Plasmonic Sensing Design for Measuring the Na⁺/K⁺ Concentration in an Electrolyte Solution Based on the Simulation of Optical Principles

Abstract

Based on the theory of optical sensing, we propose a high-precision plasmonic refractive index nanosensor, which consists of a symmetric rectangular waveguide and a circular ring containing a rectangular cavity. The designed novel tunable micro-resonant circular cavity filter based on surface plasmon excitations is able to confine light to sub-wavelength dimensions. The data show that different geometrical factors have different effects on sensing, with the geometry of the rectangular cavity and the radius of the circular ring being the key factors affecting the Fano resonance. Furthermore, the resonance bifurcation enables the structure to achieve a tunable dual Fano resonance system. The structure was tuned to obtain optimal sensitivity (S) and figure of merit values up to 3066 nm/RIU and 78. The designed structure has excellent sensing performance with sensitivities of 0.4767 nm·(mg/d${\mathrm{L}}^{-1}$) and 0.6 nm·(mg/d${\mathrm{L}}^{-1}$) in detecting Na⁺ and K⁺ concentrations in the electrolyte solution, respectively, and can be easily achieved by the spectrometer. The wavelength accuracy of 0.001 nm can be easily achieved by a spectrum analyzer, which has a broad application prospect in the field of optical integration.

1. Introduction

Surface plasmon polaritons (SPPs) are a unique phenomenon arising from the coupling of photons and electrons at the interface of a metal surface, leading to distinctive characteristics, with their remarkable field confinement capability being the most notable [1,2,3]. Unlike conventional optical waves, SPPs can confine light to the nanoscale, even surpassing the diffraction limit of traditional optical waves. This ability makes SPPs crucial in nanophotonics, providing a vital means for achieving optical control at the nanoscale [4].

Due to their unique properties, a wide range of photonic devices, such as SPP filters, optical switches, and nanoscale sensors, have found extensive applications. SPP filters exploit the specific spectral properties of SPPs to selectively transmit or block light of particular wavelengths, allowing precise control over the spectral characteristics of optical signals [5]. Optical switches utilize the strong beam confinement capability of SPPs to modulate light transmission, enabling a rapid and efficient control of optical signals. Furthermore, SPP-based nanoscale sensors leverage the sensitivity of SPPs to changes in the surrounding medium, facilitating the highly sensitive detection of molecular interactions, biomolecules, and nanoparticles [6].

In the field of optical integration, SPP-based technology offers unique advantages and characteristics [7]. Firstly, the high sensitivity of SPPs enables SPP-based biosensors to achieve the rapid and accurate detection of biomolecules, providing essential tools for biomedical research and clinical diagnostics. Secondly, SPP-based biosensors exhibit high selectivity, allowing for the selective recognition and detection of specific biomolecules, supporting molecular diagnostics and drug screening. Additionally, SPP-based biosensors can achieve high-resolution imaging of biological samples, providing important means for studying the distribution and interactions of biomolecules.

The propagation of SPP in nanostructures is guided by surface plasmon waveguides (SPWS) [7,8,9]. Among many SPWS devices, metal–insulator–metal (MIM) SPWS have the advantages of easy fabrication, strong local field constraints, small size, and low power consumption [10,11]. Yan et al. designed a structure with a sensitivity S of 1071.1 nm/RIU. The structure consists of a stub and a notched ring resonator [12]. Yun et al. proposed a nano-refractive index sensor with a sensitivity of 938 nm/RIU [13], which consists of a stub and a square resonator. Zhang et al. proposed a novel nanosensor with double rectangular cavities, which has a sensitivity of 596 nm/RIU [11]. We compared these different structures of optical sensors to further verify the superior performance of our designed sensor.

Hassan et al. investigated a refractive index sensor with three rectangular cavities containing nanodots, which had a sensitivity (S) and quality factor (FOM) of 7564 nm/RIU and 120, respectively. It was investigated that the addition of nanodots resulted in enhanced light–matter interaction. Applying this sensor to the detection of Na⁺ in human blood, the maximum shifts of the transmittance peaks were 0.83 nm for a concentration change of 1 mg/dL [14]. Sun et al. designed a plasmonic sensor based on a MIM waveguide system with an annular cavity containing a short cutoff line (RCS) with a maximum sensitivity (S) of 2010 nm/RIU and a maximum quality factor of 49,219.04 RIU⁻¹. The addition of a ring cavity above the straight waveguide allows for multiple independently tunable resonances. This feature was used to detect electrolyte sample (Na⁺) in blood with a biosensing sensitivity of 0.1833 nm·(mg/d${\mathrm{L}}^{-1}$) [15].

