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Generating and Manipulating High Quality Factors of Fano Resonance in Nanoring Resonator by Stacking a Half Nanoring
Nanoscale Research Lettersvolume 12, Article number: 578 (2017)
Abstract
We demonstrate the existence of Fano resonance spectral response in a system of nanoscale plasmonic resonant ring stacked by means of a half nanoring. Our proposed scheme exploits the stacked method under normal incidence to excite the subradiant mode. The nanostructure, which utilizes the combination of Fano resonance and polarizationresolved, has a new rotation mode and high tunability, providing a dynamic control of plasmonic spectral response. Highquality resonant line shapes corresponding to the different order modes of Fano structures are readily achieved at nearinfrared wavelengths, which is a benefit to the application for nanosensor in highly integrated circuits.
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Background
Surface plasmon polaritons (SPPs) have attracted great interest over the past years because of its capability manipulating lightmatter interaction in nanoscale dimensions [1,2,3,4,5,6]. Owing to the fact that the advances in nanofabrication, nanooptical characterization, and improvements in fullfield computational electromagnetics, which has led to the emergence of the field of nanoplasmonics, more insight and control has been gained on localized plasmon resonances in metallic nanostructures. In general, plasmon resonances of isolated nanostructures such as disks [7], triangles [8, 9], rods [10, 11], and rings [12, 13] are naturally analyzed. As a fundamental resonant effect, Fano resonances resulting from interference of broad and narrow excitation modes are typically generated in the ringrod nanostructures [14], plasmonic oligomer clusters [15], nonspherical assemblies [16], graphenebased structures [17], quantum dots [18], etc. In spite of the fact that there are many research efforts, the formation of Fano resonances at specific wavelengths in plasmonic nanostructures is a challenging task because of their complex nature corresponding to the hybridization of the available modes [19,20,21]. In addition, retardation effects [22, 23] can be varied by the angle of incidence, allowing the existence of dark multipolar modes [24,25,26,27], which has recently been exploited in metamaterial context [28,29,30]. However, this is difficult in systems where higher order modes are excited in the spectral range of interest [31] or when the modes are very complex and spatially extend over a large part of the nanostructure [32]. And the plasmonic nanostructures barely have been studied in a spatially revolved fashion on a subwavelength scale. Information about the spatial distribution of plasmonic nanostructures is crucial to unravel the mechanism that leads to mode generation from plasmonic structures. Furthermore, we can provide a recipe for how one plasmonic element can be efficiently coupled to the other plasmonic component.
In this article, we demonstrate different Fano resonances in a stacked nanostructure composed of individual nanoring and half nanoring. Numerical results from finitedifference timedomain (FDTD) simulations show that the evenorder mode of Fano resonance is particularly excited and controlled by stacking method under normal incidence rather than a general method with oblique incidence. Our approach provides new insights into the spectral features of the Fano resonance. The different spectral features associated with multiple Fano resonances each correspond to distinct plasmonic modes. Quite remarkably, the multiple Fano resonances involving the rotation modes, which are based on the different orientation angle of half nanoring, will be achieved. Two high quality factors of Fano resonances with effective dephasing time are simultaneously achieved at spectrum. These results may have potential applications for nanosensor in highly integrated circuits. Furthermore, we show how the geometry of the structure determines the Fano resonance and then how the existent initial modes convert to the different modes for controlling it. This control, which is associated with the properties of the nanostructure, is important very much for practical applications since it provides high design flexibility, remarkable and robust tunability, and excellent performance.
Methods
The proposed concentric system composed of a silver (Johnson and Christy) nanoring stacked by a silver half nanoring, as shown schematically in Fig. 1, is investigated to exhibit different radiant modes. Here, the radius of the nanoring/half nanoring inner radius (Rin) and outer radius of the ring (Rout) are 310, 400 nm, respectively. For our platform, the amount of the structural handedhelix [33] is determined by the angle θ, which is the orientation angle of the half nanoring shifting from the axle wire (along the ydirection) of the concentric system. For the structure, the nanoring and half nanoring with the thickness (t) are placed on a substrate that the period is p and refractive index is set to be 1. The corresponding geometric parameters are given as follows: t = 40 nm and p = 1000 nm. To perform our numerical calculations by the Lumerical FDTD Solutions, the grid sizes in the x and y and z directions are chosen to be Δx = Δy = Δz = 1 nm [16] and Δt = Δx/2c; here, c is the velocity of light in a vacuum. The incident plane wave illumination is taken to be along the backward zdirection with the polarization along the ydirection in the simulations. In addition, the computational domain is truncated by perfectly matched layers (PMLs) in the zdirection and the periodical boundary in the x and ydirections.
