Metal‐Insulator‐Metal Waveguide Plasmonic Sensor System for Refractive Index Sensing Applications

Plasmonic sensors are well known for their miniaturized size and high sensitivity. Herein, a numerical analysis of a metal‐insulator‐metal (MIM) waveguide (WG) for refractive index (RI) sensing applications is proposed. The sensing device is composed of a MIM bus WG with a semicircular formation side coupled to a semicircular cavity. This configuration provides a transmission dip with a high extinction ratio as compared to the standard MIM WG side‐coupled to a semicircular cavity. Moreover, the mode converters are also embedded in the sensing system solving the obstacle of light coupling to the MIM plasmonic WG. The sensitivity of the proposed device is ≈941.33 nm RIU−1, making it a promising candidate to be employed in point‐of‐care (POC) testing. This typically involves the use of portable or handheld diagnostic devices that can quickly analyze samples of blood, urine, or other bodily fluids to diagnose diseases or conditions such as infections, diabetes, or heart disease.


Introduction
Due to their distinctive characteristics, plasmonic-based tools have fascinated a lot of interest in recent years, allowing for a considerable improvement in the sensitivity of photonic sensing devices. [1,2] Metals' anticipated role in the creation of innovative optical devices that rely on plasmonic phenomena like surface plasmon polaritons (SPPs) is changing because of ongoing advances in nanofabrication. [3,4] These are appealing for application in a wide range of fields, including nanophotonics, biosensing, electronics, imaging, and many more. [5][6][7] SPPs are tightly bonded to the metal-dielectric contacts, penetrating as deep as 10 nm (the skin depth) in metal and frequently more than 100 nm in the dielectric material. For use in integrated photonic circuits, the metal-insulator-metal (MIM) waveguide (WG) system is one of the most frequently used plasmonic-based structures. Plasmonic sensors are exceptionally enticing and in high demand because they have a smaller footprint and more powerful sensing capabilities than sensors built on other platforms. SPP WG structures, especially MIM WGs, have drawn a lot of attention because they can break through the diffraction limit of light. [8,9] Because of their small size, simplicity of integration, and good balance between light localization and transmission loss, MIM WGs are expected to produce highly integrated optical circuits. [10,11] MIM WGs have a wide variety of applications in various fields, as well as sensing, spectroscopy, optical communication, filtering, and photonic integrated circuits. [12][13][14][15][16] MIM WGs can be used as sensors for identifying slight changes in refractive index (RI) or surface binding events. The high sensitivity of plasmonic modes to changes in the dielectric environment of the WG makes them ideal for sensing applications. MIM WGs can be integrated with other photonic components, such as modulators and detectors, to form complete photonic circuits. [11] The plasmonic fields associated with MIM WGs can be used to achieve subwavelength imaging of objects placed on or near the WG surface. The high field intensity associated with plasmon modes in MIM WGs can be used to enhance nonlinear optical effects such as second-harmonic generation, sum-frequency generation, and four-wave mixing. [17] Generally, MIM WGs offer a highly versatile platform for a wide range of optical applications due to their unique plasmonic properties and compatibility with existing photonic technologies.
