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Abstract
Long-range surface plasmon resonances (LRSPRs) are featured with longer propagation and deeper penetration, compared with conventional surface plasmon resonances (SPRs). Thus, LRSPR-based fiber sensors are considered to have great potential for highly sensitive detection in chemistry or biomedicine areas. Here, we propose and demonstrate a near-infrared LRSPR sensor based on a D-shaped honeycomb microstructured optical fiber (MOF) directly coated with gold film. Although there is no additional heterogeneous buffer layer, the optical field of the long-range surface plasmon polariton (LRSPP) mode penetrates strongly into the analyte region. Thus the effective refractive index of the LRSPP mode depends highly on the analyte’s material refractive index and an abnormal dispersion relationship between the LRSPP mode and MOF’s y-polarized core mode is observed. The mechanism of the LRSPR excitation in the coupling zone is attributed to an avoided crossing effect between these two modes. It also results in the generation of a narrow-bandwidth peak in the loss spectrum of the core mode. Further discussion shows that the resonance wavelength is mainly determined by the core size that is contributed by the MOF’s cladding pitch, silica-web thickness and planar-layer-silica thickness together. It indicates that the operation wavelength of the proposed LRSPR device can be flexibly tuned in a broadband wavelength range, even longer than 2 µm, through appropriately designing the MOF’s structural parameters. Finally, the proposed LRSPR sensor shows the highest wavelength sensitivity of 14700 nm/RIU and highest figure of merit of 475 RIU−1 for the analyte refractive index range from 1.33 to 1.39.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Surface plasmon polaritons (SPPs) are coupled surface excitations from the electromagnetic fields in a dielectric to the charge-density oscillations in a conductor, typically a metal, and then propagate along the conductor-dielectric interface [1]. These surface waves peak at the boundary and decay exponentially into both the media. Considering a very thin metal film sandwiched between two dielectrics with similar refractive indices, SPPs can be excited at both conductor-dielectric interfaces and then coupled to each other, forming two bound supermodes. Their main transverse electric field components distributed symmetrically or asymmetrically across the interfaces, denoted as symmetric mode and asymmetric mode (sometimes as odd and even modes) [2]. The symmetric mode shows much lower attenuation compared with conventional single-interface SPP, resulting in propagating over a longer distance and penetrating deeper into dielectrics. Thus, such mode is named as long-range surface plasmon polariton (LRSPP) mode. On the contrary, the asymmetric mode, named as short-range surface plasmon polariton (SRSPP) mode, exhibits increasing attenuation and better confinement in the metal film. Due to lower attenuation and deeper penetration into dielectrics, LRSPPs show intrinsically stronger interaction with the dielectrics. Consequently, a device based on the resonance of LRSPPs, i.e. long-range surface plasmon resonance (LRSPR), should be much more sensitive to the change of the boundary compared with conventional single-interface SPR based device. It indicates that the LRSPR-based devices have greater potentials for applications in high-performance chemical or biomedical detection [2–4].
Considering a classical scenario of liquid chemical sensing, the analyte can be treated as one dielectric to cover the metal thin film which is coated on a substrate or waveguide. Since the waveguide or substrate for guiding incident light is usually made of a certain glass, of which the material refractive index (RI) deviates considerably from that of the analyte. Such deviation causes difficulty for generating LRSPP directly in the analyte-metal-waveguide structure. To overcome this difficulty, a buffer layer with a similar refractive index as the analyte is introduced between the metal film and the waveguide [5,6]. For most of aqueous or alcohol solvent based analytes, their refractive indices range from 1.33 to 1.40. Thus, some transparent materials with low refractive indices, such as Teflon, Cytop, MgF$_{2}$, are employed as the buffer layer for enhancing the excitation of LRSPP [7–9].
From the point view of light coupling, LRSPR-based devices are commonly constructed with a prism or fiber coupling scheme. Although the former has been widely demonstrated in various LRSPR sensors [7,8,10,11], optical fiber based LRSPR sensor receives increasing attention due to fiber’s intrinsic advantages of miniaturization, remote and in situ sensing capability [3]. Many LRSPR sensors based on different fiber structures, such as D-shaped fiber [12], hollow fiber [13], H-shaped fiber [6], tapered fiber [14], have been proposed. Microstructured optical fiber (MOF), featured with fine arrangement of air holes or high-index rods in solid background, arouses particular interest in constructing fiber-based SPR sensors thanks to its great flexibility in designing and tailoring fiber’s property. Various MOF-based SPR sensors with different structures or materials have been demonstrated [15–21]. Moreover, their operating wavelength can be extended to communication bands and even longer wavelength region through properly designed structure [22,23]. However, the design on MOF-based LRSPR device is almost missing.
