- Email: [email protected]
Fano resonances of a ring-shaped “hexamer” cluster at near-infrared wavelength
Physica B: Condensed Matter 533 (2018) 63–68
Contents lists available at ScienceDirect
Physica B: Condensed Matter journal homepage: www.elsevier.com/locate/physb
Fano resonances of a ring-shaped “hexamer” cluster at near-infrared wavelength Tong-Tong Liu a, b, Feng Xia a, b, Peng Sun a, b, Li-Li Liu a, b, Wei Du a, b, Meng-Xue Li a, Wei-Jin Kong a, Yong Wan a, Li-Feng Dong c, d, Mao-Jin Yun a, b, * a
College of Physics Science, Qingdao University, Qingdao, 266071, China Key Laboratory of Photonics Materials and Technology in Universities of Shandong, Qingdao University, Qingdao, 266071, China Department of Physics, Hamline University, Saint Paul, MN, 55104, USA d Department of Chemical Engineering, Taishan Medical University, Taian, 271016, China b c
A R T I C L E I N F O
A B S T R A C T
Keywords: Fano resonances The Fano line width A contrast ratio The effective mode volume
Fano resonances have been studied intensely in the last decade, since it is an important way to decrease the resonance line width and enhance local electric field. However, achieving a Fano line-shape with both narrow line width and high spectral contrast ratio is still a challenge. In this paper, we theoretically predict the Fano resonance induced by the extinction of normal plane wave in a ring-shaped hexamer cluster at near-infrared wavelength. In order to obtain the narrow Fano line width and high spectral contrast ratio, the relationships between the Fano line-shape and the parameters of the nanostructure are analyzed in detail. The nanostructure is simulated by using commercial software based on finite element method. The simulation results show that when the structural parameters are optimized, the Fano line width can be narrowed down 0.028 eV with a contrast ratio of 86%, and the local electric field enhancement factor at the Fano resonance wavelength can reach to 36. Furthermore, the effective mode volume of the structure is 3:9 1023 m3 which is lower than the available literature. These results indicate many potential applications of the Fano resonance in multiwavelength surfaceenhanced Raman scattering and biosensing.
1. Introduction Fano resonances in metallic nanoparticles have been found promising in a wide range of potential applications in optical filters, polarization selectors, sensors, lasers, modulators and nonlinear optic devices. In particular, as the Fano resonance is sharp and sensitive to refractive index changes of the surrounding environment, such tunability and local electric field (LFE) properties of plasmonic structures have been remarkably explored in high sensitivity refractive index chemical and biological sensors. In atomic and molecular spectroscopy [1,2], it is often to observe a pronounced asymmetric spectral line-shape, which results from the overlapping between two competing pathways, one associated with discrete states and the other with a continuum of states, to generate quantum interferences and cause zero absorption phenomenon at a specific frequency. The phenomenon of this interference is known as the Fano resonance which was put forward by U. Fano in 1961. Similarly, Fano resonances in plasmonic nanostructures originate from the interference of bright and dark plasmon modes of individual constituent
components of nanostructures. Bright plasmon modes, which are analogous to the continuum state, have finite dipole moments and can be efficiently excited by incident light. So, the bright modes are radiative and have a large scattering cross section and broad line width. On the contrary, the dark modes, which possess zero dipole moments, cannot be excited by incident light. So, the dark modes are weakly radiative and have narrow line width, which is analogous to discrete states. Fano resonances generated from various nanostructures have been widely studied in recent years. For example, deep Fano resonance in the transparency spectrum is realized in the dolmen-type arranged slab structures proposed by Zhang et al. [3]. Hao et al. theoretically investigated the plasmon coupling in metallic nanorod dimer and found a pronounced dip in the extinction spectrum which is induced by destructive interference between a bright dipole plasmon and a dark quadrupole plasmon [4]. The narrow Fano line shapes in planar multilayer structures was demonstrated experimentally by Hayashi et al. [5]. A planar-engineered metamolecule that generates Fano resonance was proposed by Le et al. [6]. Fano resonance in compound resonant
* Corresponding author. College of Physics Science, Qingdao University, Qingdao, 266071, China. E-mail address: [email protected] (M.-J. Yun). https://doi.org/10.1016/j.physb.2017.12.069 Received 20 November 2017; Received in revised form 28 December 2017; Accepted 29 December 2017 Available online 30 December 2017 0921-4526/© 2018 Elsevier B.V. All rights reserved.
T.-T. Liu et al.
Physica B: Condensed Matter 533 (2018) 63–68
Fig. 1. (a) Schematic 3D illustration of the symmetric plasmonic hexamers and the incident light. Top view (b) and side view (c) of the symmetric plasmonic hexamers with geometric.
width and high spectral contrast ratio (CR) is still a challenge. Furthermore, the underlying physics that generates the Fano resonance is not always understood. In this paper, we propose a ring-shaped “hexamer” cluster consisting of six nanorings for Fano resonance generation in near-infrared regions. The near-infrared spectral range, where blood and tissue are mostly
waveguide gratings for optical sensing was investigated by Liu et al. [7]. Fang et al. introduced a remarkably simple planar nanostructure, a single metallic nanodisk with a missing wedge-shaped slice that exhibits the Fano resonance [8]. Hao et al. reported a tunable Fano resonance in plasmonic nanocavities by symmetry breaking. In spite of the intensive work about the Fano resonance, Fano line-shape with both narrow line
Fig. 2. (a) The scattering spectra of hexamers. (b) The charge densities at λ ¼ 1122 nm on the top surface. (c) The charge distribution at the wavelength of 1300 nm. (d) The electric field intensity distribution in the middle section (z ¼ h/2) at λ ¼ 1000 nm, 1122 nm, 1300 nm. 64
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Physica B: Condensed Matter 533 (2018) 63–68
Fig. 3. (a) The scattering spectra of hexamers range from 1050 nm to 1200 nm with different gap width g. (b) The Fano line width and contrast ratio as a function of the gap width g. (c) The ratio coefficient m with the change of the gap width g.