Rakib et al. studied a round-edged hexagonal plasmonic refractive index sensor consisting of nanorods embedded in a straight waveguide and resonator using the finite element method (FEM). This optimal sensor was applied to cellular protein concentration and salinity measurements and its sensitivity was 19.05 nm/g/100 mL and 1476.6 nm/ppm, respectively [16]. Qu et al. designed an independently tunable MIM for high sensitivity sensing. The sensitivity of the two peaks of this structure reached 2780 nm/RIU and 3580 nm/RIU, respectively. The simulation results were analyzed and it was found that the two peak wavelengths do not affect each other and can be tuned independently. Meanwhile, the structure proved to be promising for practical application by determining the concentration of sodium chloride solution and glucose solution [17].

In this study, we propose a plasmonic sensing model consisting primarily of a double rectangular ring resonator (DRRR) coupled with a waveguide featuring symmetric rectangular stubs. Compared with traditional single-ring configurations, the introduction of symmetric rectangular cavities on both sides of the DRRR significantly enhances the confinement and manipulation of optical waves, resulting in a more asymmetric transmission spectrum and a more pronounced Fano resonance (FR). This geometrical asymmetry strengthens the interaction between discrete and continuum states, which is crucial for achieving high-sensitivity sensing. Compared with circular and hexagonal cavity designs, the proposed DRRR structure demonstrates superior performance in mode coupling control. Although circular and hexagonal resonators can support plasmonic modes, their smooth boundaries and less concentrated localized fields often lead to limited tunability and broader resonance linewidths. In contrast, rectangular cavities—with their sharp corners and well-defined boundaries—enable a stronger field localization, thereby significantly improving sensitivity. More importantly, the resonance response of the sensor can be flexibly tuned by adjusting the dimensions of the rectangular cavities, allowing for the optimization of the sensing performance. The influence of structural parameters on the FR-based transmission characteristics is systematically investigated. After optimization, the proposed sensor exhibits a sensitivity of up to 3066 nm/RIU and a figure of merit (FOM) of 78. Compared with other plasmonic sensors, the novel tunable micro-resonant ring–cavity filter developed in this work not only confines light within subwavelength scales, but also achieves highly sensitive detection of sodium and potassium ion concentrations in electrolyte solutions, with detection sensitivities of 0.4767 nm·(mg/d${\mathrm{L}}^{-1}$) and 0.6 nm·(mg/d${\mathrm{L}}^{-1}$), respectively.

2. Model Structure and Analytical Method

The height of the designed structure is much larger than the surface depth of surface plasmon resonance (SPP), which has a negligible effect on the sensing performance. Therefore, we used a planar model for the depth simulation. Additionally, the waveguide height is effectively infinite, and the material loss remains constant, which further justifies treating it as a planar simulation.

The blue area represents the silver layer. Silver was chosen as the filler metal due to its high electric field enhancement and low power consumption. The electromagnetic response is relatively low with respect to the imaginary part of the dielectric constant. This is mainly because the propagation of electromagnetic waves in a plasmonic structure is primarily influenced by transverse planar properties. Variations along the height direction have minimal effect on material losses. This justifies simplifying the analysis and design to a planar model. Due to nanotechnology limitations, the performance of actual fabricated sensors in the future may differ from our simulations, but this difference will diminish with the development of nanofabrication technology.

The structure contains a ring resonator and a MIM waveguide with a symmetric rectangular stub. The designed device is illustrated in Figure 1. The whole structure is symmetrical. The default parameters of the structure are as follows: R = 230 nm, r = 180 nm, L = 200 nm, d = 50 nm, H = 200 nm, g = 10 nm, φ = 30°. The height of the symmetric stub is denoted by h. L.

