fig. 1(b). The width and length of rectangular cavity B are D2 and LB, the gap between rectangular cavity A and rectangular cavity B is g. In consideration of the application in biotechnology, the dielectric in the waveguides and cavities are chosen to be water (n = 1.33). The metal is sliver, of which the permittivity is characterized by the Drude model [26]: εm=εωp2/(ω2+jγω) with ε=3.7,ωp=9.1eV,γ=0.018eV.

 figure: Fig. 1

Fig. 1 Schematic diagram of the asymmetric plasmonic structure composed of (a) two MIM waveguides and one rectangular cavity and (b) two MIM waveguides and two rectangular cavities.

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In order to investigate the optical responses of the proposed structure, the transmittance are numerically calculated using commercial software (COMSOL Multiphysics) of the finite-element analysis method (FEM) [4]. The transmittance of the SPPs in plasmonic structure is defined as the quotient between the SPP power flows (obtained by integrating the Poynting vector over the cross section of the MIM waveguide) of the observing port with cavities and without cavities, that is T=P/P0 [18, 19]. In order to excite the SPPs, the input light is set to be transverse magnetic (TM) plane wave obtained from boundary mode analysis.

3. MICMT analysis

In coupled plasmonic resonator system, the total field can be expressed as the field superposition of the resonant modes. For single mode coupling, if the choice of the reference plane is appropriate, the coupling phase between waveguide and resonant cavity will be zero and has no effect on the transmittance of the coupled plasmonic resonator system. For multiple modes coupling, the coupling phases of different modes in waveguide and resonant cavity are different at the same reference plane. Because of the interference between different modes, the transmittance of the coupled plasmonic resonator system will be influenced by these coupling phases, so that the relationship between these coupling phases need be considered. Based on single mode coupled mode theory(CMT), the MICMT equations including coupling phases are given as follows

dandt=(jωn1τn01τn11τn2)an+κn1s1++κn2s2+
s1=s1++nκn1γnanejφn1
s2=s2++nκn2γnanejφn2
Where an and ωn are the field amplitude and resonant frequency of the nth resonant mode, γn is the normalized coefficient which is approximated as 1. τn0 is the decay time of internal loss of the nth resonant mode in resonant cavity. τn1 and τn2 are the decay time of the coupling between the resonant cavity and waveguides (S1 and S2), θn1 and θn2 are the coupling phases of the nth resonant mode. φn1 and φn2 are the complex amplitude phases of the nth resonant mode coupled to the waveguides (S1 and S2). si± are the field amplitudes in each waveguide (i=1,2, for outgoing (-) or incoming ( + ) from the resonator). According to MICMT equations, when s2+=0, the complex amplitude transmission coefficient from waveguide S1 to waveguide S2 can be expressed as follows
t=s2s1+=nγn|κn1||κn2|ejφnj(ωωn)+1τn0+1τn1+1τn2,φn=φn2+θn1θn2
Then, the corresponding transmittance of the plasmonic system isT=|t|2. And φn is the coupling phase difference of the nth resonant mode.

In theory, there are a number of resonant modes in plasmonic resonator. Here, we only consider the interference between the modes of which the resonant wavelengths are in and adjacent to the spectral range that we are interested in, and ignoring the influences of other modes. Because of the input light is set to be transverse magnetic (TM) plane wave, the resonant modes can be classified using TMm,n, m, n are integers and indicate the x- and y-directional resonant orders, respectively. The resonant wavelengths of two modes TM0,3 and TM1,0 are in the spectral range of 600 nm ~900 nm that we are interested in, as shown in Figs. 2(a) and 2(b). Two modes of which the resonant wavelengths are adjacent to the spectral range of 600 nm ~900 nm are TM0,2 and TM0,4, as shown in Figs. 2(c) and 2(d). So within the spectral range of 600 nm ~900 nm, the transmission response of the plasmonic structure shown in Fig. 1 (a) is mainly related to the four resonant modes. The four resonant modes TM0,2, TM0,3, TM1,0 and TM0,4, of which the magnetic field (Hz) distributions are given in Fig. 2, are expressed as a1, a2, a3 and a4. The resonant wavelengths of the four resonant modes are about λ1=1105nm, λ2=788nm, λ3=734nm and λ4=593nm, respectively. Waveguides S1 and S2 with the widths both are D1 are symmetrical about rectangular cavity A, so τn1=τn2=τn and θn1=θn2, the transmittance formula of the plasmonic system is simplified as

 figure: Fig. 2

Fig. 2 The distribution of the normalized magnetic field (Hz) of the resonant modes (a) TM1,0 mode at 734 nm, (b) TM0,3 mode at 788 nm, (c) TM0,2 mode at 1105 nm and (d) TM0,4 mode at 593 nm respectively in the rectangular cavity A with LA = 220 nm, H = 760 nm in Fig. 1(a).

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T=|t|2=|n=142γnejφnj(ωωn)τn+2+τnτn0|2,φn=φn2

4. Simulation results and discussions

Before the coupled plasmonic resonator system in Fig. 1(b) is investigated, the coupled plasmonic resonator system in Fig. 1(a) needed to be investigated first. When the parameters of the structure are LA = 220 nm, H = 760 nm, ΔH = 0 and D1 = 50 nm, the system is symmetric in y-direction. In this case, the y-directional asymmetric mode(TM0,3) cannot be excited, only the y-directional symmetric modes exist in this system. In the four modes that we are concerned about, there are three y-directional symmetric modes TM0,2, TM1,0 and TM0,4 of which the resonant wavelengths are 1105 nm, 734 nm and 593 nm, respectively. Thus, the subscript m,n in the transmittance formula Eq. (4) and Eq. (5) just take 1,3,4. The decay time of the coupling and internal loss can be obtained by curve fitting, which are τ1=10.3fs, τ3=179fs, τ4=21fs and τ10=911fs, τ30=496fs, τ40=53.8fs, respectively. In order to facilitate the calculation, the coupling phase difference φn(ω) can be approximately considered as a constant in very narrow wavelength range. Then, the coupling phase differences are about φ1=0.3π, φ3=0.58π and φ4=0.89π near the resonant wavelength of 734 nm. The simulation curve and theoretical curve of the transmittance of this plasmonic system are given in Fig. 3(a).

 figure: Fig. 3

Fig. 3 The FEM simulation results (blue lines) and MICMT results (red lines) of the transmission spectrum of the asymmetric plasmonic system with H = 760 nm, LA = 220 nm and (a) ΔH = 0, (b) ΔH = 15 nm, (c) ΔH = 30 nm. The phase curves of the complex amplitude transmission coefficients of the four modes TM0,2, TM0,3, TM1,0 and TM0,4 in the asymmetric plasmonic system with H = 760 nm, LA = 220 nm and (d) ΔH = 0, (e) ΔH = 15 nm, (f) ΔH = 30 nm.

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When the symmetry-breaking parameter of the structure respectively is ΔH=15nm and ΔH=30nm, the simulation curve and theoretical curve of the transmittance are given in Figs. 3(b) and 3(c). Here, the left Fano resonance is called FR1, and the right Fano resonance is called FR2 [5]. When the symmetry-breaking of the plasmonic structure was induced, the y-directional asymmetric mode TM0,3 at about 788 nm in the rectangular cavity A is excited, which is apparent in symmetrical plasmonic structure. The FR 2 originates from the interference between the asymmetric mode TM0,3 and the symmetric modes TM0,2, TM1,0, TM0,4. By curve fitting, it can be obtained that τ2|ΔH=15nm=1565fs, τ2|ΔH=30nm=1565fs andτ20=478fs. The coupling phase differences are about φ2|ΔH=15nm=0.11π, φ2|ΔH=30nm=0.06π. Through comparing Figs. 3(b) and 3(c), it can be seen that the transmittance difference between the peak and dip of FR2 when ΔH=15nm is smaller than that when ΔH=30nm, the reason will be illustrated in the analysis of Argand diagram latter. Moreover, the reason of the deviation between the simulation and theoretical curves is that the coupling phase difference φn(ω) is approximately considered as a constant, actually it is the function of angular frequency(ω).

