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Abstract
In this paper, we design and investigate a binary elliptical nanoring resonator array on a gold conducting layer, which can generate two optical Fano-like resonant modes in the visible light range under normal incidence. The gold conducting layer underneath the nanoring resonator array strongly enhances the coupling and hybridization among different resonant modes. These two distinct Fano-like resonances originate from the interactions of dipolar antibonding and bonding modes, and dipolar bonding and propagating surface plasmon modes, respectively, which provide as high a refractive index sensitivity as 620 nm/RIU, and achieve high figures of merit, 78 and 154, separately in a refractive index range of 1.33~1.40. Compared to the circular nanoring array, the elliptical structure we demonstrate here can generate shaper resonant modes that can be used for high sensitivity measurement. The designed binary elliptical nanoring resonator array is very promising for dual-channel biosensing application.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Due to their attractive optical characteristics, nanoring array have been widely investigated in many respects [1–6], particularly its particularly enhanced optical transmission performance. For example, Wu et al. experimentally inquiry the enhanced optical transmission of circular nanoring array due to the excitation of both surface plasmon polaritons and localized surface plasmon [1]. Subsequently, they also investigate the optical properties of elliptical nanoring array and a simple analysis model is presented to explain the modification of the transmission spectrum due to the hole shape change [2]. In addition, nanoring array also have been applied in the field of device design, such as the color filter [3,4], thresholdless nanolaser [5], and quarter-wave plates [6]. Another major reason of nanoring array widely studied is that it provides additional degrees of freedom for optimizing their optical properties. However, there are seldom reports about their biosensing application. A big restriction is that the resonant mode of nanoring array is accompanied by relative broad line shape, which constraints to its sensing properties [7].
In order to achieve narrow spectral width, an effective approach is to excite Fano-like resonance in the nanoring array. Fano-like resonance in metallic nanostructures has attracted significant interest in the field of biosensors due to its asymmetric sharper line shape and high quality factors resonance [8–13]. The Fano-like resonance resulting from the coupling and hybridization of different plasmonic modes (bright and dark modes) has become ideal candidates to be used for sensing applications with high refractive index sensitivity and low limit of detection [14–16]. How to trigger Fano-like resonance of nanoring array is a crucial question need to be resolved.
In this paper, we design a binary elliptical nanoring array (BENA) on a conducting gold layer under vertical incidence to demonstrate two Fano-like resonances. In this structure, two combined rectangle arrays with different sizes of nanoring hybridized generate two Fano-like resonant modes with sharper spectral features and higher refractive index sensitivity, which can be used for a double channel biosensor. Due to their sharper spectral features, these two Fano-like resonances with asymmetric line shape profile exhibit high figure of merits (FOM) 78 and 154, respectively, which are higher than previously reported plasmonic sensors [12,13,17]. Compared to the circle shape, the role of elliptical geometric shape we demonstrated here can generate shaper resonant modes at the resonant position.
2. Structure and simulation method
Figures 1(a) and 1(b) illustrate three-dimensional diagram of the proposed structure and the unit cell of structure, where two sets of elliptical nanoring array with different sizes interlace with each other in the x - y plane and the position of all elliptical nanoring arrange in a hexagonal lattice. Therefore, the periods of the two arrays are P (720 nm) in the y direction and P in the x direction. The structure parameters of elliptical nanoring in one set of rectangle array are defined as follows: the outer semi-major axis A1 = 280 nm, inner semi-major axis A2 = 180 nm, the outer semi-minor axis B1 = 160 nm, and inner semi-minor axis B2 = 100 nm, respectively. The difference of elliptical nanoring between two sets of rectangle arrays depends on ΔR = A1 - a1 = B1 - b1 = A2 - a2 = B2 - b2. The thickness of the BENA (H) and the conducting metal layer is 90 and 150 nm, respectively. Here, the thickness of conducting metal layer with 150 nm is completely opaque to incident light and other structure parameters are optimized for achieving two Fano-like resonances with narrow linewidth and high dip depth. This structure can be fabricated by a combination of thin-film deposition and focused ion beam (FIB) technologies. Its optical properties are investigated by using a finite-difference time-domain (FDTD) software package from Lumerical Inc. In the calculations, a single unit cell of structure is simulated with period boundary condition applied in the x and y direction. Perfectly matched layers are used in the z direction. The numerical calculations are performed with a small uniform mesh size of 2 nm in the metal region in order to obtain extremely well convergence. The upper and lower sides of the structure are air and quartz, and their refractive indexes (RI) are chosen as 1 and 1.46. The dielectric permittivity of gold is extracted from experimental data [18].
