Optimized hybrid plasmonic waveguide-based ring resonator for advanced refractive index sensing

In this study, we conducted a comprehensive numerical analysis employing the finite element method to explore the characteristics of a hybrid plasmonic waveguide (HPWG)-based ring resonator (RR) structure. Our investigation reveals that the device’s sensitivity can be significantly augmented through strategic geometric modifications. The device exhibits sensitivities of approximately 176 nm RIU−1 and 238 nm RIU−1 when utilizing WG widths of 300 nm and 270 nm, respectively, in forming the ring structure. Through optimization efforts aimed at enhancing the overlap between the dielectric and plasmonic modes, the device’s sensitivity reaches an optimized level of around 316 nm RIU−1 by reducing the ring width to 250 nm. Overall, our findings underscore the potential for leveraging geometric adjustments to enhance the sensitivity and functionality of HPWG-based RRs, thereby advancing their utility in diverse sensing applications.


Introduction
Hybrid plasmonic waveguides (HPWGs) mark a pioneering leap forward in photonics and sensing technology [1,2].By merging the strengths of dielectric and plasmonic materials, these WGs facilitate efficient light confinement and propagation on a nanoscale level [3,4].Their significance in sensing devices is profound, as they excel in boosting light-matter interactions, thereby enabling highly sensitive and specific detection of analytes.Leveraging the potent field confinement and localization attributes of plasmonic structures, HPWGs attain unparalleled sensitivity in discerning changes within * Author to whom any correspondence should be addressed.
Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. the surrounding environment, such as fluctuations in refractive index or molecular binding events [5].Consequently, their utility extends to critical domains like biosensing, environmental monitoring, and medical diagnostics, where swift and precise identification of trace analytes stands as a pivotal requirement [6].
The hybrid plasmonic mode propagating in HPWG exhibits enhanced sensitivity when compared to the dielectric WG mode, primarily attributed to its unique capacity to tightly confine electromagnetic fields within plasmonic structures while engaging with the surrounding medium [5].Plasmonic structures, distinguished by their support for surface plasmon polaritons (SPPs), manifest robust field enhancement effects at the nanoscale, effectively amplifying the light-matter interaction [7].This amplified field confinement fosters increased overlap between the evanescent field and analyte molecules, thus elevating sensitivity in detecting subtle variations in refractive index or molecular adsorption [8].Moreover, the inherent subwavelength confinement of plasmonic modes facilitates efficient coupling with nanoscale sensors, further bolstering sensitivity and enabling the detection of individual molecules or nanoparticles.In contrast, dielectric WGs typically feature larger mode volumes and weaker field confinement, resulting in comparatively low sensitivity to fluctuations in the surrounding medium [9,10].In recent years, several photonic devices have been realized utilizing HPWG structures enhanced device performance [1,5,[11][12][13][14][15][16].
Ring resonator (RR)-based sensors play a fundamental role in the detection of refractive index changes owing to their exceptional sensitivity, compact form factor, and adaptability to various environments [17,18].These sensors leverage the principle of confining light within a ring-shaped structure, where alterations in the refractive index of the surrounding medium induce shifts in either the resonant wavelength or intensity [19].This heightened sensitivity enables the detection of minute variations in refractive index, rendering RRbased sensors indispensable across a wide spectrum of applications including biomedical sensing, environmental monitoring, and chemical analysis [20].Moreover, their compact design facilitates seamless integration into portable and miniaturized devices, facilitating real-time and on-site measurements.Furthermore, RR-based sensors offer the added advantage of label-free and non-destructive detection, eliminating the necessity for supplementary chemical labels or sample preparation [21].In essence, the amalgamation of their superior sensitivity, compactness, and versatility positions RRbased sensors as indispensable tools for the precise and efficient detection of refractive index changes across diverse application domains [22].
In this study, we undertook a comprehensive numerical investigation focusing on the utilization of a HPWG-based RR tailored specifically for refractive index sensing applications.We rigorously analyzed the intricate characteristics of the device by employing the finite element method (FEM).Our research delves into strategic geometric parametric optimization aimed at optimizing the sensitivity of the resonator, thereby enhancing its performance in refractive index sensing applications.As a result, the enhanced sensitivity and Q-factor of 316 nm RIU −1 and 392.8 are obtained, respectively.