And d denotes the length and width of the rectangular cavity, and the outer and inner radii of the double rectangular ring resonant cavity are denoted by R and r, respectively. φ is the rotation angle of the rectangular cavity. The gap between the double rectangular ring resonant cavity and the waveguide is denoted by g. W is the width of all waveguides in the system (w = 50 nm), which ensures that only transverse magnetic fields exist in the system [18,19,20,21]. P_in and P_out denote the input and output ports. The blue area is the silver layer, and the white area is the air. The relative permittivity of Ag was obtained using the Debye–Drude dispersion model [22,23]:

$${\epsilon }_{Ag}(\omega )={\epsilon }_1(\omega )+{\epsilon }_2(\omega )\mathrm{i}=1-{\displaystyle \frac{{\omega }_{\mathrm{p}}^2{\tau }^2}{1+{\omega }_{\mathrm{p}}^2{\tau }^2}}+(1-{\displaystyle \frac{{\omega }_{\mathrm{p}}^2{\tau }^2}{\omega \left(1+{\omega }_{\mathrm{p}}^2{\tau }^2\right)}})$$

(1)

In Equation (1), ${\mathsf{\omega }}_{\mathrm{p}}$ is the plasmonic frequency of silver (${\mathsf{\omega }}_{\mathrm{p}}$= 1.38 ×${10}^{16}\mathrm{r}\mathrm{a}\mathrm{d}/\mathrm{s}$); and ω denotes the incident angular frequency. τ stands for the relaxation time (τ = 7.35 ×${10}^{-15}\mathrm{s})$.

Due to its inherent low dielectric constant, silver maintains a high field and low power consumption, which facilitates the excitation of SPP, an advantage unique to silver [23,24,25]. Nanostructures can be obtained by focused ion beam sputtering on a silver film. In addition, we used an ultra-fine grid to ensure the accuracy of the data and selected perfectly matched layers to prevent light spillover [26,27,28]. P_in and P_out in Figure 1 represent the light input and output ports, respectively. When the light wave propagates along the waveguide, part of the energy is transferred into the double rectangular ring resonant cavity through the waveguide. The FR phenomenon is formed and finally output from P out in the waveguide. The SPP propagates the output expression as in Equation (2) [29,30]:

$$\tan \left(kw\right)=-{\displaystyle \frac{{2k\alpha }_c}{k^2+p^2{\alpha }_c}}$$

(2)

$\mathrm{k}$ represents the wave vector,${\mathsf{\alpha }}_{\mathrm{c}}={[{\mathrm{k}}_0^2\times ({\mathsf{\epsilon }}_{\mathrm{i}\mathrm{n}}-{\mathsf{\epsilon }}_{\mathrm{m}})+\mathrm{k}]}^{{\displaystyle \frac{1}{2}}},$ and ${\mathrm{k}}_0={\displaystyle \frac{2\mathsf{\pi }}{{\mathsf{\lambda }}_0}}$. $\mathrm{P}={\displaystyle \frac{{\mathsf{\epsilon }}_{\mathrm{i}\mathrm{n}}}{{\mathsf{\epsilon }}_{\mathrm{o}\mathrm{u}\mathrm{t}}}}$, and ${\mathsf{\epsilon }}_{\mathrm{i}\mathrm{n}}$ and ${\mathsf{\epsilon }}_{\mathrm{o}\mathrm{u}\mathrm{t}}$ represent the dielectric constants of the insulator and metal, respectively.

In addition, due to the asymmetry and sharp linearity of the Fano resonance, it is susceptible to the influence of the refractive index of the medium and the shape of the structure. There are two important parameters to evaluate the sensing performance of the Fano system: sensitivity (S) and figure of merit (FOM), which are expressed as follows [31,32].

$$S={\displaystyle \frac{\Delta \lambda }{\Delta n}}$$

(3)

$$FOM={\displaystyle \frac{S}{FWHM}}$$

(4)

where $∆\lambda$ and $\mathsf{\Delta }n$ are the changes in resonant wavelength and refractive index, respectively; $S$ is the sensitivity of the sensor; and $FWHM$ is the full-width at half-maximum.