Fig. 1 The designed structure and its optical features. (a) Three-dimensional view and geometrical parameters. (b) The unit cell of structure. (c) Reflectance spectra of BENA for the difference ΔR = 30 nm (blue line) and ΔR = 0 nm (pink line). (d) Reflectance spectra of binary circular nanoring array (pink line) and binary elliptical nanoring array (blue line) for the difference ΔR = 30 nm.
3. Theoretical analysis of resonant modes
Figure 1(c) shows the calculated reflectance spectra from BENA on the gold layer with ΔR = 30 nm (blue line), and a symmetric hexagonal array with ΔR = 0 nm (pink line). There are two Fano-like dips around the wavelengths of 642 and 742 nm (marked by C and F) observed, but dip F is not found in the symmetric hexagonal array (pink line). For the sake of brevity, two sets of rectangular arrays from larger to smaller size of nanoring are termed as RAL, and RAS, respectively. It is worth noting that full widths at half maximum (FWHM) of dips C, D, and F are 7.3, 43.6, and 3.2 nm, respectively, dips C and F of which are narrower than those from the previous nanostructures [5,6]. As a comparison, the case for binary circular nanoring array (BCNA) with A1 = B1 = 280 nm, A2 = B2 = 180 nm, and ΔR = 30 nm is shown in Fig. 1(d). The FWHM of three resonant dips are 12.8, 44.5, and 5.6 nm, respectively. In addition, compared to BENA on the dielectric substrate without a layer of gold film, the gold film under BENA 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 BENA; 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.
In experiment, we know that the resolution of the sensor depends on the standard deviation of the noise. However, the FWHM of resonant mode is closely related to the standard deviation of the sensor noise. The narrower the FWHM of resonant mode is, the smaller the standard deviation of noise is. Therefore, narrow line width of resonant dip is very important for improving the sensitivity of biochemical sensing platforms. It is observed clearly that the FWHM of resonant dips in the BENA structure is narrower compared to that of BCNA structure although the depth of dip F is reduced. Therefore, to obtain sharper spectral feature at resonant dips, geometric shape of ellipse is a good candidate. The validity of results from FDTD method is further confirmed by finite element method (data not shown).
The Fano-like resonances are closely associated with the size of nanoring in the binary array. Figure 2(a) demonstrates the evolution of reflectance spectra as the difference ΔR increases from 0 to 50 nm, while structure parameters A1, A2, B1, and B2 are fixed at 280, 180, 160, and 100 nm, respectively. As the magnitude of ΔR increases gradually, the Fano-like line shape at dip F becomes more and more distinct due to the dark mode excited and the strong cancellation of resonant mode (dip E) in the binary array. As the magnitude of ΔR continues to increase, dip D is excited and dip E is weakened. However, due to the coupling of plasmonic modes C and D, resonant dip C is weakened gradually and asymmetric line shape become more and more evident. So the dip C is also regarded to a Fano-like resonance in the binary array. For the case of ΔR = 0 nm and a hexagonal array, the Fano-like resonance dip F disappears because the dark mode cannot be directly excited, and however, with the increase of the magnitude of ΔR, the bright mode (dip D) is excited, and the Fano-like resonance dip F becomes obvious. Figure 2(b) shows the influence of various outer semi-major axis A1 and inner semi-major axis A2 on the resonant modes with fixed B1 = 160 nm, B2 = 100 nm, and ΔR = 30 nm. It is observed that the change of structure parameters A1 and A2 plays a critical role in the generation of two Fano-like resonances in the binary array. When parameters A1 and A2 are fixed at 320 and 220 nm, dip D cannot be excited and dip C is almost a symmetric line shape profile. As the magnitudes of A1 and A2 decrease gradually, dip D is excited and the asymmetric profile of dip C appears, which is an obvious indicator of the Fano-like resonance. However, when parameters A1 and A2 are fixed at 260 and 160 nm, two Fano-like resonances nearly disappear simultaneously due to the strong cancellation of resonant modes C and E. In addition, the period of the arrays has little impact on the lineshape of two Fano-like resonances, However, the wavelength position of Fano-like resonance has a remarkable redshift with the increase of arrays period.
