We put forward a theoretical analysis of the optical properties of an asymmetric nanoring array on a gold metal layer. We show that for normal incidence, the spectrum of the symmetric system is characterized by a general dipolar ring resonance. For the asymmetric nanoring with an offset inner surface, obviously both dark monopolar and quadrupolar ring resonances can be generated under a normal incidence, which depends sensitively on the asymmetry of the structure. Meanwhile, the symmetry breaking of the structure provides the desirable near-field characteristics for biosensing. As a result, monopolar and multipolar modes reveal ultrahigh refractive sensitivities as large as 792 nm/RIU and 742 nm/RIU, respectively. Furthermore, due to their subradiant features, the resulting FOM is 72 RIU−1 for the monopolar mode and the record high value of 137.4 RIU−1 for the quadrupolar mode in a wide refractive index range of 1.33-1.38. These results indicate that an asymmetric ring system could be promising for biosensing applications with high performance.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Metallic nanostructures supporting plasmon resonances have recently attracted widespread interest because of many promising applications in areas such as chemical and biological sensing , negative index materials  and plasmonic waveguiding [3,4]. Since the rapid development in technologies for the fabrication (electron-beam and ion-beam lithography) and characterization (scanning electron and atomic force microscopy) of plasmonic nanostructures opens the door to new sensing concepts and applications, various nanostructures have been fabricated and studied in recent years using nanolithographic [5,6] and chemical processes . The plasmon energy and local field enhancement are highly dependent on the size and shape of nanostructures and the surrounding medium environment. The large electromagnetic fields increasing the interaction volume of analyte and optical fields and useful for sensing applications can be achieved using either some structures of much smaller dimensions than the wavelength, such as nanocubes on dielectric substrates , dual-disk ring plasmonic nanostructures  and nanoparticle clusters [10–13], or very spectrally narrow shape such as elliptical annular aperture arrays [14,15], ring/disk plasmonic nanocavities on conducting substrates  and plasmonic nanohole arrays on a hybrid substrate .
Several recent studies have shown that nanostructures that are small compared to the wavelength of incident light, only electric dipole moments can be excited. An important topic in the field of plasmonic is the effect of symmetry breaking. For highly symmetric nanoring under normal incidence, the quadrupolar mode cannot be excited due to the symmetric charge distribution which makes the total dipole moment zero . When an incident angle is introduced, the quadrupolar mode is excited through retardation effects. By breaking the symmetry of a nanostructure, nondipolar plasmon modes can be excited because of the hybridization of plasmons of different multipolar symmetry. In addition, symmetry breaking also results in much larger electromagnetic fields enhancements than symmetric structures [19,20].
In this Letter, we present a theoretical investigation of optical properties of asymmetric nanoring array (ANRA) on conducting metal layer under normal incidence in optical frequency range. In addition, compared to ANRA on the dielectric substrate without a layer of gold film, the gold film under ANRA has three advantages: First, the high reflectance of gold film impedes incident light forward into the dielectric substrate to increase the interaction of incident light and ANRA; Second, the gold film can also boost local field enhancement on the top surface; Third, the presence of gold film can increase the coupling between different modes [16,21]. We show that by varying the displacement of the inner surface with respect to the outer surface of nanoring it is possible to generate multipolar plasmon resonance in a controlled manner. For the symmetric gold nanoring, only one dipolar resonance appears in the reflection spectrum under normal incidence. As the inner surface offset of nanoring increases, the quadrupolar ring plasmon resonance gradually appears. Meanwhile, the monopolar mode associated with localized surface plasmon resonance (LSPR) of the narrow region of asymmetric structure appears in the spectrum with intensity that increases monotonously as offset parameter increases.
2. Theorical approach
The reflection spectra, electric field distribution and charge distribution of the ANRA at normal incidence are calculated using the finite-difference time-domain (FDTD) method. The periodic boundary conditions are applied in both x and y direction and perfectly matched layers (PML) are set for z direction. The grid size along x, y and z direction is 3 nm 3 nm 3 nm, respectively. The dielectric permittivity of bulk gold in the visible and near-infrared region is from Johnson and Christy .