contrast ratio and the maximum local electric field enhancement at near-infrared regions. COMSOL Multiphysics based on FEM is used to calculate the scattering spectra, the electric filed and charge distribution of the designed symmetric plasmonic hexamer model. The normally incident light is polarized along the x direction in Fig. 1. And perfectly matched layer absorbing boundary is adopted in the simulation domain. Scattering and absorption cross section are given by
transparent and light can penetrate tissues deeply, is technologically important for a number of applications, including surface-enhanced Raman scattering, biological and bio-chemical sensing [9–11]. In the symmetric plasmonic hexamers, the Fano resonance is from the interference between superradiant mode and subradiant mode. And the Fano resonance can be tuned by changing the geometric parameters or the surrounding refractive index of the designed hexamers. Fano line width (FLW), which is the most important factor to determine the performance of Fano resonances, can be narrowed to 0.028 eV with CR of 86% which the CR is better than the results in Ref. [12]when the FLW is similar, and the LFE factor at the Fano resonance wavelength reaches 36. The devices based on our tunable Fano resonance can be used in highly integrated plasmonic devices with excellent performance, such as surface-enhanced spectroscopy and sensor.
σs
c a
¼
1 ∫ ∫ ðn⋅Ssca ÞdS I0
(1)
Here, n is the normal vector pointing outwards from the nanodisk, Ssca is the scattered intensity (Poynting) vector, and I0 is the incident intensity. The integral is taken over the closed surface of the scatter. 3. Results and discussion
2. Structure and computational methods First, we perform an analysis to identify Fano resonance features of the designed symmetric plasmonic hexamer. In the calculation model, the identical inner and outer diameter d and D of the six nanorings is 60 nm and 80 nm, and the gap width g between the edge of each ring is 20 nm. The calculated scattering and absorption spectra of the hexamer structure are shown in Fig. 2(a). Obviously, there is a strong Fano dip at the wavelength of 1122 nm in the scattering spectrum, which arises mainly from the interference between superradiant and subradiant mode. It can be better understood by demonstrating the surface charge distribution. So, the induced surface charges on the top surface of the hexamers at resonance peak λ ¼ 1122 nm is given in Fig. 2(b). It can be clearly found that dipoles of the left and right nanorings (nanorings 1, 4) oscillate out of phase with that of four nanorings on the top and bottom (nanorings 2, 3, 5, 6) in the horizontal direction, and dipoles of nanorings (nanorings 2, 5) oscillate out of phase with that of nanorings (nanorings 3, 6) in the vertical direction. Such distribution of the dipoles indicates
Fig. 1 shows the three-dimensional schematic of the designed symmetric plasmonic hexamer model which consists of six nanorings. The hexamer's geometry is characterized by four parameters: the inner and outer diameter d and D of the six rings, the distance R between the center of the ring and the center of the whole structure, and the height h of the metal layer, which is equivalent to the height of each ring. The wall thickness of the nanoring is t ¼ ðD dÞ=2, and the gap between the edge of each ring is g ¼ R D. The hexamer which is embedded in a gain media doped silica layer is deposited on the glass substrate whose refractive index is set to a constant value of 1.5 with the neglect of frequency change. Since the Fano dip arises from weakly dissipated material, silver (Ag) is selected as the plasmonic material. The dielectric permittivity of silver is taken from Johnson and Christy's experimental data [13]. In this work, structure dimension can be manipulated by tuning geometric parameters to get narrow Fano resonances with high 65
T.-T. Liu et al.
Physica B: Condensed Matter 533 (2018) 63–68
there is an almost perfect net dipole moment which can be treated as subradiant behavior. By contrast, the induced surface charges distribution at the wavelength of 1300 nm is shown in Fig. 2(c), obviously the dipoles of all constituent particles oscillate in the same direction. This behavior is called as superradiant mode, which results in increasing radiation damping. The coupling between subradiant and superradiant mode results in the characteristic Fano line shape in the scattering spectra. The electric field intensity distribution diagrams in the middle section (z ¼ h=2) with the wavelength of 1000 nm, 1122 nm, 1300 nm respectively are shown in Fig. 2(d). Apparently, the electric field intensity at Fano resonance dip (1122 nm) is stronger than the other two wavelengths. In other words, the Fano resonant cluster structure has the feature of high field enhancement, which is mainly localized between the nanorings. For Fano resonances, two extremely important parameters have influence on the sensitivity of detection: FLW and CR. FLW is described as the full width at half maximum of the Fano dip, and CR is defined as the ratio of the difference between the minimum and maximum to the maximum value. In Fig. 3, a series of FEM spectral computations are presented to illustrate the dependence of Fano resonance on the geometric parameters of the designed hexamer. Fig. 3(a) displays the scattering spectrum with different gap g. It can be found that if all other parameters keep the same, there is a slight blue shift of the Fano resonance wavelengths from 1154 nm to 1128 nm with increasing gap g from 3 nm to 25 nm. Fig. 3(b) shows FLW decreases exponentially from 109 nm to 25 nm, and CR of Fano resonance decreases greatly from 91.7% to 67.2% with increasing gap g from 3 nm to 25 nm. Since the gap g determines the size of the coupling strength, the coupling strength becomes weaker with the increase of the gap, which is consistent with other studies [3,12]. In this paper, our interest is to achieve the narrow FLW and high CR. Therefore, a ratio coefficient m is defined to optimize the structure.