To ensure the accuracy and reliability of computational results, a super-triangular mesh was employed within the MIM waveguide and double rectangular ring resonant cavity (DRRR) structures, enabling the precise capture of nanoscale details and boundary effects. The mesh size was adaptively varied, ranging from nanometers to sub-nanometers, with finer grids applied to regions featuring narrower gaps and coarser grids in areas with larger intervals. Boundary conditions were carefully established to maintain consistency at structural interfaces, with perfectly matched layers (PMLs) applied at the top and bottom of the simulation domain to absorb outgoing waves and suppress spurious boundary reflections, thereby minimizing artificial interference effects. The simulation model dimensions were set to 1320 nm × 950 nm, with a PML thickness of 200 nm. A hyfine mesh configuration was adopted, featuring a mesh size of λ/100 and a total degree of freedom of 12,356, ensuring accurate resolution of field variations across the structure. It should be noted that the numerical accuracy of the simulation may be influenced by factors such as mesh size sensitivity and material loss assumptions. Although a fine mesh was applied, further refinement could potentially affect resonance precision. Additionally, the optical properties of silver were modeled based on frequency-dependent experimental data, without introducing extra damping terms, which may lead to slight deviations from real-world behavior. These limitations should be considered when interpreting the simulation results. Numerical simulations were conducted using COMSOL Multiphysics 5.4, leveraging the “Electromagnetic Waves, Frequency Domain” interface to investigate the optical transmission behavior of the planar DRRR structure. Considering the high fabrication cost of nanoscale photonic devices, we use simulation for parameter tuning and performance calculation.

The simulation parameters included the refractive indices of the core and cladding layers, waveguide geometry, incident wavelength, frequency, and wave number. Both standard Maxwell’s equations and custom partial differential equations were implemented where necessary. The incident laser source, characterized by a narrow linewidth and high coherence, was introduced to minimize monochromatic aberration. The simulation results reveal that incident light propagates predominantly along the high-index core layer, with evanescent leakage decaying rapidly in the surrounding cladding. The electric field distribution, polarized in the out-of-plane (z) direction, was analyzed, where the red and blue regions in the field maps correspond to the wave peaks and troughs, respectively. The simulation setup thus achieves a continuous, reflection-suppressed environment, enabling the precise observation of light–matter interactions within the nanoscale resonant cavity.

3. Results

To illustrate the advantages of this design, we discuss the symmetric rectangular waveguide structure, the double rectangular ring resonant structure, and the entire structure. The symmetric rectangular stub structure and the double rectangular ring resonant cavity are demonstrated in Figure 2. The black, red, and blue lines in the figure stand for the transmission spectra of the overall system, the single double rectangular ring resonant cavity, and the rectangular waveguide, respectively. The spectrum of the single double rectangular ring resonant structure has low transmittance and a symmetric shape; so, it can be seen as a narrow-band mode excited directly by the incident light.

The blue curve represents the transmission spectrum of the waveguide structure, and this curve shows a positive slope and high transmittance. It also shows that the waveguide structure supports continuous broadband modes. The interaction between the multiple modes within the waveguide leads to this continuous transmission spectrum through the multiple modes in the waveguide and the propagation properties in the waveguide. In this case, the characteristic dimensions and material parameters of the waveguide are critical in determining the shape and properties of the transmission spectrum.

Additionally, the asymmetric curve presented by the overall structure suggests that this waveguide structure produces a Fano resonance phenomenon. It results from the interaction of the optical field in the waveguide with the external environment. In this situation, the interaction between the modes in the waveguide structure and the external environment results in an asymmetric characterization of the spectrum. This asymmetry can be modulated by factors such as the shape of the waveguide structure, the material parameters, and the refractive index of the external medium.

To conduct an in-depth analysis of the Fano resonance mechanism, we investigated the variations in the magnetic and electric field distributions of a single waveguide, a single circular ring, a metal–insulator–metal (MIM) waveguide with a single ring resonator, a MIM waveguide with a rectangular cavity, as well as the field distributions at different tilted positions during the resonance process.

