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Multipolar Fano resonances in concentric semi-disk ring cavities
Optik - International Journal for Light and Electron Optics 200 (2020) 163416
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Optik journal homepage: www.elsevier.com/locate/ijleo
Original research article
Multipolar Fano resonances in concentric semi-disk ring cavities ⁎
Xingfang Zhang , Fengshou Liu, Xin Yan, Lanju Liang
T
School of Opt-Electronic Engineering, Zaozhuang University, Zaozhuang, 277160, China
A R T IC LE I N F O
ABS TRA CT
Keywords: Fano resonance Localized surface plasmon Resonance Cavity Finite difference time domain Scattering cross section
The plasmon properties of the concentric cavity consisting of a semi-disk inside a thin ring are theoretically investigated by the finite difference time domain and plasmon hybridization methods. According to the simulated absorption and scattering spectra, electric field distributions and charge diagrams, multiplar Fano resonances are successfully generated, mainly due to the coupling between the dark multipolar modes and the bright dipolar mode originating from the hybridization between the primitive modes of the semi-disk and the ring. Moreover, the intensities and spectral positions of the Fano resonances can be manipulated by modifying the geometric parameters of the cavity. The cavity for potential use as a multi-wavelength biochemical sensor is evaluated with the refractive index sensitivity and figure of merit.
1. Introduction Localized surface plasmon resonances in the noble metal such as gold or silver nanostructures, originating from the collective oscillation of free electrons in response to the applied electromagnetic waves, have gained considerable attention due to the interesting physics and wide prominent fields in biochemical sensors [1], solar cells [2], micro-nano photonic devices [3], and surface enhanced Raman scattering [4]. As the surface plasmon resonances interact between bright (superradiation) modes and dark (subradiation) modes that are spectrally and spatially overlapping due to the near-field coupling, plasmonic Fano resonances can be successfully formed, and hence sharp and asymmetric line profiles are observed in the absorption, scattering or extinction spectrum [5]. The Fano resonance is a special electromagnetic mode with a very high quality factor of merit (FOM) and environmental sensitivity because of its narrow spectral bandwidth. It is also presented that the reduction of the scattered light at the frequency corresponding to the Fano dip maximizes energy coupling into the plasmonic nanostructures, thereby generating a highly localized and huge electric field. In the last few years, plasmonic Fano resonances have shown a variety of applications including slow light photonic devices [6], optical switches [7], biosensors [8], waveguides [9], plasmon lasers [10], and so on. In the field of plasmonic nanomaterials, a great number of Fano-type nanostructures have been explored and investigated in both numerical simulations and experiments, such as multi-layered nanoshells [11], asymmetric nanoparticle dimers [12], nanoparticle clusters [13], nanorod complexes [14], non-concentric ring-disk nanocavities [15–20], and other arrangements. Among them, ringdisk cavities have been intensively studied because of the simple structure and wide spectral regulation. Sonnefraud et al. [15] found that when the disk was deviated from the center of the ring or the uniformity of the ring was destroyed, the Fano resonance can be observed from the interference between the dark quadrupolar ring mode and the bright mode formed by the hybridized dipolar mode of the whole ring-disk cavity. Li et al. [16] pointed out that tunable higher order Fano resonance can be achieved in disk-ring cavity with double symmetry breaking, due to the destructive interference between the bright mode of the displaced disk and the dark mode of the asymmetric ring. Other investigations showed that a rich set of tunable Fano line-shapes was provided in the dual-disk ring
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Corresponding author. E-mail address: [email protected] (X. Zhang).
https://doi.org/10.1016/j.ijleo.2019.163416 Received 11 March 2019; Received in revised form 19 August 2019; Accepted 13 September 2019 0030-4026/ © 2019 Elsevier GmbH. All rights reserved.
Optik - International Journal for Light and Electron Optics 200 (2020) 163416
X. Zhang, et al.
Fig. 1. Schematic of a concentric semi-disk ring cavity, where the geometrical parameters r, R1 and R2 are defined.