Fig. 2 The effect of various structure parameters on resonant dips in the designed structure. (a) Reflectance spectra for various ΔR with fixed A1 = 280 nm, A2 = 180 nm, B1 = 160 nm, and B2 = 100 nm. (b) Reflectance spectra for different outer semi-major axis A1 and inner semi-major axis A2 with fixed B1 = 160 nm, B2 = 100 nm, and ΔR = 30 nm. The reflectance spectra are offset 0.5 for better visibility.
As shown in Fig. 1(a), the designed structure support multiple resonant modes, including multiple dipolar modes, propagating surface plasmon (PSP) mode, the coupling and hybridization of which results in new coupled resonant modes explained by using plasmonic hybridization theory [19]. Fano-like resonance with an asymmetric line shape occurs in the presence of interference between a broad and a narrow resonant mode. In the designed structure, there are two distinct Fano-like asymmetric resonances arising from the overlap between super-radiant hybridized bright mode and narrow dark mode. For the case of dip C, the dipolar antibonding mode in the rectangle array RAS and dipolar bonding mode in the binary array act as bright and dark modes, respectively. Furthermore, for the case of dip F, the dipolar bonding mode in the binary array and propagating surface plasmon (PSP) mode in the rectangle array RAL acts as bright and dark mode, respectively. The different plasmonic modes in the designed structure couple and hybridize to form two Fano-like resonances.
To interpret the generation of two distinct Fano resonances more clearly, the real part of electric field Ez taken as a slice at the 4 nm distant from top surface of the structure for a unit cell and corresponding charge distributions at two dips are investigated firstly in the symmetric hexagonal arrays (ΔR = 0 nm). Figure 3(a) depicts the real part of Ez at the dip C corresponding to a dipolar antibonding mode (λ = 638 nm). The direction of Ez at the left and right rims of disk and hole are opposite, which is in agreement with charge distribution at the left and right rims of disk and hole in Fig. 3(a). It illustrates that the dipolar modes of elliptical disk and elliptical hole at λ = 638 nm couple and hybridize to form an antibonding mode, in which the dipolar disk and dipolar hole is out of phase. This dipolar antibonding mode has narrow line shape due to less radiative damping. It is observed that the real part of Ez at dip E corresponding to a dipolar bonding mode (λ = 710 nm). The direction of Ez at the left and right rims of disk and hole are same, which illustrates that the dipolar disk and dipolar hole is same. Compared to the dipolar antibonding mode of dip C, this dipolar bonding mode at dip E can generate a large radiative damping, leading to relative broad line shape.
Fig. 3 Electric field Ez and charge distributions in the symmetric hexagonal array (ΔR = 0 nm) for (a) dip C and (b) dip E.