m¼
c lnðlÞ
(2)
in which c represents the CR, and l indicates the FLW. As shown in Fig. 3(c), it can generate a B-spline curve by interpolating it over about 5 points covering the minimum to maximum values. This curve indicates that the maximum value of the ratio coefficient m corresponds to g ¼ 12 nm. Fig. 4(a) presents the influence of the metal layer height h on the Fano resonances. From the scattering spectra of the hexamers, we can conclude that if all other parameters are held constant, the Fano resonance wavelengths take on a slight blue shift from 1080 nm to 1310 nm with the metal layer height h changing from 30 nm to 80 nm. As shown in Fig. 4(b), the FLW decreases from 48 nm to 21 nm with the height h increasing from 30 nm to 80 nm. However, CR increases from 68.2% to 77.3% as the height h increasing from 30 nm to 50 nm, and then decreases to 56.1% greatly when the height h increases to 80 nm. Since the height h is relevant to active area of the coupling, the coupling strength makes a difference with the increase of the height, which corresponds to a sensitivity of hexamers. The high sensitivity of the Fano resonance scattering dip in the hexamer indicates its strong potential for biosensing applications. And Fig. 4(c) illustrates that the maximum value of the ratio coefficient m corresponds to h ¼ 56 nm. In Fig. 5, the relationship between the Fano resonance features and the thickness t of the nanorings is exploited. With the parameter t increasing from 15 nm to 30 nm, the scattering spectrum shows the Fano resonant dip has blue-shifts from 1240 nm to 998 nm obviously in Fig. 5(a). As displayed in Fig. 5(b), CR first increases from 70.4% to 74.0% and then drops to 35.4% with the increasing thickness of annular wall, and the FLW declines from 43 nm to 22 nm exponentially. This is because that thicker nanoring has more oscillating electrons and therefore provides stronger plasmonic response, which accords with the
Fig. 4. (a) The scattering spectra of hexamers with different height h of the metal layer on Fano resonance dip. (b) The Fano line width and contrast ratio as a function of the height h. (c) The ratio coefficient m with the change of the height. 66
T.-T. Liu et al.
Physica B: Condensed Matter 533 (2018) 63–68
Fig. 5. (a) The scattering spectra of hexamers with different thickness t of annular wall. (b) The Fano line width and contrast ratio as a function of the thickness t. (c) The ratio coefficient m with the change of the thickness t.
results in Ref. [13]. With the changes of the ratio coefficient m by the parameter t, we can draw the conclusion that t ¼ 21 nm appears to be the best choice for balancing the FLW and the CR, as shown in Fig. 5(c). Fano resonance is ultra-sensitive to the dielectric refractive index changes of the surrounding environment, such tunability and LFE properties of plasmonic structure have been remarkably explored in high sensitivity refractive index chemical and biological sensors [14,15]. Therefore, it is necessary to analyze the relation between Fano resonance and surrounding environment's refractive indices of the designed hexamers. As seen in Fig. 6, the Fano resonance presents a high sensitivity to the change of the surrounding's refractive index within the range of 1.1–1.5. Apparently, the Fano resonant dip show a red shift with increase of the refractive index as discussed in Refs. [12,16,17], which is potential for biosensing application.
According to the above analysis results, we propose a computational model of hexamers with optimized parameters g ¼ 12 nm, h ¼ 56 nm, and t ¼ 21 nm, which are based on scattering spectra and the defined ratio coefficient m. The computation results show that the CR can reach 85.8% and the FLW is 0.0287 eV. It means that Fano line-shape with both narrow line width and high spectral contrast ratio is obtained with the designed hexamers. So, the designed hexamers have potential applications in high sensitivity refractive index chemical and biological sensors. It is well known that the sharpening of Fano line width is crucial to the enhanced absorption. In order to illustrate LFE properties of the designed hexamers, LFE factor and effective mode volume are shown in Fig. 7. LFE factor is defined as the ratio of the maximum electric field to the intensity of incident light, indicating the ability of enhancing local electric field. Effective mode volume is calculated by Ref. [18]:
Fig. 6. The scattering spectra of hexamers with different surrounding refractive index.
