1. Introduction

The unique optical properties of noble metals have attracted great attention during the past decades. These optical properties rely on the Localized Surface Plasmon Resonance (LSPR), which is the collective oscillations of electrons at a metal-dielectric interface. LSPR results in sharp absorption peaks and strong field-enhancement which opened the gate for various applications, such as biosensing, surface-enhanced spectroscopy, near-field scanning microscopy, detection of molecular binding events and optical trapping.

Different shapes of nanostructures have been studied numerically and experimentally thanks to the significant advances in the nanofabrication technology. These shapes include symmetric structures such as nanodisks [1–4], nanocrescents [5–7], nanorings [8–12], nanodipoles [13], bowties [14] and nanocrosses [15] and asymmetric structures such as fano-resonant based structures [16–18] and electromagnetically induced transparency (EIT) based structures [19–21]. Fano resonant structures are asymmetric structures in which constructive and destructive interference occur between the broad (bright mode) resonance and the narrow (dark mode) resonance forming an asymmetric line-shape (fano) resonance. Fano resonant asymmetric structures suppress the radiative losses producing highly sensitive sharp peaks. EIT-based structures are another type of asymmetric structures that exhibit non-linearity. The EIT phenomenon allows for a very narrow transparency window in the absorption spectrum as well as a highly confined electromagnetic field, which increase the sensitivity of this type of structures.

Recently, a great attention has been directed towards a new class of nanostructures which is the complex metallic nanostructures consisting of multiple individual plasmonic metals. In such structures, coupling between elemental plasmon resonances results in tunable optical response and strong field enhancement. This phenomenon is described by the plasmon hybridization model [22]. According to this model, hybridization between plasmons of the metallic elements results in splitting the resonances into bonding and antibonding modes. The strength and energy of these modes depend on the energy matching and the spatial position of the resonances of individual elements [23]. These structures proved to achieve high sensitivity towards changes in the surrounding medium which make them good candidates for biosensing applications. In addition, they are important for developing artificial materials known as metamaterials at the infrared and optical range including left handed metamaterials which exhibit negative refractive index.

In [24], the hybridization effect in nanorice has been studied which combines the plasmon resonances of nanorods and nanoshells. Its sensitivity was measured numerically and experimentally. The maximum sensitivity reported experimentally is 800 nm/RIU while that obtained from the numerical analysis reached 1060 nm/RIU. Additionally, the plasmon hybridization in multilayer metal-dielectric nanocups was studied in [25] showing a high sensitivity reaching 942 nm/RIU which was obtained via numerical simulation. Gold-silica-gold nanosandwich is another common type of hybrid nanostructures. Nanosandwiches exhibit dipolar plasmon hybridization and strong magnetic response in the optical range. Moreover, nanosandwiches have high tunability of their plasmon resonances and can be easily fabricated [26].

In this paper, a highly sensitive array of split ring nanosandwiches (SRNS) arranged on a silica substrate is presented. It is composed of a stack of two gold split rings separated by a ${\text{SiO}}_2$ disk spacer. This structure makes use of the fact that split rings excite different modes according to the polarization of the incident wave. The gaps in the lower and upper gold split rings are perpendicular to each other so that they excite even and odd modes. The coupling effect between the two gold split rings is discussed using the plasmon hybridization model. In addition, the sensitivity of the structure is studied while varying its dimensions. The split ring nanosandwich is characterized by its bimodal resonant behavior where the hybridization results in the formation of high and low energy resonances. It has very high sensitivity compared to structures reported in literature which reaches 3024 nm/RIU. This is due to its large field enhancement that is in considerable contact with the analyte. The tunability of its optical response and the highly sensitive resonant peaks of the SRNS make it very suitable for use in biomedical sensing applications. In the next section, the SRNS structure is presented and its numerical model is described. In Section 3, the plasmon hybridization model is used to explain the structure. The tunability in the optical response of the SRNS is discussed in Section 4. A parametric study on the SRNS together with the parameters that lead to a sensitivity of 3024 nm/RIU are presented in Section 5. The paper is concluded in Section 6.