In this paper, a D-shaped honeycomb-lattice MOF with coating a thin gold film is proposed to achieve long-range surface plasmon resonances from telecom band to 2 $\mu$m. Different from previous fiber-based LRSPR devices, the LRSPP mode in the proposed configuration is obtained without the assistance of additional low-RI buffer layer (e.g. Teflon, Cytop). By using a full-vector finite-element method (FEM), the electric field distribution, effective refractive index ($n_{\textrm{eff}}$ ), confinement loss of the LRSPP mode and core mode are numerically investigated and followed with a comprehensive discussion about the influence of the structural parameters on the LRSPR. The simulation results illustrate that the electric field of the LRSPP mode distributes mostly in the analyte, pushing the $n_{\textrm{eff}}$ of LRSPP mode close to the level of analyte’s material RI. Moreover, an abnormal dispersion relationship, in which the $n_{\textrm{eff}}$ of the LRSPP mode varies much flatter than that of MOF’s y-polarized core mode, is observed. The mechanism of the LRSPR excitation in the coupling region is proven to be related to an avoided crossing between the LRSPP mode and MOF’s core mode [24–26]. Further discussions show that the LRSPR coupling wavelength can be flexibly tuned by the MOF’s cladding pitch, the thickness of the silica web and the thickness of the planar-layer silica, but it is not sensitive to the thickness of gold film. Finally, the sensing performance of the proposed device is characterized by varying the analyte’s RI from 1.33 to 1.39. It shows an average wavelength sensitivity of 10607 nm/RIU and the corresponding resolution of 9.43$\times 10^{-7}$ RIU. More intriguingly, it’s highest sensitivity and FOM reach 14700 nm/RIU and 475 $ \textrm{RIU}^{-1}$, respectively.
2. Configuration and methodology
The configuration of the proposed D-shaped honeycomb-structure MOF LRSPR sensor is illustrated in Fig. 1. The preparation of this MOF is similar with the fabrication of a side-channel MOF [27] and described as follows. Firstly, some long silica capillaries are used to stack half of holey cladding and the central one is replaced with a solid silica rod. Secondly, some short capillaries with the same outer diameter as the long ones are used to stack the rest half of cladding at both ends. Thirdly, the stacked capillaries are inserted into a silica tube to form a preform. Since the long capillaries are fasten by the short ones at both ends of the preform, their position are kept steadily during the drawing process. After fiber drawing, the empty part forms a large semicircular air channel inside the MOF, while the adjacent capillaries adhere to each other and generate a D-shaped holey structure and a big smooth silica surface due to surface tension under high temperature. By properly controlling the air pressure and drawing speed, the surface will be close to a plane and the air holes in the inner cladding deforms into hexagonal shape. After the MOF fabrication, the outer cladding connected to the empty semicircular air channel is removed by side polishing [17,28] or chemical etching [29–32] techniques to expose the planar silica surface for coating a thin layer of gold film. Compared with previous endless single-mode MOF with triangular arrangement of circular air holes, hexagonal air holes structure will provide higher air-filling ratio. Hence, the optical field diffusion in the lattice cladding is less than that in circular air-holes MOF, resulting in stronger interaction between the light in the planar-layer silica and gold film. To mimic the scenario of practical sensing, the proposed device is immersed into the liquid of analyte. It can be viewed as another dielectric layer. The thin-layer Au is sandwiched between the planar-layer silica and the analyte. As shown in Fig. 1, the center part of the planar-layer silica is attached to the MOF’s core, while the remain of the thin-layer silica is partially attached to the air holes. Due to the high difference on refractive index at the silica-air interface, especially the two half hexagonal air holes flanking MOF’s core (A1 and A2 in Fig. 1), electromagnetic field will bounce back to metal. It forms a quasi dielectric-metal-dielectric-waveguide configuration. The surface plasmon polaritons (SPPs) will be excited on both sides of the metal layer and then coupled to each other, generating a deeply-penetrating LRSPP mode.