When the wavelength λ = 1870 nm, by comparing Figure 3b,c at positions A and C, it can be observed that the introduction of the rectangular waveguide enables magnetic fields to couple within the dual rectangular waveguide regions, with energy also concentrated within these regions. Comparing Figure 3a,b at positions A and C reveals that the addition of the entire cavity allows the magnetic field to be evenly concentrated within both the cavity and the waveguide, with more energy confined inside the cavity. At λ = 2203 nm, comparing Figure 3a,b at positions B and D shows that normalized magnetic fields are present in both the left rectangular waveguide and the ring resonator, with the magnetic field predominantly concentrated within the cavity, and the energy more strongly confined there as well. Furthermore, comparing Figure 3b,c at positions B and D demonstrates that introducing a rectangular cavity into the ring resonator further enhances both the magnetic field distribution and energy within the cavity. This indicates that the incident surface plasmon polaritons (SPPs) interact with the waveguide, propagating from the waveguide to the MIM waveguide and then coherently enhancing through the interactions between the SPPs and the MIM waveguide. In this case, the resonator can be regarded as a Fabry–Perot (FP) cavity, which consists of an air dielectric layer sandwiched between two silver layers. Additionally, compared with any grating, an FP interferometer (FP cavity) can measure wavelengths with greater precision. This structure ensures that incident light undergoes diffraction, thereby exciting propagation modes within the waveguide. This facilitates interference between the diffracted light and directly transmitted light, which also explains the near absence of SPP resonance in the rectangular stub. Compared with position B in Figure 3b, the circular resonator exhibits a stronger resonance after the addition of a right-angled waveguide, which is beneficial for generating Fano resonance. Moreover, when strong resonance occurs, the resonance within the circular resonator becomes almost confined, resulting in a lower transmittance at the resonance tilt angle.

From Figure 3, it can be concluded that, when no rectangular waveguide is present, the magnetic field distribution and energy within the ring cavity are relatively weak, while the magnetic field and energy within the waveguide remain strong and evenly distributed, indicating poor coupling efficiency. However, after introducing dual rectangular waveguides, the situation changes significantly. Comparing positions B and D in Figure 3a,b, it is clear that the magnetic field inside the ring cavity is enhanced, while the structure on the right side of the waveguide shows weaker magnetic fields and energy, indicating a significantly improved coupling effect. The dual rectangular waveguides play a crucial role in the coupling performance of the structure, making it necessary to incorporate rectangular waveguides.

Due to the small size of the nanostructure, the operating wavelength is about 1840 nm, and the imaginary part of ${\epsilon }_{Ag}$ (ω), which represents the absorption loss, should be considered when ω < ${\mathsf{\omega }}_{\mathrm{p}}$. The calculated value of dielectric loss is about 0.13. The surface depth of silver is summarized as ${\epsilon }_{\mathrm{A}\mathrm{g}}={\displaystyle \frac{\lambda }{4\pi p\left|\epsilon \right(\omega \left)\right|}}$, which is 0.77 nm. Additionally, it indicates that the SPP is bonded to the metal surface.

First, the refractive index (RI) of the medium has an essential effect on the Fano resonance transmission spectrum. The Fano resonance spectra are highly sensitive to variations in refractive index (RI); so, we modeled six different values of the refractive index (RI). The refractive index (RI) was 1.00, 1.01, 1.02, 1.03, 1.04, and 1.05. The default parameters of the nanostructures were as follows: R = 230 nm, H = 200 nm, L = 220 nm, φ = 30, d = 50 nm, r = 180 nm, and g = 10 nm; and the transmission curves are illustrated in Figure 4a. With the increase in RI, the transmission spectrum undergoes an approximately isometric redshift. This shows that the transmission spectrum has a linear relationship with the refractive index. As illustrated in Figure 4b, the tilted wavelength shift is closely related to the refractive index. By linear fitting, the maximum sensitivity of the structure is 3066 nm/RIU and the FOM is 78.

From the data analysis, we understand that the refractive index is part of the influence on the Fano resonance effect and that the structural parameters have a significant effect on the inclination wavelength. In order to further understand the factors influencing the Fano resonance, it is necessary to investigate the effects of specific parameters of the structure, and firstly, the outer radius R of the annular cavity was adjusted. The setting range was 190–230 nm with a step size of 10 nm, and the rest of the structural parameters were kept unchanged. The transmission spectra are illustrated in Figure 5a. With the increase in R, we find that the tilted position of the resonance line is significantly red-shifted and the resonance peak on their curve becomes more and more obvious with the increase in R.