2. Split ring nanosandwich structure and numerical model

A schematic of the proposed SRNS array is shown in Fig. 1. The SRNS consists of a stack of two gold split rings separated by a ${\text{SiO}}_2$ disk. The array is arranged on a silica substrate and its periodicity is denoted by p, which is chosen to be 1031 nm to avoid lateral coupling between the neighboring SRNS cells. Split rings are used instead of complete rings due to the fact that split rings are polarization anisotropic leading to the excitation of even and odd modes according to the orientation of the gaps. The SRNS array is excited by a plane wave propagating normal to the array with the electric field polarized parallel to the gaps in the upper gold split ring. The lower split ring is rotated such that the E-field is polarized perpendicular to its gaps. The geometry of the SRNS unit cell is demonstrated in Fig. 2. The three layers of the SRNS have the same diameter denoted by d. The width of the gaps in the lower and upper split rings are equal and denoted by g while the ring width is w. The thicknesses of the lower and upper gold split rings are $h_1$and $h_3$, respectively, while that of the silica disk is $h_2$.

 

Fig. 1 SRNS array schematic. The periodicity of the SRNS array is denoted by p.

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Fig. 2 Geometry of the SRNS unit cell. (a) Side view of the SRNS unit cell, (b) top view of the upper gold ring, (c) top view of the intermediate silica disk, and (d) top view of the lower gold ring. The geometric parameters $d=526 \text{nm}$, $w=53 \text{nm}$, $G=50 \text{nm}$ and $h_1=h_2=h_3=20 \text{nm}.$

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The design and parametric study of the presented SRNS structure are carried out by using the software package CST Microwave Studio [27]. The dimensions of the SRNS are chosen such that it resonates in the visible and infrared regions. The diameter d is 526 nm and the ring width w is 53 nm. The SRNS layers have the same thickness of 20 nm and the gap width is 50 nm for both, the upper and lower split rings. It is worth noting that the optical response of this structure is insensitive to variations in the dimensions in order of 1 nm. The SRNS is simulated in water ($n=1.33$). The permittivity of gold is modeled with the Drude formula $\epsilon \left(\omega \right)={\epsilon }_{\infty }-{\omega }_p^2/\omega (\omega +i\gamma )$ with the infinite permittivity ${\epsilon }_{\infty }=9.069$, plasma frequency ${\omega }_p=1.354 \times {10}^{16}$ rad/s, and the collision frequency $\gamma =1.2\times {10}^{14}$ rad/s. The structure was simulated using the frequency domain solver with periodic boundary conditions and hexahedral mesh where the minimum mesh size is 8 nm. The freedom provided by the novel nanofabrication techniques allows for designing and fabricating more complicated structures with improved sensitivity. This structure can be easily fabricated using colloidal lithography [28].

3. Plasmon hybridization in SRNS

The energy diagram shown in Fig. 3 describes the plasmon hybridization in the SRNS structure. The electric field is polarized parallel to the gaps of the upper split ring in which it excites an odd mode of energy $|{\omega }_{odd}〉$. Being perpendicular to the gaps in the lower split ring, leads to the excitation of an even mode $|{\omega }_{even}〉$ . The interaction between these modes results in a new coupled mode pair: symmetric high energy mode $|{\omega }_{+}〉$ and antisymmetric low energy mode $|{\omega }_{-}〉$.

 

Fig. 3 The energy diagram describing the plasmon hybridization in a SRNS. The coupling between the odd mode ($|{\omega }_{odd}〉$) and even mode ($|{\omega }_{even}〉$) of the upper and lower split rings, respectively, results in two new modes: symmetric plasmon mode ($|{\omega }_{+}〉$) and antisymmetric plasmon mode ($|{\omega }_{-}〉$).