To understand the origin of two Fano-like resonances in the binary arrays, we plot the real part of electric field Ez taken as a slice at the 4 nm distant from top surface of the structure for a unit cell. Figures 4(a-c) correspond to the electric field Ez distribution at the dips C, D, and F in the binary arrays with ΔR = 30 nm, respectively. It is observed that the dipolar bonding mode is only excited in the RAS, not in the RAL. So the excitation of dipolar bonding mode in the RAS results in the generation of dip D. It is easy to understand that electromagnetic field and charge are more inclined to accumulate around the tip of structure. We find that the electric field Ez distribution in Fig. 4(a) is almost identical to that of Fig. 3(a). A major difference between them is that the dipolar mode of elliptical disk in the RAS is greatly enhanced, which is the result of coupling and hybridization of the dipolar bonding mode in the RAS and dipolar antibonding mode in the binary arrays. They overlap and bring out an interference, which results in the Fano resonance dip C. In addition, it is noteworthy that the interference of these two modes increases the asymmetry of line shape at dip C.
Fig. 4 Electric field Ez distributions in the binary array with ΔR = 30 nm for (a) dip C, (b) dip D, and (c) dip F.
Moreover, the real part of electric field Ez at dip F (λ = 742 nm) is shown in Fig. 4(c). The Ez distribution of dip F is distinct from that of dips C and D in Fig. 4. Obviously, the characteristics of PSP mode in the RAL are shown. For a rectangle array, the excitation of PSP mode at the dielectric/gold interface satisfies the condition below [20]:
where P is period of rectangle arrays, εm and εd represent the permittivity of the gold and dielectric, and i and j are integers. ns is refractive index of incident space, θ is incident angle, and λ is incidence wavelength. According to Eq. (1), the wavelength for (1, 0) PSP mode is 742 nm. It completely agrees with the wavelength of dip F, which verifies that the generation of dip F is closely associated with the excitation of PSP mode in the rectangle arrays, not in the hexagonal arrays. Furthermore, the dipolar bonding mode in the binary arrays is also observed clearly. However, this mode is weakened significantly compared to that of Fig. 3(b). Thus, Fano-like resonance at the wavelength λ = 742 nm (dip F) is the result of coupling between dipolar bonding mode in the binary arrays and PSP mode in the RAL. We find that dipolar bonding mode in the binary arrays has a minor effect on the position of dip F and has a significant role in the line shape of dip F. This can be explained as follows: the dipolar bonding mode in the binary arrays is regarded as localized surface plamon (LSP) mode. The structure parameters have a minor effect on the wavelength position of this LSP mode, but can change the intensity of this LSP mode. Moreover, the wavelength position of PSP mode in the RAL dependents on the array period. In our design, the array period always keeps a constant. Therefore, it is impossible that the wavelength positions of dipolar bonding mode in the binary arrays and PSP mode in the RAL have a crossing point to induce the position change of dip F. However, the intensity change of this LSP mode will has an effect on the lineshape of dip F. In addition, dip E has not been observed in the reflectance spectrum of binary arrays with ΔR = 30 nm, which can be explained as follows: firstly, when the difference ΔR equals to 30 nm, the resonant positions (dips D and E) of dipolar bonding mode in the binary arrays and in the RAS is close to each other. The resonant intensity of dip D is larger than that of dip E. As a result, the spectrum line of dips D and E overlap, and dip E disappears in the reflectance spectrum.As the difference ΔR continues to increase, dip D has a blue-shift, and both dips D and E appear simultaneously in the reflectance spectrum of binary arrays with ΔR = 50 nm. To further reveal the nature of two Fano-like resonances, Fig. 5 depicts electric field Ez distributions at the dips C, D, E, and F. It is observed that the coupling and hybridization of the dipolar bonding mode in the RAS and dipolar antibonding mode in the binary arrays are further reinforced, which can be clearly observed in Figs. 5(a) and 5(b). Figure 5 demonstrates the bright modes and dark modes of two Fano-like resonances in the designed structure.
Fig. 5 Electric field Ez distributions in the binary array with ΔR = 50 nm for (a) dip C, (b) dip D, (c) dip E, and (c) dip F.
