1. Introduction

Metallic nanostructures, through the excitation of localized surface plasmon resonances (LSPRs), have the ability to concentrate light into nanoscale spatial regions with the local field enhancement, which enables their use in a wide range of nanophotonics technologies and devices [1,2]. The plasmonic properties have been demonstrated to be efficiently engineered by controlling the size, shape, composition of the metallic nanostructures, and the refractive index of the surrounding environment as well [3]. In particular, this last characteristic of the LSPRs in turn allows label-free and real-time detection of local refractive index changes by monitoring the resonance spectral shifts, leading to the application of metallic nanostructures as LSPR-based sensors [4–15]. The widely adapted metric for the performance of the biosensors is the figure of merit (FOM), defined as the refractive index sensitivity (S = dλ/dn) divided by the linewidth of the plasmonic resonance [9]. Compared with conventional propagating surface plasmon resonances (PSPRs) based sensors which usually operate with a prism coupling in the Kretschmann configuration [16,17], the advantages of the LSPR sensors are simple, cost-effective and suitable for detecting changes in the dielectric environment of the metallic nanostructures. However, the LSPRs exhibit broad linewidths due to the strong radiative damping and dissipation losses, and consequently, result in only small FOM values [9–12], which are generally 1-2 orders of magnitude smaller than the theoretically estimated upper limits (FOM ≈108) of the conventional PSPR-based sensors [16,17].

A possible way to increase the FOM of a LSPR-based sensor is to increase its refractive index sensitivity (S). For example, by lifting metallic nanoparticles above substrates with pillars [18,19] or by constructing a quasi-three-dimensional metallic nanohole array [20], the sensitivity could be immediately increased owing to the reduced substrate effect, where a large fraction of the spatial region with enhanced local electric fields is exposed to the environment. Recently, more efforts have been made to increase the FOM values by alternatively reducing the linewidth (FWHM) of the LSPRs. The Fano interference between subradiant and superradiant plasmon modes has been suggested as a promising technique to narrow the linewidth of plasmon resonances and therefore improve the FOM of the LSPR sensors [21–28]. However, even with such metallic Fano resonant systems, the achievable FOM are limited to 5~20. Although periodically patterned metal mushrooms [29] and perforated metal films [30] have been reported to show sharp Fano resonances with narrow linewidths of ~10 nm or even below 5 nm, resulting in high FOM values comparable to or even exceeding the theoretically estimated upper limits of the prism coupled PSPR sensors, they are based on diffractive coupling mechanism [31], which requires a near-perfect periodic arrangement of the metallic elements and an extremely precise angular alignment of the incident light with respect to the plasmonic nanostructures.

In this paper, we theoretically examine the sensing performance of the dielectric-metal core-shell resonators (DMCSRs) that support multipolar sharp magnetic and electric-based cavity plasmon resonances. We demonstrate that due to the strong confinement of resonant optical fields within the space enclosed by the metal shell layer the DMCSRs exhibit high refractive index sensitivities of 700 ~1200 nm/RIU. With the practical consideration, we also investigate the plasmonic properties of the non-perfect DMCSRs with nano-openings in the metal shell layer, which could be used to introduce specimen into the cavities. We demonstrate that the ability of DMCSRs to confine the resonant optical fields within the cavity is quite robust against the existence of nano-openings and thus high refractive index sensitivities could be well maintained even in the non-perfect DMCSRs. Based on this characteristic, we also propose a microfluidic refractive index sensor consisting of an array of non-perfect DMCSRs connected with each other via the nano-openings. The narrow linewidths of the cavity plasmon resonances coupled with their high index sensitivities make the proposed microfluidic sensors possess high FOM values up to ~88.

