A Coupled Resonator Optical Waveguide-Based Refractive Index Sensor Employing Sagnac Loop Reflectors

A Coupled Resonator Optical Waveguide-Based Refractive Index Sensor Employing Sagnac Loop Reflectors | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article A Coupled Resonator Optical Waveguide-Based Refractive Index Sensor Employing Sagnac Loop Reflectors Muhammad Ali Butt, Bartosz Janaszek This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8253816/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This work presents a silicon-on-insulator (SOI) refractive index sensor based on a coupled resonator optical waveguide (CROW) architecture employing two inversely coupled Sagnac loop reflectors (SLRs) connected through a self-coupled feedback waveguide. The structure exploits bidirectional propagation and discrete–continuum interference to produce sharp Fano-type asymmetric resonances with steep spectral slopes, enabling enhanced wavelength sensitivity. Numerical analysis demonstrates that tuning the loop radius, directional-coupler length, coupling gap, and feedback-path length provides precise control over free spectral range (FSR), resonance asymmetry, and spectral sharpness. The sensor exhibits stable and reproducible resonance shifts for refractive index variations from 1.33 to 1.36, achieving sensitivities between 106 and 120 nm/RIU for the ridge-feedback configuration. Sensitivity is further improved by introducing a subwavelength-grating (SWG) segment into the feedback waveguide, which enhances evanescent-field interaction and increases the overlap factor without compromising compactness or Fano asymmetry. The SWG-assisted design attains sensitivities of 185.8–212.2 nm/RIU, nearly doubling responsivity. The proposed coupled-SLR CROW exhibits strong fabrication tolerance, high Q-factor, and compact footprint, outperforming conventional microring and cascaded resonator sensors in robustness and tunability. These characteristics establish the coupled-SLR and SWG-enhanced CROW as a promising platform for high-resolution, low-limit-of-detection photonic refractive index sensing applications on SOI. Physical sciences/Optics and photonics Physical sciences/Physics Sagnac loop reflector refractive index sensor subwavelength grating silicon-on-insulator coupled resonator optical waveguide Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 1. Introduction Silicon (Si) photonics has emerged as a leading platform for on-chip refractive index sensing due to its CMOS compatibility, high index contrast, and ability to support compact interferometric and resonant structures with strong light–matter interaction[ 1 – 4 ]. Among the various integrated sensing approaches, resonator-based devices such as microring resonators[ 5 , 6 ], Sagnac interferometers[ 7 , 8 ], and cascaded resonant networks[ 9 , 10 ] have received significant attention owing to their high spectral resolution and suitability for label-free biochemical detection. However, many of these architectures suffer from sensitivity limitations, fabrication-induced phase errors, or restricted tunability, which can limit their performance in practical applications requiring high resolution, robustness, and compactness. As sensing requirements continue to advance, there is a growing need for architectures that combine structural simplicity with enhanced field confinement and improved control over spectral response[ 11 , 12 ]. Coupled-resonator optical waveguides (CROWs) have recently gained interest as promising candidates for high-performance refractive index sensing because they leverage multi-cavity interference to achieve sharp resonances and flexible spectral engineering within a small footprint[ 13 , 14 ]. When properly configured, CROW structures can exhibit steep transmission slopes and strong phase sensitivity, attributes that are particularly advantageous for wavelength-interrogated sensors[ 15 ]. Integrating Sagnac loop reflectors (SLRs) into CROW networks further expands their capabilities by enabling bidirectional propagation and discrete-continuum interference, giving rise to Fano-type resonances that enhance detection accuracy[ 16 , 17 ]. These features motivate the exploration of coupled-SLR-based CROW topologies to achieve robust, highly sensitive, and fabrication-tolerant refractive index sensors on the SOI platform[ 18 ]. An important motivation for adopting coupled-SLR with a feedback-loop configuration for refractive-index sensing lies in its inherent fabrication robustness[ 19 ]. Because the resonant cavity is formed through a single, continuous waveguide rather than several fully isolated resonators, random dimensional variations in either SLR