The results show that the sensitivity of the nanosensor keeps increasing with the increase in the R value. Meanwhile, the resonant tilt wavelength is affected by the radius, and the fitted lines of sensitivity for different half-ring radii are illustrated in Figure 5b. The results illustrated indicate that R is a topical parameter affecting the sensing accuracy of this structure. Furthermore, by analyzing the relationship between the resonance tilt angle and R, a linear correlation between them is apparent. Therefore, R can be adjusted appropriately to obtain the desired accuracy. We found that, when R = 230 nm, not only the sensitivity and FOM of the structure reached the maximum, but also the transmittance decreased. The sensitivity at R = 230 nm is 240 higher than that at 220 nm. In summary, the radius R of the double rectangular ring resonant cavity structure should be selected from a wide range. In this paper, a ring radius R = 230 nm was selected.

In the simulation experiments, the resonance spectra when the parameter L is 180 nm, 190 nm, 200 nm, 210 nm, and 220 nm are shown in Figure 6a. As L increases, the left resonance peak is only slightly red-shifted, while the red shift of the right resonance peak is more significant. Figure 6b demonstrates the effect of rectangular cavity width on the resonance peaks, where the left-tilted wavelength remains almost unchanged while the right-tilted wavelength undergoes a significant redshift, indicating that the Fano resonance can be effectively attained by adjusting the width of the rectangular cavity to achieve the crossover frequency modulation. Since different resonant modes respond differently to changes in structural parameters, the length L and width W were chosen as the modulation parameters based on their high sensitivity and strong adjustability to the resonance peaks, so that the resonance peaks at two different positions can be controlled separately to achieve the fine modulation of the Fano resonance. The sensitivity fitting curves corresponding to the length and width variations are shown in Figure 6c,d, respectively.

According to the above analysis, when the length and width of the rectangular cavity keep changing, the sensitivity is still in the range of 2800 nm/RIU ~ 3066 nm/RIU, which indicates that it has little influence on the sensitivity. By observing Figure 6a,b, it can be seen that the change has a great effect on different for resonance peaks. Therefore, the length l and width d on the rectangular cavity are important parameters affecting the resonance curve. Based on the fitted lines in Figure 6, the sensitivity corresponds to a maximum FOM of 78, L = 220 nm, and d = 50 nm, which is the optimum selection for structure and structure.

The effect of the symmetric rectangular strut height h on the transmission spectra was analyzed, with h varying between 150 and 200 nm. As shown in Figure 7a, the lines of the transmission spectra change significantly as h increases, red-shifting during the increase in h, and the Fano resonance effect becomes more and more obvious. This indicates that the height of the strut is closely related to the line shape of the Fano resonance curve. In conclusion, the height h of the symmetric rectangular pillars has a significant effect on the resonance line shape, but the full-width half-height (FWHM) gradually becomes wider with the increase in the pillar height h, which leads to a decrease in the sensitivity factor (FOM) value. Appropriate height has a facilitating effect on the optical coupling, but a too strong coupling leads to an increase in the half-width, and the simulation results are consistent with this law. Taking all the considerations into account, we obtained the optimal structural parameter as h = 200 nm.

Then, we studied the influence of the coupling gap. We gradually adjusted the coupling distance g in the range of 10–30 nm, keeping other structural parameters unchanged. The coupling results between the double rectangular ring resonant cavity and waveguide are shown in Figure 7b. This indicates a significant weakening of the coupling properties. It will unavoidably lead to a sharp drop in the sensor performance. Additionally, the blue shift of the resonance curve increases, the transmittance increases, the FWHM increases, the resonance fluctuation decreases, and the resonance fluctuation range decreases. This is because the farther the coupling distance g, the lower the coupling strength.

Finally, we investigated the effect of the angle φ on the performance. Since the cavity adheres at 0° and 80°, we chose to study it between 10° and 70°, and the range of φ was 10–70°, and four sets of experimental transmission spectra were set up with 20° as a step, as shown in Figure 7c. From the figure, it can be seen that the change in angle has a nonlinear effect on the transmission spectra, due to the sharp structure having a certain effect on the parameters, and in the process of changing the angle, the sharp structure and the area of the cavity will change at the same time, and this linkage change also leads to the specificity of the transmission spectra. Although the spectra at 10° have more redshift but the half-width increases, and the redshift at φ = 30° is also more redshifted but the half-width is the smallest, and considering the overall performance, we chose φ = 30° and φ = 70° to be the best choice for the transmission spectra. For the overall performance, we chose φ = 30°.