In order to facilitate the theoretical analysis, the complex amplitude transmission coefficient of each mode is set as tn=2ejφn/[j(ωωn)τn+2+τn/τn0]. From Eq. (5), it is known that the transmission response of the plasmonic system can be expressed as the ‘interference’ between the transmission coefficients tn of the four resonant modes. The phase curve ϕn of the transmission coefficient tn is given in Figs. 3(d)-3(f). As shown in Figs. 3(e) and 3(f), the phase mutation occurred in t3 is about π near the resonant wavelength of 734 nm, while the phases of t1, t2 and t4 almost remain unchanged; the phase mutation occurred in t2 is also about π near the resonant wavelength of 788 nm, while the phases of t1, t3 and t4 almost remain unchanged. In this case, the coherence properties (destructive or constructive) of transmission coefficients are reverse near the opposite sides of the two resonant wavelengths, thereby forming the asymmetric double Fano resonances line-shape.

The Argand diagrams of the transmission coefficients tn at the peak and dip of FR1 and FR2 are given in Fig. 4. Here, the phase ϕ1 of the transmission coefficient t1 is taken as the reference zero point. As shown in Figs. 4(a)-4(d), FR1 is mainly the result of the interference between the transmission coefficients t1, t3 and t4, the influence of the transmission coefficient t2 on FR1 is so little that it can be neglected. Figures 4(d) and 4(e) show that the transmission coefficients of the four modes all have effect on FR2. And we have already mentioned that the transmittance difference between the peak and dip of FR2 when ΔH=15nm is smaller than that when ΔH=30nm, the reason is that the amplitudes and phases of the transmission coefficients t1, t3 and t4 when ΔH=15nm are basically identical with those when ΔH=30nm and only the phase change of the transmission coefficient t2 is obvious. The amplitudes of the transmission coefficients t2|ΔH=15nm are 0.22 and 0.27 at the peak and dip of FR2 respectively, and the amplitudes of the transmission coefficients t2|ΔH=30nm are 0.25 and 0.27, they are basically identical. While the phase ϕ2 of t2|ΔH=15nm are 0.34π and 0.78π at the peak and dip of FR2 respectively, and that of t2|ΔH=30nm are 0.31π and 0.90π respectively. This is the reason why the difference of the transmittance between the peak and dip of FR2 induced by the change of ΔH is different.

 figure: Fig. 4

Fig. 4 Argand diagrams of the transmission coefficients t1, t2, t3 and t4 of the four resonant modes TM0,2, TM0,3, TM1,0 and TM0,4 at the peak (red lines) and dip (blue lines) of FR1 and FR2 in the plasmonic system shown in Fig. 1(a) with H = 760 nm, LA = 220 nm and (a, e) ΔH = 15nm, (c, f) ΔH = 30 nm. (b) and (d): The detailed transmission coefficients t1, t2 and t3 in the areas selected by rectangular boxes in (a) and (c), respectively.

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The transmission responses of the asymmetric plasmonic system shown in Fig. 1(b) will be investigated next. The parameters of the plasmonic structure are ΔH = 30 nm, g = 10 nm, H = 760 nm, LA = 220 nm, LB = 500 nm and D1 = D2 = 50 nm, respectively. Figure (5) shows the simulation and theoretical curves of the transmittance and the distribution of the normalized magnetic field (Hz) in the plasmonic system shown in Fig. 1(b). As shown in Figs. 5(c) and 5(d), a new resonant mode appears in the range of 600 nm ~900 nm after the rectangular cavity B is added to the plasmonic structure in Fig. 1(a), of which the resonant wavelength has significant relationship with rectangular cavity B and the upper part of rectangular cavity A. Here, the new added resonant mode is considered as the fifth resonant mode a5 of the plasmonic system, and its resonant wavelength is about 672 nm. According to MICMT, the numbers of the resonant modes increase to 5, that is n=1,2,,5. The simulation and theoretical curves of the transmittance is shown in Fig. 5(d), and the Fano resonance on the left of FR1 is called FR3. It can be known from Fig. 5(c) that the resonant wavelength of the fifth resonant mode a5 has significant relationship with LA and LB.

 figure: Fig. 5

Fig. 5 The distribution of the normalized magnetic field (Hz) of the resonant modes at (a) 791 nm, (b) 788 nm and (c) 1105 nm in the asymmetric plasmonic system respectively, when ΔH = 30 nm, H = 760 nm, LA = 220 nm, LB = 500 nm, g = 10 nm and D1 = D2 = 50 nm. (d) The FEM simulation results (blue lines) and MICMT results (red lines) of the transmission spectrum of the asymmetric plasmonic system.

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The figure of merit (FOM) is a key parameter for Fano resonance, which can be defined as FOM*=ΔT/TΔn at a fixed wavelength and FOM=max|FOM*| near a fixed wavelength [27], where T denotes the transmittance in the proposed structure. Figure 3(a) shows the transmission spectra for different refractive indexes of the dielectric in the waveguides and cavities with the structure parameters of ΔH = 30 nm, g = 10 nm, H = 760 nm, LA = 220 nm, LB = 500 nm and D1 = D2 = 50 nm. With the increasing of n from 1.33 to 1.34, the peaks of FR1, FR2 and FR3 are all red shift, the peaks of FR 1 red shifts from about 733 nm to 739 nm, the peaks of FR 2 red shifts from about 791 nm to 796 nm and the peaks of FR3 red shifts from about 672 nm to 677 nm. The FOM*curve of this plasmoic system is given in Fig. 6(b), and the maximum FOMs of FR1, FR2 and FR3 are about 3803, 816 and 2947 respectively.

 figure: Fig. 6

Fig. 6 (a) The transmission spectra of the plasmonic structure with H = 760 nm, LA = 220 nm, LB = 500 nm, D1 = D2 = 50 nm, g = 10 nm, ΔH = 30 nm, and different refractive indexes of the dielectric in the waveguides and cavities, n = 1.33 (blue line), n = 1.34 (red line). (b) The FOM* curve of this plasmonic structure.

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When ΔH = 30 nm, g = 10 nm and D1 = D2 = 50 nm are fixed value, the influence of the structure parameters on the transmission spectrum profile is studied in detail and the results are shown in Fig. 7. Figure 7(a) depicts that the position of FR2 can be tuned by the height (H) of the rectangular cavity A. As shown in Fig. 7(a), with H increasing from 730 nm to 770 nm, the position of FR2 changes from 763 nm to 800 nm, while the positions of FR1 and FR3 almost have no change(< 1 nm), this kind of tuning is called ‘independent tuning’. Figure 7(b) shows that the position of FR3 can be tuned by the length (LB) of the rectangular cavity B. As shown in Fig. 7(b), with LB increasing from 490 nm to 530 nm, the position of FR3 changes from 667 nm to 687 nm, while the positions of FR1 and FR2 also almost have no change(< 1 nm), so the tuning of FR2 is also ‘independent tuning’. Figure 7(c) depicts that the position of FR1 can be tuned by the length (LA) of the rectangular cavity A. As shown in Fig. 7(c), with LA increasing from 215 nm to 227 nm, the position of FR1 changes from 722 nm to about 750 nm, and the position of FR3 changes from 665 nm to about 682 nm, while the positions of FR2 has a little change about 3 nm. So, the tuning of FR1 has little effect on FR2 but evident on FR3, this kind of tuning is called ‘semi-independent tuning’. And as shown in Fig. 7(d), with the change of the height (H) of rectangular cavity A, the FOMs of FR1, FR2 and FR3 change slightly, no more than 25%. In Fig. 7(e), with the change of the length LB, the FOMs of FR1 and FR2 almost have no change, no more than 9%, but the FOM of FR3 increase by about 55%. In Fig. 7(f), with the change of the length LA, the FOMs of FR2 and FR3 change a little, no more than 27%, but the FOM of FR1 increase by about 1.2 times. This means that the FOMs of the triple Fano resonances keep high value in the tuning process.