2. Sensing performance of the individual perfect DMCSRs

We first consider a perfect DMCSR consisting of a spherical specimen cavity (dielectric core) surrounded by a concentric gold shell layer, as schematically depicted in the inset of Fig. 1(a). The calculated absorption efficiency spectrum of a DMCSR with a cavity radius of R = 500 nm, the refractive index of the material inside the cavity n = 1.57, and the gold shell thickness of t = 50 nm is shown in Fig. 1(a). The calculations throughout this paper are conducted using the three-dimensional finite-element-method (FEM) software COMSOL Multiphysics, where the nanostructures under investigation are embedded in the air (n = 1.0) and illuminated by a plane wave. The permittivity of gold is taken from the experimental data by Johnson and Christy [32]. The computational domain is a 3-μm-radius sphere surrounded by a spherical Perfectly Matched Layer (PML). Scattering boundary condition is imposed at the outer boundary of the computational domain. Free tetrahedral meshes with a maximum mesh size of 10 nm and an element growth rate of 1.4 are applied to the dielectric-core subdomain. Both the gold shell and PML are sweep meshed with 5 layers. The remaining subdomains are restricted to a maximum mesh size of 200 nm with the element growth rate of 1.5. The most remarkable spectral features in Fig. 1(a) are the four distinct absorption peaks locating at the wavelengths of λ = 1915, 1387, 1145, and 1095 nm, respectively. As already have been demonstrated in previous studies, when the core size of the DMCSRs is extending beyond the quasistatic regime, cavity plasmons can interact strongly with the incident optical field because of the phase retardation effect [33–35]. The electric field intensity enhancement distributions are calculated at the peak positions and shown in Fig. 1(b), in which optical fields are found to be mostly confined within the cavity and thus demonstrating typical features of the cavity plasmons. Moreover, Fig. 1(b) shows that the electric fields exhibit single-lobed, four-lobed, six-lobed and circulated distributions within the cavity, confirming that the observed absorption peaks are a result of the excitations of the electric-based dipolar (TM₁), electric quadrupolar (TM₂), electric octupolar (TM₃), and magnetic-based dipolar (TE₁) cavity plasmon resonances. Our previous experiments have shown that the cavity plasmon resonances could initially present a progressive decrease in the linewidth and a gradual blue-shift upon increasing the shell thickness due to the stronger confinement of the cavity plasmon modes at larger shell thickness [36]. As the shell thickness increases beyond the optical skin depth of metal, the linewidth narrowing and the resonance shift begin to converge because the additional increment in the shell thickness can no longer increase the optical field confinement [33, 36]. Therefore, to obtain cavity plasmons with narrow spectral linewidths, the gold shell thickness in this paper is chosen to be t = 50 nm, which extends well beyond the skin depth for gold in the range of near-infrared.

 

Fig. 1 (a) Calculated absorption efficiency spectrum of a DMCSR consisting of a spherical cavity (radius: R = 500 nm; refractive index of the material inside the cavity: n = 1.57) wrapped by a gold shell layer (thickness: t = 50 nm). The inset schematically shows the structure of the DMCSR. (b) Electric field intensity enhancement distributions of the four cavity plasmon resonances. The dashed lines represent the enhancement factor of 10. (c) Calculated absorption efficiency spectra of the DMCSRs with different refractive indices of the material inside the cavity. The spectra are vertically shifted with respect to each other by 0.3 for clarity. (d) Relationship between the resonance wavelength and the refractive index (solid symbols). Sensitivities are obtained using a linear fitting (dashed lines).

Download Full Size | PDF

In order to examine the performance of the perfect DMCSR as a refractive index sensor, the absorption efficiency spectra of the DMCSRs with the same structural parameters R = 500 nm and t = 50 nm but different refractive indices of the material inside the cavity are calculated and shown in Fig. 1(c). Since the cavity plasmon resonances are associated with the surface charges on the inner surface of the metal shell, they should be sensitive to the refractive index of the material inside the cavity [34]. Indeed, it is seen from Fig. 1(c) that all the four cavity plasmon resonances (absorption peaks) blue-shift to a shorter wavelength with decreasing the refractive index, which forms the basis of a LSPR sensor. The spectral positions of the absorption peaks are summarized in Fig. 1(d) versus the refractive index. High refractive index sensitivities of S = 1228, 895, 696, and 736 nm/RIU are obtained from linear fitting for the cavity plasmon resonances TM₁, TM₂, TM₃, and TE₁, respectively.