[17,18] or asymmetric split-ring-disk nanostructures [19,20]. In addition, it is proved that the introduction perturbations into a plasmonic system such as an asymmetric dielectric environment [21] or oblique incidence [15,20] can be the efficient ways to excite Fano resonances in metal nanostructures. In this paper, we study the excitation of Fano resonances in a concentric semi-disk ring cavity by employing the finite difference time domain (FDTD) method. It is found that multipolar Fano resonances arise due to the destructive interference between the dark multipolar modes and the bright dipolar mode originating from the hybridization between the primitive modes of the semi-disk and the ring. The effects of geometric parameters on the generation and evolution of Fano resonances are discussed in detail on the basis of plasmon hybridization theory. The potential of using such cavities as biosensors is evaluated with the values of the refractive index (RI) sensitivity and FOM. 2. Model and theoretical calculation The 2D model of the concentric semi-disk ring cavity under consideration is shown in Fig. 1, where the radius of the gold semidisk is r = 150 nm, the inner and outer radii of the gold ring are R2 = 170 nm and R1 = 200 nm, respectively, and the heights of the semi-disk and ring are equal to H = 40 nm. The surrounding dielectric environment is assumed to be air with the refractive index of n = 1 if without special description, and the dielectric function used to model gold is obtained from the experimental data of Johnson and Christy [22]. The cavity is illuminated by a normal incident plane wave with the electric and magnetic fields polarized along the y and x directions, respectively. Its optical properties are investigated by using the three-dimensional FDTD method [23]. In the numerical simulation, a plane wave total field-scattered field source ranging from 400 to 2500 nm is utilized as the incident light, and perfectly matched layers in all directions are used as absorption boundary to prevent reflections of scattered waves back into the simulation domain. According to Courant stability, the size of spatial step is defined at Δx = Δy = Δz = 2.5 nm, and a time step Δt = 4.5 × 10−18s is adopted, then cΔ t≤ Δx / 3 in the three-dimensional coordinates is able to obtain extremely well convergence [24]. Here, c is the velocity of light in a vacuum. Two boxes of monitors, one in the scattered field region and the other in the total field region, are defined to calculate the scattering and absorption cross sections, and all of the surface charge and near-field distributions are taken at the center cross sections of the cavities. The plasmon hybridization theory is usually adopted to describe the optical properties of the metallic nanostructures [25]. According to the theory, the plasmonic resonance of the semi-disk ring cavity can be considered as an interaction between the primitive plasmon responses of individual semi-disk and ring. The energy level diagram of plasmon hybridization between semi-disk modes (|ωl > , l = 1, 2, etc.) and symmetric ring modes (|ω-l' > , l' = 1, 2, etc.) is shown in Fig. 2(a). Due to the asymmetry of the cavity, the primitive semi-disk modes and symmetric ring modes with different angular momenta can hybridize with each other, i.e., the dipole mode of the semi-disk (l = 1) will not only couple to the dipole symmetric ring mode (l' = 1) but also with the quadrupole and higher order ring modes (l' = 2, 3, etc.), and vice versa, resulting in low energy bonding modes |ω–ll' > and high energy antibonding modes |ω-+ll' > . Similarly, there are two modes for each plasmon hybridization between semi-disk modes (|ωl > , l = 1, 2, etc.) and antisymmetric ring modes (|ω+l' > , l' = 1, 2, etc.): a low-energy bonding mode |ω+-ll' > and a higher energy antibonding mode |ω++ll' > . The induced dipole moments at the interfaces are shown schematically in Fig. 2(b). For clarify, higher order polar moments are not shown. 3. Results and discussion 3.1. Fano resonances in the semi-disk ring cavity Fig. 3 shows the calculated absorption (dashed) and scattering (solid) spectra of our proposed semi-disk ring cavity with the values of structural parameters given in the above section. It is found that two typical Fano-like resonance spectral response with dips around 796 nm and 1002 nm (denoted as dips M1 and M2) appear in broad scattering spectrum, respectively. According to plasmon hybridization, the plasmon resonance at 2015 nm (|ω–11' >), referred to as the DBR mode [15,26], resulting from a bonding 2
Optik - International Journal for Light and Electron Optics 200 (2020) 163416
X. Zhang, et al.
Fig. 2. Plasmon hybridization diagram in a semi-disk ring cavity and induced dipole polarizations of the cavity.
Fig. 3. The absorption (dotted line) and scattering (solid line) spectra of the semi-disk ring cavity embedded in air with r = 150 nm, R2 = 170 nm, R1 = 200 nm and H = 40 nm. Inset shows the charge diagram for central cross section of the cavity at 2015 nm as indicated by the arrow.
combination of the disk dipole and the bonding-type ring dipole, exhibits a spectrally sharper line width and has acquired a dark character due to an antiparallel coupling between the dipolar modes of the parent disk and ring plasmons. This interpretation is well supported by the surface charge plots at the associated resonance wavelength, depicted in the inset. Conversely, the higher energy mode around 1000 nm (|ω+-11' >), referred to as the DAR mode [15,26], is mainly a bonding combination of the disk dipole and the antibonding ring dipole, leading to an increased net dipole moment. Hence the DAR mode has a bright character, and is reflected in the broader line width with greater radiative losses. In order to reveal further the physical origin of the two Fano resonances, we investigate the surface charge and electric field distributions at the wavelengths corresponding to dips M1 and M2, which are presented in Fig. 4(a–d), respectively. As for the dip M1, the charge diagram in Fig. 4(a) indicates that the induced charge of ring on both sides are in phase, and out of phase with that of the center semi-disk. According to plasmon hybridization, M1 shows an obvious quadrupole-octupole bonding mode (|ω–23′ >) pattern, corresponding to a dark mode generated from the semi-disk quadrupolar mode and ring octupolar bonding mode. The Fano resonance near 796 nm hence results from the destructive interference of the dark quadrupole-octupole mode with the bright DAR mode. It can be seen from the electric field distribution in Fig. 4(c) that four hot spots exist in the gap between disk and ring. Charge diagram in Fig. 4(b) clearly demonstrates that quadrupole mode of the semi-disk and quadrupole bonding mode of the ring are excited simultaneously. This means that the Fano resonance M2 results from the coupling between the dark quadrupolequadrupole bonding mode (|ω–22′ >) and bright DAR mode. The electric field distribution in Fig. 4(d) has a similar feature as that shown in Fig. 4(b), showing four hot spots existing in the gap except for the stronger field enhancement not near the two vertices.