Fig. 7. The LFE factor and the effective mode volume around the Fano resonance. 67
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Veff ¼ ∫ V εðrÞjEðrÞj2 d3 r
Physica B: Condensed Matter 533 (2018) 63–68
max εðrÞjEðrÞj2
References
(3)
[1] U. Becker, T. Prescher, E. Schmidt, B. Sonntag, H. Wetzel, Decay channels of the discrete and continuum Xe 4d resonances, Phys. Rev. A Gen. Phys. 33 (1986) 3891–3899. [2] U. Fano, Effects of configuration interaction on intensities and phase shifts, Phys. Rev. 124 (1961) 1866–1878. [3] S. Zhang, D.A. Genov, Y. Wang, M. Liu, X. Zhang, Plasmon-induced transparency in metamaterials, Phys. Rev. Lett. 101 (2008), 047401. [4] Z.J. Yang, Z.S. Zhang, L.H. Zhang, Q.Q. Li, Z.H. Hao, Q.Q. Wang, Fano resonances in dipole-quadrupole plasmon coupling nanorod dimers, Optic Lett. 36 (2011) 1542–1544. [5] S. Hayashi, D.V. Nesterenko, A. Rahmouni, Z. Sekkat, Observation of Fano line shapes arising from coupling between surface plasmon polariton and waveguide modes, Appl. Phys. Lett. 108 (2016) 2257. [6] T.K. Nguyen, T.D. Le, P.T. Dang, K.Q. Le, Asymmetrically engineered metallic nanodisk clusters for plasmonic Fano resonance generation, J. Opt. Soc. Am. B 34 (2017) 668. [7] J.H. Hu, X.H. Liu, J.J. Zhao, J. Zou, Investigation of Fano resonance in compound resonant waveguide gratings for optical sensing, Chin. Optic Lett. (2017) 60–63. [8] Z. Fang, J. Cai, Z. Yan, P. Nordlander, N.J. Halas, X. Zhu, Removing a wedge from a metallic nanodisk reveals a Fano resonance, Nano Lett. 11 (2011) 4475. [9] C. Lu, J. Yao, L. Zhao, Y. Cui, Z. Qi, Tunable double-resonance dimer structure for surface-enhanced Raman scattering substrate in near-infrared region, Photon. Res. 3 (2015) 313. [10] M. Shioi, H. Jans, K. Lodewijks, P.V. Dorpe, L. Lagae, T. Kawamura, Tuning the interaction between propagating and localized surface plasmons for surface enhanced Raman scattering in water for biomedical and environmental applications, Appl. Phys. Lett. 104 (2014), 1667-R. [11] K.M. Mayer, J.H. Hafner, Localized surface plasmon resonance sensors, Chem. Rev. 111 (2011) 3828–3857. [12] Y. Huo, T. Jia, Y. Zhang, H. Zhao, S. Zhang, D. Feng, Z. Sun, Narrow and deep Fano resonances in a rod and concentric square ring-disk nanostructures, Sensors 13 (2013) 11350–11361. [13] P.B. Johnson, Optical constants of the noble metals, Phys. Rev. B 6 (1972) 4370–4379. [14] Y. Zhan, D.Y. Lei, X. Li, S.A. Maier, Plasmonic Fano resonances in nanohole quadrumers for ultra-sensitive refractive index sensing, Nanoscale 6 (2014) 4705–4715. [15] K.L. Lee, J.B. Huang, J.W. Chang, S.H. Wu, P.K. Wei, Ultrasensitive biosensors using enhanced Fano resonances in capped gold nanoslit arrays, Sci. Rep. 5 (2015) 8547. [16] K. Liu, X. Xue, V. Sukhotskiy, E.P. Furlani, Optical Fano resonance in self-assembled magnetic–plasmonic nanostructures, J. Phys. Chem. C 120 (2016) 27555–27561. [17] L. Niu, J.B. Zhang, Y.H. Fu, S. Kulkarni, A.B. Luky, Fano resonance in dual-disk ring plasmonic nanostructures, Opt. Express 19 (2011) 22974–22981. [18] P.T. Kristensen, V.C. Van, S. Hughes, Generalized effective mode volume for leaky optical cavities, Optic Lett. 37 (2012) 1649–1651. [19] Y. Huo, T.Q. Jia, Y. Zhang, H. Zhao, S.A. Zhang, D. Feng, Z.R. Sun, Spaser based on Fano resonance in a rod and concentric square ring-disk nanostructure, Appl. Phys. Lett. 104 (2014), 113104.
in which εðrÞ is the dielectric coefficient, jEðrÞj is the absolute value of electric field intensity and the region V is covering metallic nanoparticles and the surrounding media. The small mode volume provides enhanced light-matter interaction and is of both fundamental and technological interest. Fig. 7 presents at the Fano resonance dip LFE factor achieves to the maximum 36 and the effective mode volume reduces to the minimum 3:9 1023 m3 that an order of magnitude is decreased comparing with Ref. [19]. At the Fano scattering dip, the incident optical field is efficiently transferred into local regions with a higher LFE factor and a lower mode volume, which contributes to the strongly concentrated local fields for enhancing surface enhanced Raman scattering signals. 4. Conclusions In conclusion, we show that the Fano resonance can be achieved in a symmetric plasmonic hexamer model composed of six nanorings at nearinfrared regions. By using COMSOL based on FEM, the scattering spectra, the charge densities and the electric field intensity distribution are simulated. According to the simulation results, the formation of the Fano resonance is analyzed in theory. The spectral dip of the structure has characteristics of a narrow line width and relatively high contrast ratio. In addition, the hexamers can achieve a higher LFE factor and a lower effective mode volume. The hexamer nanostructure has potential applications as a sensitive sensor, since it is sensitive to the changes of the surrounding media refractive index. For the proposed hexamer, it also has an ability of enhancing electric field intensity that can apply to surface enhanced Raman scattering signals. Acknowledgments This work was supported by the National Natural Science Foundation of China (51472174, 11144007, and 11274188); Natural Science Foundation of Shandong Province under Grant ZR2017MF059; Optoelectronics Think Tank Foundation of Qingdao; the Malmstrom Endowment Fund of Hamline University.