Sensor design and numerical model
The sensor design comprises a silicon bus WG, which is sidecoupled to a silicon ring with a defined gap (g).The width of the bus WG is denoted as W bus which is tapered at the coupling junction to facilitate the maximum coupling of light to the ring due to the extension of the evanescent field in the medium.The radius of this ring is represented as R, while the width of the WG forming the ring is denoted as W ring .Within the ring, a gold (Au) disk is intricately embedded at its center, with a nanometer-scale gap (s) maintaining separation from the silicon ring.This configuration facilitates the creation of an HPWG, optimizing the confinement of hybrid modes upon meeting resonance conditions.To elevate the sensitivity of the device, a HPWG structure is introduced.This structure entails the addition of a semi-circular Au ring positioned adjacent to one side of the silicon ring, also separated by a nanometerscale gap (s).The graphical illustration of the HPWG-based RR structure is presented in figures 1(a) and (b) and the geometric parameters used to optimize the device are specified in table 1.This augmentation enhances the sensor's capability to detect and analyze minute changes in its surroundings.
Employing COMSOL Multiphysics 6.1 software (RF, electromagnetic waves, Frequency domain (emw)), we conducted simulations to analyze transmittance and field distributions utilizing the 2D-FEM.The refractive index of the materials such as silicon, air and Au are obtained from the materials library available in COMSOL software.The TE-polarized light is coupled to the 600 nm wide bus WG to warrant the easy coupling and propagation of the single mode in the near-IR spectrum.To ensure precision, the sub-domains of our device design were precisely subdivided into triangular mesh elements, each boasting a grid size of λ/200.This meticulous meshing strategy proved indispensable in yielding highly accurate simulation results while optimizing the utilization of our computing resources, comprising an 8-core Processor (3.8 GHz) and 128 GB of RAM.In the realm of electromagnetic wave phenomena analysis, establishing an open-bounded domain is paramount.Such a domain provides a computational space where emw propagate devoid of reflections.To emulate this scenario, we implemented scattering boundary conditions judiciously along the outer borders of the FEM simulation window.Through this strategic approach, we attained comprehensive and dependable simulations that closely mirror real-world wave behavior.