Table 1. Comparison with other structural data.

References	Structure	Detection Limit (RIU)	Sensitivity (nm/RIU)	Figure of Merit
[33]	E-shaped resonator	4.07 × 10−5	2453.75	-
[34]	Unique half-ring and half-square split	1.6 × 10−4	620.24	13.88
[35]	H-shaped	4.4 × 10−5	1960	-
[36]	Consisting of the SRCSB, ITC and the bus waveguide	4.4 × 10−5	2259.56	-
This work	DRRR structure	3.26 × 10−5	3066	78

shows the comparison of our structure with structural data from other studies.

4. Application

In order to further explore how this structure could be used as a sensor for detecting electrolyte solutions, we need to gain a deeper understanding of the important role of electrolytes in our lives. Electrolytes are a class of compounds that can dissociate into ions in water, including sodium, potassium, and chloride.

Common electrolyte solutions include sports drinks, oral rehydration salts (ORSs), and medical saline solutions. Among them, sports drinks usually contain electrolytes such as sodium, potassium, magnesium, and calcium, which are used to replenish electrolytes lost by the body due to sweating during exercise. They help maintain fluid balance, maintain muscle function, and prevent cramps. Oral rehydration salts are used to treat dehydration, especially in cases of electrolyte loss due to diarrhea or vomiting. They contain moderate amounts of sodium, potassium, and glucose, which help to quickly replenish the body’s electrolytes and balance body fluids. Saline (0.9% sodium chloride solution) is a common electrolyte solution used in medical care, usually for intravenous infusion to replenish body fluids and electrolytes, maintain blood volume, or as a drug diluent.

Electrolytes play an important role in the human body, maintaining charge balance inside and outside cells, and are involved in several physiological processes such as nerve conduction, muscle contraction, and cell signaling. Of these, the sodium ion (Na⁺) is particularly important. Sodium is a major cation and a key factor in the maintenance of osmotic pressure and acid–base balance of body fluids. It affects cellular water balance and regulates blood pressure and heart function. Normally, the body absorbs the right amount of sodium ions through the diet. The excess sodium is then excreted through sweat and urine to keep the body’s sodium concentration stable. However, when the concentration of sodium ions is abnormal, it may lead to a number of health problems, such as increased blood pressure and increased heart burden, especially cardiovascular disease. Potassium ions (K⁺) play a key role in nerve conduction and muscle contraction, and an imbalance in potassium ion concentration can lead to abnormal nerve and muscle function.

However, reliable electrolyte solution sensors not only help medical and healthcare professionals monitor electrolyte levels in patients and healthy populations in real time, ensuring timely intervention and maintenance of electrolyte balance, but also enhance the safety of food and drinking water, optimize agricultural and industrial process control, promote scientific research and environmental protection, and provide vital support for the overall improvement of public health and quality of life.

The linear relationship between refractive index and Na⁺ and K⁺ concentration at constant temperature is written as Equations (5) and (6) [18,37,38]:

$$n_{N{a}^{+}}=1.3373+1.768\times {10}^{-3}\left({\displaystyle \frac{C_1\times k_1}{393}}\right)-5.8\times {10}^{-6}{\left({\displaystyle \frac{C_1\times k_1}{393}}\right)}^2$$

(5)

$$n_{K^{+}}=1.3352+1.6167\times {10}^{-3}\left({\displaystyle \frac{C_2\times k_2}{530}}\right)-4\times {10}^{-7}{\left({\displaystyle \frac{C_2\times k_2}{530}}\right)}^2$$

(6)

where $C_1$ and $C_2$ is the concentration of the liquid to be measured, and ${\mathrm{k}}_1$ and ${\mathrm{k}}_2$ are specific values at room temperature (${\mathrm{k}}_1$ = 30 and ${\mathrm{k}}_2$ = 50). Assuming an electrolyte solution with different levels of sodium and potassium ions, the refractive indices for sodium ion concentrations (C₁) ranging from 0 to 300 mg/dL are 1.3373, 1.3452, 1.3531, 1.361, 1.3689, and 1.3768, according to the formula above. The refractive indices for potassium ion concentrations (C₂) ranging from 0 to 75 mg/dL are 1.3352, 1.3376, 1.34, 1.3425, 1.3449, and 1.3473.