68
Contents lists available at ScienceDirect
Physica B: Condensed Matter journal homepage: www.elsevier.com/locate/physb
Fano resonances of a ring-shaped “hexamer” cluster at near-infrared wavelength Tong-Tong Liu a, b, Feng Xia a, b, Peng Sun a, b, Li-Li Liu a, b, Wei Du a, b, Meng-Xue Li a, Wei-Jin Kong a, Yong Wan a, Li-Feng Dong c, d, Mao-Jin Yun a, b, * a
College of Physics Science, Qingdao University, Qingdao, 266071, China Key Laboratory of Photonics Materials and Technology in Universities of Shandong, Qingdao University, Qingdao, 266071, China Department of Physics, Hamline University, Saint Paul, MN, 55104, USA d Department of Chemical Engineering, Taishan Medical University, Taian, 271016, China b c
A R T I C L E I N F O
A B S T R A C T
Keywords: Fano resonances The Fano line width A contrast ratio The effective mode volume
Fano resonances have been studied intensely in the last decade, since it is an important way to decrease the resonance line width and enhance local electric field. However, achieving a Fano line-shape with both narrow line width and high spectral contrast ratio is still a challenge. In this paper, we theoretically predict the Fano resonance induced by the extinction of normal plane wave in a ring-shaped hexamer cluster at near-infrared wavelength. In order to obtain the narrow Fano line width and high spectral contrast ratio, the relationships between the Fano line-shape and the parameters of the nanostructure are analyzed in detail. The nanostructure is simulated by using commercial software based on finite element method. The simulation results show that when the structural parameters are optimized, the Fano line width can be narrowed down 0.028 eV with a contrast ratio of 86%, and the local electric field enhancement factor at the Fano resonance wavelength can reach to 36. Furthermore, the effective mode volume of the structure is 3:9 1023 m3 which is lower than the available literature. These results indicate many potential applications of the Fano resonance in multiwavelength surfaceenhanced Raman scattering and biosensing.
1. Introduction Fano resonances in metallic nanoparticles have been found promising in a wide range of potential applications in optical filters, polarization selectors, sensors, lasers, modulators and nonlinear optic devices. In particular, as the Fano resonance is sharp and sensitive to refractive index changes of the surrounding environment, such tunability and local electric field (LFE) properties of plasmonic structures have been remarkably explored in high sensitivity refractive index chemical and biological sensors. In atomic and molecular spectroscopy [1,2], it is often to observe a pronounced asymmetric spectral line-shape, which results from the overlapping between two competing pathways, one associated with discrete states and the other with a continuum of states, to generate quantum interferences and cause zero absorption phenomenon at a specific frequency. The phenomenon of this interference is known as the Fano resonance which was put forward by U. Fano in 1961. Similarly, Fano resonances in plasmonic nanostructures originate from the interference of bright and dark plasmon modes of individual constituent
components of nanostructures. Bright plasmon modes, which are analogous to the continuum state, have finite dipole moments and can be efficiently excited by incident light. So, the bright modes are radiative and have a large scattering cross section and broad line width. On the contrary, the dark modes, which possess zero dipole moments, cannot be excited by incident light. So, the dark modes are weakly radiative and have narrow line width, which is analogous to discrete states. Fano resonances generated from various nanostructures have been widely studied in recent years. For example, deep Fano resonance in the transparency spectrum is realized in the dolmen-type arranged slab structures proposed by Zhang et al. [3]. Hao et al. theoretically investigated the plasmon coupling in metallic nanorod dimer and found a pronounced dip in the extinction spectrum which is induced by destructive interference between a bright dipole plasmon and a dark quadrupole plasmon [4]. The narrow Fano line shapes in planar multilayer structures was demonstrated experimentally by Hayashi et al. [5]. A planar-engineered metamolecule that generates Fano resonance was proposed by Le et al. [6]. Fano resonance in compound resonant
* Corresponding author. College of Physics Science, Qingdao University, Qingdao, 266071, China. E-mail address: [email protected] (M.-J. Yun). https://doi.org/10.1016/j.physb.2017.12.069 Received 20 November 2017; Received in revised form 28 December 2017; Accepted 29 December 2017 Available online 30 December 2017 0921-4526/© 2018 Elsevier B.V. All rights reserved.
T.-T. Liu et al.
Physica B: Condensed Matter 533 (2018) 63–68
Fig. 1. (a) Schematic 3D illustration of the symmetric plasmonic hexamers and the incident light. Top view (b) and side view (c) of the symmetric plasmonic hexamers with geometric.
width and high spectral contrast ratio (CR) is still a challenge. Furthermore, the underlying physics that generates the Fano resonance is not always understood. In this paper, we propose a ring-shaped “hexamer” cluster consisting of six nanorings for Fano resonance generation in near-infrared regions. The near-infrared spectral range, where blood and tissue are mostly
waveguide gratings for optical sensing was investigated by Liu et al. [7]. Fang et al. introduced a remarkably simple planar nanostructure, a single metallic nanodisk with a missing wedge-shaped slice that exhibits the Fano resonance [8]. Hao et al. reported a tunable Fano resonance in plasmonic nanocavities by symmetry breaking. In spite of the intensive work about the Fano resonance, Fano line-shape with both narrow line
Fig. 2. (a) The scattering spectra of hexamers. (b) The charge densities at λ ¼ 1122 nm on the top surface. (c) The charge distribution at the wavelength of 1300 nm. (d) The electric field intensity distribution in the middle section (z ¼ h/2) at λ ¼ 1000 nm, 1122 nm, 1300 nm. 64
T.-T. Liu et al.