3. Sensing performance of the individual non-perfect DMCSRs with nano-windows in the metal shell layer

Although perfect DMCSRs exhibit high refractive index sensitivities, they are fully closed, which prevents direct entry of the specimen into the cavity. In order to make the DMCSRs suitable for sensing applications, small through-holes are introduced in the metal shell layer to provide the accessibility inside the cavity. Figure 2(a) schematically shows a non-perfect DMCSR with six nano-windows that are characterized by an opening angle of γ. The nano-windows are arranged along the same equator and equally spaced with angular separation between two adjacent nano-windows equal to 60°. The incident plane wave propagates along the z-axis (i.e. normal to the equatorial plane containing six nano-windows) with its electric fields lying in the xy-plane, at an orientation angle of φ from the x-axis [Fig. 2(a)]. To demonstrate the effect of the existence of the nano-windows on the plasmonic properties of the DMCSRs, the absorption efficiency spectra are first calculated at φ = 0° for the DMCSRs with different opening angles ranging from γ = 0° to 30° and shown in Fig. 2(b), in which the core radius, the shell thickness and the refractive index of the material inside the cavity are fixed to R = 500 nm, t = 50 nm, and n = 1.57, respectively. Figure 2(b) clearly demonstrates that the multipolar cavity plasmon resonances could be well sustained in the non-perfect DMCSRs and exhibit a gradual red-shift with increasing the opening angle. Moreover, Fig. 2(b) shows that the cavity plasmon resonances (absorption peaks) present a progressive increase in the linewidth upon increasing the opening angle. Due to the interference between the sphere and cavity plasmon resonances of the same multipolar order supported by the DMCSRs [34–37], the absorption peaks exhibit asymmetric Fano-type line shapes [Figs. 1(c) and 2(b)]. To precisely describe the resonance broadening effect, the absorption efficiency spectra are fitted in the vicinity of each cavity plasmon resonance using a Fano formula , where σ_bg and σ₀ are the background and normalized efficiency, q is the asymmetry parameter, and ε = 2(λ - λ_res)/Γ with λ_res and Γ being the resonance position and linewidth, respectively. Figure 2(c) summarizes the extracted linewidths for the non-perfect DMCSRs with different opening angles. It is seen from Fig. 2(c) that when the opening angle is increased from γ = 0° to 10° the linewidths of the cavity plasmon resonances TM₁, TM₂, TM₃ and TE₁ keep almost constant values as narrow as Γ ≈22 nm, 17 nm, 13 nm and 5 nm, respectively, demonstrating that the DMCSRs with small opening angles (γ < 10°) could effectively act as a closed cavity with losses only determined by the absorption in the metal and not by radiation losses into the far field [33]. After that, the resonance linewidths begin to broaden upon increasing the opening angle. For example, as the opening angle is increased to γ = 20°, the linewidths of the resonances TM₁, TM₂, TM₃ and TE₁ are increased to Γ ≈24 nm, 25 nm, 14 nm and 7 nm, respectively.

 

Fig. 2 (a) Schematic illustration of the non-perfect DMCSR having six nano-windows (opening angle: γ) that are arranged along the same equator and equally spaced with angular separation between two adjacent nano-windows equal to 60°. (b) Calculated absorption efficiency spectra of the non-perfect DMCSRs at the electric field orientation angle of φ = 0° for varying the opening angles. The spectra are vertically shifted by 0.22 for clarity. (c) Extracted linewidths of multipolar cavity plasmon resonances for the non-perfect DMCSRs with different opening angles. (d) Calculated absorption efficiency spectra of the non-perfect DMCSR with an opening angle of γ = 20° at three different electric field orientation angles of φ = 0°, 15° and 30°. The spectra are vertically shifted by 0.3 for clarity. (e) Electric field intensity enhancement distributions of the cavity plasmon resonances supported by the non-perfect DMCSR with an opening angle of γ = 20° at φ = 0°. The dashed lines represent the enhancement factor of 10.