Fig. 1. Configuration of the proposed D-shaped honeycomb microstructured optical fiber (MOF) LRSPR sensor, surrounded with a liquid analyte and then a perfectly-matched layer (PML). $\Lambda$ denotes the pitch of MOF’s air-hole cladding; $d$ denotes the thickness of silica wall; $t_{\textrm{Au}}$ denotes the thickness of gold film; $t_{\textrm{SiO}_{2}}$ denotes the thickness of the planar silica layer; A1 and A2 denote two half-hexagonal air holes attached to the core.
The key parameters to characterize the MOF structure include the MOF’s pitch $\Lambda$, the thickness of silica wall $d$ , the thickness of metal layer $t_{\textrm{Au}}$, and the thickness of the planar-layer silica $t_{\textrm{SiO}_{2}}$, as shown in Fig. 1. The MOF’s pitch $\Lambda$ refers to the distance between the centers of two adjacent air holes. The diameters of the whole fiber, analyte and perfectly-matched layer (PML) are appropriately set to circle the microstructure, since they affect the guiding property slightly but consume the computing resource.
The material refractive index of silica can be described by a Sellmeier equation with the corresponding coefficients [33,34]:
The LRSPR excitation in the proposed device and the followed analyses about the optimization of the structural parameters and the sensing performance is investigated by using a commercial FEM software (COMSOL Multiphysics). In order to enhance simulation accuracy, the maximum element size of the meshes in the gold film is set to be 10 nm, whereas those of the meshes in the silica wall and fiber core are no more than 50 nm. With mode analysis, a series of complex eigenvalues ($N_{\textrm{eff}}$) of different modes are calculated. The real part of each eigenvalue represents the effect refractive index ($n_{\textrm{eff}}$) of the corresponding mode, whereas the imaginary part is related to its confinement loss $\alpha (\lambda )$ through the following expression [36,37]:
Fig. 2. (a) Dispersion relationship of the y-polarized core mode (red), LRSPP mode (blue), and the corresponding attenuation spectrum of the y-polarized core mode (black); (b) The electric field profile along y axis of the LRSPP mode at 1970 nm; (c-1)-(c-5) and (d-1)-(d-5) are the electric field distributions of the y-polarized core mode and LRSPP mode at the wavelength of 1950 nm, 1970nm, 1977 nm, 1980 nm and 2000 nm, respectively. The red arrows in (c-1)-(c-5) and (d-1)-(d-5) denote the directions of electric field.
As for the operation principle of LRSPR based refractive index sensor, the widely-adopted methods includes wavelength interrogation and amplitude interrogation [23,37]. The practical scheme is basically similar with the experimental setup used in conventional fiber-based SPR sensors [6,17,38]. The MOF is spliced with two single-mode fibers. One is connected with a polarizer and a polarization controller and then linked with a broadband light source, while the other one is connected with an optical spectrum analyzer. The sensor head, D-shaped region, is kept straight and immersed into a groove inscribed on a substrate. Then, the transmission spectrum of the sensor can be real-time monitored by filling different analytes into the groove. By following the central wavelength and amplitude of the LRSPR peak under different analyte refractive index, the wavelength sensitivity ($S_{\lambda }$) and amplitude sensitivity ($S_{\textrm{A}}$) can be evaluated with Eq. (4) and (5), respectively.
Besides, the performance of a SPR-based sensor can be further evaluated by its resolution ($R$) and figure of merit (FOM). They are respectively defined as follows [23,37]
where $\Delta \lambda _{\textrm{min}}$ stands for the minimum discernible wavelength of an optical spectrum analyser.3. Results and discussions
3.1 LRSPR excitation and property
At first, an example with $\Lambda =2600$ nm, $t_{\textrm{Au}}=70$ nm, $t_{\textrm{SiO}_{2}}=250$ nm, is simulated for demonstrating the excitation of LRSPR in the proposed MOF. The diameters of the fiber’s outer cladding, analyte, and PML are set to 36 $\mu$m, 40 $\mu$m, and 42 $\mu$m, respectively. The refractive index of analyte and PML are both set to 1.33. By sweeping wavelength from 1850 nm to 2100 nm, the eigenvalues of the guided core modes and several SPP modes are simulated. Due to geometric asymmetry, this MOF shows a significant birefringence in the investigated spectral region. The x-polarized core mode has higher $n_{\textrm{eff}}$ and better confinement. But it hardly interacts with SPP modes due to considerable difference between their $n_{\textrm{eff}}$ and poor mode overlap. Thus, only the y-polarized core mode is considered. Its electric field distribution is shown in Fig. 2(c-1). A part of field is bounced from the interface between the metal and planar-layer silica, and then extends into the fiber’s core since the planar layer has the same material property with the fiber’s core. The SPP mode, taking the picture in Fig. 2(d-1) as an example, illustrates some distinct characteristics from those conventional SPP modes of gold film: 1) the optical field distributes in the analyte (one dielectric layer) significantly, while that in the metal film is nearly empty; 2) the penetrating depth in the analyte is almost 10 $\mu$m, as shown in Fig. 2(b); 3) its effective refractive index is very close to the material refractive index of the analyte from the weighted index point of view [2,6], and is much smaller than that of conventional SPP mode [39,40]. Regarding to these distinguish features, the SPP mode excited in the proposed configuration can be viewed as a type of LRSPP mode, although there is no additional low-RI buffer layer between metal film and analyte [3]. Since the heterogeneous buffer layer is not necessary any more, the device fabrication, especially the coating process, can be simplified greatly. Moreover, the stability and robustness of the whole device might be improved as well.