3.2. Effects of geometric parameters on Fano resonances As we know, Fano resonances depend not only on the metallic materials but also on the size of nanostructure elements, gap distances and the surrounding dielectric media. To obtain the influences of geometric parameters on Fano resonances, the semi-disk r, 3
Optik - International Journal for Light and Electron Optics 200 (2020) 163416
X. Zhang, et al.
Fig. 4. Charge diagrams and electric field distributions of the semi-disk ring cavity in the x–y plane corresponding to dips M1 and M2 at 796 and 1002 nm, respectively.
the ring radii R1, R2 and cavity height H are varied in our study to examine the modulation response of Fano resonances, respectively. We first discuss the dependence of the semi-disk size on the plasmonic properties of the cavity. Fig. 5 presents the simulated scattering spectra for various r from 110 nm to 150 nm with an increment of 20 nm, respectively. As shown in Fig. 5, we can see that dips M1, M2 and DBR mode are blue shift as r decreases, M1 is disappeared completely and M2 is almost invisible when r = 110 nm. Based on the plasmon hybridization, the coupling between the semi-disk and ring becomes weaker with decreasing r, resulting in the blue shift of the |ω–11′ > 、|ω–22′ > and |ω–23′ > modes of the cavity. Meanwhile, the decrease in the size of the semi-disk causes the decrease in the amount of collective oscillating electrons, which not only weakens the intensities of the |ω–22′ > and |ω– 23′ > modes, but also decreases the net dipole moment of the DAR mode. The blue-shifted and weakened dark modes are superimposed on the reduced spectral envelope of the bright mode, thereby producing two diminishing Fano dips in scattering spectrum. Fig. 6 shows the scattering spectra of the cavity with the radius R2 varying from 160 nm to 190 nm. Fano dips M1 and M2 appear near 809 and 1005 nm, respectively, when R2 = 160 nm, as shown in Fig. 6. With an increase in R2, dips M1, M2 and DBR mode are blue shift slightly and then red shift. As R2 increases to 190 nm, the dips M1 and M2 are very weak. This phenomenon may be
Fig. 5. Scattering spectra of the cavity embedded in air for different values of semi-disk size r with R2 = 170 nm, R1 = 200 nm and H = 40 nm. 4
Optik - International Journal for Light and Electron Optics 200 (2020) 163416
X. Zhang, et al.
Fig. 6. Scattering spectra of the cavity embedded in air with inner radii of the Au ring R2 = 160, 170, 180 and 190 nm. The other geometric parameters size r, R1 and H are fixed at 150, 200 and 40 nm, respectively.
attributed to the red shift of the ring mode competes with the spectral shifts induced by the diminishing hybridization between semidisk and ring modes with the increase in the inner radius of the ring. As R2 increases, the resonance frequencies of the ring modes |ωl' > decrease [25], resulting in the decreased frequencies of |ω–11′ > , |ω–22′ > and |ω–23′ > modes. Meanwhile, the increase in R2 leads to the weakening hybridization between the semi-disk and ring, resulting in blue shift of the |ω–11′ > , |ω–22′ > and |ω– 23′ > modes. It is reported that a closer distance between nanoparticles gives rise to the stronger hybridization, and the resonance wavelength shift exhibits a near-exponential decay with increasing inter-particle distance [27]. Therefore, as R2 increases, the Fano dips are blue shift due to the reduction of dominant hybridization between ring and semi-disk when R2 is relatively small, but when R2 is large enough, the Fano dips are red shift owing to the reduction in the frequency of the ring. Moreover, with a lager R2, there is less coupling between dark |ω–22′ > , |ω–23′ > modes and bright BAR mode, hence the Fano dips are gradually diminishing. Fig. 7 displays the simulated scattering spectra with different R1 varying from 190 nm to 210 nm. It can be clearly seen in Fig. 7 that the wavelengths corresponding to Fano dips M1, M2 and DBR mode occur around 852 nm, 1077 nm and 2175 nm, respectively, as R1 = 190 nm. With an increase in R1, the width of the ring becomes thicker, which leads to a weaker interaction between the electrons at the outer and inner surface of the ring, resulting in blue shift of |ω–11′ > 、|ω–22′ > and |ω–23′ > modes and hence blue shift of Fano resonances. Obviously, the |ω–22′ > mode is always in the spectral envelope of bright DAR mode, hence the Fano resonance M2 changes little, while |ω–23′ > mode gradually moves away from the spectral envelope of DAR mode, thereby the coupling between them decreases and the Fano dip M1 decreases. We have further investigated the influence of the cavity height on Fano resonances. In Fig. 8, the solid, dashed, and dotted lines represent the scattering spectra of the cavity with the height H of 20, 30, and 40 nm, respectively. By increasing the height H, Fano dips M1, M2 and DBR mode are red shift. A simple interpretation is that as the height increases, the amount of charges induced by the incident electric field increases while the cavity size is fixed. As a result, the displaced electron experiences a larger restoring force, leading to a higher resonance frequency [28]. Furthermore, when the height increases to a certain extent, more Fano resonances may occur. For example, the dipole bright mode supported by nanostructures and the quadrupole dark mode caused by the phase retardation could become non-orthogonal and interfere strongly with each other, leading to both Fano-like resonance and superscattering in a single subwavelength nanodisk [29].
Fig. 7. Scattering spectra of the cavity embedded in air with outer radii of the Au ring R1 = 190, 200, and 210 nm. The other geometric parameters size r, R2 and H are fixed at 150, 170 and 40 nm, respectively. 5
Optik - International Journal for Light and Electron Optics 200 (2020) 163416
X. Zhang, et al.
Fig. 8. Scattering spectra of the cavity embedded in air with cavity heights H = 20, 30, and 40 nm. The other geometric parameters size r, R1 and R2 are fixed at 150, 170 and 200 nm, respectively.