Download Full Size | PDF

In addition to the electric field orientation angle of φ = 0°, the absorption efficiency spectra are also calculated for a non-perfect DMCSR with an opening angle of γ = 20° under other two different electric field orientation angles of φ = 15° and 30°, and plotted in Fig. 2(d), in which three absorption spectra are found to be almost exactly the same regardless of the incident electric field orientations. Figure 2(e) shows the spatial distributions of the electric field intensity enhancement calculated at the cavity plasmon resonances of the non-perfect DMCSR with an opening angle of γ = 20° under the electric field orientation angle of φ = 0°. It is seen from Fig. 2(e) that near field enhancements could occur around the edges of the nano-openings, implying the excitations of the rim plasmon modes. In the non-perfect DMCSRs with nano-openings, such rim plasmon modes may interact with the cavity plasmons [38–41], which could induce additional radiation losses and therefore should be responsible for the resonance red-shift and linewidth broadening upon increasing the opening angle as shown in Fig. 2(b). Apart from the feature of the rim plasmons, the fields within the cavity of the non-perfect DMCSR [Fig. 2(e)] have nearly the same distribution patterns as those of the perfect DMCSR [Fig. 1(b)], demonstrating that the ability of DMCSRs to confine the resonant optical fields within the cavity is quite robust against the existence of nano-openings.

Figure 3(a) shows the calculated absorption efficiency spectra of the non-perfect DMCSRs with the same structural parameters (R = 500 nm, t = 50 nm, γ = 20°) but different core refractive indices. It is clearly seen from Fig. 3(a) that the cavity plasmon resonances supported by the non-perfect DMCSRs occur a red-shift with increasing the core refractive index. Figure 3(b) plots the absorption peak positions as a function of the core refractive index. By linearly fitting the dependence of the spectral position on the core refractive index, the cavity plasmon resonances TM₁, TM₂, TM₃, and TE₁ supported by the non-perfect DMCSRs are found to exhibit refractive index sensitivities of S = 1237, 900, 700, and 733 nm/RIU, respectively, which are almost the same as those obtained from the perfect DMCSRs [Fig. 1(c)], demonstrating that high refractive index sensitivities could be maintained in the non-perfect DMCSRs. Overall performances of the biosensors are often quantified by a general figure of merit (FOM) defined as the refractive index sensitivity divided by the resonance linewidth, which has been widely accepted as a proper measure for the performance of both LSPR-based and PSPR-based sensors. According to the obtained refractive index sensitivities [Fig. 1(c)] and the corresponding linewidths [Fig. 2(c)], the FOM values of the cavity plasmon resonances TM₁, TM₂, TM₃, and TE₁ supported by the perfect DMCSRs (γ = 0°) are determined to be FOM = 56, 53, 54, and 147, respectively. For the non-perfect DMCSRs (γ = 20°), due to the nano-windows induced linewidth broadening [Fig. 2(c)], the FOM values of the cavity plasmon resonances TM₁, TM₂, TM₃, and TE₁ are decreased to FOM = 52, 36, 50, and 105, respectively. Furthermore, in both the perfect and non-perfect DMCSRs, the magnetic-based cavity plasmon resonance TE₁ is found to have a much higher FOM value compared to the electric-based cavity plasmons (TM₁, TM₂, TM₃), because it produces relatively smaller field enhancements near the inner surface of the shell [Figs. 1(b) and 2(e)] and thus there are less power penetration into the metal walls.

 

Fig. 3 (a) Calculated absorption efficiency spectra of the non-perfect DMCSRs with the same structural parameters R = 500 nm and t = 50 nm but different refractive indices of the material inside the cavity. The spectra are vertically shifted by 0.36 for clarity. (b) Relationship between the resonance wavelength and the refractive index (solid symbols). Sensitivities are obtained using a linear fitting (dashed lines).

