1. Introduction

Surface plasmon polaritons (SPPs) are surface waves that are bound to and propagate along metal-insulator interfaces, when incident electromagnetic waves are coupled into the collective oscillations of free electrons in a metal [1]. A variety of metal-insulator-metal (MIM)-based plasmonic nanostructures have been designed for guiding SPP modes so far, such as metallic gap (hetero)waveguides, slot waveguides, trench waveguides and V-shaped grooves [2]. Since surface evanescent waves have electric field components polarized perpendicular to the propagation direction, SPP-based plasmonic waveguides can show ultra-compact mode area, strongly enhanced mode field and high sensitivity to the refractive index (RI) variation of surrounding dielectrics [3]. However, the only disadvantage of these traditional plasmonic waveguides (TPWs) is their intrinsic absorption loss caused by metals [4]. Conversely, photonic modes guided in dielectric waveguides present extremely low propagation loss and relatively large mode area. Therefore, incorporating the advantages of both SPP modes and photonic modes, the hybrid plasmonic waveguides (HPWs) based on metal-insulator-semiconductor structures becoming an excellent alternative are extensively investigated [5–9]. Typically, the HPWs are horizontally or vertically slotted slab structures including a metal cladding, an in-between low-index insulator slot and a high-index semiconductor substrate, presenting mode properties dependent on the slot size and substrate dimensions. Metal cladding and high-index semiconductor substrate can squeeze light power into the very thin low-index slot, in which an extremely low-loss and sensitive hybrid mode is established [10]. Physically, this feature can be explained from two aspects. On the one hand, owing to the insulator-semiconductor interface is instead of an insulator-metal one in the TPWs, the hybrid mode has low losses. Thus, the electric field components can spread over the insulator region rather than tightly bounding to the metal surface. On the other hand, the discontinuity of electric field components at high-index-contrast interfaces can generate polarization charges, which will effectively interact with plasmon oscillations excited at the metal-insulator interface [11]. In other words, the hybrid mode is a result of coupling between two evanescent waves with discontinuous transverse electric field components.

In recent years, a great many HPWs-based functional components have been investigated, for example, directional couplers [12], polarization beam splitters [13], nanolasers [14], power splitters [15] and plasmonic sensors [16–24]. Regarding plasmonic RI sensors, by modulating surface plasmon resonances (SPRs) including propagating surface plasmon resonances (PSPRs) and localized surface plasmon resonances (LSPRs), a linear relationship between resonant wavelength of spectral shift and RI of material under detection can be established for realizing RI sensing, which is the most commonly used modulation method [11]. As [19–24] illustrated, many RI sensors are designed by exploiting SPRs-based gratings and periodic nanostructures, like metallic slit (nanoring) arrays acting as perfect absorbers to confine light. However, compared with those complex structures, a combination of HPWs and resonant nanocavities (denoted as waveguide-cavity system for short) is of absolute superiority because of its excellent spectral properties and thus sensing performance. Firstly, featuring best trade-off between propagation loss and mode confinement, HPWs can give rise to extremely confined and enhanced hybrid mode that are very sensitive to the RI change of surrounding medium. Secondly, the high-quality cavity with metallic walls can pick out the required wavelength accurately, showing favorable spectral properties like narrow line-width. Thirdly, this type of RI sensors is more ease of integration. For example, in the case that the incoming light signal is TE-polarized, a polarization converter [25] is only required to integrate ahead with the input waveguide of RI sensor, enabling the TE-polarized signal to convert into the desired TM-polarized one for RI sensing. Therefore, plasmonic RI sensors based on the waveguide-cavity system are essential components with high-performance and easy-to-integrate features, which are deserving of particularly investigated.

In this paper, by sandwiching a rectangular cavity between two vertically slotted hybrid plasmonic waveguides (VSHPWs), a novel near-infrared plasmonic RI sensor with excellent performance (high sensitivity, narrow line-width and good degree of linearity) is proposed and investigated. Compared with other types of waveguide-cavity system-based RI sensors, we introduce a mechanism of synergy between LSPRs and PSPRs that can further improve the sensitivity to as high as 2647.5nm/RIU from 1817.5nm/RIU. With CMOS-compatible technology, the proposed RI sensor can be designed and fully realized on the silicon-on-insulator (SOI) platform.