 figure: Fig. 7

Fig. 7 The dependence of transmittance on the structure parameters, when ΔH = 30 nm, g = 10 nm, n = 1.33 and D1 = D2 = 50 nm. (a) Different H with fixed LA = 220 nm and LB = 500 nm; (b) different LB with fixed H = 760 nm, LA = 220 nm; (c) different LA with fixed H = 760 nm and LB = 500 nm. (d) ~(f) The change curves of FOM of FR 1 (blue line), FR 2 (green line) and FR 3 (red line) with the change of the structure parameters H, LB and LA, respectively.

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As shown in Fig. 8, attribute to the tunability of FR 1 and FR 2 and the reversed ‘direction’ of Fano asymmetry, the transmission window can be constructed with the position and the full width at half maximum (FWHM) can be adjusted freely. And because FR3 is independently tunable, after the position and FWHM of the first Lorentzian-like line-shape transmission window is determined, then the tuning for FR3 is proceeded, so that the ‘M’ type double Lorentzian-like line-shape transmission windows of which the peak interval and FWHMs are respectively less than 20nm and 8nm can be constructed. And the Lorentzian-like line-shape on the right is called LL1, the Lorentzian-like line-shape on the left is called LL2. As shown in Fig. 8(a), the position of the ‘M’ type double Lorentzian-like line-shape transmission window can be adjusted freely, and Fig. 8(b) shows that the FWHM of each line-shape can also be adjusted freely. This kind of transmission window, whose position and FWHM can be adjusted freely, can be used in filters, enhanced bio-chemical sensors, nonlinear and slow-light devices.

 figure: Fig. 8

Fig. 8 The dependence of the ‘M’ type of double Lorentzian-like line-shape transmittance on the structure parameters, when ΔH = 30 nm, g = 10 nm, n = 1.33 and D1 = D2 = 50 nm are fixed values. H = 709 nm, LA = 225 nm, LB = 600 nm (blue line); H = 698 nm, LA = 221 nm, LB = 590 nm (green line); H = 708 nm, LA = 225 nm, LB = 610 nm (red line).

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5. Conclusion

In summary, we report an asymmetric plasmonic structure composed of two MIM waveguides and two rectangular cavities. And the multimode interference coupled mode theory including coupling phases is proposed based on single mode coupled mode theory. The MICMT is used for describing and explaining the origin of the multiple Fano resonances in coupled plasmonic resonator systems. Our proposed structure can support triple Fano resonances originating from three different mechanisms. One mechanism originates from the interference between the symmetric modes, and another is induced by the interference between the symmetric and anti-symmetric modes. The third one originates from the coupling between the resonant modes of the two cavities. The triple Fano resonances can be well tuned independently or semi- independently by changing the parameters of the two rectangular cavities, and the FOMs of the triple Fano resonances remain keep large values, all larger than 725. By tuning the positions of the three Fano resonances, the transmission spectra can be well tailored and the narrow ‘M’ type of double Lorentzian-like line-shape transmission windows can be constructed. Benefit from the different ‘direction’ of Fano asymmetry, the large FOM, independent tunability and the compactness, the triple Fano resonances can find widely applications in switches, bio-chemical sensors, slow-light devices and modulator of high density nano-photonic integrated circuits devices with excellent performance.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant 11374041, Grant 11574035 and Grant 11404030), Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Tele-communications), PR China.

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24. G. Lai, R. Liang, Y. Zhang, Z. Bian, L. Yi, G. Zhan, and R. Zhao, “Double plasmonic nanodisks design for electromagnetically induced transparency and slow light,” Opt. Express 23(5), 6554–6561 (2015). [CrossRef]   [PubMed]  

25. J. J. Chen, Z. Li, Y. J. Zou, Z. L. Deng, J. H. Xiao, and Q. H. Gong, “Response line-shapes in compact coupled plasmonic resonator systems,” Plasmonics 8(2), 1129–1134 (2013). [CrossRef]  

26. X. S. Lin and X. G. Huang, “Tooth-shaped plasmonic waveguide filters with nanometeric sizes,” Opt. Lett. 33(23), 2874–2876 (2008). [CrossRef]   [PubMed]  

27. M. Bera and M. Ray, “Circular phase response based analysis for swapped multilayer metallo-dilelectric plasmonic structures,” Plasmonics 9(2), 237–249 (2014). [CrossRef]  

References

  • View by:

  1. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
    [Crossref] [PubMed]
  2. A. D. Khan and G. Miano, “Plasmonic Fano resonances in single-layer gold conical nanoshells,” Plasmonics 8(3), 1429–1437 (2013).
    [Crossref]
  3. J. Shu, W. Gao, and Q. Xu, “Fano resonance in concentric ring apertures,” Opt. Express 21(9), 11101–11106 (2013).
    [Crossref] [PubMed]
  4. J. J. Chen, Z. Li, Y. J. Zou, Z. L. Deng, J. H. Xiao, and Q. H. Gong, “Coupled-resonator-induced Fano resonances for plasmonic sensing with ultra-high figure of merits,” Plasmonics 8(4), 1627–1632 (2013).
    [Crossref]
  5. J. Chen, Z. Li, S. Yue, J. Xiao, and Q. Gong, “Plasmon-induced transparency in asymmetric T-shape single slit,” Nano Lett. 12(5), 2494–2498 (2012).
    [Crossref] [PubMed]
  6. J. Wang, C. Fan, J. He, P. Ding, E. Liang, and Q. Xue, “Double Fano resonances due to interplay of electric and magnetic plasmon modes in planar plasmonic structure with high sensing sensitivity,” Opt. Express 21(2), 2236–2244 (2013).
    [Crossref] [PubMed]
  7. D. Wang, X. Yu, and Q. Yu, “Tuning multiple Fano and plasmon resonances in rectangle grid quasi-3D plasmonic-photonic nanostructures,” Appl. Phys. Lett. 103(5), 053117 (2013).
    [Crossref]
  8. Y. Y. Zhang, S. L. Li, X. Y. Zhang, Y. Y. Chen, L. L. Wang, Y. Zhang, and L. Yu, “Evolution of Fano resonance based on symmetric/asymmetric plasmonic waveguide system and its application in nanosensor,” Opt. Commun. 370, 203–208 (2016).
    [Crossref]
  9. C. Wu, A. B. Khanikaev, and G. Shvets, “Broadband slow light metamaterial based on a double-continuum Fano resonance,” Phys. Rev. Lett. 106(10), 107403 (2011).
    [Crossref] [PubMed]
  10. Z. Chen, J. J. Chen, L. Yu, and J. H. Xiao, “Sharp trapped resonances by exciting the anti-symmetric waveguide mode in a metal-insulator-metal resonator,” Plasmonics 10(1), 131–137 (2015).
    [Crossref]
  11. K. H. Wen, Y. H. Hu, L. Chen, J. Y. Zhou, L. Lei, and Z. M. Meng, “Single/dual fano resonance based on plasmonic metal-dielectric-metal waveguide,” Plasmonics 11(1), 315–321 (2016).
    [Crossref]
  12. Z. Chen, W. H. Wang, L. N. Cui, L. Yu, G. Y. Duan, Y. F. Zhao, and J. H. Xiao, “Spectral splitting based on electromagnetically induced transparency in plasmonic waveguide resonator system,” Plasmonics 10(3), 721–727 (2015).
    [Crossref]
  13. Y. Xu and A. E. Miroshnichenko, “Reconfigurable non reciprocity with a nonlinear fano diode,” Phys. Rev. B 89(13), 1361–1377 (2014).
    [Crossref]
  14. K. H. Wen, L. S. Yan, W. Pan, B. Luo, Z. Guo, Y. H. Guo, and X. G. Luo, “Electromagnetically induced transparency-like transmission in a compact side-coupled T-shaped resonator,” J. Lightwave Technol. 32(9), 1701–1707 (2014).
    [Crossref]
  15. T. R. Liu, Z. K. Zhou, C. Jin, and X. Wang, “Tuning triangular prism dimer into fano resonance for plasmonic sensor,” Plasmonics 8(2), 885–890 (2013).
    [Crossref]
  16. G. Zhan, R. Liang, H. Liang, J. Luo, and R. Zhao, “Asymmetric band-pass plasmonic nanodisk filter with mode inhibition and spectrally splitting capabilities,” Opt. Express 22(8), 9912–9919 (2014).
    [Crossref] [PubMed]
  17. T. Wu, Y. Liu, Z. Yu, Y. Peng, C. Shu, and H. Ye, “The sensing characteristics of plasmonic waveguide with a ring resonator,” Opt. Express 22(7), 7669–7677 (2014).
    [Crossref] [PubMed]
  18. Z. Chen and L. Yu, “Multiple fano resonances based on different waveguide modes in a symmetry breaking plasmonic system,” IEEE Photonics J. 6(6), 1–8 (2014).
  19. Z. Chen, L. Yu, L. L. Wang, G. Y. Duan, Y. F. Zhao, and J. H. Xiao, “A refractive index nanosensor based on fano resonance in the plasmonic waveguide system,” IEEE Photonics Technol. Lett. 27(16), 1695–1698 (2015).
    [Crossref]
  20. H. Lu, X. Liu, L. Wang, Y. Gong, and D. Mao, “Ultrafast all-optical switching in nanoplasmonic waveguide with Kerr nonlinear resonator,” Opt. Express 19(4), 2910–2915 (2011).
    [Crossref] [PubMed]
  21. S. E. Harris, J. E. Field, and A. Imamoglu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64(10), 1107–1110 (1990).
    [Crossref] [PubMed]
  22. K. Totsuka, N. Kobayashi, and M. Tomita, “Slow light in coupled-resonator-induced transparency,” Phys. Rev. Lett. 98(21), 213904 (2007).
    [Crossref] [PubMed]
  23. B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
    [Crossref] [PubMed]
  24. G. Lai, R. Liang, Y. Zhang, Z. Bian, L. Yi, G. Zhan, and R. Zhao, “Double plasmonic nanodisks design for electromagnetically induced transparency and slow light,” Opt. Express 23(5), 6554–6561 (2015).
    [Crossref] [PubMed]
  25. J. J. Chen, Z. Li, Y. J. Zou, Z. L. Deng, J. H. Xiao, and Q. H. Gong, “Response line-shapes in compact coupled plasmonic resonator systems,” Plasmonics 8(2), 1129–1134 (2013).
    [Crossref]
  26. X. S. Lin and X. G. Huang, “Tooth-shaped plasmonic waveguide filters with nanometeric sizes,” Opt. Lett. 33(23), 2874–2876 (2008).
    [Crossref] [PubMed]
  27. M. Bera and M. Ray, “Circular phase response based analysis for swapped multilayer metallo-dilelectric plasmonic structures,” Plasmonics 9(2), 237–249 (2014).
    [Crossref]

2016 (2)

Y. Y. Zhang, S. L. Li, X. Y. Zhang, Y. Y. Chen, L. L. Wang, Y. Zhang, and L. Yu, “Evolution of Fano resonance based on symmetric/asymmetric plasmonic waveguide system and its application in nanosensor,” Opt. Commun. 370, 203–208 (2016).
[Crossref]

K. H. Wen, Y. H. Hu, L. Chen, J. Y. Zhou, L. Lei, and Z. M. Meng, “Single/dual fano resonance based on plasmonic metal-dielectric-metal waveguide,” Plasmonics 11(1), 315–321 (2016).
[Crossref]

2015 (4)

Z. Chen, W. H. Wang, L. N. Cui, L. Yu, G. Y. Duan, Y. F. Zhao, and J. H. Xiao, “Spectral splitting based on electromagnetically induced transparency in plasmonic waveguide resonator system,” Plasmonics 10(3), 721–727 (2015).
[Crossref]

Z. Chen, J. J. Chen, L. Yu, and J. H. Xiao, “Sharp trapped resonances by exciting the anti-symmetric waveguide mode in a metal-insulator-metal resonator,” Plasmonics 10(1), 131–137 (2015).
[Crossref]

Z. Chen, L. Yu, L. L. Wang, G. Y. Duan, Y. F. Zhao, and J. H. Xiao, “A refractive index nanosensor based on fano resonance in the plasmonic waveguide system,” IEEE Photonics Technol. Lett. 27(16), 1695–1698 (2015).
[Crossref]

G. Lai, R. Liang, Y. Zhang, Z. Bian, L. Yi, G. Zhan, and R. Zhao, “Double plasmonic nanodisks design for electromagnetically induced transparency and slow light,” Opt. Express 23(5), 6554–6561 (2015).
[Crossref] [PubMed]

2014 (6)

M. Bera and M. Ray, “Circular phase response based analysis for swapped multilayer metallo-dilelectric plasmonic structures,” Plasmonics 9(2), 237–249 (2014).
[Crossref]

G. Zhan, R. Liang, H. Liang, J. Luo, and R. Zhao, “Asymmetric band-pass plasmonic nanodisk filter with mode inhibition and spectrally splitting capabilities,” Opt. Express 22(8), 9912–9919 (2014).
[Crossref] [PubMed]

T. Wu, Y. Liu, Z. Yu, Y. Peng, C. Shu, and H. Ye, “The sensing characteristics of plasmonic waveguide with a ring resonator,” Opt. Express 22(7), 7669–7677 (2014).
[Crossref] [PubMed]

Z. Chen and L. Yu, “Multiple fano resonances based on different waveguide modes in a symmetry breaking plasmonic system,” IEEE Photonics J. 6(6), 1–8 (2014).