Download Full Size | PDF

4. Sensing performance of the array of non-perfect DMCSRs

In the following, we demonstrate that an array of non-perfect DMCSRs could act as a high performance microfluidic refractive index sensor. As schematically shown in Fig. 4(a), non-perfect DMCSRs are hexagonally close-packed and connected with each other via the nano-windows. The proposed array of non-perfect DMCSRs could be readily prepared by physically depositing metal onto a self-supporting monolayer of dielectric colloids, followed by dissolving the supporting dielectric cores [36]. In this method, due to the direct contact between adjacent dielectric colloids, the metal film cannot be fully deposited onto those contact areas so that six nano-windows with an opening angle of γ = 20° could be formed in each of the DMCSRs [36]. Figure 4(b) shows the calculated zeroth-order normal-incidence transmission spectra of the array of non-perfect DMCSRs with the same structural parameters of R = 500 nm, t = 50 nm, and γ = 20° but different core refractive indices. For 500-nm-radius non-perfect DMCSRs, an opening angle of 20° corresponds to a nano-window with a diameter of ~170 nm, which is large enough to let fluid enter inside the cavity [42]. The simulated domain is a cuboid containing one complete and four separate one-quarter of the non-perfect DMCSRs, its four sides (xz- and yz-planes) are applied with periodic boundary conditions and its top and bottom boundaries (xy-planes) are terminated with PML to absorb reflected and transmitted light in the z-axis (k-direction) [Fig. 4(a)]. It is worth noting that the same simulation model has been applied in our previous studies and the calculated results have shown an excellent agreement with the measurements [36]. It is seen from Fig. 4(b) that in each case there are four distinct Fano-like resonances. As mentioned above, the coupling between sphere and cavity plasmon resonances supported by an individual perfect or non-perfect DMCSR could result in the formation of plasmonic Fano resonances [Fig. 2(b)], in which the cavity plasmon resonances act as a narrow discrete resonance and the sphere plasmon modes provide a broad super-radiant continuum [33,35,36]. When the DMCSRs are closely packed like in Fig. 4(a), the sphere plasmons of adjacent DMCSRs may strongly interact because their surface charges are predominantly located on the outer surface of the shell [43]. However, the optical fields associated with the cavity plasmons are tightly confined within the cavity [Fig. 2(e)], which can prevent cavity plasmons in adjacent DMCSRs from interacting with each other [36], provided that the metal shell thickness is larger than the optical skin depth of the metal. Therefore, the Fano resonances observed in the individual DMCSRs [Figs. 1(c) and 2(b)] and the array of DMCSRs [Fig. 4(b)] are expected to have in common that the cavity plasmons supported by the single DMCSR act as the discrete states. The only difference is that the broad super-radiant continuum are provided by the sphere plasmons supported by the individual DMCSR in the former case, while they are provided by the coupled sphere plasmons arising from the coupling between adjacent DMCSRs in the latter case. Indeed, the electric field intensity enhancement distributions within the cavity associated with the cavity plasmon resonances in the array of non-perfect DMCSRs [Fig. 4(c)] are almost the same as that in the individual non-perfect DMCSR [Fig. 2(e)].

 

Fig. 4 (a) Schematic illustration of an array of non-perfect DMCSRs that are hexagonally close-packed and connected with each other via the nano-windows (left side). The simulated domain is a cuboid containing one complete and four separate one-quarter of the non-perfect DMCSRs (right side). (b) Calculated zeroth-order normal-incidence transmission spectra of the array of non-perfect DMCSRs with the same structural parameters of R = 500 nm, t = 50 nm, and γ = 20° but different core refractive indices. The spectra are vertically shifted by 0.36 for clarity. (c) Electric field intensity enhancement distributions of the cavity plasmon resonances supported by the array of non-perfect DMCSRs with the core refractive index of n = 1.55. The dashed lines represent the enhancement factor of 10. (d) Relationship between the resonance wavelength and the refractive index (solid symbols). Sensitivities are obtained using a linear fitting (dashed lines). (e) Calculated transmission spectra of the array of non-perfect DMCSRs with different radii of the cavity. The spectra are vertically shifted with respect to each other by 0.45. The arrows indicate the spectral positions of TE₁ and TM₃.