3.3. RI sensitivity and FOM of the cavity The plasmonic properties of the Fano resonance are likely to be strongly influenced by the RI of the surrounding medium. In order to investigate the sensing performance of the cavity, we compare the scattering spectra with complete dielectric filling of four different media (refractive indices n = 1, 1.1, 1.2 and 1.3), respectively. As shown in Fig. 9, dips M1, M2 and DBR mode exhibit an obvious red shift with an increase in the RI of the dielectric environment. This can be understood by the fact that the resonance wavelength is proportional to the dielectric screening effect [30]. Thereby the semi-disk ring cavity can be employed as a tunable multi-wavelength RI based sensor. Here, RI sensitivity (defined as S = δλ/δn) and FOM (FOM = S/Δλ) are taken into account to evaluate the sensing performance of the cavity [31]. where δλ is the shift quantity of the resonance peak (dip), δn is the quantity of the refractive of medium, and is the full width at half maximum of the resonance line. For Fano-like resonances, the Δλ can be defined as the energy difference between the Fano dip and the closest neighboring peak. we calculate Fano dips M1, M2 and DBR mode shift versus the RI of the surrounding medium, as shown in the inset of Fig. 9. A linear fit to the data gives a large RI sensitivity of 674 nm/ RIU, 914 nm/RIU and 1839 nm/RIU for dips M1, M2 and DBR mode, respectively, and the corresponding FoMs are about 6.8, 8.9 and 9.0 with the Δλ values around 99, 103 and 208 nm, respectively. The results show that the semi-disk ring cavity can be used for the multi-wavelength high sensitive sensing in near-infrared region. Next, we examine the RI sensitivity and FOM of the cavity for partial insertion of a dielectric medium into the gap between the semi-disk and ring, where small molecules are expected to concentrate because of strong gradient forces induced by plasmons. Fig. 10 shows the scattering spectral variations with different media and partial filling of the cavity. It can be seen in Fig. 10 that when the RI of the dielectric increases from 1 to 1.3, Fano dips M1, M2 are red shift from 796 nm, 1002 nm to 844 nm, 1050 nm, respectively, and the calculated RI sensitivities are about 160 nm/RIU and 158 nm/RIU, respectively. The corresponding FOMs are obtained to be 1.8 and 1.6, respectively. As discussed before, the sharp Fano resonances are very sensitive to the variation of the local refractive indices. By using the Fano resonances, a small variation of the local refractive indices in narrowest part of the gap between the ring and the semi-disk can bring a remarkable and observable wavelength shift change. Lastly, we compare the performance of our proposed cavity with analogous developed nanostructures as given in Table 1. For double split-ring resonators, the Fano resonance exceeds the sensitivity of 605 nm/RIU and the FOM of 4.8 [32]. The split-ring disk
Fig. 9. Scattering spectra of the cavity with changed refractive indices of surrounding media of 1, 1.1, 1.2, and 1.3, respectively, while keeping the geometry parameters unchanged. Inset shows the resonance wavelengths shift of the M1, M2 and DBR modes with different surrounding refractive indices. 6
Optik - International Journal for Light and Electron Optics 200 (2020) 163416
X. Zhang, et al.
Fig. 10. Scattering spectra of the cavity for partial dielectric filling in the gap between semi-disk and ring. The refractive indices are n = 1, 1.1, 1.2 and 1.3, respectively. The schematic shows that yellow represents gold, gray is for dielectrics, and white is for air. Inset displays the zoom-in on the M1 and M2 modes showing the spectral shifts in more detail (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article). Table 1 Comparison of the cavity performance with previous work. Ref.
Structure
Filling
Sensitivity
FOM
[32] [33] [34]
Double split-ring Split-ring disk Nonconcentric ring/disk
[35]*
Double split nanoring
This work
Semi-disk ring
complete complete complete partial complete partial complete partial
605 282 534 129 1200 110 674, 914 160, 158
4.8 4 3.2 0.95 8.5 0.66 6.8, 8.9 1.8, 1.6
The mark * indicates that the sensitivities and FOMs in this paper are the response of the bonding mode to the environment.
nanocavity is reported to obtain a sensitivity of ∼282 nm/RIU with a figure of merit ∼4 in near-infrared regime [33]. Hao et al. described that the sensitivity and FOM were 129 nm/RIU and 0.95 for partially filled cavity, and 534 nm/RIU and 3.2 for a completely filled cavity in a nonconcentric ring/disk cavity [34]. Liu et al. found that the sensitivity of bonding mode exceeding 1200 nm/RIU with a FOM exceeding 8.5 were obtained with a Au double split nanoring cavity for complete filling, and 110 nm/RIU and 0.66 for partial filling [35]. Our results are similar to those mentioned above, and the sensitivity and FOM could be further improved by optimizing the cavity size, or breaking the symmetry of cavity.
4. Conclusion In conclusion, we have investigated the multipolar Fano properties in a plasmonic semi-disk ring cavity based on FDTD and plasmon hybridization methods. Results show that two Fano dips are obtained due to the destructive interference between the bright mode and two dark modes originating from the interaction of semi-disk quadrupolar with ring octupolar or quadrupolar bonding modes, respectively. Moreover, the intensities and spectral positions of the two Fano resonances can be manipulated by modifying the geometric parameters of the cavity. By decreasing the semi-disk size, or increasing the cavity height and the outer ring radius, the two Fano dips are blue shift in the scattering spectra. With an increase in the inner radius of the ring, the two Fano dips are blue shift firstly and then red shift because the redshift of the dipole bonding ring mode competes with the spectral shifts induced by the diminishing hybridization between semi-disk and ring modes. Furthermore, the two Fano dips exhibit high RI sensitivities of 674 and 914 nm/RIU as well as high FoMs of 6.8 and 6.9 for a completely filled cavity, 160 and 158 nm/RIU as well as FoMs of 1.8 and 1.6 for partially filled cavity. The proposed cavity with two Fano resonances maybe an effective platform for multi-wavelength biochemical sensing.