Results and Discussion
Figure 2a, c shows the optical properties of the plasmonic nanostructures, which is considered singly. Because the nanostructures exhibited only odd modes of plasmonic resonances at normal incidence [25], the thirdorder mode of the nanoring at 1027 nm A can be excited under the normal illumination with polarization along the yaxis, which implies thirdorder resonance mode of the nanoring is superradiant. In this geometry, the Fano line shape arises from the hybridized coupling between a plasmon resonance of the disk and a plasmon resonance supported by the slice of antidot [34, 35], which can be qualitatively described as the dipolar plasmon disk associated with a diskshaped hole in a metallic film (hole structure) [36], as is shown explicitly in Fig. 2b. From Fig. 2b, we can clearly utilize the plasmon hybridization concept to explain the origin of the thirdorder Fano resonance where the plasmon modes can be understood as bonding (D_{ B }) or antibanding (D_{ AB }) mode combination of the nanodisk (D_{ D }) and the antidot (D_{ H }) plasmon modes. Furthermore, the dipole of single half nanoring firstorder mode at 1297 nm B is clearly observed, as shown explicitly in Fig. 2c.
To further elucidate transmission characteristics of the stacked nanostructure, we also calculated that the spectral response of stacked system is a combination of the individual layers modes, as shown in Fig. 3a. In order to completely offset the positive and negative dipole moment, a secondorder mode Fano resonance cannot be directly stimulated except for the way of an oblique incidence [22]. Figure 3b shows the thirdorder mode (m = 3) Fano resonance is similar to the previously analyzed case in Fig. 2b. When the half nanoring standing on the nanoring was investigated, the thirdorder mode (m = 3) Fano resonance almost remains invariant. In addition to this, the secondorder mode (m = 2) Fano resonance efficiency was achieved at a wavelength of 1160 nm, as shown explicitly in Fig. 3c. Comparing the superradiant plasmon resonance modes, we can conclude the Fano resonance arises from stacking influence. And a modification of the circumstance in or around the nanorings affects the resonant mode [10]: its resonance wavelength will change compared with that of the single nanoring or half nanoring. The stacking contact causes a strong blueshift of the fundamental firstorder mode, while the geometrical shape of the stacking nanoring/half nanoring still allows for an efficient excitation of higher order modes. These two plasmon resonant firstorder modes of the stacking nanoring/half nanoring are blueshifted to 1160 nm, resulting in the existence of secondorder mode (m = 2) Fano resonances, where the firstorder mode of the nanoring at a relatively long wavelength shifts more than the half nanoring’s. We demonstrate that new Fano type resonant modes are excited due to the hybridization between the firstorder mode of the nanoring and the half nanoring. Since these two modes can influence each other, it can be ascribed to the compensation of the retardation effect during Fano interference. It is obvious to get that secondorder mode (m = 2) Fano resonance is governed by the stack of the half nanoring because of the different transmission distributions and propagation characteristics of the nanostructure. As it can be observed, on the one hand, the existence of the half nanoring has little influence on the thirdorder mode (m = 3) Fano resonance, which retains the great characteristics. On the other hand, it shows that the half nanoring has a positive influence on the secondorder mode (m = 2) Fano resonance. Noticeably, the full width at halfmaximum (FWHM) of secondorder resonance is 14 nm, showing a quality factor (Qfactor) up to 82.8. And we calculated the FWHM of the thirdorder resonance in the stacked nanostructure to be 9 nm, which is located at 1027 nm effectively with a high quality factor of 114. Two high quality factors in the stacked are achieved by the stacking between its constituting elements, which is larger than 20 [37], 50 [38], and 62 [10]. Furthermore, the dephasing time of the induced resonant mode can crucially influence its properties of the resonances. We calculated the dephasing time of the induced resonant mode via T _{ r } = 2 ℏ/Γ _{ L } (r = 2, 3) [39,40,41], where ℏ is the reduced Planck’s constant and Γ _{ L } is the homogeneous line width of the Fano resonance. The dephasing time of secondorder resonant mode (m = 2) T _{2} is estimated as 0.10 ps, and the thirdorder resonant mode (m = 3) T _{3} is estimated as 0.12 ps. Since the Fano resonances, dephasing times T _{0} are believed to be on the order of 10 fs [41] and are thus too short to be reliably resolved with available laser pulses. Both T _{2} and T _{3} are larger than the general Fano resonances dephasing times T _{0,} which can be easily realized.