Physica B: Condensed Matter 533 (2018) 63–68
Fig. 3. (a) The scattering spectra of hexamers range from 1050 nm to 1200 nm with different gap width g. (b) The Fano line width and contrast ratio as a function of the gap width g. (c) The ratio coefficient m with the change of the gap width g.
contrast ratio and the maximum local electric field enhancement at near-infrared regions. COMSOL Multiphysics based on FEM is used to calculate the scattering spectra, the electric filed and charge distribution of the designed symmetric plasmonic hexamer model. The normally incident light is polarized along the x direction in Fig. 1. And perfectly matched layer absorbing boundary is adopted in the simulation domain. Scattering and absorption cross section are given by
transparent and light can penetrate tissues deeply, is technologically important for a number of applications, including surface-enhanced Raman scattering, biological and bio-chemical sensing [9–11]. In the symmetric plasmonic hexamers, the Fano resonance is from the interference between superradiant mode and subradiant mode. And the Fano resonance can be tuned by changing the geometric parameters or the surrounding refractive index of the designed hexamers. Fano line width (FLW), which is the most important factor to determine the performance of Fano resonances, can be narrowed to 0.028 eV with CR of 86% which the CR is better than the results in Ref. [12]when the FLW is similar, and the LFE factor at the Fano resonance wavelength reaches 36. The devices based on our tunable Fano resonance can be used in highly integrated plasmonic devices with excellent performance, such as surface-enhanced spectroscopy and sensor.
σs
c a
¼
1 ∫ ∫ ðn⋅Ssca ÞdS I0
(1)
Here, n is the normal vector pointing outwards from the nanodisk, Ssca is the scattered intensity (Poynting) vector, and I0 is the incident intensity. The integral is taken over the closed surface of the scatter. 3. Results and discussion
2. Structure and computational methods First, we perform an analysis to identify Fano resonance features of the designed symmetric plasmonic hexamer. In the calculation model, the identical inner and outer diameter d and D of the six nanorings is 60 nm and 80 nm, and the gap width g between the edge of each ring is 20 nm. The calculated scattering and absorption spectra of the hexamer structure are shown in Fig. 2(a). Obviously, there is a strong Fano dip at the wavelength of 1122 nm in the scattering spectrum, which arises mainly from the interference between superradiant and subradiant mode. It can be better understood by demonstrating the surface charge distribution. So, the induced surface charges on the top surface of the hexamers at resonance peak λ ¼ 1122 nm is given in Fig. 2(b). It can be clearly found that dipoles of the left and right nanorings (nanorings 1, 4) oscillate out of phase with that of four nanorings on the top and bottom (nanorings 2, 3, 5, 6) in the horizontal direction, and dipoles of nanorings (nanorings 2, 5) oscillate out of phase with that of nanorings (nanorings 3, 6) in the vertical direction. Such distribution of the dipoles indicates
Fig. 1 shows the three-dimensional schematic of the designed symmetric plasmonic hexamer model which consists of six nanorings. The hexamer's geometry is characterized by four parameters: the inner and outer diameter d and D of the six rings, the distance R between the center of the ring and the center of the whole structure, and the height h of the metal layer, which is equivalent to the height of each ring. The wall thickness of the nanoring is t ¼ ðD dÞ=2, and the gap between the edge of each ring is g ¼ R D. The hexamer which is embedded in a gain media doped silica layer is deposited on the glass substrate whose refractive index is set to a constant value of 1.5 with the neglect of frequency change. Since the Fano dip arises from weakly dissipated material, silver (Ag) is selected as the plasmonic material. The dielectric permittivity of silver is taken from Johnson and Christy's experimental data [13]. In this work, structure dimension can be manipulated by tuning geometric parameters to get narrow Fano resonances with high 65
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Physica B: Condensed Matter 533 (2018) 63–68
there is an almost perfect net dipole moment which can be treated as subradiant behavior. By contrast, the induced surface charges distribution at the wavelength of 1300 nm is shown in Fig. 2(c), obviously the dipoles of all constituent particles oscillate in the same direction. This behavior is called as superradiant mode, which results in increasing radiation damping. The coupling between subradiant and superradiant mode results in the characteristic Fano line shape in the scattering spectra. The electric field intensity distribution diagrams in the middle section (z ¼ h=2) with the wavelength of 1000 nm, 1122 nm, 1300 nm respectively are shown in Fig. 2(d). Apparently, the electric field intensity at Fano resonance dip (1122 nm) is stronger than the other two wavelengths. In other words, the Fano resonant cluster structure has the feature of high field enhancement, which is mainly localized between the nanorings. For Fano resonances, two extremely important parameters have influence on the sensitivity of detection: FLW and CR. FLW is described as the full width at half maximum of the Fano dip, and CR is defined as the ratio of the difference between the minimum and maximum to the maximum value. In Fig. 3, a series of FEM spectral computations are presented to illustrate the dependence of Fano resonance on the geometric parameters of the designed hexamer. Fig. 3(a) displays the scattering spectrum with different gap g. It can be found that if all other parameters keep the same, there is a slight blue shift of the Fano resonance wavelengths from 1154 nm to 1128 nm with increasing gap g from 3 nm to 25 nm. Fig. 3(b) shows FLW decreases exponentially from 109 nm to 25 nm, and CR of Fano resonance decreases greatly from 91.7% to 67.2% with increasing gap g from 3 nm to 25 nm. Since the gap g determines the size of the coupling strength, the coupling strength becomes weaker with the increase of the gap, which is consistent with other studies [3,12]. In this paper, our interest is to achieve the narrow FLW and high CR. Therefore, a ratio coefficient m is defined to optimize the structure.