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Another illustration of the plasmon hybridization in the SRNS is depicted in Fig. 4 where the extinction spectrum of the upper and lower split rings are compared to that of the SRNS. The extinction spectrum of the upper split ring in Fig. 4(a) shows a resonance at 1965.9 nm which is $|{\omega }_{odd}〉$. The inset of Fig. 4(a) shows the E-field distribution of the excited odd mode in the upper split ring. Figure 4(b) shows the extinction spectrum of the lower split ring which has a peak resonance at 3000 nm that is the $|{\omega }_{even}〉$ and the inset shows the E-field distribution of the excited even mode. It is observed that $|{\omega }_{odd}$ is much higher than $|{\omega }_{even}〉$ as demonstrated in Fig. 3. The extinction spectrum of the SRNS with the incident field parallel to the gap in the upper split ring is shown in Fig. 4(c). Coupling occurs between the even and odd modes of the upper and lower split rings producing two resonances: a high energy resonance ($|{\omega }_{+}〉$) at 2220 nm due to symmetric coupling and a low energy resonance ($|{\omega }_{-}〉$) at 3492 nm due to antisymmetric coupling. The inset shows the E-field distribution of the symmetric and antisymmetric modes in the stacked upper (left) and lower (right) split rings of the SRNS.

 

Fig. 4 Plasmon hybridization in SRNS. The Simulated extinction spectra as function of wavelength for (a) the upper split ring, (b) the lower split ring and (c) the SRNS structure. The insets show the simulated E-field distribution $E_r$ of the corresponding modes in the $xy$ plane. The insets of (c) displays $E_r$ for the upper split ring (on the left) and lower split ring (on the right) for $|{\omega }_{+}〉$ and $|{\omega }_{-}〉$.

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The effect of increasing the intermediate silica disk thickness $h_2$ on the plasmon hybridization in the SRNS is investigated in Fig. 5. Figures 5(a)-(c) show the extinction spectra of the SRNS at silica disk thickness of 20 nm, 50 nm and 200 nm. The extinction spectra of the upper and lower split rings are given for comparison and the corresponding plasmon hybridization energy diagrams are shown beside the extinction spectra for illustration. As shown in Fig. 5(a), as the split rings are closely placed, strong coupling occurs between the odd and even modes of the upper and lower split rings, respectively, which makes the hybridization and splitting of the plasmon modes very strong. In this case, the hybridized plasmon modes, $|{\omega }_{+}〉$ and $|{\omega }_{-}〉$, are highly shifted from the isolated split rings’ plasmon modes, $|{\omega }_{odd}〉$ and $|{\omega }_{even}〉$ In addition, the amplitude of the extinction cross section at the high energy resonance $|{\omega }_{+}〉$ is much higher than that of the low energy resonance $|{\omega }_{-}〉$. The reason for that is that $|{\omega }_{+}〉$ is due to the symmetric coupling between the two split rings while $|{\omega }_{-}〉$ is due to the antisymmetric coupling between the two split rings. Figure 5(b) depicts the SRNS with a weaker coupling between the split rings’ plasmon modes due to the larger spacing between the upper and lower split rings (50 nm). Because the hybridization is weaker in this case, the SRNSplasmon modes are at small shifts from the isolated split rings’ plasmon modes and the amplitude of the lower energy resonance $|{\omega }_{-}〉$ increases. Figure 5(c) shows a SRNS with a completely decoupled plasmon response where the spacing between the two split rings is increased to 200 nm. In this case, it is observed that the plasmon hybridization in the SRNS plasmon modes has completely vanished. Hence, $|{\omega }_{+}〉$ is identical to $|{\omega }_{odd}〉$and $|{\omega }_{-}〉$ is identical to $|{\omega }_{even}〉$, in terms of plasmon energy and amplitude of the extinction cross section.