In order to figure out the mechanism of the LRSPP mode generation in the proposed configuration, the dispersion curves of the y-polarized core mode and the LRSPP mode are simulated and plotted in Fig. 2(a). And the evolutions of their electric field are monitored with the sweeping step as fine as 1 nm in the coupling region. It is interesting to observe an abnormal dispersion relationship between the core mode and LRSPP mode, in which the $n_{\textrm{eff}}$ of core mode declines more sharply than the LRSPP mode with the increment of wavelength. Aforementioned, the $n_{\textrm{eff}}$ of the LRSPP mode is close to the analyte’s RI according to effective-medium theory, whereas the $n_{\textrm{eff}}$ of core mode is determined by the material dispersion of silica and MOF’s waveguide dispersion. Such strong dependence of SPP mode $n_{\textrm{eff}}$ on environmental material RI was experimentally demonstrated in the research on parity-time phase transition [41]. For a given wavelength span and fixed ambient temperature, the RI variation of an aqueous or alcohol solvent based analyte is much smaller than that of silica [42]. It might be the main reason that the dispersion curve of the LRSPP mode is flatter than that of the core mode. Moreover, there is a break in their dispersion curves, in which avoided crossing occurs between these two modes. As the pictures shown in Fig. 2(c-1)-(c-5), the electric field of the core mode is gradually transferred from the core region to the analyte as increasing wavelength. It means that the core mode is converted into the LRSPP mode. Meanwhile, the LRSPP mode is transformed into the y-polarized core mode step-by-step as the pictures shown in Fig. 2(d-1)-(d-5). Such bidirectional conversion is completed around 2000 nm. It is noteworthy that two modes have nearly identical field profile at 1977 nm, as shown in Fig. 2(c-3) and (d-3), but their $n_{\textrm{eff}}$ are different. It is corresponding to the avoided-crossing point, at which the core mode and the LRSPP mode exchange their roles and then diverge from each other [25]. Accordingly, the attenuation spectrum is composed of the confinement loss of the core mode before the avoided-crossing point and the converted “core mode” after the avoided-crossing point, as the red dot-dash curve shown in Fig. 2(a). The curve inclines at the beginning of the resonant zone and then declines sharply when the converted “core mode” dominates the fiber’s core, resulted in a narrow bandwidth peak in the attenuation spectrum [26]. Meanwhile, the loss variations of the LRSPP mode and the converted “LRSPP mode” are illustrated as the black dot-dash curve in Fig. 2(a). Such special discontinuance of their attenuation spectra is consistent with the exchange of two modes.
3.2 Influence of MOF’s pitch on resonance
By tracking the variation of the LRSPR peak, the discussion on the MOF’s structural parameters is addressed as follows. At first, the pitch $\Lambda$ of the honeycomb-structure cladding of the MOF is reducing from 2600 nm to 2200 nm with the step of 200 nm, while the other parameters keep the same as those in Section 3.1. As shown in Fig. 3, the LRSPR excitation can be found in all four MOFs with different pitches. And the resonance occurs at the shorter wavelengths with reducing the pitch. Since the core size is highly determined by the pitch, it will reduce in accordance with the decrement of the pitch. Consequently, the $n_{\textrm{eff}}$ of the core mode at each wavelength decreases at the similar pace [43,44], while the corresponding $n_{\textrm{eff}}$ of LRSPP mode is still around the value of analyte’s material refractive index. It indicates that the avoided crossing will be fulfilled at the shorter wavelength. Particularly, it offers great flexibility to tune LRSPR wavelength in a very broad span by simply designing the MOF with different pitches.