Y. Xu and A. E. Miroshnichenko, “Reconfigurable non reciprocity with a nonlinear fano diode,” Phys. Rev. B 89(13), 1361–1377 (2014).
[Crossref]

K. H. Wen, L. S. Yan, W. Pan, B. Luo, Z. Guo, Y. H. Guo, and X. G. Luo, “Electromagnetically induced transparency-like transmission in a compact side-coupled T-shaped resonator,” J. Lightwave Technol. 32(9), 1701–1707 (2014).
[Crossref]

2013 (7)

T. R. Liu, Z. K. Zhou, C. Jin, and X. Wang, “Tuning triangular prism dimer into fano resonance for plasmonic sensor,” Plasmonics 8(2), 885–890 (2013).
[Crossref]

J. Wang, C. Fan, J. He, P. Ding, E. Liang, and Q. Xue, “Double Fano resonances due to interplay of electric and magnetic plasmon modes in planar plasmonic structure with high sensing sensitivity,” Opt. Express 21(2), 2236–2244 (2013).
[Crossref] [PubMed]

D. Wang, X. Yu, and Q. Yu, “Tuning multiple Fano and plasmon resonances in rectangle grid quasi-3D plasmonic-photonic nanostructures,” Appl. Phys. Lett. 103(5), 053117 (2013).
[Crossref]

A. D. Khan and G. Miano, “Plasmonic Fano resonances in single-layer gold conical nanoshells,” Plasmonics 8(3), 1429–1437 (2013).
[Crossref]

J. Shu, W. Gao, and Q. Xu, “Fano resonance in concentric ring apertures,” Opt. Express 21(9), 11101–11106 (2013).
[Crossref] [PubMed]

J. J. Chen, Z. Li, Y. J. Zou, Z. L. Deng, J. H. Xiao, and Q. H. Gong, “Coupled-resonator-induced Fano resonances for plasmonic sensing with ultra-high figure of merits,” Plasmonics 8(4), 1627–1632 (2013).
[Crossref]

J. J. Chen, Z. Li, Y. J. Zou, Z. L. Deng, J. H. Xiao, and Q. H. Gong, “Response line-shapes in compact coupled plasmonic resonator systems,” Plasmonics 8(2), 1129–1134 (2013).
[Crossref]

2012 (1)

J. Chen, Z. Li, S. Yue, J. Xiao, and Q. Gong, “Plasmon-induced transparency in asymmetric T-shape single slit,” Nano Lett. 12(5), 2494–2498 (2012).
[Crossref] [PubMed]

2011 (2)

C. Wu, A. B. Khanikaev, and G. Shvets, “Broadband slow light metamaterial based on a double-continuum Fano resonance,” Phys. Rev. Lett. 106(10), 107403 (2011).
[Crossref] [PubMed]

H. Lu, X. Liu, L. Wang, Y. Gong, and D. Mao, “Ultrafast all-optical switching in nanoplasmonic waveguide with Kerr nonlinear resonator,” Opt. Express 19(4), 2910–2915 (2011).
[Crossref] [PubMed]

2010 (1)

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[Crossref] [PubMed]

2008 (1)

2007 (1)

K. Totsuka, N. Kobayashi, and M. Tomita, “Slow light in coupled-resonator-induced transparency,” Phys. Rev. Lett. 98(21), 213904 (2007).
[Crossref] [PubMed]

2003 (1)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

1990 (1)

S. E. Harris, J. E. Field, and A. Imamoglu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64(10), 1107–1110 (1990).
[Crossref] [PubMed]

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

Bera, M.

M. Bera and M. Ray, “Circular phase response based analysis for swapped multilayer metallo-dilelectric plasmonic structures,” Plasmonics 9(2), 237–249 (2014).
[Crossref]

Bian, Z.

Chen, J.

J. Chen, Z. Li, S. Yue, J. Xiao, and Q. Gong, “Plasmon-induced transparency in asymmetric T-shape single slit,” Nano Lett. 12(5), 2494–2498 (2012).
[Crossref] [PubMed]

Chen, J. J.

Z. Chen, J. J. Chen, L. Yu, and J. H. Xiao, “Sharp trapped resonances by exciting the anti-symmetric waveguide mode in a metal-insulator-metal resonator,” Plasmonics 10(1), 131–137 (2015).
[Crossref]

J. J. Chen, Z. Li, Y. J. Zou, Z. L. Deng, J. H. Xiao, and Q. H. Gong, “Coupled-resonator-induced Fano resonances for plasmonic sensing with ultra-high figure of merits,” Plasmonics 8(4), 1627–1632 (2013).
[Crossref]

J. J. Chen, Z. Li, Y. J. Zou, Z. L. Deng, J. H. Xiao, and Q. H. Gong, “Response line-shapes in compact coupled plasmonic resonator systems,” Plasmonics 8(2), 1129–1134 (2013).
[Crossref]

Chen, L.

K. H. Wen, Y. H. Hu, L. Chen, J. Y. Zhou, L. Lei, and Z. M. Meng, “Single/dual fano resonance based on plasmonic metal-dielectric-metal waveguide,” Plasmonics 11(1), 315–321 (2016).
[Crossref]

Chen, Y. Y.

Y. Y. Zhang, S. L. Li, X. Y. Zhang, Y. Y. Chen, L. L. Wang, Y. Zhang, and L. Yu, “Evolution of Fano resonance based on symmetric/asymmetric plasmonic waveguide system and its application in nanosensor,” Opt. Commun. 370, 203–208 (2016).
[Crossref]

Chen, Z.

Z. Chen, J. J. Chen, L. Yu, and J. H. Xiao, “Sharp trapped resonances by exciting the anti-symmetric waveguide mode in a metal-insulator-metal resonator,” Plasmonics 10(1), 131–137 (2015).
[Crossref]

Z. Chen, W. H. Wang, L. N. Cui, L. Yu, G. Y. Duan, Y. F. Zhao, and J. H. Xiao, “Spectral splitting based on electromagnetically induced transparency in plasmonic waveguide resonator system,” Plasmonics 10(3), 721–727 (2015).
[Crossref]

Z. Chen, L. Yu, L. L. Wang, G. Y. Duan, Y. F. Zhao, and J. H. Xiao, “A refractive index nanosensor based on fano resonance in the plasmonic waveguide system,” IEEE Photonics Technol. Lett. 27(16), 1695–1698 (2015).
[Crossref]

Z. Chen and L. Yu, “Multiple fano resonances based on different waveguide modes in a symmetry breaking plasmonic system,” IEEE Photonics J. 6(6), 1–8 (2014).

Chong, C. T.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[Crossref] [PubMed]

Cui, L. N.

Z. Chen, W. H. Wang, L. N. Cui, L. Yu, G. Y. Duan, Y. F. Zhao, and J. H. Xiao, “Spectral splitting based on electromagnetically induced transparency in plasmonic waveguide resonator system,” Plasmonics 10(3), 721–727 (2015).
[Crossref]

Deng, Z. L.

J. J. Chen, Z. Li, Y. J. Zou, Z. L. Deng, J. H. Xiao, and Q. H. Gong, “Coupled-resonator-induced Fano resonances for plasmonic sensing with ultra-high figure of merits,” Plasmonics 8(4), 1627–1632 (2013).
[Crossref]

J. J. Chen, Z. Li, Y. J. Zou, Z. L. Deng, J. H. Xiao, and Q. H. Gong, “Response line-shapes in compact coupled plasmonic resonator systems,” Plasmonics 8(2), 1129–1134 (2013).
[Crossref]

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

Ding, P.

Duan, G. Y.

Z. Chen, W. H. Wang, L. N. Cui, L. Yu, G. Y. Duan, Y. F. Zhao, and J. H. Xiao, “Spectral splitting based on electromagnetically induced transparency in plasmonic waveguide resonator system,” Plasmonics 10(3), 721–727 (2015).
[Crossref]

Z. Chen, L. Yu, L. L. Wang, G. Y. Duan, Y. F. Zhao, and J. H. Xiao, “A refractive index nanosensor based on fano resonance in the plasmonic waveguide system,” IEEE Photonics Technol. Lett. 27(16), 1695–1698 (2015).
[Crossref]

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

Fan, C.

Field, J. E.

S. E. Harris, J. E. Field, and A. Imamoglu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64(10), 1107–1110 (1990).
[Crossref] [PubMed]

Gao, W.

Giessen, H.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[Crossref] [PubMed]

Gong, Q.