RI sensing is a method that measures changes in the RI of a material or medium. This technique has various applications in several fields, including, 1) biosensing: RI sensing is used in biosensors to detect and quantify biological molecules such as proteins, DNA, and cells. The technique can distinguish changes in the RI instigated by the binding of these molecules to a sensing surface, providing a label-free method for detecting and quantifying the biomolecules; [18] 2) environmental sensing: RI sensing is used to detect variations in the RI of environmental pollutants, such as oil spills, and can provide real-time monitoring of water quality in rivers and lakes; [19] 3) food industry: RI sensing is used in the food industry to measure the sugar content of fruit juices, which is an important parameter in determining the quality of the product; [20] 4) chemical sensing: RI sensing can be used in chemical sensors to detect the presence of specific chemicals in a sample. This technique is particularly useful for monitoring chemical reactions and identifying unknown substances. [21] The biosensors are now a trendy area of study because of their numerous uses in areas including food quality management, health, illness detection, and environmental and molecular monitoring. [19,22,23] The two primary categories of biosensors are label-based and label-free sensors. Due to its propensity to alter the binding characteristics of the molecule, the first one is less reliable than the second. The label-free biosensors, which feature benefits like real-time surveillance without a label, work like other SPR-based sensors and find changes in the test medium's RI. Some of the unique advantages of the SPR-based label-free biosensors that have been extensively considered for medical applications include label-free detection, direct and quick response, spectral tunability, strong augmentation of a local electric field, and compliance with modern nanotechnology. [24,25] In this work, a MIM WG-based plasmonic sensor is proposed for RI sensing application and numerically investigated via the finite element method (FEM). Most of the previous research publications on MIM WG-based-plasmonic sensors have utilized 2D numerical simulations, [12,26] which treat one dimension as infinity. This facilitates an analysis of the sensor performance with much shorter computational time and lower loss, and so is this work. Though, the height of the MIM WG has a significant effect on the loss of the system, which should be considered for practical processing. The issue related to the light coupling mechanism to the MIM WG has also been addressed. Silicon nitride (Si 3 N 4 )-based mode converters are embedded at the input and output of the MIM WG to couple the light in and out of the MIM WG. Moreover, the sensitivity of the MIM WG is compared with the sensitivity offered by Si 3 N 4 ridge and slot WGs. The sensitivity of the proposed device is %941.33 nm RIU À1 which makes it suitable as a biochemical sensor for the recognition of minute variations in the analytes.

Device Design and Numerical Model
In this article, an attractive plasmonic sensor configuration is proposed, and its transmission spectrum and H-field mapping are compared with standard plasmonic sensor design. In a standard sensor configuration, the semicircular cavity is side-coupled to a MIM WG as indicated in Figure 1a. The width of the MIM WG is denoted as W and the gap between the MIM WG and the cavity is represented as g. The radius and width of the semicircular cavity are expressed as R and W 1 , respectively. The MIM WG is made up of a nano air slot that is encased on either side by metal layers. Gold (Au) is an excellent choice for plasmonic sensors because it has a strong surface plasmon resonance (SPR) response in the visible and near-infrared regions of the EM spectrum. This response is due to the unique electronic structure of gold, which makes it possible for the electrons in the metal to resonate with light waves. In addition to its optical properties,  Au is also biocompatible and chemically stable, making it a good alternative for use in biological sensing applications.
The Lorentz-Drude model is used to calculate the permittivity of Au, [27] as indicated in Equation (1) where ε ∞ ¼ 9.0685, ω p = 135.44 Â 10 14 rad s À1 , and γ ¼ 1.15 Â 10 14 rad s À1 . Due to its ability to support a fundamental TM 0 mode, W is fixed at 50 nm for simplification. Nanogaps can be designed using focused ion beam lithography (FIBL) [28] or E-beam lithography (EBL), [29] which can achieve a better resolution of s0 nm. Additionally, a modified configuration of the plasmonic sensor is also proposed for better device performance. The MIM bus WG consists of a semicircular formation and is side-coupled to a semicircular cavity as displayed in Figure 1b. In general, the size, shape, and orientation of the cavity in plasmonic sensors based on MIM WG play an important role in light-matter interaction which in turn influences the sensing capability of the device. That is why several attractive plasmonic sensor designs are recently proposed which include a circularshaped cavity, [30] an elliptical-shaped cavity, [31] a bow-tie-shaped resonator, [5,32] a hollow rectangular cavity with a metallic island, [33] and a T-shaped resonator. [34] A plane wave is coupled at the input port (P in ) and the light is collected at the output port (P out ) of the bus WG. The transmission spectrum of both sensor configurations is plotted in Figure 1c. The structural variables such as R = 310 nm, g = 20 nm, W = 50 nm, and W 1 = 200 nm are fixed which are obtained during the initial optimization process. From the transmission spectrum, it can be seen that sensor design with standard MIM WG can generate resonance dip I and resonance dip II with extinction ratio (ER) of À8.96 and À13.88 dB, respectively. Whereas sensor design having a MIM WG with semicircular formation produces a single resonance dip with an ER of À23.13 dB within the spectral range of 750 to 1,000 nm. The ER of an optical ring resonator refers to the ratio of the intensity of the resonant output light to the intensity of the nonresonant output light. In other words, it is a measure of how much the resonant output dominates over the nonresonant output. A higher ER indicates a stronger resonant response, and therefore a more effective device. Typically, ER of À20 dB or higher is desired for most applications. However, achieving high ERs can be challenging, as it requires careful design and optimization of the resonator geometry, materials, and fabrication process. The H-field mapping in the sensor configuration with standard MIM WG at resonance dip II, resonance dip I, and nonresonant state for the wavelength of 776, 872, and 905 nm is presented in Figure 1d-f, respectively. Whereas the H-field mapping in the sensor configuration where MIM WG with semicircular formation at on-resonance and off-resonance states are demonstrated for the wavelength of 872.6 and 908 nm in Figure 1g,h, respectively. It can be seen that the light is strongly confined in the cavity when the resonance condition is satisfied resulting in a strong dip in the transmission spectrum. The structural variables of the device used in this study are listed in Table 1.