 

Fig. 5 Series of simulated extinction spectra of the SRNS (solid black curves) compared to the upper split ring (dashed blue curves) and lower split ring (dot-dashed red curves) at different intermediate silica disk thickness to track the plasmon hybridization in SRNS. The thickness of the silica disk is varied from (a) 20 nm; (b) 50 nm; and (c) 200 nm. The corresponding SRNS structure and the plasmon hybridization energy diagrams are shown adjacent to the extinction spectra.

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It can be concluded that the SRNS can be described as a collection of plasmons arising from the hybridization between the plasmons of the individual split rings. It is clear that the coupling strength of these plasmons varies according to the spacing between the two split rings. Also, as will be discussed in the next section, the coupling strength varies by tuning the plasmon resonance of any of the individual split rings through changing its dimensions.

4. Tunability of the optical response of SRNS

The tunability of the optical response of the SRNS is investigated in this section. The effect of tuning the plasmon resonances of the individual split rings by changing their thicknesses, $h_1$and $h_3$, on the plasmon modes of the SRNS is discussed in Fig. 6. Figure 6(a) shows the extinction spectra of the SRNS at different thickness of the lower split ring $h_1$: 10 nm, 20 nm and 30 nm while setting the other geometrical parameters to their values in the initital design presented in Section 2. It is clear that increasing $h_1$ leads to increasing the resonance frequency of the lower split ring ${\omega }_{even}$ which affects the antisymmetric plasmon resonance frequency ${\omega }_{+}$ by increasing it as well. In which case, the two split rings become nearly resonant with each other which strengthens their coupling. This is illustrated in Fig. 6(c) which shows the plasmon energy shift as function of $h_1$, where the plasmon energy shift is defined as $\Delta E=\left||{\omega }_{+}-|{\omega }_{-}\right|-\left||{\omega }_{odd}-|{\omega }_{even}\right|$. It is observed that $\Delta E$increases from −60 meV at $h_1=$10 nm to 22 meV at $h_1=$40 nm. This shows a stronger coupling between the two split rings in the latter case. The amplitudes of the SRNS plasmon resonances in the extinction cross-section are also influenced by the coupling strength between the two split rings. As $h_1$increases, the amplitude of $|{\omega }_{+}〉$in the extinction cross section increases to be higher than that of $|{\omega }_{-}〉$ indicating strong symmetric and antisymmetric coupling between the two split rings. Thus, the difference in amplitudes between $|{\omega }_{+}〉$ and $|{\omega }_{-}〉$in the extinction cross section increases from 2 dB at $h_1=$10 nm to 4.4 dB at $h_1=$30 nm.

 

Fig. 6 Tunability of the optical response of the SRNS. The extinction spectra of the SRNS at different values of (a) the lower split ring thickness $h_2$, and (b) the upper split ring thickness $h_2$ while the other dimensions are remained constants and set to their initial design values. The plasmon energy shift (in meV) at different values of (c) $h_2$, and (d) $h_2$.

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On the other hand, Fig. 6(b) presents the extinction spectra of the SRNS at different values of $h_3$. The rest of the geometrical parameters remained constants and set to their values in the initial design. It is shown that increasing the thickness of the upper split ring shifts ${\omega }_{+}$ to higher frequencies. This is attributed to the fact that increasing $h_3$ leads to increasing ${\omega }_{odd}$. In this case, the upper and lower split rings plasmon resonances are detuned from each other in frequency which weakens their plasmon hybridization. Figure 6(d) shows that $\Delta E$ decreases from 45 meV at $h_3=$ 10 nm to −28 meV at $h_3=$40 nm which emphasizes the decrease in the coupling strength between the two split rings. In consequence, the amplitude of $|{\omega }_{+}〉$ in the extinction cross section is not much higher than that of $|{\omega }_{-}〉$ where the difference in their amplitudes is reduced from 5 dB at $h_3=$ 10 nm to 3.3 dB at $h_3=$30 nm. The locations of the individual split rings’ plasmon resonances have shown to highly influence the plasmon modes of the SRNS in terms of spectral location and amplitude of extinction cross-section. It is observed that ${\omega }_{-}$ is dominated by ${\omega }_{even}$while ${\omega }_{+}$is dominated by ${\omega }_{odd}$. This is consistent with the observation in Fig. 5 which demonstrated that in case of no plasmon hybridization, ${\omega }_{-}$ becomes identical to ${\omega }_{even}$ and ${\omega }_{+}$ becomes identical to ${\omega }_{odd}$.