Results and discussion
Hybrid modes emerge within an HPWG because of the intricate interaction between guided electromagnetic fields and SPPs propagating along its structure.In contrast to conventional dielectric WGs, HPWGs are typically composed of a dielectric core enclosed by metal layers, fostering robust interactions between guided modes and surface plasmons.This unique configuration enables the coupling of both dielectric and plasmonic modes, giving rise to hybrid modes with distinct characteristics.These hybrid modes amalgamate features from both dielectric and plasmonic WGs, including enhanced field confinement from plasmonic effects and extended propagation lengths stemming from the dielectric core [23].The formation and properties of hybrid modes are intricately influenced by parameters such as WG geometry, material properties, and operating wavelength [1].
In figure 2(a), we observe the intensity distribution line graph captured at H/2 of the HPWG for varying values of s: 50 nm, 60 nm, 70 nm, 80 nm, 90 nm, and 100 nm.Analysis of the graph reveals that the intensity distribution within the HPWG is notably robust at s = 50 nm, progressively diminishing by half as s increases towards 100 nm.This observation underscores the importance of minimizing s, contingent  upon the fabrication's resolution, to achieve enhanced confinement of the hybrid mode within the HPWG structure for strong light-matter interaction.Afterwards, a systematic investigation was conducted into the impact of W ring on the intensity of the hybrid mode confinement within the RR at its resonance wavelength.Remarkably, as W ring undergoes a gradual increase from 200 nm to 250 nm, we observe a notable blueshift in the resonance wavelength concomitant with the enhancement in the strength of the hybrid mode due to the optimum overlap between dielectric and plasmonic mode, as illustrated in figure 2(b).Subsequently, we delved into the impact of the nano-slot width (s) on the confinement strength of the hybrid mode at the onresonance state.By plotting the transmission spectrum across a range of s from 50 nm to 100 nm, as depicted in figure 2(c), we discerned interesting trends.Notably, the HPWG structure with an s of 50 nm exhibited a significantly higher extinction ratio (ER) compared to configurations with s > 50 nm.ER can be calculated as [20]: where P out and P in are the output power and input power, respectively.This observation underscores the pivotal role of nano-slot dimensions in modulating the coupling efficiency and confinement properties of the hybrid mode, offering valuable insights for optimizing the performance of HPWG-based devices in various photonic applications [24,25].
The bus WG undergoes tapering from 600 nm to 240 nm at the coupling segment to enhance the evanescent field, thus maximizing the E-field power transfer to the ring at its resonance wavelength.This strategic tapering ensures efficient light coupling between the WG and the resonator.To comprehensively evaluate the impact of W bus on coupling power, we investigate the confinement of the electric field within the HPWG-based RR.Our analysis spans W bus values ranging from 240 nm to 300 nm, allowing us to delineate the relationship between WG width and the extent of E-field confinement within the resonator.As depicted in figure 3(a), the level of field confinement within the RR is notably pronounced when W bus is set to 240 nm.However, as W bus is gradually increased to 300 nm, a discernible reduction in field confinement becomes evident.This observation underscores the critical role of W bus in determining the spatial distribution and extent of the electric field within the RR.Modification in the WG width allows for precise control over the coupling efficiency and overall performance of the device, highlighting its significance in the design and optimization of integrated photonic systems [26].
The real part of the effective refractive index (Re(n eff )) of the bus WG is methodically analyzed across a spectrum of W bus values ranging from 240 nm to 600 nm, focusing on an operational wavelength of 1550 nm. Figure 3(b) vividly illustrates how Re(n eff ) escalates with increasing W bus , indicating robust confinement of the mode within the WG.Notably, at W bus = 600 nm, the mode is tightly confined within the WG, whereas at W bus = 240 nm, a significant portion of the  mode's power extends into the cladding.This nuanced behavior facilitates seamless power transfer from the bus WG to the RR.Furthermore, figure 3(c) portrays the normalized Efield distribution at various sections of the bus WG, offering invaluable insights into the evolution of the electromagnetic field along its length.These analyses collectively contribute to a comprehensive understanding of the WG's behavior and aid in the refinement of photonic device design for enhanced performance.
The distance (g) between a bus WG and a ring in an optical system is crucial for achieving optimum coupling efficiency.This distance determines the extent of interaction between the light propagating through the bus WG and the resonant modes supported by the RR.When the distance is properly adjusted, it allows for efficient transfer of optical power from the bus WG into the RR, enabling strong coupling between them.This optimal coupling is essential for various applications such as signal modulation, filtering, and switching in integrated photonic circuits.Too large a distance may result in weak coupling, leading to significant power loss and reduced device performance.Conversely, if the distance is too small, it can cause excessive coupling, leading to unwanted crosstalk and interference effects.