3. Results and discussions
3.1 Optical responses of the ANRA system
In Fig. 1(a), we schematically illustrate the structural parameters used to model ANRA on a conducting metal layer, which can be experimentally fabricated using thin film deposition and E-beam lithography (EBL). Here, the outer radius (R) and inner radius (r) of the ring is 230 nm and 150 nm, respectively. For our system, the amount of the structural symmetry-breaking is determined by ∆y, which is the offsetting amount of the inner surface of ring from the center of the concentric system along the polarization direction. For the nonconcentric system presented in this picture, ∆y = 60 nm. The thickness (H) of the ring and the period of the ANRA is 100 nm and 740 nm, respectively. The structure was illuminated-perpendicularly by y-polarized electromagnetic waves from the analyte side.
In Fig. 2(b), we obtain the optical responses for different values of offset parameters ∆y of the designed structure for normal incidence. The black solid line in the spectra is the reflection spectrum for the concentric structure (∆y = 0 nm). In the circumstance, the spectrum is characterized by a single resonance which is a symmetric dipolar ring mode. As the shifting amount parameter ∆y increases, two plasmon resonances with related to the structural asymmetry appear at wavelengths of 757 nm and 871 nm, respectively, and corresponding peak-dip contrast gradually deepens, which is beneficial to increase resolution of biosensing system. For our structure with ∆y = 60 nm, three resonant dips in the reflection spectrum (blue curve) is indicated by blue symbol A、B and C, respectively.
3.2 Electromagnetic near-field and charge distributions
To interpret the generation of each plasmon resonance dip more clearly in the ANRA system, the electric near-field and surface charge distributions at the spectral specific position of resonances at 2 nm distant from top surface of the designed for four unit cells are calculated.
3.2.1 The mechanism behind of the generation of the plasmonic dips A and C
The upper row in Fig. 2 displays the profiles of the electric field intensity |E|2 and the bottom row shows the normalized surface charge distributions. As shown in Fig. 2, a typical narrow quadrupolar ring mode is formed clearly in the ANRN system at a wavelength of 757 nm, acting as dark state, which always occurs in the high photon-energy region. Since the “dark” plasmon mode characterized by hybrid subradiant mode possesses nearly zero dipole moments, do not couple efficiently to incident light, and are not radiatively broadened. In the low-energy region, a symmetric ring dipolar mode with irrelevance to structural symmetry is excited at λ = 871 nm, which is classified as bright mode. Bright plasmon modes possess finite dipole moments and can therefore be efficiently excited by incident light. Since the bright modes couple to light, they also radiate, and their spectral features can be significantly broadened due to radiative damping . As seen in Fig. 1(b), the multipolar ring mode exhibits more spectrally sharper features than the dipolar plasmon mode in our proposed structure, because of the imaginary part of the dielectric function of the metal, the main damping mechanism of dark modes is their inherent broadening: therefore, this hybrid subradiant mode can be significantly narrower than bright plasmon mode.
3.2.2 Monopolar plasmon resonance for plasmonic dip B
The computed cross-sectional field profiles at the wavelength of 828 nm (resonance dip B) in ANRA on a conducting metal layer is shown in Fig. 3. We observe that the narrow region of the asymmetric structure displays a higher local field enhancement, which is possible to excite the narrow plasmonic resonance for dip B. Filed profiles the dark mode conforming its monopole character is given in this picture. In-direct coupling of the incident light to the subradiant mode through the superradaint mode is negligible. This leads to narrow spectral feature with high-quality factor resonance. In addition, propagating surface plasmons can also exist on the air/metal interface, because of presence of the conducting metal layer. As shown in this picture, the electric field at y-z plane exhibit a characteristic of surface waves that have their maximum at metal/air interfaces and exponentially decaying fields apart from it.
An advantage of using the asymmetry of nanoring is the desirable local field enhancements for biosensing applications. For our proposed structure, symmetry breaking results in much larger electromagneitic field enhancements than concentric system. More importantly, these large local electromagnetic fields are easily accessible to the surrounding medium. As seen in Fig. 4, we compute the near-field intensity (|E|2) of ANRA on a conducting metal substrate at the plasmonic dip B with various ∆y values. The calculation shows very large field intensity enhancements, of manitudes comparable with those attainable in nanoparticle dimer junctions and fabricated bowtie nanoantennas. However, in contrast to those geometries, here the region of maximum field enhancement is located on the open, exterior surface of an individual nanostructure and not within a narrow confined gap or junction.