Varying the gap width g in the upper and lower split rings (while keeping all other geometrical parameters constants with their initial design values) also affects the hybridized plasmon modes of the SRNS as presented in Fig. 7. Upon removing the gaps (g$=0$), the upper and lower split rings become identical complete rings leading to the excitation of an even mode in both. The excitation of the same mode in both rings breaks the plasmon hybridization model described earlier. Now, the two individual rings are decoupled from each other having the same resonance frequency at 98.07 THz (wavelength of 3060 nm). However, stacking them results in shifting this resonance frequency to 116.5 THz (wavelength of 2575 nm).

 

Fig. 7 Extinction spectra of the SRNS at different values of the gap width in both split rings g while other dimensions are remained constants.

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At g$<0$, odd and even modes are excited in the upper and lower split rings, respectively. As a result, the plasmon hybridization between the two split rings starts to appear and the splitting of the SRNS plasmon resonances becomes stronger producing ${\omega }_{+}$ and ${\omega }_{-}$. It is shown in Fig. 7 that ${\omega }_{+}$ and ${\omega }_{-}$ shift to higher frequencies as g increases. The reason for that is that increasing the gap width in both split rings results in decreasing their gap capacitances. The gap capacitance of the split ring is defined as: $C={\epsilon }_{r}wh/\text{g}$, where ${\epsilon }_r$is the dielectric constant of the medium filling the gap (which is water in our case), w is the ring width and h is the ring thickness. According to the LC circuit model, the resonance frequency is inversely proportional to the square root of the gap capacitance ($\omega \alpha 1/\sqrt{LC}$). Hence, the resonance frequencies of the upper and lower split rings (${\omega }_{odd}$ and ${\omega }_{even}$) increase as a result of decreasing their gap capacitances. Since ${\omega }_{+}$(${\omega }_{-}$) is dominated by ${\omega }_{odd}$(${\omega }_{even}$) as concluded earlier, it increases as well.

It can be concluded that tuning the plasmon resonances of the individual split rings by either changing their thicknesses or their gap widths can affect the coupling efficiency between them. Changing the gaps’ alignment and locations also changes in the optical response of the SRNS and its sensitivity to the surrounding medium as discussed in [29]. This tunability of the optical response makes the SRNS highly desirable for sensing applications.

5. Sensitivity of SRNS

In this section, the LSPR sensitivity of the SRNS to refractive index changes is investigated. We also explore the sensitivity of the SRNS as a function of its dimensions where the dimensions having the highest sensitivity are concluded. By performing numerical simulations on the SRNS design, the sensitivity can be calculated as the peak wavelength shift per unit refractive index change (nm/RIU). Figure 8(a) presents the extinction spectra of the SRNS at different refractive indices n. It is observed that the wavelengths of ${\omega }_{+}$ and ${\omega }_{-}$ red shift as n increases. However, Fig. 8(b) shows that ${\omega }_{-}$ has larger peak wavelength shift ($\Delta {\lambda }_{peak}$) relative to water than ${\omega }_{+}$. This is attributed to the fact that the field distribution at ${\omega }_{-}$ is more spread to the surrounding medium which makes it in good contact with the analyte as will be discussed later. The full width at half maximum (FWHM) is shown in Fig. 8(c) for ${\omega }_{+}$ and ${\omega }_{-}$ at different values of n. It is observed that ${\omega }_{-}$has broader peak width than ${\omega }_{+}$ which makes its FWHM larger, this decreases its figure of merit (FOM) where FOM is defined as the ratio between the sensitivity (nm/RIU) and the FWHM (nm).