Using COMSOL Multiphysics software, the transmittance and field mappings are modeled using the finite element method (FEM). With the help of the available computing resources, the subdomains of the device design are divided up into triangle mesh elements with a grid size of λ/150. This aids in producing accurate simulation results. When analyzing electromagnetic wave problems, it is preferable to create an open-bounded domain, or limit of the computation domain, where an EM wave flows without any reflection. For the FEM simulation window's outer edges to represent an open geometry, scattering boundary conditions (SBC) are used.

Device Optimization
To obtain the best sensor performance, it is crucial to optimize the structural variables of the device. Because the transformation of the variables will cause a change in the effective length of the resonator resulting in a change in the λ res . In the proposed sensor design, three variables such as W 1 , R, and g must be adjusted for a narrow transmission dip with a high extinction ratio (ER). In the first step, W 1 is optimized by keeping the remaining geometric variables such as W, R, and g fixed at 50, 300, and 20 nm, respectively. W 1 is varied in the range of 100 and 300 nm to select an optimum effective length of the cavity for the maximum confinement of the λ res . From Figure 2a, it can be seen that a sharp resonance dip is obtained in the spectrum of 750 to 1000 nm when W 1 = 200 nm. Whereas at W 1 = 100, 150, 250, and 300 nm, the E-field confinement in the cavity is not too strong resulting in the broader transmission dip with a low ER. In the second step, the effect of R on the λ res is determined, as indicated in Figure 2b. The R is varied between 280 nm and 320 nm, whereas the remaining structural variables such as W, W 1 , and g are fixed at 50, 200, and 20 nm, respectively. The λ res performs a redshift as R increases from 280 to 320 nm due to an increase in the effective length of the cavity. [35] The maximum ER = À23.13 dB is obtained at λ = 872.6 nm when R = 310 nm. In the last step, the distance between the cavity and the bus WG is explored to find the optimum value of g. In the previous steps, W 1 and R are optimized at 200 and 310 nm, respectively, whereas g is varied between 10 and 35 nm to find the optimum value for the effective coupling of light from the bus WG to the cavity. From Figure 2c, it can be seen that the maximum ER = À23.13 dB is obtained at g = 20 nm, which indicates that there is a maximum transfer of incoming light from the bus WG to the cavity at λ res . To sum up, the optimum geometric variables of the device are as follows: W = 50 nm, W 1 = 200 nm, g = 20 nm, and R = 310 nm. For further investigation, these variables are used to plot the H-field mappings and to explore the sensing capabilities of the device. As we have mentioned in the previous section, MIM WGs are highly attractive due to their large light-matter interaction resulting in the enhanced sensitivity of the device. Here, we analyzed a sensitivity of a widely used Si 3 N 4 ridge WG and Si 3 N 4 slot WG and compared them with a MIM WG. Si 3 N 4 slot WGs are a type of integrated photonic WG that consist of a Si 3 N 4 core layer with a thin slot etched through the center. The slot is typically filled with a low-index material such as SiO 2 or air, which creates a high-index contrast between the core and the cladding regions of the WG. These WGs offer several advantages over other WG technologies, including low propagation loss, high confinement of light, and compatibility with complementary metal-oxide-semiconductor (CMOS) fabrication processes. They are particularly useful for nonlinear optics and sensing applications, such as optical frequency comb generation, fourwave mixing, and biochemical sensing. [36][37][38] The Si 3 N 4 ridge WG is designed for single-mode operation for the wavelength range of 800 to 1000 nm by keeping the width and height of the WG to 600 and 220 nm, respectively. Also, the Si 3 N 4 slot WG has a height, rail width, and slot fixed to 220, 355, and 50 nm, respectively. The MIM WG with height = 220 nm and slot width (W) = 50 nm is selected which can support TM fundamental mode. The schematic representation of Si 3 N 4 ridge WG, slot WG, and MIM WG is presented in Figure 3a-c, respectively. Additionally, the E-field mapping in the respective WGs