3.3 Geometrical parameters
Changing the geometrical parameters of the system and observing the evolution of the plasmon resonances provides further insight into their nature and formation. Here, the outer radius (R), inner radius (r) and shifting amount (∆y) of nanoring are fixed as 230, 150 and 60 nm. Then, we demonstrate the effect of the periodicity (P) and the thickness (H) of the ANRA on the optical responses of the structure. Figure 5(a) shows the evolution of reflection spectra as the thickness H increases from 80 to140 nm, while the periodicity is 740 nm. As the thickness of nanoring increases, the contrast of dips B and C disappears gradually, because the cavity mode of ANRA system is excited and monopolar mode is weakened, leading to the contrast of dip A first increases then nearly keeps as a constant. So, in order to ensure each resonance dip with narrow full widths at half maximum (FWHM) and high contrast, the thickness H = 100 nm of nanoring should be chosen. The effect of period P on three resonant dips is exhibited in Fig. 5(b). The dips A, B and C have obvious red-shifted resonances with the increase of the structural period, while the changes of dips A and B are more significant, indicating that they are closely related to the propagating surface plasmon mode of the upper surface of the metal layer substrate.
In addition, the monopolar mode (indicated by gray dashed line) changes linearly by adjusting the outer and inner radius ([R, r]) of the nanoring. As shown in Fig. 5(c), unlike the red-shift behavior of quadrupolar and dipolar modes with increasing [R, r], the monopolar mode blue-shift distinctly when the parameter [R, r] is changed from [R, r] = 220, 140 nm to [R, r] = 270, 190 nm (P = 740 nm, H = 100 nm and ∆y = 60 nm). Meanwhile, the spectral contrast of the monopolar mode degrades with increasing [R, r]. These appearances are caused by the coupling of monopolar mode in the ring cavity, which means the large-sized annular cavity weakens the interaction between the monopolar pattern between the narrow and the wide regions along the polarization direction of the light source. Since the spectra that are spectrally close to each other will not be suit for biosensing applications requiring reliable and accurate identification of spectral shifts, the parameters R = 230 and r = 150 nm should be chosen. .
3.4 Sensing performance
In order to evaluate the sensing performance of the ANRA on the gold layer with 60 nm offset, we qualitatively and quantitatively analyze the refractive index (RI) sensitivity of the reflection spectrum to the analyte above the structure surface in a range of 1.33-1.38. The results are shown in Fig. 6(a). It is seen that three resonant modes exhibit a significant red shift with respect to a small fluctuation in refractive index of surrounding medium and always maintain constant line-shape in the wide RI range of 1.33-1.38. Figure 5(b) illustrates the RI sensitivities of three resonant modes, which is defined as the resonant wavelength shift per RI unit (S = Δλ/Δn). In this structure, compared to that of other metal structures, three plasmonic modes support higher RI sensitivities as SA = 742 nm/RIU, SB = 792 nm/RIU, and SC = 840 nm/RIU, simultaneously. For these modes, three fitted curves show a linear dependency of the shift on the refractive index, which is in well agreement with the results in previous work .
Another important criterion for advanced biosensing is figure of merits (FOM = S/FWHM). As shown in Fig. 6(c), apparently, the resulting FOM is 19.5 for the dipolar mode and an ultra-high value of 137.4 for the quadrupolar mode. The high FOM of the quadrupolar mode is attributed to its sub-radiant feature, significantly reduces the radiative damping and greatly enhances localized electric field intensity. Exhibiting the superior sensing performance together, this device demonstrates its capability for ultrasensitive bio-detection.
In summary, we theoretically and numerically investigated the optical properties of the designed platform based on periodic arrays of asymmetric nanorings on a single metal sheet. The optical responses are influenced by various phenomena, such as localized surface plasmons of nanoring and propagating surface plasmons on the dielectric/metal interface. It is demonstrated that the excitations of both quadrupolar and dipolar modes under normal incidence in the visible light range, providing a novel multi-channel sensing technique. Appearance of the sharper spectral feature through smaller structural asymmetry on a gold surface indicates that this is partly facilitated by the contribution of propagating surface plasmons on the metal layer and air interface excited by the grating effect. The resulting that this device can be used for high performances biosensor application.
National Natural Science Foundation of China (NSFC) (61675065, 61705100, 61627818, 11474043, 61475043); Doctoral Scientific Research Foundation of Henan Normal University (5101029170305); Youth Science Foundation of Henan Normal University (5101029170408); Key Scientific Research Programs of Institutions of Higher Education of Henan Province of China (19A416005).
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