Acknowledgements This work was financially supported by the National Natural Science Foundation of China (No.61701434), the Natural Science Foundation of Shandong Province, China (Nos.ZR2017MF005, ZR2018LF001) and the Project of Shandong Province Higher Education Science and Technology Program, China (No. J17KA087). 7
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Optik journal homepage: www.elsevier.com/locate/ijleo
Original research article
Multipolar Fano resonances in concentric semi-disk ring cavities ⁎
Xingfang Zhang , Fengshou Liu, Xin Yan, Lanju Liang
T
School of Opt-Electronic Engineering, Zaozhuang University, Zaozhuang, 277160, China
A R T IC LE I N F O
ABS TRA CT
Keywords: Fano resonance Localized surface plasmon Resonance Cavity Finite difference time domain Scattering cross section
The plasmon properties of the concentric cavity consisting of a semi-disk inside a thin ring are theoretically investigated by the finite difference time domain and plasmon hybridization methods. According to the simulated absorption and scattering spectra, electric field distributions and charge diagrams, multiplar Fano resonances are successfully generated, mainly due to the coupling between the dark multipolar modes and the bright dipolar mode originating from the hybridization between the primitive modes of the semi-disk and the ring. Moreover, the intensities and spectral positions of the Fano resonances can be manipulated by modifying the geometric parameters of the cavity. The cavity for potential use as a multi-wavelength biochemical sensor is evaluated with the refractive index sensitivity and figure of merit.
1. Introduction Localized surface plasmon resonances in the noble metal such as gold or silver nanostructures, originating from the collective oscillation of free electrons in response to the applied electromagnetic waves, have gained considerable attention due to the interesting physics and wide prominent fields in biochemical sensors [1], solar cells [2], micro-nano photonic devices [3], and surface enhanced Raman scattering [4]. As the surface plasmon resonances interact between bright (superradiation) modes and dark (subradiation) modes that are spectrally and spatially overlapping due to the near-field coupling, plasmonic Fano resonances can be successfully formed, and hence sharp and asymmetric line profiles are observed in the absorption, scattering or extinction spectrum [5]. The Fano resonance is a special electromagnetic mode with a very high quality factor of merit (FOM) and environmental sensitivity because of its narrow spectral bandwidth. It is also presented that the reduction of the scattered light at the frequency corresponding to the Fano dip maximizes energy coupling into the plasmonic nanostructures, thereby generating a highly localized and huge electric field. In the last few years, plasmonic Fano resonances have shown a variety of applications including slow light photonic devices [6], optical switches [7], biosensors [8], waveguides [9], plasmon lasers [10], and so on. In the field of plasmonic nanomaterials, a great number of Fano-type nanostructures have been explored and investigated in both numerical simulations and experiments, such as multi-layered nanoshells [11], asymmetric nanoparticle dimers [12], nanoparticle clusters [13], nanorod complexes [14], non-concentric ring-disk nanocavities [15–20], and other arrangements. Among them, ringdisk cavities have been intensively studied because of the simple structure and wide spectral regulation. Sonnefraud et al. [15] found that when the disk was deviated from the center of the ring or the uniformity of the ring was destroyed, the Fano resonance can be observed from the interference between the dark quadrupolar ring mode and the bright mode formed by the hybridized dipolar mode of the whole ring-disk cavity. Li et al. [16] pointed out that tunable higher order Fano resonance can be achieved in disk-ring cavity with double symmetry breaking, due to the destructive interference between the bright mode of the displaced disk and the dark mode of the asymmetric ring. Other investigations showed that a rich set of tunable Fano line-shapes was provided in the dual-disk ring
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Corresponding author. E-mail address: [email protected] (X. Zhang).
https://doi.org/10.1016/j.ijleo.2019.163416 Received 11 March 2019; Received in revised form 19 August 2019; Accepted 13 September 2019 0030-4026/ © 2019 Elsevier GmbH. All rights reserved.
Optik - International Journal for Light and Electron Optics 200 (2020) 163416
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Fig. 1. Schematic of a concentric semi-disk ring cavity, where the geometrical parameters r, R1 and R2 are defined.