2. Horizontally slotted hybrid plasmonic waveguide (HSHPW)

2.1 Hybrid structure

Figure 1 shows the cross-sectional view of a HSHPW with fabrication procedure on the right. For such a commonly used multilayer slab structure, as described in [26–28], the fabrication technology is CMOS-compatible and fully realizable. With a high-index Si substrate, different combinations of metals (such as gold, silver, copper and aluminum) and insulators (such as SiO₂, SiC and MgF₂) can present diverse mode and transmission characteristics. More detailed descriptions about these combinations can be found in [29]. The heights of Si rib, SiO₂ slot and metal cladding are h_rib = 300nm, h_slot = 50nm and h_m = 100nm, respectively. The widths of Si rib, SiO₂ slot and metal cladding are w_rib = 250nm. The dielectric constants of air, Si and SiO₂ are ε_air = 1, ε_si = 12.11, and ε_SiO2 = 2.25. Metal of silver (Ag) is selected due to its smallest imaginary part in the near-infrared region (NIR), which leads to relatively low absorption loss. Here, Ag is characterized by the Drude model $\epsilon (\omega )={\epsilon }_{\infty }-{\omega }_p{}^2/[\omega (\omega +i\gamma )]$, where ε_∞ = 3.7, ω_p = 9.1[eV], and γ = 0.018[eV] [30].

 

Fig. 1 (Left) Cross-sectional view of the HSHPW structure. (Right) CMOS-compatible fabrication technology a-d in terms of the practical procedure.

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2.2 Mode characteristic

By varying slot size, the HSHPW can support three modes: Si-based photonic mode (mode S), SPP-based plasmonic mode (mode P) and HSHPW-based hybrid mode (mode H). As eigenmodes existing in the Si rib and at the Ag-SiO₂ interface, mode S and mode P are featured by nearly lossless propagation and nanosize mode confinement, respectively. As an efficient hybridization of mode P and leaky mode S, mode H exhibits extremely low loss, ultra-compact mode area and high sensitivity to RI change. In addition, field evolution from mode H to mode S is shown in Fig. 2. For h_slot < 50nm, mode H presenting more plasmonic-like is mainly confined in the slot. However, for 50nm < h_slot <300nm, mode H starts to leak into the Si rib, thus presenting more photonic-like. Finally, for h_slot = 500nm, a pure mode S is formed in the Si rib. To show mode S clearly, the field evolution distributions are all solved in a symmetric HSHPW structure being outlined in Fig. 2(a), where we use a SiO₂ substrate with width w_rib instead of the previous SOI platform. Here, the incident wavelength is 1550nm.

 

Fig. 2 (a)-(f) Field evolution of the SPP modes from hybrid mode H to pure photonic mode S. Values of h_slot are marked in the yellow blocks.

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Next, based on the finite element method, effective mode index (denoted as n_eff) of the HSHPW is calculated by mode solver. With simulation domain enclosed by perfectly matched layers, free triangular meshing with maximum (minimum) element size of 10nm (1nm) is used for calculation convergence. Since the SiO₂ slot plays an important role in controlling the coupling effect, n_eff-w_rib relationships for different h_slot are plotted in Fig. 3(a). Thinner slot has larger n_eff because more power penetrates into metal. Figure 3(b) shows that thicker metal cladding has no impact on n_eff as long as h_m is larger than silver’s skin depth (typically about 20nm in the NIR). In Fig. 3(c), for constant h_slot, slot with larger w_HPW tends to concentrate more power, resulting in larger n_eff. In Fig. 3(d), P_norm-w_rib relationships are plotted for indicating power confinement capability of the slot. As defined in [31], surface integrals of the merely slot domain and whole simulation domain are introduced to calculate the power values of P_slot and P_total, respectively. Then the power density in slot is defined as P_density = P_slot / A_slot, where A_slot is the area of slot domain. Therefore, the normalized power density is calculated by P_norm = P_density / P_total. For h_slot = 10nm, P_norm = 156[1/μm²] is larger than P_norm values obtained in [27,28].