In our study, we systematically explore the effect of g on the transmission spectrum within a range of 100 nm to 180 nm, while keeping other geometric parameters such as W bus , W ring , s, and R fixed at 240 nm, 250 nm, 50 nm, and 3 µm, respectively, as illustrated in figure 4(a).The transmission spectrum demonstrates how the ER of the resonance dips fluctuates with variations in g from 100 nm to 180 nm.Notably, the optimal field coupling between the bus WG and the RR is achieved at g = 120 nm, yielding a significantly enhanced ER of −12.31 dB when resonance conditions are satisfied.Contrastingly, when g is set to 180 nm, a suboptimal coupling occurs, resulting in a poorer ER of −6.22 dB.These findings underscore the critical importance of precisely tuning the g to maximize coupling efficiency and ensure robust performance in integrated photonic devices.
The free spectral range (FSR) of an RR is a fundamental parameter that holds significant importance in various optical applications [27].FSR represents the frequency spacing between adjacent resonance peaks or dips in the transmission spectrum of the RR.The significance of FSR lies in its ability to determine the spectral resolution and selectivity of the resonator [28].A larger FSR implies a broader frequency range over which the resonator can operate without interference between adjacent resonances.This broad spectral coverage is valuable for applications such as wavelength filtering, signal demultiplexing, and frequency stabilization in optical communication systems.Moreover, FSR directly influences the device's ability to resolve closely spaced spectral lines or distinguish between different wavelengths of light.Fine-tuning the FSR allows tailoring the performance of RRs according to specific application requirements, enabling precise control over signal processing and manipulation in integrated photonic circuits.Finally, we investigate the impact of R on the FSR of the device, as illustrated in figure 4(b).With the geometric parameters W bus , W ring , g, and s fixed at their optimized values of 240 nm, 250 nm, 120 nm, and 50 nm, respectively.The FSR analysis reveals significant variations: the device exhibits FSR values of 52 nm, 40 nm, 32 nm, 28 nm, and 25 nm for R = 2 µm, 2.5 µm, 3 µm, 3.5 µm, and 4 µm, respectively.These results underscore the pivotal role of R in determining the spectral behavior and performance characteristics of the device.
The resonance wavelength of an optical RR can be approximated by the formula: where R eff , n eff , and m are the effective radius of the RR, effective refractive index of the resonator, and an integer representing the mode number, respectively.Variations in the ambient medium can cause shifts in the resonance wavelength of a RR through changes in the effective optical path length and refractive index.When the refractive index of the surrounding medium changes, it alters the phase accumulation and interference of light waves circulating within the resonator.This change in phase affects the resonance condition, leading to a shift in the resonant wavelength.Additionally, variations in the refractive index influence the optical confinement and mode distribution within the resonator, further impacting the resonance characteristics.For instance, an increase in the refractive index of the surrounding medium generally redshifts the resonant wavelength, while a decrease blueshifts it.These shifts in resonance wavelength are crucial in applications such as biochemical sensing, where minute changes in the ambient medium's refractive index can be detected through precise monitoring of the resonator's optical response.The sensitivity of a refractive index sensor, commonly symbolized as S, plays a pivotal role in evaluating its capability to detect alterations in refractive index.This sensitivity is typically determined by examining how the sensor's response changes concerning variations in refractive index.In mathematical terms, sensitivity is represented by the formula [29]: where ∆λ signifies the alteration in the resonance wavelength, and ∆n denotes the change in refractive index.This equation illuminates how the sensor's output adjusts when the refractive index of the surrounding medium is modified.A higher sensitivity indicates the sensor's capacity to perceive minute variations in refractive index, rendering it particularly appropriate for precise applications like biochemical sensing and environmental monitoring.The refractive index range of biological analytes, such as cells, tissues, and biofluids, varies significantly depending  on their composition and molecular structure.Generally, the refractive index of biological materials falls within the range of approximately 1.33-1.55,with variations observed based on factors like hydration level, protein content, and lipid composition.This range is crucial in various biomedical applications, particularly in microscopy and optical sensing techniques, where precise measurements of refractive indices help in distinguishing different biological components and elucidating their properties.The transmission spectrum of the HPWG-based RR structure is precisely plotted across the wavelength spectrum spanning from 1480 nm to 1580 nm, showcasing its response under slight variation of refractive index conditions, as depicted in figure 5(a).For this purpose, we have meticulously chosen a relatively narrow refractive index range spanning from 1.33 to 1.35, with a precise step size of 0.005.Throughout this analysis, the geometric parameters of the device remain constant, with R = 3 µm, g = 120 nm, s = 50 nm, W bus = 240 nm, and W ring = 250 nm.Notably, the resonance wavelength consistently demonstrates a discernible redshift phenomenon as the ambient refractive index ascends from 1.33 to 1.35, underscoring the sensitivity of the device to minute