 

Fig. 8 (a) Extinction spectra of the SRNS at different surrounding media, (b) peak wavelength shift relative to water ($\text{n}=1.33$) and (c) full width half maximum versus n.

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One of the main objectives in designing nanoantennas for biosensing is to find the geometry that achieves the maximum bulk sensitivity. In order to find the design parameters that satisfy the highest sensitivity of the SRNS, we calculate the sensitivity of its plasmon modes by varying the following dimensions: $h_1$, $h_2$ and $h_3$. Additionally, we discuss the relationship between the sensitivity behavior and the strength of the plasmon hybridization between the split rings in order to provide a guide for designing metal-dielectric composite nanostructures for biosensing applications. Figure 9 presents the sensitivity and FOM of the SRNS while varying $h_1$ and $h_3$. The sensitivity versus $h_1$ at $h_3=$ 10 nm, 20 nm and 30 nm is shown in Fig. 9(a). It is observed that the maximum sensitivity is always obtained for ${\omega }_{-}$ when the two split rings have the same thickness. At $h_1=h_3$, the two split rings become closely resonant resulting in a strong coupling between them which produces highly sensitive hybridized plasmon modes. As shown, the antisymmetric resonance has often higher sensitivity than the symmetric one due to the nature of the field distribution at this resonance which is more spread in the surrounding medium. It is also noticed that the ranges of $h_1$ for which the sensitivity of ${\omega }_{-}$ is higher than that of ${\omega }_{+}$ change with the value of $h_3$.

 

Fig. 9 (a) Sensitivity, and (b) FOM of the SRNS vs $h_2$at different values of $h_2$.

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Another phenomenon that is observed is that a maximum sensitivity of the antisymmetric resonance is always met with a minimum sensitivity of the symmetric one and vice versa. This can be attributed to the energy conservation between the two hybridized modes. For example, at $h_1=h_3$, most of the energy is transferred from ${\omega }_{+}$ to ${\omega }_{-}$ resulting in a maximum sensitivity at ${\omega }_{-}$ and a minimum sensitivity at ${\omega }_{+}$. A similar behavior is shown in Fig. 9(b) where the FOM is presented versus $h_2$ at different values of $h_3$. The FOM of ${\omega }_{-}$ is higher than that of ${\omega }_{+}$at certain range of $h_1$, specifically at 10 nm < $h_1$< 20 nm when $h_3=$ 10 nm. While at $h_3=$ 30 nm, this range shifts to 27 nm < $h_1$< 36 nm. However, ${\omega }_{+}$ is in general characterized by its higher FOM than ${\omega }_{-}$due to its narrower peak width. Since the maximum sensitivity is always achieved at $h_1=h_3$, the sensitivity and FOM versus $h_1$ at different values of $h_1$ while maintaining $h_1=f$ are presented in Fig. 10(a) and Fig. 10(b), respectively. As shown in Fig. 10(a), the range of $h_1$for which ${\omega }_{-}$ has higher sensitivity than ${\omega }_{+}$ is nearly constant while increasing $h_1$ and $h_3$. It is observed that the highest sensitivity is always obtained at the smaller values of $h_1$. This is due to the stronger hybridization between the two split rings at smaller intermediate disk thickness. Figure 10(b) shows a similar behavior where the smaller values of $h_2$ has higher FOM for ${\omega }_{-}$ than that of ${\omega }_{+}$.

 

Fig. 10 (a) Sensitivity, and (b) FOM of the SRNS vs $h_2$at different values of $h_2$and $h_2$.