is also presented in Figure 3d-f. The real part of the effective refractive index (Re(n eff )) of the Si 3 N 4 ridge WG, Si 3 N 4 slot WG, and MIM WG is determined for the ambient RI of 1.0 and 1.33 as demonstrated in Figure 4a-c, respectively. The Re(n eff ) of the WGs is calculated by utilizing the "Mode analysis" study in the COMSOL Multiphysics software where the desired number of modes is searched near the refractive index of the core layer. It can be seen that n eff of the MIM WG has a large shift in the presence of a small variation in the ambient index as compared to Si 3 N 4 ridge and slot WGs. The sensitivity of the WG is calculated by using Equation (2).
where Δn eff is the variation in the effective index caused by the change in ambient RI, i.e., Δn. From Figure 4d, it can be noticed that the MIM WG has a sensitivity of %1.23 n eff RIU À1 which is much higher than the sensitivity offered by the Si 3 N 4 ridge WG and Si 3 N 4 slot WG which is %0. 16   www.advancedsciencenews.com www.adpr-journal.com

Results and Discussion
The detection of variations in the λ res is the interrogation technique used the most frequently in ring resonators based on plasmonic structures. [39] Most wavelengths interrogation-based optical systems employ polychromatic light sources, such as halogen lamps or super luminescent diodes (SLEDs), that cover the entire spectrum where λ res is expected to be observed. Halogen lamp technology is superior in terms of light spectrum. This light source is preferred when using the wavelength interrogation method and fixed incidence angle configuration. The strong electromagnetic field confinement within the WG structure, which causes a high overlap between the sensing area and the field, results in high sensitivity for MIM WG-based plasmonic sensors. Light coupling into the WG generates a potent electromagnetic field inside the insulating layer that is extremely responsive to   www.advancedsciencenews.com www.adpr-journal.com changes in the RI of the surrounding medium. A target analyte, such as a biomolecule or gas, may be present close to the WG and cause this change in RI. [7,40] A plasmonic RI sensor with a RI sensitivity of 596 nm RIU À1 and a figure of merit of 7.5 was developed by Zhang et al. using MIM WG-coupled double rectangular cavities. [41] Using a MIM stub resonator and plasmonic square cavity resonator, Yun et al. demonstrated a device with a 938 nm RIU À1 sensitivity to RI. [42] A RI sensor with a figure of merit of 75 was developed by Tang et al. using a MIM WG connected to a rectangle and ring resonator. [43] The resonant cavity has a significant impact on the device's characteristics. Consequently, the plasmonic resonator optimization technique is essential for increasing the sensor's sensitivity. The sensitivity of the plasmonic sensing device is estimated by using Equation (3).
where Δλ and Δn are the change in the resonant wavelength and ambient RI, respectively. The transmission spectrum is plotted for the wavelength range of 800-1000 nm as shown in Figure 5a. The RI of the material under observation is selected in the range of 1.33-1.37 which refers to various biological materials such as cells, tissues, and blood plasma. [44] If the RI of the sensing material increases, it can cause a redshift in the transmission spectrum of a sensing device. This is because the λ res of the resonators is influenced by the effective RI of the WG, which is manipulated by the RI of the ambient medium. When the ambient RI increases, it effectively increases the effective RI of the cavity, which causes the λ res of the ring resonator to increase, or "redshift". The λ res versus refractive index unit (RIU) is plotted in Figure 5b. Linear fitting also known as linear regression, is a statistical method used to model the relationship between two variables by fitting a linear equation to the observed data. In other words, it is a way to determine how well a straight line can approximate the relationship between two variables. The linear equation is of the form y = mx þ b, where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept. The slope of the line is around 941.33 nm RIU À1 which defines the sensitivity of the proposed device. Table 2 provides a comparison of the sensing performance of the suggested sensing device with the previously published plasmonic sensors established on MIM WGs.