changes in the surrounding refractive index.Furthermore, we delve into the impact of varying W ring on the device's sensitivity, exploring values of 250 nm, 270 nm, and 300 nm.Through careful analysis, we plot the change in resonance wavelength against the refractive index, discerning the subtle nuances in device performance.The slope of this plot unveils the rate of change of resonance wavelength, directly correlating with the sensitivity of the device as shown in figure 5(b).Remarkably, we observe sensitivity values of 176 nm RIU −1 , 238 nm RIU −1 , and 316 nm RIU −1 for W ring values of 300 nm, 270 nm, and 250 nm, respectively.This detailed examination underscores that a W ring of 250 nm stimulates superior field confinement of the hybrid mode within the HPWG.Consequently, this configuration maximizes lightmatter interaction, culminating in heightened sensitivity.Such findings accentuate the pivotal role of W ring in optimizing device performance for refractive index sensing applications.
The quality factor (Q-factor) plays a pivotal role in assessing the effectiveness of an RR.It serves as a fundamental parameter delineating the resonance's sharpness and selectivity, offering insights into sensitivity, stability, and energy storage capacities [30].Determining the Q-factor entails measuring the resonance linewidth, defined as the width of the resonance dip at half its maximum intensity (FWHM).Typically, this factor is computed as [20]: where λ res is the resonance wavelength and FWHM is the full width at half maximum.A higher Q-factor signifies a narrower resonance linewidth, leading to a more precise and stable resonant frequency.Various experimental techniques, such as optical transmission measurements, ring-down measurements, and fitting methodologies applied to the resonator's transmission spectrum, can be employed to determine the Q-factor accurately [31].This meticulous determination of the Q-factor is crucial for refining the design and manufacturing processes of RRs across diverse applications, thereby ensuring optimal performance and functionality.The vital parameters such as FWHM, Q-factor and sensitivity of the proposed RR design are presented in table 2.  In the end, we plotted the normalized H-field distribution within the HPWG-based ring structure at optimized dimensions including R = 3 µm, W bus = 240 nm, W ring = 250 nm, s = 50 nm, and g = 120 nm, while maintaining an ambient refractive index of 1.33.As illustrated in figure 6, our findings unveil intriguing behaviors of light within the device.In figure 6(a), under on-resonance conditions at the operational wavelength of 1528.9 nm, the H-field distribution demonstrates significant confinement within the HPWGbased ring, indicative of resonant behavior.Conversely, in figure 6(b), for off-resonance conditions at the operational wavelength of 1544.5 nm, the H-field distribution illustrates minimal confinement within the ring, with light predominantly passing through the bus WG.These observations elucidate the dynamic interplay between resonance states and light propagation within the HPWG structure, highlighting its potential for versatile photonic applications.Table 3 presents a comparative analysis of the sensitivity exhibited by the proposed HPWG-based RR structure in contrast to several leading RR sensors across various platforms.
The proposed fabrication method for a HPWG-based RR structure follows steps akin to those in the fabrication processes of certain HPWGs [40] or metal-insulator-siliconinsulator-metal WGs [41].This method leverages materials carefully chosen to enhance overall appeal, particularly in terms of compatibility with standard CMOS microelectronics and photonics technology [42,43].Initially, a conventional SOI wafer undergoes electron beam lithography (EBL) and plasma etching processes to replicate the pattern of the SOI structure.EBL offers a myriad of advantages in the realm of nanofabrication and device manufacturing.Firstly, its unparalleled resolution capability enables the creation of intricate nanostructures with feature sizes down to a few nanometers [44].This precision is invaluable in fields such as semiconductor technology, where miniaturization is a constant pursuit.Secondly, EBL provides exceptional flexibility and versatility, allowing for rapid prototyping and quick design iterations without the need for costly mask fabrication.Furthermore, the direct-write nature of EBL eliminates the constraints imposed by traditional photolithography techniques, enabling the fabrication of non-conventional patterns and complex geometries.
Reactive ion etching (RIE) is a highly precise and controlled process used in semiconductor manufacturing and microfabrication.It involves bombarding a substrate with a directed plasma of reactive ions, typically containing a mixture of gases such as fluorine or chlorine, in a low-pressure environment [45].These reactive ions chemically react with the material on the substrate surface, forming volatile byproducts that are subsequently removed, leaving behind a patterned structure.RIE offers several advantages, including high etch selectivity, excellent anisotropy, and fine-tuned process control.Its ability to etch precise patterns with high aspect ratios makes it indispensable in creating microstructures and integrated circuits with nanometer-scale features.The deposition of the gold layer involves lithography, etching, and liftoff steps.Notably, a process like that described by Kwon [41], involving the partial removal of insulator layers, may also yield satisfactory outcomes and warrants consideration.Subsequently, an additional material (upper cladding) is deposited onto the surface, and a sensing window is prepared where analytes are injected for sensing.