m¼
c lnðlÞ
(2)
in which c represents the CR, and l indicates the FLW. As shown in Fig. 3(c), it can generate a B-spline curve by interpolating it over about 5 points covering the minimum to maximum values. This curve indicates that the maximum value of the ratio coefficient m corresponds to g ¼ 12 nm. Fig. 4(a) presents the influence of the metal layer height h on the Fano resonances. From the scattering spectra of the hexamers, we can conclude that if all other parameters are held constant, the Fano resonance wavelengths take on a slight blue shift from 1080 nm to 1310 nm with the metal layer height h changing from 30 nm to 80 nm. As shown in Fig. 4(b), the FLW decreases from 48 nm to 21 nm with the height h increasing from 30 nm to 80 nm. However, CR increases from 68.2% to 77.3% as the height h increasing from 30 nm to 50 nm, and then decreases to 56.1% greatly when the height h increases to 80 nm. Since the height h is relevant to active area of the coupling, the coupling strength makes a difference with the increase of the height, which corresponds to a sensitivity of hexamers. The high sensitivity of the Fano resonance scattering dip in the hexamer indicates its strong potential for biosensing applications. And Fig. 4(c) illustrates that the maximum value of the ratio coefficient m corresponds to h ¼ 56 nm. In Fig. 5, the relationship between the Fano resonance features and the thickness t of the nanorings is exploited. With the parameter t increasing from 15 nm to 30 nm, the scattering spectrum shows the Fano resonant dip has blue-shifts from 1240 nm to 998 nm obviously in Fig. 5(a). As displayed in Fig. 5(b), CR first increases from 70.4% to 74.0% and then drops to 35.4% with the increasing thickness of annular wall, and the FLW declines from 43 nm to 22 nm exponentially. This is because that thicker nanoring has more oscillating electrons and therefore provides stronger plasmonic response, which accords with the
Fig. 4. (a) The scattering spectra of hexamers with different height h of the metal layer on Fano resonance dip. (b) The Fano line width and contrast ratio as a function of the height h. (c) The ratio coefficient m with the change of the height. 66
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Physica B: Condensed Matter 533 (2018) 63–68
Fig. 5. (a) The scattering spectra of hexamers with different thickness t of annular wall. (b) The Fano line width and contrast ratio as a function of the thickness t. (c) The ratio coefficient m with the change of the thickness t.
results in Ref. [13]. With the changes of the ratio coefficient m by the parameter t, we can draw the conclusion that t ¼ 21 nm appears to be the best choice for balancing the FLW and the CR, as shown in Fig. 5(c). Fano resonance is ultra-sensitive to the dielectric refractive index changes of the surrounding environment, such tunability and LFE properties of plasmonic structure have been remarkably explored in high sensitivity refractive index chemical and biological sensors [14,15]. Therefore, it is necessary to analyze the relation between Fano resonance and surrounding environment's refractive indices of the designed hexamers. As seen in Fig. 6, the Fano resonance presents a high sensitivity to the change of the surrounding's refractive index within the range of 1.1–1.5. Apparently, the Fano resonant dip show a red shift with increase of the refractive index as discussed in Refs. [12,16,17], which is potential for biosensing application.
According to the above analysis results, we propose a computational model of hexamers with optimized parameters g ¼ 12 nm, h ¼ 56 nm, and t ¼ 21 nm, which are based on scattering spectra and the defined ratio coefficient m. The computation results show that the CR can reach 85.8% and the FLW is 0.0287 eV. It means that Fano line-shape with both narrow line width and high spectral contrast ratio is obtained with the designed hexamers. So, the designed hexamers have potential applications in high sensitivity refractive index chemical and biological sensors. It is well known that the sharpening of Fano line width is crucial to the enhanced absorption. In order to illustrate LFE properties of the designed hexamers, LFE factor and effective mode volume are shown in Fig. 7. LFE factor is defined as the ratio of the maximum electric field to the intensity of incident light, indicating the ability of enhancing local electric field. Effective mode volume is calculated by Ref. [18]:
Fig. 6. The scattering spectra of hexamers with different surrounding refractive index.