 

Fig. 3 Real part of n_eff varies as a function of (a) w_rib and (b)-(c) h_slot, for varying (a) h_slot (b) h_m and (c) w_rib. (d) P_norm varies as a function of w_rib for different h_slot.

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3. Near-infrared plasmonic RI sensor based on VSHPWs-nanocavity system

3.1 Structure design

The cross-sectional and three dimensional views of the proposed RI sensor based on VSHPWs-nanocavity system are shown in Fig. 4(a) and 4(b), respectively. The geometric parameters are set as l₁ = l₂ = 500nm, w_slot = 25nm, w_rib = 50nm, w_HPW = 100nm, w_m = 100nm and h_rib = 250nm. In Fig. 4(b), the sensing cavity is sandwiched by input VSHPW₁ and output VSHPW₂. With the metal gaps, an incident power with P_in and y-polarized electric field can be efficiently coupled into and out of the cavity. Note that, the cavity length l_c is calculated by the expression ${\lambda }_m=n_{eff}s/m$ derived in [30], together with n_eff-n₀ relationships shown in Fig. 4(d). The hollow sensing cavity has n_eff = 1.2 and n₀ = 1.0, where n₀ is the RI of material under detection. Thus, the cavity length (l_c = s/2) is calculated as 646nm using a near-infrared resonant wavelength λ_m = 1550nm. Here, l_c is set as 650nm. In Fig. 4(c), for w_slot = 25nm, the h_rib = 240nm is corresponds to the minimum of imag(n_eff) and thus a maximum of transmission efficiency.

 

Fig. 4 (a) Cross-sectional and (b) three dimensional views of the proposed RI sensor. (c) Effective mode index behavior of the VSHPW with different w_slot for varying h_rib. (d) Linear relationship between n_eff of the cavity and n₀ of the material under detection, for several random incident wavelength λ₀ (For clarity, small vertical displacements are made and labeled on the right side of each curve).

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3.2 Spectral property

In our simulation, on the basis of boundary mode analysis, P_out is calculated as an integral of Poynting vector’s x-component along the output boundary of VSHPW₂. P_in is set as the default value of 1[W] [30]. Experimentally, the incident power can be injected into VSHPW₁ by a nanofiber, while the output power can be detected from VSHPW₂ by a spectrometer [32]. As shown in Fig. 5(a), adjusting width d of two metal gaps for desirable coupling effect and resonant peak profile, transmission efficiency T (defined as T = P_out / P_in) of the whole system reduces to 65% from 97.6% as d increases from 5nm to 30nm [33]. For d = 30nm, line-widths of the first-order (mode 1 at λ_m = 1667nm) and second-order (mode 2 at λ_m = 841nm) resonant peaks are 7.4nm and 10.3nm, respectively. This can be physically explained that narrower metal gap leads to more power penetration into dielectrics, resulting in lower absorption loss, larger T and wider line-width. However, slightly wider metal gap can support efficiently excited and coupled SPP modes, showing decreased T and narrower line-width. Thus, moderate d contributes to acceptable T and small FWHM (defined in section 3.4). In subsequent investigations, as sensing indicator, mode 1 peak for d = 30nm is selected for its good optical resolution. Next, for several w_slot, spectral shifts of mode 1 caused by the RI variation of different material is demonstrated in Fig. 5(b). By following the direction of black solid arrows, there is a one-to-one correspondence between peaks under n₀ = 1.0 (n₀ = 1.4) tag and w_slot values listed above the top arrow. Notice that for smaller w_slot the λ₀ is getting larger, because constant l_c and smaller w_slot can result in larger n_eff and thus λ₀.

 

Fig. 5 (a) The dependence of transmission efficiency T on λ₀ for different metal gap width d. (b) Spectral shifts caused by RI change as n₀ increases from 1.0 to 1.4, for varying w_slot (d = 30nm).