In order to further verify the generation of two Fano-like resonances in this structure, we fit reflectance spectrum of the binary structure with ΔR = 50 nm from FDTD simulation to the analytical model of Eq. (2) [21]:
where the parameters a, ωs, and Ws are used to reconstruct bright mode. And the parameters ωa, Wa, q, and b are used to constitute the dark state. The results from FDTD method are almost in agreement with that of analytical model in Fig. 6(a). Figure 6(b) shows the dependence of reflectance spectra on the incident angle (the magnetic field parallel to the x direction). The two blue solid lines are calculated from Eq. (1), which further confirms that the appearance of dip F is closely related to the PSP mode of rectangle arrays. It is also noted that dip D has a good angular tolerance with the increase of incident angle, which is due to the excitation of magnetic resonance in the metallic grooves. Figure 6(c) shows the electric and magnetic fields at the wavelength 690 nm for metallic grooves. As the figure shows, strong magnetic field is confined in the grooves, and a closed induced current loop is formed around two grooves. These further illustrate that dips D and E stem from the excitation of electric and magnetic dipoles in the designed structure.Fig. 6 (a) Comparison of FDTD simulation and analytical model of Fano-like resonance in the binary structure with ΔR = 50 nm. (b) Optical properties at different incident angles in the binary structure with ΔR = 30 nm. (c) Electromagnetic field taken as a slice through the center of binary structure with ΔR = 30 nm at the wavelength 690 nm.
4. Sensing performance
For the design of sensing application, RI sensitivity and FOM are two major criteria to evaluate qualitatively and quantitatively its performance. Figure 7(a) shows the evolution of reflectance spectra in the binary array with the difference ΔR = 40 nm for the sample with different RIs in a range of 1.33~1.40. Two Fano-like resonances (dips C and F) always exhibit narrow spectral features (narrow FWHM and big depth) in the wide RI range. However, dips D and E (not marked) have a wide FWHM compared to that of dips C and F. Figure 7(b) illustrates the RI sensitivity of two Fano-like resonances, which is defined as the resonant wavelength change respect to the bulk RI changes (S = Δλ/Δn). In this structure, compared to that of other metal nanostructures, two Fano-like resonances support higher RI sensitivities as SC = 620, and SF = 723 nm/RIU simultaneously, and they also have good linear approximations in the whole RI range. Dip F supports highest RI sensitivity, because it supports higher near-field intensity enhancement compared to that of dip C, as shown in Figs. 4 and 5. High near-field intensity increases the interaction volume of the sample and optical fields.
Fig. 7 (a) Reflectance spectra for the sample with different RIs on the upper side of structure. (b) Linear response of wavelength positions of two Fano-like resonances (dips C and F) on RIs. (c) Calculated FOM for two Fano-like resonant modes.
Another important criterion for advanced biosensing is figure of merits (FOM = S / FWHM). As shown in Fig. 7(c), the FOMs of dips C and F are extremely high and remain constant in the whole RI range. High FOMs of dips C and F are attributed to sharper spectral features of two Fano-like resonances, which can significantly reduce the limit of detection. Moreover, the FOM of dip F (FOM = 154) is nearly 2 times larger than that of dip C (FOM = 78). Exhibiting high FOM and RI sensitivity at two Fano-like resonant modes simultaneously, the designed structure demonstrates its good performance for multi-channel ultrasensitive bio-detection.
5. Conclusion
We demonstrate the optical properties of BENA on a conducting gold layer. It can generate two obvious Fano-like resonant modes under normal incidence in the visible light range, which provides a novel double channel sensing technique. The two Fano-like resonant modes originate from the interactions of dipolar antibonding and bonding modes, and dipolar bonding and PSP modes, respectively, which contributes high RI sensitivity and high FOM. In this nanostructure, the important reason of elliptical geometric shape used is that it can generate sharper line shape than that of circle shape. This device can be used for high-performance biosensor application.
Funding
National Natural Science Foundation of China (NSFC) (Grant Nos. 61675065, 61705100, 61627818, 11474043 and 61475043); Doctoral Scientific Research Foundation of Henan Normal University (Grant Nos. 5101029170305);Youth Science Foundation of Henan Normal University (Grant Nos. 5101029170408).
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