Fig. 3. The variation of loss spectrum with respect to different pitch of honeycomb structure cladding, when $d=500$ nm, $t_{\textrm{Au}}=70$ nm, $t_{\textrm{SiO}_{2}}=250$, $n_{\textrm{ana}}=1.33$.
3.3 Influence of silica-web thickness on resonance
Then, the silica-web thickness $d$ in the honeycomb structure cladding is discussed. In order to maintaining consistency, only $d$ is changed from 600 nm to 100 nm while the other parameters are the same as those in Section 3.1. With the decrement of silica-web thickness, the LRSPR peak keeps its profile well and shifts to the shorter wavelength as shown in Fig. 4. Similar with the cladding pitch, the essence of the influence of silica-web thickness on the resonant wavelength is also related to the fiber’s core size and the corresponding waveguide dispersion. Because the fiber’s core is basically composed of a hexagonal region with the side length of $\left (\Lambda +d \right ) /2$ and a small part of the planar-layer silica. It means that the silica-web thickness in the proposed device can also be applied to tune the LRSPR wavelength in the proposed device.
Fig. 4. The variation of loss spectrum with respect to the change of the thickness of silica web, when$d=2600$ nm, $t_{\textrm{Au}}=70$ nm, $t_{\textrm{SiO}_{2}}=250$, $n_{\textrm{ana}}=1.33$.
3.4 Influence of planar-silica-layer thickness on resonance
The top-layer silica not only provides a flat plane for coating metal film, but also plays an important role in this device. In order to analyze the influence of the planar silica on the LRSPR, its thickness varies from 250 nm to 100 nm with the step of 50 nm and the other parameters are the same as those in Section 3.1. As the results shown in Fig. 5, the resonant peak shifts to the shorter wavelengths with the decrement of the thickness of planar-layer silica. Meanwhile, the resonant peak tend to be more asymmetric and its relative amplitude is enhanced. It indicates that both the peak wavelength and the FWHM can be tuned by varying the thickness of the planar-layer silica.
Fig. 5. The variation of loss spectrum with respect to the change of the thickness of planar-layer silica, when $\Lambda =2600$ nm, $t_{\textrm{Au}}=70$ nm, $t_{\textrm{SiO}_{2}}=250$, $n_{\textrm{ana}}=1.33$.
3.5 Influence of metal-layer thickness on resonance
Finally, the fiber’s geometrical parameters used in Section 3.1 are remained, but the thickness of gold film varies from 50 nm to 90 nm. As the result shown in Fig. 6, the LRSPRs in all five simulation models peak at the almost same wavelength. From this point of view, the proposed device is find another merit to lessen the critical requirement of coating process. Moreover, the amplitude of the resonant peak declines obviously with the increment of the thickness of Au film, and the width decreases as well. It might be related to the generation of LRSPP mode, in which the resonance coupling between metal’s upper and lower surfaces is weaken as increasing the thickness of metal film [2,3].
3.6 Sensing performance
Based on the interrogation methods mentioned in Section 2, the sensing performance of the proposed LRSPR sensor is characterized by following the variation of the resonant peak under the analytes with different RIs. Taking the model used in Section 3.1 as an example, the attenuation spectra are simulated by changing the analyte’s RI from 1.33 to 1.39 with the interval of 0.01, as shown in Fig. 7. With the increment of the analyte’s RI, the resonant peak shifts to the shorter wavelengths and the amplitude increases apparently. By extracting the peak wavelengths and then fitting linearly, as the inset shown in Fig. 7, the average wavelength sensitivity to the external RI is calculated around 10607 nm/RIU. Referring to a typical $\Delta \lambda _{\textrm{min}}$ of a commercial optical spectrum analyser ($\Delta \lambda _{\textrm{min}}=0.01$ nm), the corresponding average resolution ($R_{\textrm{avg}}$) of this sensor is around 9.43$\times 10^{-7}$ RIU. It is worth noting that the linearity of the wavelength shift is not good enough within the RI range from 1.33 to 1.39. Thus, the wavelength sensitivity $S_{\lambda }$ to analyte’s RI is further recalculated piecewise based on Eq. (4). As the bar chart shown in Fig. 8, the $S_{\lambda }$ in the range of 1.33-1.34 is of 8700 nm/RIU, and then increases monotonically for the higher RI spans. The maximum $S_{\lambda }$ is found in the range of 1.38-1.39, which reaches up to 14700 nm/RIU. The corresponding minimum resolution is 6.80$\times 10^{-7}$ RIU. Moreover, the FWHM of each resonant peak is measured from the loss spectra in Fig. 7. To ensure consistency with the piecewise $S_{\lambda }$, the equivalent FWHM is defined as the average of the FWHMs of adjacent two resonant peaks. They are calculated at 18.31 nm, 19.40 nm, 21.89 nm, 27.54 nm, 35.89 nm, and 48.20 nm, successively. The corresponding FOMs are computed as well and shown as the red curve in Fig. 8. The highest FOM is of 475 $\textrm{RIU}^{-1}$, achieved in the RI range of 1.33-1.34. With the increment of analyte’s RI, the FOM declines gradually and reaches the lowest value of 305 $\textrm{RIU}^{-1}$ in the RI range of 1.38-1.39.