[17,18] or asymmetric split-ring-disk nanostructures [19,20]. In addition, it is proved that the introduction perturbations into a plasmonic system such as an asymmetric dielectric environment [21] or oblique incidence [15,20] can be the efficient ways to excite Fano resonances in metal nanostructures. In this paper, we study the excitation of Fano resonances in a concentric semi-disk ring cavity by employing the finite difference time domain (FDTD) method. It is found that multipolar Fano resonances arise due to the destructive interference between the dark multipolar modes and the bright dipolar mode originating from the hybridization between the primitive modes of the semi-disk and the ring. The effects of geometric parameters on the generation and evolution of Fano resonances are discussed in detail on the basis of plasmon hybridization theory. The potential of using such cavities as biosensors is evaluated with the values of the refractive index (RI) sensitivity and FOM. 2. Model and theoretical calculation The 2D model of the concentric semi-disk ring cavity under consideration is shown in Fig. 1, where the radius of the gold semidisk is r = 150 nm, the inner and outer radii of the gold ring are R2 = 170 nm and R1 = 200 nm, respectively, and the heights of the semi-disk and ring are equal to H = 40 nm. The surrounding dielectric environment is assumed to be air with the refractive index of n = 1 if without special description, and the dielectric function used to model gold is obtained from the experimental data of Johnson and Christy [22]. The cavity is illuminated by a normal incident plane wave with the electric and magnetic fields polarized along the y and x directions, respectively. Its optical properties are investigated by using the three-dimensional FDTD method [23]. In the numerical simulation, a plane wave total field-scattered field source ranging from 400 to 2500 nm is utilized as the incident light, and perfectly matched layers in all directions are used as absorption boundary to prevent reflections of scattered waves back into the simulation domain. According to Courant stability, the size of spatial step is defined at Δx = Δy = Δz = 2.5 nm, and a time step Δt = 4.5 × 10−18s is adopted, then cΔ t≤ Δx / 3 in the three-dimensional coordinates is able to obtain extremely well convergence [24]. Here, c is the velocity of light in a vacuum. Two boxes of monitors, one in the scattered field region and the other in the total field region, are defined to calculate the scattering and absorption cross sections, and all of the surface charge and near-field distributions are taken at the center cross sections of the cavities. The plasmon hybridization theory is usually adopted to describe the optical properties of the metallic nanostructures [25]. According to the theory, the plasmonic resonance of the semi-disk ring cavity can be considered as an interaction between the primitive plasmon responses of individual semi-disk and ring. The energy level diagram of plasmon hybridization between semi-disk modes (|ωl > , l = 1, 2, etc.) and symmetric ring modes (|ω-l' > , l' = 1, 2, etc.) is shown in Fig. 2(a). Due to the asymmetry of the cavity, the primitive semi-disk modes and symmetric ring modes with different angular momenta can hybridize with each other, i.e., the dipole mode of the semi-disk (l = 1) will not only couple to the dipole symmetric ring mode (l' = 1) but also with the quadrupole and higher order ring modes (l' = 2, 3, etc.), and vice versa, resulting in low energy bonding modes |ω–ll' > and high energy antibonding modes |ω-+ll' > . Similarly, there are two modes for each plasmon hybridization between semi-disk modes (|ωl > , l = 1, 2, etc.) and antisymmetric ring modes (|ω+l' > , l' = 1, 2, etc.): a low-energy bonding mode |ω+-ll' > and a higher energy antibonding mode |ω++ll' > . The induced dipole moments at the interfaces are shown schematically in Fig. 2(b). For clarify, higher order polar moments are not shown. 3. Results and discussion 3.1. Fano resonances in the semi-disk ring cavity Fig. 3 shows the calculated absorption (dashed) and scattering (solid) spectra of our proposed semi-disk ring cavity with the values of structural parameters given in the above section. It is found that two typical Fano-like resonance spectral response with dips around 796 nm and 1002 nm (denoted as dips M1 and M2) appear in broad scattering spectrum, respectively. According to plasmon hybridization, the plasmon resonance at 2015 nm (|ω–11' >), referred to as the DBR mode [15,26], resulting from a bonding 2
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Fig. 2. Plasmon hybridization diagram in a semi-disk ring cavity and induced dipole polarizations of the cavity.
Fig. 3. The absorption (dotted line) and scattering (solid line) spectra of the semi-disk ring cavity embedded in air with r = 150 nm, R2 = 170 nm, R1 = 200 nm and H = 40 nm. Inset shows the charge diagram for central cross section of the cavity at 2015 nm as indicated by the arrow.
combination of the disk dipole and the bonding-type ring dipole, exhibits a spectrally sharper line width and has acquired a dark character due to an antiparallel coupling between the dipolar modes of the parent disk and ring plasmons. This interpretation is well supported by the surface charge plots at the associated resonance wavelength, depicted in the inset. Conversely, the higher energy mode around 1000 nm (|ω+-11' >), referred to as the DAR mode [15,26], is mainly a bonding combination of the disk dipole and the antibonding ring dipole, leading to an increased net dipole moment. Hence the DAR mode has a bright character, and is reflected in the broader line width with greater radiative losses. In order to reveal further the physical origin of the two Fano resonances, we investigate the surface charge and electric field distributions at the wavelengths corresponding to dips M1 and M2, which are presented in Fig. 4(a–d), respectively. As for the dip M1, the charge diagram in Fig. 4(a) indicates that the induced charge of ring on both sides are in phase, and out of phase with that of the center semi-disk. According to plasmon hybridization, M1 shows an obvious quadrupole-octupole bonding mode (|ω–23′ >) pattern, corresponding to a dark mode generated from the semi-disk quadrupolar mode and ring octupolar bonding mode. The Fano resonance near 796 nm hence results from the destructive interference of the dark quadrupole-octupole mode with the bright DAR mode. It can be seen from the electric field distribution in Fig. 4(c) that four hot spots exist in the gap between disk and ring. Charge diagram in Fig. 4(b) clearly demonstrates that quadrupole mode of the semi-disk and quadrupole bonding mode of the ring are excited simultaneously. This means that the Fano resonance M2 results from the coupling between the dark quadrupolequadrupole bonding mode (|ω–22′ >) and bright DAR mode. The electric field distribution in Fig. 4(d) has a similar feature as that shown in Fig. 4(b), showing four hot spots existing in the gap except for the stronger field enhancement not near the two vertices.