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In addition, the normalized electric field E_norm (defined as E_norm = |E| / |E|_max) and power flux density (x-component) distributions of mode1, mode2, mode3 and a non-resonant mode are presented in Fig. 6(a)-6(d), respectively. We can see clearly the PSPRs distributions in cavity and transmission behaviors of the SPP modes from VSHPW₁ to VSHPW₂.

 

Fig. 6 Normalized E_norm and power flux density (x-component) distributions of the (a) first-order (b) second-order (c) third-order resonant SPP modes and (d) non-resonant SPP modes.

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3.3 Sensing performance

The sensing performance can be characterized by three performance indices. First, the wavelength sensitivity S of a RI sensor is defined as $\Delta {\lambda }_{\text{m}}/\Delta n_0$ (nm/RIU), representing the amount of resonant spectral shifts per refractive index unit. Second, the line-width of a resonant peak is indicated by FWHM (full width at half maximum), showing how accurate is the λ_m can be identified. Third, however, figure of merit FOM that defined as the ratio of S to FWHM is the most comprehensive one to evaluate the sensing performance. The larger FOM is, the better trade-off between sensitivity and resolution is achieved. Concluded from the spectral shifts shown in Fig. 5(b), the detailed sensing behaviors are listed in Table1. With w_slot increasing from 5nm to 45nm, S (FWHM) decreases from 1817.5nm/RIU (11.8nm) to 1587.5nm/RIU (7.4nm). As a result, the proposed RI sensor with FOM as high as 224.3 can be achieved for w_slot = 25nm. The last but equally important is, except for S, FWHM and FOM, the good degree of linearity of λ_m-n₀ curves shown in Fig. 7(a). Beyond the NIR, a simple prediction of λ_m for different l_c can be realized by the linear relationship of λ_m-l_c curves presented in Fig. 7(b).

Table 1. Sensing Performance of the Proposed Plasmonic RI Sensor

View Table

 

Fig. 7 (a) Linear relationship between λ_m and n₀ for different w_slot. (b) Linear relationship between λ_m of mode 1 and cavity length l_c (n₀ = 1.0).

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Considering practical application, the perfect symmetry of the structure may get broken for the precision limitation during fabrication process. Thus the fabrication tolerance and alignment tolerance are calculated. First, concluded from Table 1, ± 5nm variations in slot width (w_slot = 25nm) can lead to average fluctuations of ± 1.45% for S, ± 8.05% for FWHM and ± 8.0% for FOM. It is acceptable that, the relatively large fabrication tolerance still maintains a FOM larger than 200. Second, numerical simulation results show that a y-direction deviation of ± 20nm between VSHPWs and cavity is acceptable, which leads to merely <1nm variation in S. In general, both fabrication tolerance and alignment tolerance are relaxed for the structure.

3.4 Further improvement

For better sensing performance, a cavity embedded with metal nanoparticles (NPs) is proposed. As shown in Fig. 8(a), within the cavity with l_c = 450nm, three Ag NPs with radius r = 45nm are placed in the cavity with equal spacing, keeping other geometric parameters unchanged. Comparing E_norm distributions shown in Fig. 6(a)-6(c) and Fig. 8(b)-8(d), as can be expected for a strongly enhanced coupling effect in the dielectric cavity, we find that most power of resonant SPP modes is concentrated in the gap region between Ag slab and NPs. When LSPRs are excited by PSPRs in the cavity, standing wave distributions are coupled with individual dipole-like LSPRs. The LSPRs-PSPRs synergy can greatly enhances coupling efficiency of SPP modes and thus the sensitivity. As the transmission spectrum presented in Fig. 8(e), mode 1 exhibits a sensitivity of 2230nm/RIU and a FWHM of 17nm. For l_c = 650nm, the sensitivity is increased from 1665nm/RIU to 2647.5nm/RIU for r increasing from 5nm to 45nm. Note that, l_c = 650nm and r = 45nm are maximal structure size due to λ_m = 2240nm of mode 1. Furthermore, a good degree of linearity of λ_m-n₀ curve is also presented in Fig. 8(f). Within the NIR, plasmonic RI sensors based on the TPWs-cavity system, can realize a S of 1496nm/RIU and a FOM of 124.6 by a fillet cavity in [30], a S of 1476.3nm/RIU by a ring cavity in [33], and a S of 1563nm/RIU and a FOM of 38.6 by a hexagonal cavity in [34]. In addition, values of S and FOM achieved by other types of nano-structured plasmonic RI sensors are concluded in [35].