Fig. 7. The LFE factor and the effective mode volume around the Fano resonance. 67
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Veff ¼ ∫ V εðrÞjEðrÞj2 d3 r
Physica B: Condensed Matter 533 (2018) 63–68
max εðrÞjEðrÞj2
References
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[1] U. Becker, T. Prescher, E. Schmidt, B. Sonntag, H. Wetzel, Decay channels of the discrete and continuum Xe 4d resonances, Phys. Rev. A Gen. Phys. 33 (1986) 3891–3899. [2] U. Fano, Effects of configuration interaction on intensities and phase shifts, Phys. Rev. 124 (1961) 1866–1878. [3] S. Zhang, D.A. Genov, Y. Wang, M. Liu, X. Zhang, Plasmon-induced transparency in metamaterials, Phys. Rev. Lett. 101 (2008), 047401. [4] Z.J. Yang, Z.S. Zhang, L.H. Zhang, Q.Q. Li, Z.H. Hao, Q.Q. Wang, Fano resonances in dipole-quadrupole plasmon coupling nanorod dimers, Optic Lett. 36 (2011) 1542–1544. [5] S. Hayashi, D.V. Nesterenko, A. Rahmouni, Z. Sekkat, Observation of Fano line shapes arising from coupling between surface plasmon polariton and waveguide modes, Appl. Phys. Lett. 108 (2016) 2257. [6] T.K. Nguyen, T.D. Le, P.T. Dang, K.Q. Le, Asymmetrically engineered metallic nanodisk clusters for plasmonic Fano resonance generation, J. Opt. Soc. Am. B 34 (2017) 668. [7] J.H. Hu, X.H. Liu, J.J. Zhao, J. Zou, Investigation of Fano resonance in compound resonant waveguide gratings for optical sensing, Chin. Optic Lett. (2017) 60–63. [8] Z. Fang, J. Cai, Z. Yan, P. Nordlander, N.J. Halas, X. Zhu, Removing a wedge from a metallic nanodisk reveals a Fano resonance, Nano Lett. 11 (2011) 4475. [9] C. Lu, J. Yao, L. Zhao, Y. Cui, Z. Qi, Tunable double-resonance dimer structure for surface-enhanced Raman scattering substrate in near-infrared region, Photon. Res. 3 (2015) 313. [10] M. Shioi, H. Jans, K. Lodewijks, P.V. Dorpe, L. Lagae, T. Kawamura, Tuning the interaction between propagating and localized surface plasmons for surface enhanced Raman scattering in water for biomedical and environmental applications, Appl. Phys. Lett. 104 (2014), 1667-R. [11] K.M. Mayer, J.H. Hafner, Localized surface plasmon resonance sensors, Chem. Rev. 111 (2011) 3828–3857. [12] Y. Huo, T. Jia, Y. Zhang, H. Zhao, S. Zhang, D. Feng, Z. Sun, Narrow and deep Fano resonances in a rod and concentric square ring-disk nanostructures, Sensors 13 (2013) 11350–11361. [13] P.B. Johnson, Optical constants of the noble metals, Phys. Rev. B 6 (1972) 4370–4379. [14] Y. Zhan, D.Y. Lei, X. Li, S.A. Maier, Plasmonic Fano resonances in nanohole quadrumers for ultra-sensitive refractive index sensing, Nanoscale 6 (2014) 4705–4715. [15] K.L. Lee, J.B. Huang, J.W. Chang, S.H. Wu, P.K. Wei, Ultrasensitive biosensors using enhanced Fano resonances in capped gold nanoslit arrays, Sci. Rep. 5 (2015) 8547. [16] K. Liu, X. Xue, V. Sukhotskiy, E.P. Furlani, Optical Fano resonance in self-assembled magnetic–plasmonic nanostructures, J. Phys. Chem. C 120 (2016) 27555–27561. [17] L. Niu, J.B. Zhang, Y.H. Fu, S. Kulkarni, A.B. Luky, Fano resonance in dual-disk ring plasmonic nanostructures, Opt. Express 19 (2011) 22974–22981. [18] P.T. Kristensen, V.C. Van, S. Hughes, Generalized effective mode volume for leaky optical cavities, Optic Lett. 37 (2012) 1649–1651. [19] Y. Huo, T.Q. Jia, Y. Zhang, H. Zhao, S.A. Zhang, D. Feng, Z.R. Sun, Spaser based on Fano resonance in a rod and concentric square ring-disk nanostructure, Appl. Phys. Lett. 104 (2014), 113104.
in which εðrÞ is the dielectric coefficient, jEðrÞj is the absolute value of electric field intensity and the region V is covering metallic nanoparticles and the surrounding media. The small mode volume provides enhanced light-matter interaction and is of both fundamental and technological interest. Fig. 7 presents at the Fano resonance dip LFE factor achieves to the maximum 36 and the effective mode volume reduces to the minimum 3:9 1023 m3 that an order of magnitude is decreased comparing with Ref. [19]. At the Fano scattering dip, the incident optical field is efficiently transferred into local regions with a higher LFE factor and a lower mode volume, which contributes to the strongly concentrated local fields for enhancing surface enhanced Raman scattering signals. 4. Conclusions In conclusion, we show that the Fano resonance can be achieved in a symmetric plasmonic hexamer model composed of six nanorings at nearinfrared regions. By using COMSOL based on FEM, the scattering spectra, the charge densities and the electric field intensity distribution are simulated. According to the simulation results, the formation of the Fano resonance is analyzed in theory. The spectral dip of the structure has characteristics of a narrow line width and relatively high contrast ratio. In addition, the hexamers can achieve a higher LFE factor and a lower effective mode volume. The hexamer nanostructure has potential applications as a sensitive sensor, since it is sensitive to the changes of the surrounding media refractive index. For the proposed hexamer, it also has an ability of enhancing electric field intensity that can apply to surface enhanced Raman scattering signals. Acknowledgments This work was supported by the National Natural Science Foundation of China (51472174, 11144007, and 11274188); Natural Science Foundation of Shandong Province under Grant ZR2017MF059; Optoelectronics Think Tank Foundation of Qingdao; the Malmstrom Endowment Fund of Hamline University.
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