And the sensitivity of checking the electrolyte concentration in the sensor can be described as follows in Equation (7):

$$S_C={\displaystyle \frac{\Delta \lambda }{\Delta C}}$$

(7)

To evaluate the detection performance, the specific experimental steps were as follows: First, the sensor surface was washed with ultrapure water to ensure that it was clean and allowed to dry in a clean environment. In the absence of any sample, the baseline response of the sensor was measured using a spectrometer. Second, a sample of the pre-treated electrolyte solution was injected into the detection region of the sensor using a nano-syringe. The injection rate should be controlled at a smooth, slow rate to avoid disturbing the sensor surface. Finally, a spectrometer was used to measure the spectral response of the sensor before and after sample injection and calculate the shift in resonance wavelength before and after sample injection.

The data simulation aims to evaluate the sensor’s detection performance at different Na⁺ and K⁺ concentrations. As the concentrations of Na⁺ and K⁺ in the electrolyte solution vary within the possible range, different changes in the transmission peaks are observed. Modern spectrometers can easily distinguish significant variations in the transmission peaks. Thanks to its nanometer-level integration, low cost, and rapid response capabilities, the sensor can achieve efficient and accurate detection.

In Figure 8a,c, the graphs demonstrate an approximately equidistant redshift of the resonance curves with the increase in ion concentration, indicating that the sensor has a sensitive response to changes in ion concentration. The linearly fitted images in Figure 8b,d show a highly linear relationship between the sensor’s spectral response and ion concentration, with changes in ion concentration leading to corresponding changes in the spectral response according to a linear trend.

The sensitivities of the sensor are 0.4767 nm·(mg/d${\mathrm{L}}^{-1}$) and 0.6 nm·(mg/d${\mathrm{L}}^{-1}$), meaning that for every 1 mg/dL increase in ion concentration, the wavelength changes detected by the sensor are 0.4767 nm and 0.6 nm, respectively. Considering that the wavelength accuracy of commercial spectral analyzers can reach up to 0.001 nm, this indicates that the sensor is fully capable of meeting the detection requirements.

5. Conclusions

In this work, a novel plasmonic structure composed of a symmetric rectangular MIM waveguide and a ring resonator is proposed, and its transmission characteristics are systematically analyzed using the finite element method. Unlike conventional toroidal cavity structures, the sensing performance is enhanced by extending the rectangular cavity to improve light confinement. The study investigates both the effect of refractive index variations in the surrounding medium and the influence of various structural parameters on the resonance transmission spectrum. Through a detailed parametric analysis involving six key parameters—the refractive index (n), ring resonator radius (R), rectangular cavity length (l), coupling distance (g), waveguide height (h), cavity width (d), and coupling angle (φ)—it was found that n, R, l, d, and φ exhibit regular trends in their impact on sensitivity and spectral characteristics. Notably, the coupling distance g causes a sudden increase in the FOM when it reaches 5 nm due to a significant broadening of the resonance linewidth. Meanwhile, increasing the waveguide height h improves sensitivity but also broadens the FWHM, ultimately reducing the FOM.

Although the proposed structures can be fabricated using chemical vapor deposition (CVD) and electron beam lithography, the nanoscale complexity—particularly in coupling regions and fine features—may introduce fabrication challenges. These may lead to structural deviations, such as edge roughness and dimensional inaccuracies, which can affect resonance behavior and cause discrepancies between the simulated and experimental results. Therefore, further investigation into fabrication tolerances and post-fabrication calibration will be essential for real-world deployment. After comprehensive optimization, the optimal structural parameters were determined as R = 230 nm, l = 200 nm, d = 50 nm, h = 200 nm, g = 10 nm, and φ = 30°. Under these conditions, the system achieves a high sensitivity of 3066 nm/RIU and a FOM of 78. Moreover, this structure demonstrates potential not only for conventional sensing applications but also for industrial detection in food products, with the maximum detectable concentrations of sodium and potassium ions reaching 0.4767 nm·(mg/d${\mathrm{L}}^{-1}$) and 0.6 nm·(mg/d${\mathrm{L}}^{-1}$), respectively. These findings broaden the application prospects of MIM waveguide-based refractive index sensors in nanophotonic and biosensing fields.