J. Chen, Z. Li, S. Yue, J. Xiao, and Q. Gong, “Plasmon-induced transparency in asymmetric T-shape single slit,” Nano Lett. 12(5), 2494–2498 (2012).
[Crossref] [PubMed]

Gong, Q. H.

J. J. Chen, Z. Li, Y. J. Zou, Z. L. Deng, J. H. Xiao, and Q. H. Gong, “Coupled-resonator-induced Fano resonances for plasmonic sensing with ultra-high figure of merits,” Plasmonics 8(4), 1627–1632 (2013).
[Crossref]

J. J. Chen, Z. Li, Y. J. Zou, Z. L. Deng, J. H. Xiao, and Q. H. Gong, “Response line-shapes in compact coupled plasmonic resonator systems,” Plasmonics 8(2), 1129–1134 (2013).
[Crossref]

Gong, Y.

Guo, Y. H.

Guo, Z.

Halas, N. J.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[Crossref] [PubMed]

Harris, S. E.

S. E. Harris, J. E. Field, and A. Imamoglu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64(10), 1107–1110 (1990).
[Crossref] [PubMed]

He, J.

Hu, Y. H.

K. H. Wen, Y. H. Hu, L. Chen, J. Y. Zhou, L. Lei, and Z. M. Meng, “Single/dual fano resonance based on plasmonic metal-dielectric-metal waveguide,” Plasmonics 11(1), 315–321 (2016).
[Crossref]

Huang, X. G.

Imamoglu, A.

S. E. Harris, J. E. Field, and A. Imamoglu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64(10), 1107–1110 (1990).
[Crossref] [PubMed]

Jin, C.

T. R. Liu, Z. K. Zhou, C. Jin, and X. Wang, “Tuning triangular prism dimer into fano resonance for plasmonic sensor,” Plasmonics 8(2), 885–890 (2013).
[Crossref]

Khan, A. D.

A. D. Khan and G. Miano, “Plasmonic Fano resonances in single-layer gold conical nanoshells,” Plasmonics 8(3), 1429–1437 (2013).
[Crossref]

Khanikaev, A. B.

C. Wu, A. B. Khanikaev, and G. Shvets, “Broadband slow light metamaterial based on a double-continuum Fano resonance,” Phys. Rev. Lett. 106(10), 107403 (2011).
[Crossref] [PubMed]

Kobayashi, N.

K. Totsuka, N. Kobayashi, and M. Tomita, “Slow light in coupled-resonator-induced transparency,” Phys. Rev. Lett. 98(21), 213904 (2007).
[Crossref] [PubMed]

Lai, G.

Lei, L.

K. H. Wen, Y. H. Hu, L. Chen, J. Y. Zhou, L. Lei, and Z. M. Meng, “Single/dual fano resonance based on plasmonic metal-dielectric-metal waveguide,” Plasmonics 11(1), 315–321 (2016).
[Crossref]

Li, S. L.

Y. Y. Zhang, S. L. Li, X. Y. Zhang, Y. Y. Chen, L. L. Wang, Y. Zhang, and L. Yu, “Evolution of Fano resonance based on symmetric/asymmetric plasmonic waveguide system and its application in nanosensor,” Opt. Commun. 370, 203–208 (2016).
[Crossref]

Li, Z.

J. J. Chen, Z. Li, Y. J. Zou, Z. L. Deng, J. H. Xiao, and Q. H. Gong, “Coupled-resonator-induced Fano resonances for plasmonic sensing with ultra-high figure of merits,” Plasmonics 8(4), 1627–1632 (2013).
[Crossref]

J. J. Chen, Z. Li, Y. J. Zou, Z. L. Deng, J. H. Xiao, and Q. H. Gong, “Response line-shapes in compact coupled plasmonic resonator systems,” Plasmonics 8(2), 1129–1134 (2013).
[Crossref]

J. Chen, Z. Li, S. Yue, J. Xiao, and Q. Gong, “Plasmon-induced transparency in asymmetric T-shape single slit,” Nano Lett. 12(5), 2494–2498 (2012).
[Crossref] [PubMed]

Liang, E.

Liang, H.

Liang, R.

Lin, X. S.

Liu, T. R.

T. R. Liu, Z. K. Zhou, C. Jin, and X. Wang, “Tuning triangular prism dimer into fano resonance for plasmonic sensor,” Plasmonics 8(2), 885–890 (2013).
[Crossref]

Liu, X.

Liu, Y.

Lu, H.

Luk’yanchuk, B.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[Crossref] [PubMed]

Luo, B.

Luo, J.

Luo, X. G.

Maier, S. A.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[Crossref] [PubMed]

Mao, D.

Meng, Z. M.

K. H. Wen, Y. H. Hu, L. Chen, J. Y. Zhou, L. Lei, and Z. M. Meng, “Single/dual fano resonance based on plasmonic metal-dielectric-metal waveguide,” Plasmonics 11(1), 315–321 (2016).
[Crossref]

Miano, G.

A. D. Khan and G. Miano, “Plasmonic Fano resonances in single-layer gold conical nanoshells,” Plasmonics 8(3), 1429–1437 (2013).
[Crossref]

Miroshnichenko, A. E.

Y. Xu and A. E. Miroshnichenko, “Reconfigurable non reciprocity with a nonlinear fano diode,” Phys. Rev. B 89(13), 1361–1377 (2014).
[Crossref]

Nordlander, P.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[Crossref] [PubMed]

Pan, W.

Peng, Y.

Ray, M.

M. Bera and M. Ray, “Circular phase response based analysis for swapped multilayer metallo-dilelectric plasmonic structures,” Plasmonics 9(2), 237–249 (2014).
[Crossref]

Shu, C.

Shu, J.

Shvets, G.

C. Wu, A. B. Khanikaev, and G. Shvets, “Broadband slow light metamaterial based on a double-continuum Fano resonance,” Phys. Rev. Lett. 106(10), 107403 (2011).
[Crossref] [PubMed]

Tomita, M.

K. Totsuka, N. Kobayashi, and M. Tomita, “Slow light in coupled-resonator-induced transparency,” Phys. Rev. Lett. 98(21), 213904 (2007).
[Crossref] [PubMed]

Totsuka, K.

K. Totsuka, N. Kobayashi, and M. Tomita, “Slow light in coupled-resonator-induced transparency,” Phys. Rev. Lett. 98(21), 213904 (2007).
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[Crossref]

Wang, J.

Wang, L.

Wang, L. L.

Y. Y. Zhang, S. L. Li, X. Y. Zhang, Y. Y. Chen, L. L. Wang, Y. Zhang, and L. Yu, “Evolution of Fano resonance based on symmetric/asymmetric plasmonic waveguide system and its application in nanosensor,” Opt. Commun. 370, 203–208 (2016).
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Z. Chen, L. Yu, L. L. Wang, G. Y. Duan, Y. F. Zhao, and J. H. Xiao, “A refractive index nanosensor based on fano resonance in the plasmonic waveguide system,” IEEE Photonics Technol. Lett. 27(16), 1695–1698 (2015).
[Crossref]

Wang, W. H.

Z. Chen, W. H. Wang, L. N. Cui, L. Yu, G. Y. Duan, Y. F. Zhao, and J. H. Xiao, “Spectral splitting based on electromagnetically induced transparency in plasmonic waveguide resonator system,” Plasmonics 10(3), 721–727 (2015).
[Crossref]

Wang, X.

T. R. Liu, Z. K. Zhou, C. Jin, and X. Wang, “Tuning triangular prism dimer into fano resonance for plasmonic sensor,” Plasmonics 8(2), 885–890 (2013).
[Crossref]

Wen, K. H.