section or in the feedback path primarily induce a uniform spectral shift. This behavior avoids distortion of the resonance lineshape. As a result, the distinct spectral characteristics of the device, including the Fano-type asymmetry, remain largely preserved even under typical silicon-on-insulator (SOI) fabrication tolerances. This stability is highly beneficial for sensing applications, as it reduces the need for post-fabrication adjustments and ensures more consistent performance between devices. By contrast, multi-resonator platforms are vulnerable to relative phase errors that can distort the spectral response and lower sensing accuracy[ 20 ]. Furthermore, the high refractive-index contrast (Δn) of the SOI platform facilitates strong optical confinement and compact loop dimensions, while also enabling enhanced evanescent-field interaction through narrow or refractive index-engineered waveguides to increase the overlap factor (Γ) and thereby enhance the wavelength sensitivity [ 21 , 22 ]. Taken together, the compact footprint, tunable lineshape characteristics, and strong tolerance to fabrication variations make this coupled-SLR and feedback-loop architecture an excellent candidate for high-performance refractive-index sensing, especially in wavelength-interrogated operation. In this paper, we proposed a compact sensing platform composed of two inversely coupled Sagnac loop reflectors linked through a feedback waveguide, and we analyze its spectral behavior using finite element method in COMSOL Multiphysics software. We identify the mechanisms governing its Fano-type resonance formation and quantify how key structural parameters influence the free-spectral range, lineshape asymmetry, and extinction characteristics. We further demonstrate that incorporating a subwavelength-grating (SWG) feedback section markedly enhances the refractive-index sensitivity. Together, these results establish a tunable and fabrication-tolerant architecture for high-performance integrated refractive-index sensing. 2. Design and numerical analysis The sensing device is designed on the SOI platform and is based on two inversely coupled Sagnac loop reflectors (denoted as, SLR-1 and SLR-2) connected through a self-coupled feedback waveguide. Each SLR consists of a directional coupler (DC) and a waveguide loop that supports counter-propagating waves. When light enters an SLR, it splits into clockwise and counterclockwise components, which accumulate phase in the loop and then recombine at the same coupler. Their recombination produces wavelength-dependent constructive or destructive interference. By placing two such SLRs in proximity and coupling them through a central DC, the structure creates coherent mixing between the optical fields of the two loops. The resonance itself follows: $$\:m\lambda\:={n}_{eff}{L}_{rt},$$ where L rt is the effective round-trip length including contributions from both SLR loops and the feedback path. Because the cavity behaves as a standing-wave resonator, its free spectral range (FSR) is determined by: $$\:\text{F}\text{S}\text{R}\approx\:\frac{{\lambda\:}^{2}}{{n}_{g}{L}_{rt}},$$ where n g is the group index. In the sensing operation, the SLR loops and the feedback waveguide are exposed to the external analyte. A change in the analyte refractive index modifies the modal effective index (n eff ) through evanescent-field interaction, and thus changes the total round-trip phase accumulated in the coupled cavity. This results in a spectral shift of the resonance, which forms the basis of refractive-index sensing. The wavelength sensitivity is expressed as $$\:{S}_{\lambda\:}=\frac{\varDelta\:\lambda\:}{\varDelta\:n};$$ Where​​ Δλ and Δn denote the change in resonance wavelength and the change in ambient refractive index, respectively. Although a Fano resonance exhibits an asymmetric lineshape due to interference between a discrete state and a continuum, the quality factor (Q-factor) is still defined using the standard resonance-width relation. The Q-factor is expressed as $$\:Q-factor=\frac{{\lambda\:}_{res}}{FWHM}$$ ; Where λ res ​ is the resonance wavelength and FWHM​ is the full width at half maximum of the Fano resonance. It is noteworthy that Fano resonances exhibit intrinsically asymmetric line shapes arising from interference between discrete and continuum modes, and, thus, the conventional symmetric Lorentzian FWHM is not directly applicable. Therefore, following the approach demonstrated in [ 23 ], we define the FWHM as the absolute spectral separation between the dip/resonance \(\:{\lambda\:}_{d}\) and the peak \(\:{\lambda\:}_{p}\) of the given resonance, i.e., \(\:FWHM=\:\left|{\lambda\:}_{d}-{\lambda\:}_{p}\right|\) , which