3.2. Effects of geometric parameters on Fano resonances As we know, Fano resonances depend not only on the metallic materials but also on the size of nanostructure elements, gap distances and the surrounding dielectric media. To obtain the influences of geometric parameters on Fano resonances, the semi-disk r, 3
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Fig. 4. Charge diagrams and electric field distributions of the semi-disk ring cavity in the x–y plane corresponding to dips M1 and M2 at 796 and 1002 nm, respectively.
the ring radii R1, R2 and cavity height H are varied in our study to examine the modulation response of Fano resonances, respectively. We first discuss the dependence of the semi-disk size on the plasmonic properties of the cavity. Fig. 5 presents the simulated scattering spectra for various r from 110 nm to 150 nm with an increment of 20 nm, respectively. As shown in Fig. 5, we can see that dips M1, M2 and DBR mode are blue shift as r decreases, M1 is disappeared completely and M2 is almost invisible when r = 110 nm. Based on the plasmon hybridization, the coupling between the semi-disk and ring becomes weaker with decreasing r, resulting in the blue shift of the |ω–11′ > 、|ω–22′ > and |ω–23′ > modes of the cavity. Meanwhile, the decrease in the size of the semi-disk causes the decrease in the amount of collective oscillating electrons, which not only weakens the intensities of the |ω–22′ > and |ω– 23′ > modes, but also decreases the net dipole moment of the DAR mode. The blue-shifted and weakened dark modes are superimposed on the reduced spectral envelope of the bright mode, thereby producing two diminishing Fano dips in scattering spectrum. Fig. 6 shows the scattering spectra of the cavity with the radius R2 varying from 160 nm to 190 nm. Fano dips M1 and M2 appear near 809 and 1005 nm, respectively, when R2 = 160 nm, as shown in Fig. 6. With an increase in R2, dips M1, M2 and DBR mode are blue shift slightly and then red shift. As R2 increases to 190 nm, the dips M1 and M2 are very weak. This phenomenon may be
Fig. 5. Scattering spectra of the cavity embedded in air for different values of semi-disk size r with R2 = 170 nm, R1 = 200 nm and H = 40 nm. 4
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Fig. 6. Scattering spectra of the cavity embedded in air with inner radii of the Au ring R2 = 160, 170, 180 and 190 nm. The other geometric parameters size r, R1 and H are fixed at 150, 200 and 40 nm, respectively.
attributed to the red shift of the ring mode competes with the spectral shifts induced by the diminishing hybridization between semidisk and ring modes with the increase in the inner radius of the ring. As R2 increases, the resonance frequencies of the ring modes |ωl' > decrease [25], resulting in the decreased frequencies of |ω–11′ > , |ω–22′ > and |ω–23′ > modes. Meanwhile, the increase in R2 leads to the weakening hybridization between the semi-disk and ring, resulting in blue shift of the |ω–11′ > , |ω–22′ > and |ω– 23′ > modes. It is reported that a closer distance between nanoparticles gives rise to the stronger hybridization, and the resonance wavelength shift exhibits a near-exponential decay with increasing inter-particle distance [27]. Therefore, as R2 increases, the Fano dips are blue shift due to the reduction of dominant hybridization between ring and semi-disk when R2 is relatively small, but when R2 is large enough, the Fano dips are red shift owing to the reduction in the frequency of the ring. Moreover, with a lager R2, there is less coupling between dark |ω–22′ > , |ω–23′ > modes and bright BAR mode, hence the Fano dips are gradually diminishing. Fig. 7 displays the simulated scattering spectra with different R1 varying from 190 nm to 210 nm. It can be clearly seen in Fig. 7 that the wavelengths corresponding to Fano dips M1, M2 and DBR mode occur around 852 nm, 1077 nm and 2175 nm, respectively, as R1 = 190 nm. With an increase in R1, the width of the ring becomes thicker, which leads to a weaker interaction between the electrons at the outer and inner surface of the ring, resulting in blue shift of |ω–11′ > 、|ω–22′ > and |ω–23′ > modes and hence blue shift of Fano resonances. Obviously, the |ω–22′ > mode is always in the spectral envelope of bright DAR mode, hence the Fano resonance M2 changes little, while |ω–23′ > mode gradually moves away from the spectral envelope of DAR mode, thereby the coupling between them decreases and the Fano dip M1 decreases. We have further investigated the influence of the cavity height on Fano resonances. In Fig. 8, the solid, dashed, and dotted lines represent the scattering spectra of the cavity with the height H of 20, 30, and 40 nm, respectively. By increasing the height H, Fano dips M1, M2 and DBR mode are red shift. A simple interpretation is that as the height increases, the amount of charges induced by the incident electric field increases while the cavity size is fixed. As a result, the displaced electron experiences a larger restoring force, leading to a higher resonance frequency [28]. Furthermore, when the height increases to a certain extent, more Fano resonances may occur. For example, the dipole bright mode supported by nanostructures and the quadrupole dark mode caused by the phase retardation could become non-orthogonal and interfere strongly with each other, leading to both Fano-like resonance and superscattering in a single subwavelength nanodisk [29].
Fig. 7. Scattering spectra of the cavity embedded in air with outer radii of the Au ring R1 = 190, 200, and 210 nm. The other geometric parameters size r, R2 and H are fixed at 150, 170 and 40 nm, respectively. 5
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Fig. 8. Scattering spectra of the cavity embedded in air with cavity heights H = 20, 30, and 40 nm. The other geometric parameters size r, R1 and R2 are fixed at 150, 170 and 200 nm, respectively.