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It can be concluded that the design parameters of the SRNS having the highest sensitivity are:$h_1=h_2=h_3=$ 10 nm at which a sensitivity of 3024 nm/RIU is obtained at ${\omega }_{-}$ while a sensitivity of 1176 nm/RIU is obtained at ${\omega }_{+}$. This is met with FOM values of 1.5 and 1.4 for ${\omega }_{+}$ and ${\omega }_{-}$, respectively. The simulated E-field lines and the E-field absolute value for ${\omega }_{-}$ and ${\omega }_{+}$ at the same dimensions are presented in Fig. 11. A large field enhancement is shown at ${\omega }_{-}$ which emerges from the gaps making more contact with the analyte. On the other hand, most of the field enhancement at ${\omega }_{+}$ is confined in the dielectric disk spacer decreasing its contact with the analyte which decreases its sensitivity. It is worth noting that changing the gap widths did not result in significant enhancement of the sensitivity of the SRNS. A summary of the SRNS design parameters having the highest sensitivity is presented in Table 1. In Table 2, the proposed SRNS is compared to other nanostructures in terms of sensitivity and FOM. It can be noticed that the sensitivity of the SRNS exceeds the sensitivities of most designs reported in literature. However, its FOM is comparatively small due to the broad peak width of its plasmon resonances.

 

Fig. 11 Calculated E-field enhancement in the vicinity of the SRNS ($xz$ plane) at the dimensions: $h_1=h_2=h_3=10$ nm. The E-field lines and E-field absolute value at (a-b) ${\omega }_{-}$ and (c-d) ${\omega }_{+}$. All amplitudes are normalized to the amplitude of the incident e-field.

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Table 1. Summary of the SRNS Highest Sensitivity Design Parameters

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Table 2. Comparison between the Sensitivity and FOM of SRNS and Other Nanostructures Reported in Literature

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Bringing the two gold nanoparticles close to each other leads to strong coupling between them and the formation of hybridized resonances. In this section, we proved that the stronger the hybridization between the two gold elements, the higher the sensitivity obtained for the composite/nanosandwich structure. This shows that the plasmon hybridization effect has contributed to increasing the sensitivity of the structure which made us wonder about how adding more elements of gold nanoparticles might affect the sensitivity. So, we have studied the effect of adding more layers of split rings on the sensitivity of the SRNS in [30]. It was shown that stacking more layers leads to increasing the number of hybridized resonances which the plasmon hybridization model can no longer describe. Measuring the maximum sensitivity at each configuration shows that increasing the number of layers does not necessarily increase the sensitivity of the SRNS as shown in Fig. 12. On the contrary, for number of layers larger than three, the sensitivity starts to decrease till we reach 7 layers then it increases again. Hence, the conclusion is that the relationship between the number of layers and the sensitivity is not a monotonic relationship as there is no obvious trend spotted. In addition, the sensitivity enhancement is not high enough so as to justify the high costs and challenges of fabricating multilayer structures.

 

Fig. 12 Maximum sensitivity versus the number of layers of SRNS [30].

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6. Conclusion

A nanosandwich structure for refractive index sensing is presented. The plasmon hybridization model is used to describe the resonant modes of the SRNS which result from the coupling between the individual split rings’ plasmons. The coupling strength between the two split rings is shown to strongly depend on the spacing between them and the spectral location of their plasmon resonances. It is also shown that the SRNS is characterized by strong field enhancement and high sensitivity to changes in the surrounding medium. The optical properties of the nanosandwich are studied showing high tunability in the optical response which is appealing for use in biosensing applications. The sensitivity of this structure is investigated as a function of its dimensions showing that the sensitivity increases as the coupling strength between the two split rings increases. It is also observed that the energy is conserved in the SRNS where it is transferred between the symmetric and antisymmetric plasmon modes. The design parameters that lead to the highest sensitivity were presented at which the sensitivity reaches 3024 nm/RIU. It can be concluded that the hybridized plasmon modes have higher sensitivity and stronger field enhancement than the individual plasmon modes. However, adding more gold elements to produce more hybridized resonances does not necessarily increase the sensitivity. On the other hand, it has been shown that there is no monotonic relationship between the sensitivity and the degree of hybridization.