Next, the dependence of Fano resonance on parameters of the system is studied as well. Indeed, as it is the case for the plasmonic resonator, one can select the spectral characteristics of the resonances by changing the handedhelix rotation angle of the half nanoring. When we consider normal incidence with linearly polarized light along the yaxis (θ = 0°), it can be seen that for θ = 0°, only the second and thirdorder resonance modes are excited, as shown in Fig. 3a. However, Fig. 4a shows spectra of a slight variation of the handedhelix rotation angle has much more impact on the nanostructures, observing that the 5° rotation of the half nanoring leads to a new mode resonance (named rotation mode m = r). Clearly, when the half nanoring are placed together with θ = 5° rotation, three asymmetric dips exist the spectrum. In order to identify the hybridized modes, we plot the surface charge distributions corresponding to the three dips in the hybridized spectrum, as shown in Fig. 4b–d. The electric field diagram describes the hybridization of the plasmon modes supported by this stacked system. Moreover, one should notice that the thirdorder mode (m = 3) as a superradiant mode under such an excitation almost no change along the yaxis of the nanostructure, whereas, the secondorder Fano resonance (m = 2) is consistent with the mechanism on above, identified as a hybridization firstorder mode of half nanoring and the nanoring. Notably, the rotation resonances mode (m = r) of the nanoring cannot be excited in a single configuration because of the retardation effect. The dip in the wavelength rotation modes (m = r) is also hybridized between resonance firstorder modes of the half nanoring and the nanoring. In the situation of rotation, the Fano resonance shows the same charge distribution with the secondorder mode (m = 2), but with a structural handedhelix rotation angle, as shown in the charge distribution in Fig. 4d. Based on the secondorder mode, the rotation mode is supported a by rotating method and show an asymmetric redshift (shift to long wavelength). The revolving half nanoring has double function that one is used as a half nanoring to generate the secondorder mode and the other is served as a revolving half nanoring to excite the rotation mode. Note that the resonance of the dip in the spectrum can strengthen or vanish, resulting in the flexible modulation in integrated circuits.
Figure 5 shows spectra of nanostructure with the same diameters but with a changing handed helix angle of the half nanoring deviating from the direction of the electric field polarization. The angle difference leads to the variation of the rotation resonant mode (m = r), which is in agreement with the above analysis of the modes. When the angle difference becomes very large, such as in the case from θ = 0° to θ = 30°, the line shape of the hybridized spectrum becomes more distinctive. It can be seen that the mode (m = r) is not dominant enough since the half nanoring has a little rotation moment due to its little angle size. And the revolving resonant mode becomes apparent increasing with the angle. Thus, the whole structure exhibits three modes. Additionally, the secondorder mode (m = 2) becomes decreased since the net moment along the yaxis is small, which results in weak interference insufficient for a distinctive Fano profile in secondorder mode (m = 2). As the angle of the half nanoring becomes larger, the resonant difference becomes obvious, so that the overlap of the two modes is prominent, making the asymmetric Fano profile (m = r) more distinctive.
It is interesting to see that for nanostructure composed of a nanoring with the same length but a half nanoring, a distinctive (actually much sharper) secondorder mode Fano resonance can also be excited, which can stimulate two highquality Fano at the same time, contributing to development of integrated circuits. This further demonstrates that the special shape of the nanoring makes different from those in other nanoparticle systems. The reason about the particular behavior of plasmon hybridization is that for the half nanoring where their ends are relatively docking nanoring, where the strong influence will induce the evenmode of the nanostructure. But as the angle of the half nanoring are varied, the rotating mode (m = r) are excited, which subsequently produces three Fano resonance profiles. Of course, when the half nanoring shift to another direction from the ydirection of the concentric system (in the case of θ = 0°, − 10°, − 20°, − 30°), the phenomenon of the nanostructure is same as in Fig. 5. We can draw the same conclusions that a slight variation of the rotation angle has much more impact on the nanoring resonant modes. There is the new mode resonance (rotation mode m = r) consistent with the descriptions before.
Conclusions
In summary, a novel silver plasmonic nanostructure that combines mode resonances into a hybrid system, which consists of nanoring stacked by a half nanoring, supporting a Fano resonance in the nearinfrared range of the spectrum, has been analyzed and investigated. The nanostructure exhibits high tunability and robust control of its spectral features with only a few structural handedhelix rotation parameters. The analysis of the electric field distribution revealed that the different modes can be excited for specific frequencies. Otherwise, multiple Fano resonances are achieved by rotating the angle of half nanoring and then the mechanisms are significantly perturbed. The stack of a half nanoring creates a path for realizing different Fano resonance modes in the plasmonic resonant system. In addition, the Fano line shapes are of high quality factor that can be easily applied for nanosensor in highly integrated circuits.
Abbreviations
 FDTD:

Finitedifference timedomain
 FWHM:

Full width at halfmaximum
 PMLs:

Perfectly matched layers
 Qfactor:

Quality factor
 SPPs:

Surface plasmon polaritons
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Acknowledgements
This work was supported by the National Natural Science Foundation of China (Grant Nos. 61505052, 61176116, 11074069, 61775055).
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MQ, LLW, and XZ designed the study and analyzed the data. LLW, DCC, and SXX supervised the writing of the manuscript. All the authors have read and approved the final manuscript.
Corresponding author
Correspondence to Lingling Wang.
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Keywords
 Optical materials and properties
 Nanoparticles
 Plasmonic metasurfaces
 Fano resonance
 Nanoring