Download Full Size | PDF

Figure 4(d) plots the transmission peak positions that are collected from Fig. 4(b) as a function of the core refractive index, in which the spectral shift of each cavity plasmon resonance is linear with respect to the core refractive index. The refractive index sensitivities for the cavity plasmon resonances TM₁, TM₂, TM₃, and TE₁ obtained from linear fitting are S = 1337, 951, 666, and 703 nm/RIU, respectively, which are expected to be similar to those obtained from the individual perfect [Fig. 1(c)] or non-perfect DMCSRs [Fig. 3(b)]. The extracted linewidths from the best fitting to the transmission spectra shown in Fig. 4(b) are Γ ≈37 nm, 74 nm, 31 nm and 8 nm for the cavity plasmon resonances TM₁, TM₂, TM₃ and TE₁, respectively. The FOM values are then determined to be FOM = 36 (TM₁), 13 (TM₂), 21 (TM₃), and 88 (TE₁). As mentioned above, in the array of the non-perfect DMCSRs the coupled sphere plasmons between adjacent DMCSRs, instead of the sphere plasmons supported by the single DMCSR, act as broad continuum, which could lead to larger radiation losses as compared with the individual DMCSRs. Therefore, the obtained FOM values for the array of the non-perfect DMCSRs are found to be smaller than those of the individual perfect and non-perfect DMCSRs. Nevertheless, at the dipolar magnetic cavity plasmon resonance TE₁ a high FOM value of ~88 is obtained for the closely packed non-perfect DMCSRs, which is much larger than the previously reported values for LSPR sensors [9–12,18–28]. It should be noted that the resonance TE₁ is spectrally close to the resonance TM₃ [Fig. 4(b)], which may make them almost indistinguishable, and thus making it difficult to exploit the TE₁ resonance for sensing applications from an experimental point of view. Therefore, it is better to increase the spectral separation between the resonances TE₁ and TM₃ so that the TE₁ resonance can be effectively available for sensing applications. A possible way to increase the spectral separation between the TE₁ and TM₃ resonances is increasing the size of the cavity of DMCSRs. Figure 4(e) shows the calculated zeroth-order normal-incidence transmission spectra of the array of non-perfect DMCSRs with the same parameters of (t = 50 nm, γ = 20° and n = 1.55) but different radii of the cavity. It is seen from Fig. 4(e) that upon increasing the cavity radius, the cavity plasmon resonances red-shift, and meanwhile the spectral separation between the two resonances becomes wider. For example, when the cavity radius is increased to R = 750 nm, the spectral separation can be increased from Δλ ≈40 nm for R = 500 nm to Δλ = 95 nm while maintaining the narrow linewidth of the TE₁ resonance (Γ ≈9 nm).

5. Conclusions

In conclusion, we demonstrate that the perfect DMCSRs consisting of a special cavity wrapped by a complete metal shell layer could support multipolar sharp cavity plasmon resonances, provide strong field confinement in the cavity, and thus exhibit high refractive index sensitivities of 700 ~1200 nm/RIU. To obtain a more realistic operational refractive index sensor, we also propose the design of the individual and closely packed non-perfect DMCSRs with nano-openings in the metal shell. We demonstrate that the ability of DMCSRs to strongly confine the optical fields inside the cavity is quite robust against with the existence of the nano-openings, thus ensuring high levels of refractive index sensitivity in the non-perfect DMCSR cases. In particular, we demonstrate that the linewidth of the magnetic dipolar cavity plasmon resonance supported by the array of non-perfect DMCSRs could be as narrow as ~8 nm, and correspondingly the FOM as large as ~88 could be obtained, which is a significant improvement over the previously reported LSPR sensors [9–12,18–28] and even approaches the theoretically estimated upper limit (FOM ≈108) for gold standard prism coupled surface-plasmon sensors [16,17]. Although the obtained FOM value (up to ~88) of the array of non-perfect DMCSRs is smaller than that of the periodically patterned metal mushrooms (~105) [29] and perforated metal films (~144) [30] which are based on the diffractive coupling mechanism, our proposed sensor relies on the cavity plasmon resonances that have been demonstrated to be independent of the incident and electric field orientation angles [34,36], and thus has no particular requirement of precise angular alignment of the incident light with respect to the structures. Furthermore, the array of non-perfect DMCSRs presented here could be readily prepared by physically depositing metal onto a self-supporting monolayer of dielectric colloids [36]. All these desirable features make the array of non-perfect DMCSRs an attractive candidate for high performance sensing applications.