 

Fig. 8 (a) Perspective view of the proposed RI sensor with a modified cavity. Top view of the E_norm distributions of the (b) first-order (c) second-order (d) third-order resonant SPP modes in cavity. (e) Spectral shifts in the transmission spectrum for l_c = 450nm and r = 45nm. (f) Linear relationship between λ_m of mode 1 and n₀ of material under detection.

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According to fabrication technologies and manipulation approaches presented in [36], we present a basically feasible manufacturing process as shown in Fig. 9. Firstly, two Si ribs with 50nm in width and 500nm in length are etched on the top of SOI platform by electron beam lithography (EBL). Secondly, SiO₂ ribs adjacent to Si ribs are fabricated by sputter coating or plasmon-enhanced chemical vapor deposition. Then EBL can be used to tailor the width and length of SiO₂ ribs. Thirdly, after placing a protection cover on the position of sensing cavity, Ag cladding can be formed by magnetron sputtering method. Finally, three prepared Ag NPs are placed one by one using contact nanomanipulation techniques, such as multi-probe scanning electron microscopy (SEM) and scanning atomic force microscopy. For example, with ultra-high resolution and relatively low energy, SEM manipulation enables good accuracy in controlling NPs within the proposed sensing cavity with moderate size. It is worth noting that repulsive interactions resulted from interparticle and metallic wall-particle gaps can provide a good force balance, which keeps the Ag NPs in a relatively steady state. As described in [37], recently the most popular way of preparing noble metal NPs is the chemical colloidal synthesis. In addition to the large fabrication tolerance analyzed above, the Ag NPs with diameters of 90nm exhibit desirable preparation feasibility and operating controllability. In general, lithography technique with ultra-high resolution and excellent chemical colloidal synthesis method contribute greatly to the manufacture and preparation of plasmonic nanostructures [37].

 

Fig. 9 (Left) Schematic views for the fabrication process. (Right) From a to e, the detailed manufacture and preparation approaches are listed according to actual operation.

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By employing PSPRs or LSPRs resulted from metallic nanostructures, the proposed NPs-embedded plasmonic sensor allows tremendous applications in environmental monitoring [38] and disease detection [39]. For example, when monitoring a liquid sample containing heavy metal ions with a certain concentration, the RI sensing can be fulfilled on a micro/nanofluidic platform with spectrum response detected by SPRs spectrometer [38].

4. Conclusion

In this paper, on the premise of CMOS-compatible fabrication feasibility, we propose a near-infrared plasmonic RI sensor based on waveguide-cavity system, which consists of two Ag-SiO₂-Si VSHPWs coupled with a rectangular cavity. By adjusting the metal gap width between VSHPWs and cavity, an extremely confined and enhanced hybrid mode can be efficiently coupled in and out of the cavity. As a result, the sensing function is realized with high-performance including high sensitivity of 1660nm/RIU, narrow line-width of 7.4nm, large FOM of 224.3 and good degree of linearity. To further improve sensitivity, a mechanism of PSPRs-LSPRs synergy is presented, which can give rise to a sensitivity as high as 2647.5nm/RIU. However, a moderate FOM of 156 is obtained because of the relatively wide line-width of 17nm. Notice that, an increasing sensitivity is always accompanying with a decreasing resolution and vice versa. Therefore, achieving good balance between sensitivity and resolution is still a significant work. In conclusion, the high sensitivity, good resolution and efficient transmission achieved by our design may pave the way for further investigations in nanophotonic circuits, environmental monitoring and even pharmaceutical research.