Challenges Associated with the Realization of MIM WG-Based Sensors
While plasmonic sensors offer several advantages such as labelfree detection, high sensitivity, and real-time monitoring, they also have certain limitations, such as limited penetration depth, limited selectivity, and limited reproducibility as the fabrication of plasmonic sensors can be challenging, and slight variations in the geometry of the metallic nanostructures can lead to variations in sensor response. Plasmonic sensors are sensitive to changes in temperature, humidity, and pH, which can affect their performance and lead to variations in the sensor response. Moreover, the fabrication of plasmonic sensors can be costly and timeconsuming, which can limit their widespread use in certain applications. Despite these limitations, plasmonic sensors have found applications in various fields such as biomedicine, environmental monitoring, and food safety, and ongoing research is addressing these limitations to improve their performance and expand their capabilities. [45] One more challenging aspect of MIM WG-based plasmonic sensors is the light coupling to the nanoscale WG which was not addressed in the previous papers. [2,9,14] However, this matter has been extensively discussed in our previous review paper. [46] To transform a signal that is moving in a dielectric WG into a plasmonic signal that can be relayed through a plasmonic WG, components known as dielectric-to-plasmonic mode converters are used. Dielectric and plasmonic WGs can be integrated into nanophotonic circuitry with the help of this kind of conversion. Dielectric WGs can accommodate modes that are mostly made up of the electric and magnetic fields present in the dielectric substance. SPPs, electromagnetic waves that travel along the boundary between a metal and a dielectric substance, sustain modes that are mainly present in plasmonic WGs. Two mode converter segments should be embedded on the chip to couple the light in and out of the MIM WG, as shown in Figure 6. For   1.330 1.335 1.340 1.345 1.350 1.355 1.360 1.365 1 [44] The H-field mapping in the sensing device at the on-resonance state and off-resonance state is shown in Figure 7a,b. It can be realized that the dielectric mode propagates in the Si 3 N 4 tapered WG and transformed into plasmonic mode as it travels in the MIM WG and coupled to the semicircular cavity when resonance condition is met at λ = 872.6 nm as shown in Figure 7a. Whereas, at λ = 908 nm, the plasmonic mode keeps traveling without coupling to the cavity as it does not satisfy the resonance condition, transforms back to dielectric mode, and is collected at the output port, as shown in Figure 7b

Conclusion
In this work, a MIM WG-based plasmonic sensor is suggested for RI sensing applications. In biochemical sensing, the RI of a liquid or a thin film is used to detect the presence and concentration of biomolecules, such as proteins, DNA, and cells, that are adsorbed onto or near the sensing surface. As the biomolecules interact with the sensing surface, they cause a change in the RI, which can be detected and quantified using different optical techniques. MIM WGs are highly attractive due to their enhanced light-matter interaction. The sensitivity offered by standard MIM WG is %7X higher as compared to the sensitivity offered by Si 3 N 4 ridge and slot WGs. Furthermore, the proposed Dielectric to plasmonic mode converter Plasmonic to dielectric mode converter Figure 6. MIM WG-based plasmonic sensor with input and output mode converters.
λ=872.6 nm λ=908 nm www.advancedsciencenews.com www.adpr-journal.com sensing device is composed of a MIM bus WG with a semicircular formation side coupled to a semicircular cavity filled with the material under observation. The proposed sensor design with a simple cavity formation provides high sensitivity in the biological refractive index range. The sensitivity of the device is %941.33 nm RIU À1 which makes it highly suitable to detect small variations in the RI of the biochemical analytes. The light coupling mechanism to the MIM WG has not been well explored in previous studies. Therefore, we proposed to integrate tapered WGs mode converters with the plasmonic sensor to effectively couple the broadband light source to the nanoscale MIM WG. We believe that this study will help in the realization of integrated plasmonic sensing devices for potential applications.