3.3. RI sensitivity and FOM of the cavity The plasmonic properties of the Fano resonance are likely to be strongly influenced by the RI of the surrounding medium. In order to investigate the sensing performance of the cavity, we compare the scattering spectra with complete dielectric filling of four different media (refractive indices n = 1, 1.1, 1.2 and 1.3), respectively. As shown in Fig. 9, dips M1, M2 and DBR mode exhibit an obvious red shift with an increase in the RI of the dielectric environment. This can be understood by the fact that the resonance wavelength is proportional to the dielectric screening effect [30]. Thereby the semi-disk ring cavity can be employed as a tunable multi-wavelength RI based sensor. Here, RI sensitivity (defined as S = δλ/δn) and FOM (FOM = S/Δλ) are taken into account to evaluate the sensing performance of the cavity [31]. where δλ is the shift quantity of the resonance peak (dip), δn is the quantity of the refractive of medium, and is the full width at half maximum of the resonance line. For Fano-like resonances, the Δλ can be defined as the energy difference between the Fano dip and the closest neighboring peak. we calculate Fano dips M1, M2 and DBR mode shift versus the RI of the surrounding medium, as shown in the inset of Fig. 9. A linear fit to the data gives a large RI sensitivity of 674 nm/ RIU, 914 nm/RIU and 1839 nm/RIU for dips M1, M2 and DBR mode, respectively, and the corresponding FoMs are about 6.8, 8.9 and 9.0 with the Δλ values around 99, 103 and 208 nm, respectively. The results show that the semi-disk ring cavity can be used for the multi-wavelength high sensitive sensing in near-infrared region. Next, we examine the RI sensitivity and FOM of the cavity for partial insertion of a dielectric medium into the gap between the semi-disk and ring, where small molecules are expected to concentrate because of strong gradient forces induced by plasmons. Fig. 10 shows the scattering spectral variations with different media and partial filling of the cavity. It can be seen in Fig. 10 that when the RI of the dielectric increases from 1 to 1.3, Fano dips M1, M2 are red shift from 796 nm, 1002 nm to 844 nm, 1050 nm, respectively, and the calculated RI sensitivities are about 160 nm/RIU and 158 nm/RIU, respectively. The corresponding FOMs are obtained to be 1.8 and 1.6, respectively. As discussed before, the sharp Fano resonances are very sensitive to the variation of the local refractive indices. By using the Fano resonances, a small variation of the local refractive indices in narrowest part of the gap between the ring and the semi-disk can bring a remarkable and observable wavelength shift change. Lastly, we compare the performance of our proposed cavity with analogous developed nanostructures as given in Table 1. For double split-ring resonators, the Fano resonance exceeds the sensitivity of 605 nm/RIU and the FOM of 4.8 [32]. The split-ring disk
Fig. 9. Scattering spectra of the cavity with changed refractive indices of surrounding media of 1, 1.1, 1.2, and 1.3, respectively, while keeping the geometry parameters unchanged. Inset shows the resonance wavelengths shift of the M1, M2 and DBR modes with different surrounding refractive indices. 6
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Fig. 10. Scattering spectra of the cavity for partial dielectric filling in the gap between semi-disk and ring. The refractive indices are n = 1, 1.1, 1.2 and 1.3, respectively. The schematic shows that yellow represents gold, gray is for dielectrics, and white is for air. Inset displays the zoom-in on the M1 and M2 modes showing the spectral shifts in more detail (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article). Table 1 Comparison of the cavity performance with previous work. Ref.
Structure
Filling
Sensitivity
FOM
[32] [33] [34]
Double split-ring Split-ring disk Nonconcentric ring/disk
[35]*
Double split nanoring
This work
Semi-disk ring
complete complete complete partial complete partial complete partial
605 282 534 129 1200 110 674, 914 160, 158
4.8 4 3.2 0.95 8.5 0.66 6.8, 8.9 1.8, 1.6
The mark * indicates that the sensitivities and FOMs in this paper are the response of the bonding mode to the environment.
nanocavity is reported to obtain a sensitivity of ∼282 nm/RIU with a figure of merit ∼4 in near-infrared regime [33]. Hao et al. described that the sensitivity and FOM were 129 nm/RIU and 0.95 for partially filled cavity, and 534 nm/RIU and 3.2 for a completely filled cavity in a nonconcentric ring/disk cavity [34]. Liu et al. found that the sensitivity of bonding mode exceeding 1200 nm/RIU with a FOM exceeding 8.5 were obtained with a Au double split nanoring cavity for complete filling, and 110 nm/RIU and 0.66 for partial filling [35]. Our results are similar to those mentioned above, and the sensitivity and FOM could be further improved by optimizing the cavity size, or breaking the symmetry of cavity.
4. Conclusion In conclusion, we have investigated the multipolar Fano properties in a plasmonic semi-disk ring cavity based on FDTD and plasmon hybridization methods. Results show that two Fano dips are obtained due to the destructive interference between the bright mode and two dark modes originating from the interaction of semi-disk quadrupolar with ring octupolar or quadrupolar bonding modes, respectively. Moreover, the intensities and spectral positions of the two Fano resonances can be manipulated by modifying the geometric parameters of the cavity. By decreasing the semi-disk size, or increasing the cavity height and the outer ring radius, the two Fano dips are blue shift in the scattering spectra. With an increase in the inner radius of the ring, the two Fano dips are blue shift firstly and then red shift because the redshift of the dipole bonding ring mode competes with the spectral shifts induced by the diminishing hybridization between semi-disk and ring modes. Furthermore, the two Fano dips exhibit high RI sensitivities of 674 and 914 nm/RIU as well as high FoMs of 6.8 and 6.9 for a completely filled cavity, 160 and 158 nm/RIU as well as FoMs of 1.8 and 1.6 for partially filled cavity. The proposed cavity with two Fano resonances maybe an effective platform for multi-wavelength biochemical sensing.
Acknowledgements This work was financially supported by the National Natural Science Foundation of China (No.61701434), the Natural Science Foundation of Shandong Province, China (Nos.ZR2017MF005, ZR2018LF001) and the Project of Shandong Province Higher Education Science and Technology Program, China (No. J17KA087). 7
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