K. H. Wen, Y. H. Hu, L. Chen, J. Y. Zhou, L. Lei, and Z. M. Meng, “Single/dual fano resonance based on plasmonic metal-dielectric-metal waveguide,” Plasmonics 11(1), 315–321 (2016).
[Crossref]

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J. Chen, Z. Li, S. Yue, J. Xiao, and Q. Gong, “Plasmon-induced transparency in asymmetric T-shape single slit,” Nano Lett. 12(5), 2494–2498 (2012).
[Crossref] [PubMed]

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Z. Chen, W. H. Wang, L. N. Cui, L. Yu, G. Y. Duan, Y. F. Zhao, and J. H. Xiao, “Spectral splitting based on electromagnetically induced transparency in plasmonic waveguide resonator system,” Plasmonics 10(3), 721–727 (2015).
[Crossref]

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[Crossref]

Z. Chen, L. Yu, L. L. Wang, G. Y. Duan, Y. F. Zhao, and J. H. Xiao, “A refractive index nanosensor based on fano resonance in the plasmonic waveguide system,” IEEE Photonics Technol. Lett. 27(16), 1695–1698 (2015).
[Crossref]

J. J. Chen, Z. Li, Y. J. Zou, Z. L. Deng, J. H. Xiao, and Q. H. Gong, “Response line-shapes in compact coupled plasmonic resonator systems,” Plasmonics 8(2), 1129–1134 (2013).
[Crossref]

J. J. Chen, Z. Li, Y. J. Zou, Z. L. Deng, J. H. Xiao, and Q. H. Gong, “Coupled-resonator-induced Fano resonances for plasmonic sensing with ultra-high figure of merits,” Plasmonics 8(4), 1627–1632 (2013).
[Crossref]

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Xu, Y.

Y. Xu and A. E. Miroshnichenko, “Reconfigurable non reciprocity with a nonlinear fano diode,” Phys. Rev. B 89(13), 1361–1377 (2014).
[Crossref]

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Y. Y. Zhang, S. L. Li, X. Y. Zhang, Y. Y. Chen, L. L. Wang, Y. Zhang, and L. Yu, “Evolution of Fano resonance based on symmetric/asymmetric plasmonic waveguide system and its application in nanosensor,” Opt. Commun. 370, 203–208 (2016).
[Crossref]

Z. Chen, J. J. Chen, L. Yu, and J. H. Xiao, “Sharp trapped resonances by exciting the anti-symmetric waveguide mode in a metal-insulator-metal resonator,” Plasmonics 10(1), 131–137 (2015).
[Crossref]

Z. Chen, W. H. Wang, L. N. Cui, L. Yu, G. Y. Duan, Y. F. Zhao, and J. H. Xiao, “Spectral splitting based on electromagnetically induced transparency in plasmonic waveguide resonator system,” Plasmonics 10(3), 721–727 (2015).
[Crossref]

Z. Chen, L. Yu, L. L. Wang, G. Y. Duan, Y. F. Zhao, and J. H. Xiao, “A refractive index nanosensor based on fano resonance in the plasmonic waveguide system,” IEEE Photonics Technol. Lett. 27(16), 1695–1698 (2015).
[Crossref]

Z. Chen and L. Yu, “Multiple fano resonances based on different waveguide modes in a symmetry breaking plasmonic system,” IEEE Photonics J. 6(6), 1–8 (2014).

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D. Wang, X. Yu, and Q. Yu, “Tuning multiple Fano and plasmon resonances in rectangle grid quasi-3D plasmonic-photonic nanostructures,” Appl. Phys. Lett. 103(5), 053117 (2013).
[Crossref]

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[Crossref]

Yu, Z.

Yue, S.

J. Chen, Z. Li, S. Yue, J. Xiao, and Q. Gong, “Plasmon-induced transparency in asymmetric T-shape single slit,” Nano Lett. 12(5), 2494–2498 (2012).
[Crossref] [PubMed]

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Zhang, X. Y.

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[Crossref]

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Y. Y. Zhang, S. L. Li, X. Y. Zhang, Y. Y. Chen, L. L. Wang, Y. Zhang, and L. Yu, “Evolution of Fano resonance based on symmetric/asymmetric plasmonic waveguide system and its application in nanosensor,” Opt. Commun. 370, 203–208 (2016).
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[Crossref] [PubMed]

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Y. Y. Zhang, S. L. Li, X. Y. Zhang, Y. Y. Chen, L. L. Wang, Y. Zhang, and L. Yu, “Evolution of Fano resonance based on symmetric/asymmetric plasmonic waveguide system and its application in nanosensor,” Opt. Commun. 370, 203–208 (2016).
[Crossref]

Zhao, R.

Zhao, Y. F.

Z. Chen, W. H. Wang, L. N. Cui, L. Yu, G. Y. Duan, Y. F. Zhao, and J. H. Xiao, “Spectral splitting based on electromagnetically induced transparency in plasmonic waveguide resonator system,” Plasmonics 10(3), 721–727 (2015).
[Crossref]

Z. Chen, L. Yu, L. L. Wang, G. Y. Duan, Y. F. Zhao, and J. H. Xiao, “A refractive index nanosensor based on fano resonance in the plasmonic waveguide system,” IEEE Photonics Technol. Lett. 27(16), 1695–1698 (2015).
[Crossref]

Zheludev, N. I.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[Crossref] [PubMed]

Zhou, J. Y.

K. H. Wen, Y. H. Hu, L. Chen, J. Y. Zhou, L. Lei, and Z. M. Meng, “Single/dual fano resonance based on plasmonic metal-dielectric-metal waveguide,” Plasmonics 11(1), 315–321 (2016).
[Crossref]

Zhou, Z. K.

T. R. Liu, Z. K. Zhou, C. Jin, and X. Wang, “Tuning triangular prism dimer into fano resonance for plasmonic sensor,” Plasmonics 8(2), 885–890 (2013).
[Crossref]

Zou, Y. J.

J. J. Chen, Z. Li, Y. J. Zou, Z. L. Deng, J. H. Xiao, and Q. H. Gong, “Coupled-resonator-induced Fano resonances for plasmonic sensing with ultra-high figure of merits,” Plasmonics 8(4), 1627–1632 (2013).
[Crossref]

J. J. Chen, Z. Li, Y. J. Zou, Z. L. Deng, J. H. Xiao, and Q. H. Gong, “Response line-shapes in compact coupled plasmonic resonator systems,” Plasmonics 8(2), 1129–1134 (2013).
[Crossref]

Appl. Phys. Lett. (1)

D. Wang, X. Yu, and Q. Yu, “Tuning multiple Fano and plasmon resonances in rectangle grid quasi-3D plasmonic-photonic nanostructures,” Appl. Phys. Lett. 103(5), 053117 (2013).
[Crossref]

IEEE Photonics J. (1)

Z. Chen and L. Yu, “Multiple fano resonances based on different waveguide modes in a symmetry breaking plasmonic system,” IEEE Photonics J. 6(6), 1–8 (2014).