provides a robust and physically meaningful measure of the effective resonance width for strongly asymmetric profiles. The architecture presented in this work is particularly advantageous for refractive-index sensing because it combines high spectral sharpness with low loss. Unlike conventional microring resonators where the standard bus–ring coupling geometry excites predominantly a single propagation direction, the SLR structure inherently generates counter-propagating waves and therefore supports richer bidirectional interference. When two SLRs are coupled, the resulting interference produces strong asymmetric resonances with very steep spectral slopes. These sharp Fano features can significantly enhance practical sensitivity, since even a small resonance shift produces a large transmission change. Furthermore, the feedback waveguide introduces an additional phase parameter that enables flexible resonance tuning without the need of complicated multi-stage structures. Compared with other higher-order filtering architectures, such as cascaded microrings[ 5 , 24 , 25 ], ring-assisted Mach–Zehnder interferometers[ 26 ], or multi SLR chains[ 27 ], this structure achieves comparable spectral control with a significantly smaller footprint and fewer constituent resonators. This reduction in complexity not only simplifies fabrication but also enhances sensing reliability by reducing phase-matching requirements and minimizing cumulative optical loss. To ensure consistent evaluation of the device behavior under variations of loop radius, coupling length, and feedback-path configuration, the geometrical parameters of the coupled-SLR CROW sensor are summarized in Table 1 . These parameters define the fundamental physical layout of the two SLRs, the inter-SLR coupling region, and the feedback waveguide. By systematically adjusting only one parameter at a time while keeping the others fixed within the ranges listed, the study isolates the individual influence of each structural component on resonance asymmetry, free spectral range, and overall spectral performance. This parameterization provides the baseline for all numerical simulations and enables a clear interpretation of the device’s spectral and sensing characteristics. All simulations in this work were carried out using the COMSOL Multiphysics® software package. The electromagnetic response of the device was modeled using the Electromagnetic Waves, Frequency Domain physics interface, which solves Maxwell’s equations in the steady-state frequency regime. A triangular finite-element mesh with a minimum element size of 50 nm was employed to accurately resolve subwavelength features and coupling regions. Scattering boundary conditions were applied at the outer domain to prevent nonphysical reflections and to emulate open-boundaries. A wavelength sweep was performed across the C-band (1530 nm to 1565 nm) to evaluate the transmission characteristics and extract the resonance behavior of the structure. The Si waveguide core and SiO 2 substrate were assigned refractive index values obtained directly from the COMSOL material library. Table 1 Geometric parameters of the device used in this study Parameter Expression Value R Radius of Sagnac loop 2 µm to 5 µm g The gap between the waveguides, and also the gap between the two SLRs 125 nm to 200 nm L DC Length of the directional coupler 2 µm to 9 µm W Width of the waveguide 400 nm L f Length of the feedback waveguide π×(R×5 + L DC + g – W) C-band Operational wavelength range 1530 nm to 1565 nm 3. Device optimization Figure 2 (a-d) presents the simulated transmission spectra of the coupled-SLR CROW structure for different SLR radii (R), while maintaining a fixed directional-coupler length L DC =5 µm and a uniform coupling gap of g = 150 nm. Four cases are examined, corresponding to R = 2, 3, 4, and 5 µm, with the feedback-waveguide length L f appropriately adjusted in each configuration to ensure efficient phase interaction within the composite cavity. As the loop radius increases, the overall round-trip optical length (L rt ) of the device which includes contributions from both SLR loops, the feedback path, and the directional couplers, also increases. The longer round-trip path leads to a systematic reduction in the free spectral range (FSR), resulting in a denser distribution of spectral resonances within the wavelength window. In the simulated structures, the FSR decreases from approximately 4.3 nm to 2.1 nm as R increases from 2 µm to 5 µm. The corresponding analytical predictions range from 4.67 nm to 2.14 nm. These results indicate percentage deviations of about 7.9% at R = 2 µm and 1.9% at R = 5 µm between the numerical and analytical