Compared with the LRSPR-based fiber sensors reported recently, as shown in Table 1, the LRSPR sensor in this work has the advantages such as higher sensitivity, higher FOM and lower resolution. More importantly, the LRSPR in the designed configuration is achieved without the additional low-RI buffer layer and not sensitive to the metal-film thickness. It indicates that the coating process in the device fabrication will be simplified greatly and the robustness of the whole device will be improved as well.
Fig. 6. The variation of loss spectrum with respect to the change of the thickness of Au film, when $\Lambda =2600$ nm, $d=500$ nm, $t_{\textrm{SiO}_{2}}=250$, $n_{\textrm{ana}}=1.33$.
Fig. 7. The variation of loss spectrum with respect to the change of the analyte’s RI; the inset shows the peak wavelengths and the corresponding linear fitting under different analyte’s RIs.
Table 1. Comparison of the performance of the proposed sensor with recently reported LRSPR sensors
4. Conclusion
In summary, an LRSPR sensor based on a D-shaped honeycomb-lattice MOF coated with gold film is proposed and designed. Different from those previously reported LRSPR sensors, the heterogeneous low-RI buffer layer is not necessary for the LRSPP mode generation in the designed configuration. The generated LRSPP wave penetrates into the analyte as deep as almost 10 $\mu$m. On the one hand, the strong penetration into the analyte will facilitate the interaction between light and analyte and consequent applications on high-accuracy detection. On the other hand, it results that the $n_{\textrm{eff}}$ of the LRSPP mode is close to the analyte’s material RI and varies much flatter than that of MOF’s core mode. This abnormal dispersion relationship is seldom reported in previous SPR-based devices. The field-distribution evolutions of the LRSPP mode and core mode reveal that the LRSPR coupling is essentially attributed to an avoided crossing between these two modes. With discussing the influences of all kinds of structural parameters, we find that the LRSPR wavelength is mainly affected by the MOF’s core size which is related to the MOF’s cladding pitch, silica-web thickness, and planar-silica-layer thickness together. The thickness of gold film contributes very little to the LRSPR wavelength but affects the amplitude and FWHM of the resonant peak notably. With appropriate structural parameters, therefore, the operation wavelength of the proposed LRSPR sensor can be flexibly tuned in a wide wavelength range, even beyond 2 $\mu$m. By following the variation of the resonant peak under the analyte’s RI range from 1.33 to 1.39, the proposed LRSPR sensor is demonstrated to have an average spectral sensitivity of 10607 nm/RIU and the corresponding resolution of 9.43$\times 10^{-7}$ RIU. Besides, its highest sensitivity and FOM reach 14700 nm/RIU and 475 $\textrm{RIU}^{-1}$, respectively. Compared with the results reported recently, the LRSPR sensor in this work provides much higher sensitivity and FOM, better resolution, and has the merit of simpler coating process in the device fabrication. Thus, the proposed LRSPR sensor is very promising to be applied for highly sensitive measurement in wide areas.
Funding
National Natural Science Foundation of China (11774102); Scientific Research Funds and Promotion Program for Young and Middle-aged Teacher in Science & Technology Research of Huaqiao University (17BS412, ZQN-YX504).
Disclosures
The authors declare no conflicts of interest.
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