Concluding remarks
In this study, we conducted a comprehensive numerical analysis to explore the impact of geometric parametric variations on the performance of HPWG-based RR structures intended for refractive index sensing applications.The proposed sensor configuration comprises a silicon ring coupled to a bus W G. To create the HPWG architecture, an Au circular disk was incorporated within the silicon ring and enclose it with a Au semi-circular ring, maintaining a nanoscale separation between them.This arrangement ensures a highly confined hybrid mode within the HPWG at its resonance wavelength, resulting in a large redshift as the refractive index of the surrounding medium varies.To enhance sensor performance, optimization of key parameters such as the width of the bus WG, the distance between the bus WG and the ring, the dimensions of the nano-slot, and the width of the ring WG is crucial.Our analysis reveals that sensitivity can be finely tuned, ranging from 176 nm RIU −1 to 316 nm RIU −1 , through the adjustment of the ring WG width, reducing it from 300 nm to 200 nm, respectively.

Figure 1 .
Figure 1.Schematic of a HPWG-based RR structure, (a) 2D representation, (b) 3D representation.The device is covered with upper cladding and a sensing area is created to inject the analytes into it.

Figure 2 .
Figure 2. (a) Line graph along the core of the HPWG versus s, (b) Influence of W ring on the resonance wavelength and field confinement in the ring, (c) transmission spectrum versus s.

Figure 3 .
Figure 3. (a) Influence of confinement in the ring at resonance wavelength versus W bus , (b) Effective refractive index of the bus WG versus W bus , (c) E-field distribution along the un-tapered and tapered segment of the bus WG.

Figure 4 .
Figure 4. Transmission spectrum of the device versus (a) g, (b) R.

Figure 5 .
Figure 5. (a) Transmission spectrum versus varying ambient refractive index, (b) sensitivity of the device versus different values of W ring .

Figure 6 .
Figure 6.Normalized H-field distribution in the HPWG-based sensor at the operational wavelength of, (a) 1528.9 nm, (b) 1544.5 nm.

Table 1 .
Geometric parameters of the HPWG-based RR structure.
ring Width of ring WG 200-250 g Gap between bus WG and ring 100-180 s Nano-slot for HPWG 50-100 R Radius of silicon ring 3000

Table 2 .
Performance indicators of the proposed RR device.

Table 3 .
Sensitivity comparison of the HPWG-based RR structure with the previously proposed RR architectures.