IEEE Photonics Technol. Lett. (1)

Z. Chen, L. Yu, L. L. Wang, G. Y. Duan, Y. F. Zhao, and J. H. Xiao, “A refractive index nanosensor based on fano resonance in the plasmonic waveguide system,” IEEE Photonics Technol. Lett. 27(16), 1695–1698 (2015).
[Crossref]

J. Lightwave Technol. (1)

Nano Lett. (1)

J. Chen, Z. Li, S. Yue, J. Xiao, and Q. Gong, “Plasmon-induced transparency in asymmetric T-shape single slit,” Nano Lett. 12(5), 2494–2498 (2012).
[Crossref] [PubMed]

Nat. Mater. (1)

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
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Nature (1)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

Opt. Commun. (1)

Y. Y. Zhang, S. L. Li, X. Y. Zhang, Y. Y. Chen, L. L. Wang, Y. Zhang, and L. Yu, “Evolution of Fano resonance based on symmetric/asymmetric plasmonic waveguide system and its application in nanosensor,” Opt. Commun. 370, 203–208 (2016).
[Crossref]

Opt. Express (6)

Opt. Lett. (1)

Phys. Rev. B (1)

Y. Xu and A. E. Miroshnichenko, “Reconfigurable non reciprocity with a nonlinear fano diode,” Phys. Rev. B 89(13), 1361–1377 (2014).
[Crossref]

Phys. Rev. Lett. (3)

S. E. Harris, J. E. Field, and A. Imamoglu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64(10), 1107–1110 (1990).
[Crossref] [PubMed]

K. Totsuka, N. Kobayashi, and M. Tomita, “Slow light in coupled-resonator-induced transparency,” Phys. Rev. Lett. 98(21), 213904 (2007).
[Crossref] [PubMed]

C. Wu, A. B. Khanikaev, and G. Shvets, “Broadband slow light metamaterial based on a double-continuum Fano resonance,” Phys. Rev. Lett. 106(10), 107403 (2011).
[Crossref] [PubMed]

Plasmonics (8)

Z. Chen, J. J. Chen, L. Yu, and J. H. Xiao, “Sharp trapped resonances by exciting the anti-symmetric waveguide mode in a metal-insulator-metal resonator,” Plasmonics 10(1), 131–137 (2015).
[Crossref]

K. H. Wen, Y. H. Hu, L. Chen, J. Y. Zhou, L. Lei, and Z. M. Meng, “Single/dual fano resonance based on plasmonic metal-dielectric-metal waveguide,” Plasmonics 11(1), 315–321 (2016).
[Crossref]

Z. Chen, W. H. Wang, L. N. Cui, L. Yu, G. Y. Duan, Y. F. Zhao, and J. H. Xiao, “Spectral splitting based on electromagnetically induced transparency in plasmonic waveguide resonator system,” Plasmonics 10(3), 721–727 (2015).
[Crossref]

J. J. Chen, Z. Li, Y. J. Zou, Z. L. Deng, J. H. Xiao, and Q. H. Gong, “Coupled-resonator-induced Fano resonances for plasmonic sensing with ultra-high figure of merits,” Plasmonics 8(4), 1627–1632 (2013).
[Crossref]

A. D. Khan and G. Miano, “Plasmonic Fano resonances in single-layer gold conical nanoshells,” Plasmonics 8(3), 1429–1437 (2013).
[Crossref]

T. R. Liu, Z. K. Zhou, C. Jin, and X. Wang, “Tuning triangular prism dimer into fano resonance for plasmonic sensor,” Plasmonics 8(2), 885–890 (2013).
[Crossref]

M. Bera and M. Ray, “Circular phase response based analysis for swapped multilayer metallo-dilelectric plasmonic structures,” Plasmonics 9(2), 237–249 (2014).
[Crossref]

J. J. Chen, Z. Li, Y. J. Zou, Z. L. Deng, J. H. Xiao, and Q. H. Gong, “Response line-shapes in compact coupled plasmonic resonator systems,” Plasmonics 8(2), 1129–1134 (2013).
[Crossref]

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Figures (8)

Fig. 1
Fig. 1 Schematic diagram of the asymmetric plasmonic structure composed of (a) two MIM waveguides and one rectangular cavity and (b) two MIM waveguides and two rectangular cavities.
Fig. 2
Fig. 2 The distribution of the normalized magnetic field (Hz) of the resonant modes (a) TM1,0 mode at 734 nm, (b) TM0,3 mode at 788 nm, (c) TM0,2 mode at 1105 nm and (d) TM0,4 mode at 593 nm respectively in the rectangular cavity A with LA = 220 nm, H = 760 nm in Fig. 1(a).
Fig. 3
Fig. 3 The FEM simulation results (blue lines) and MICMT results (red lines) of the transmission spectrum of the asymmetric plasmonic system with H = 760 nm, LA = 220 nm and (a) ΔH = 0, (b) ΔH = 15 nm, (c) ΔH = 30 nm. The phase curves of the complex amplitude transmission coefficients of the four modes TM0,2, TM0,3, TM1,0 and TM0,4 in the asymmetric plasmonic system with H = 760 nm, LA = 220 nm and (d) ΔH = 0, (e) ΔH = 15 nm, (f) ΔH = 30 nm.
Fig. 4
Fig. 4 Argand diagrams of the transmission coefficients t1, t2, t3 and t4 of the four resonant modes TM0,2, TM0,3, TM1,0 and TM0,4 at the peak (red lines) and dip (blue lines) of FR1 and FR2 in the plasmonic system shown in Fig. 1(a) with H = 760 nm, LA = 220 nm and (a, e) ΔH = 15nm, (c, f) ΔH = 30 nm. (b) and (d): The detailed transmission coefficients t1, t2 and t3 in the areas selected by rectangular boxes in (a) and (c), respectively.
Fig. 5
Fig. 5 The distribution of the normalized magnetic field (Hz) of the resonant modes at (a) 791 nm, (b) 788 nm and (c) 1105 nm in the asymmetric plasmonic system respectively, when ΔH = 30 nm, H = 760 nm, LA = 220 nm, LB = 500 nm, g = 10 nm and D1 = D2 = 50 nm. (d) The FEM simulation results (blue lines) and MICMT results (red lines) of the transmission spectrum of the asymmetric plasmonic system.
Fig. 6
Fig. 6 (a) The transmission spectra of the plasmonic structure with H = 760 nm, LA = 220 nm, LB = 500 nm, D1 = D2 = 50 nm, g = 10 nm, ΔH = 30 nm, and different refractive indexes of the dielectric in the waveguides and cavities, n = 1.33 (blue line), n = 1.34 (red line). (b) The FOM* curve of this plasmonic structure.
Fig. 7
Fig. 7 The dependence of transmittance on the structure parameters, when ΔH = 30 nm, g = 10 nm, n = 1.33 and D1 = D2 = 50 nm. (a) Different H with fixed LA = 220 nm and LB = 500 nm; (b) different LB with fixed H = 760 nm, LA = 220 nm; (c) different LA with fixed H = 760 nm and LB = 500 nm. (d) ~(f) The change curves of FOM of FR 1 (blue line), FR 2 (green line) and FR 3 (red line) with the change of the structure parameters H, LB and LA, respectively.
Fig. 8
Fig. 8 The dependence of the ‘M’ type of double Lorentzian-like line-shape transmittance on the structure parameters, when ΔH = 30 nm, g = 10 nm, n = 1.33 and D1 = D2 = 50 nm are fixed values. H = 709 nm, LA = 225 nm, LB = 600 nm (blue line); H = 698 nm, LA = 221 nm, LB = 590 nm (green line); H = 708 nm, LA = 225 nm, LB = 610 nm (red line).

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

d a n dt =( j ω n 1 τ n0 1 τ n1 1 τ n2 ) a n + κ n1 s 1+ + κ n2 s 2+
s 1 = s 1+ + n κ n1 γ n a n e j φ n1
s 2 = s 2+ + n κ n2 γ n a n e j φ n2
t= s 2 s 1+ = n γ n | κ n1 || κ n2 | e j φ n j( ω ω n )+ 1 τ n0 + 1 τ n1 + 1 τ n2 , φ n = φ n2 + θ n1 θ n2
T= | t | 2 = | n=1 4 2 γ n e j φ n j( ω ω n ) τ n +2+ τ n τ n0 | 2 , φ n = φ n2

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