calculations. In all four cases, the device preserves a high-contrast Fano-type lineshape in the vicinity of each resonance. This asymmetric spectral response originates from the interference between discrete resonance pathways supported by the Sagnac loops and the quasi-broadband pathway enabled through the central coupling section and the feedback waveguide. Because L DC and g are kept constant for all configurations, the coupling strength between waveguides remains nearly identical, isolating the effect of increased loop perimeter as the dominant mechanism governing changes in spectral characteristics. The observed increase in resonance density with larger R therefore directly reflects the longer accumulated phase per round-trip rather than variations in coupling efficiency. Furthermore, the persistence of the Fano asymmetry across all loop radii highlights the structural robustness of the coupled-SLR configuration. Even as the cavity size grows, constructive and destructive interference among counter-propagating fields within each SLR, together with the feedback-mediated mixing between the loops, yields similarly sharp spectral features. These steep resonance slopes are advantageous for refractive-index sensing, as they enhance wavelength-shift detectability and enable high-resolution measurements. Figure 3 (a-f) shows the simulated transmission spectra of the coupled-SLR CROW structure for different directional-coupler lengths (L DC )​, while keeping the loop radius fixed at R = 3 µm and the coupling gap at g = 150 nm. Six values of L DC ​ are investigated: 9, 8, 6, 5, 3, and 2 µm, with corresponding feedback-waveguide lengths L f​ adjusted to maintain phase matching within the composite cavity. A clear evolution of the spectral response is observed as L DC ​ is varied. When L DC is relatively long, as in Fig. 3 (a), the resonance profile becomes more symmetric and the characteristic Fano asymmetry is significantly diminished. This indicates that the extended coupling region suppresses the phase imbalance between the discrete resonant path and the broadband background pathway. As L DC ​ decreases, the interference between these pathways strengthens, leading to increasingly asymmetric Fano resonances. The most pronounced Fano lineshape appears when L DC ​=2 µm to 6 µm, as seen in Fig. 3 (c)-(f), where the transmission exhibits sharp asymmetric dips with steep slopes. Throughout Fig. 3 , the free spectral range (FSR) remains nearly unchanged, since the total round-trip length is dominated by the fixed loop perimeter and the feedback-waveguide section, while variations in L DC contribute only marginally to L rt ​. Thus, the primary effect of changing L DC is not resonance-spacing modification but lineshape control. These results demonstrate that L DC acts as an effective tuning parameter for engineering spectral asymmetry and resonance sharpness. In particular, shorter coupler lengths enable stronger Fano interference, offering steeper resonance slopes advantageous for high-resolution refractive-index sensing. Figure 4 investigates how a uniform change of the coupling gap (g) across all three coupling regions (the two SLR directional couplers and the inter-SLR coupling section) modifies the transmission response of the coupled-SLR CROW. For the smallest gaps, g = 125 nm in Fig. 4 (a) and g = 150 nm in Fig. 4 (b), the evanescent overlap is strong, enabling efficient loading of the resonant pathway and appreciable mixing with the broadband transmission channel. Under these conditions, the spectrum displays pronounced Fano resonances: asymmetric line profiles with steep slopes and high extinction (13 dB to 25.5 dB), including the characteristic double-dip structure that arises from two interference solutions (two hybridized resonant conditions) within one free-spectral interval. The asymmetry and depth here indicate that both the discrete (cavity) and continuum (bus/feedback) pathways contribute comparably, maximizing the interference contrast. As the gap (g) increases to 175 nm (Fig. 4 (c)) and further to 200 nm (Fig. 4 (d)), the coupling weakens across all sections, which suppresses the discrete–continuum interference responsible for Fano lineshapes. Consequently, the spectral response transitions to more symmetric, weakly modulated features (and eventually to near-flat transmission), with the earlier double-dip behavior disappearing. In this weak-coupling regime, only a small fraction of the field is coupled into the resonant loop and inter-SLR mixing is minimal; the response is therefore dominated by the broadband path rather than by interference between comparable channels. Figure 5 illustrates the influence of the feedback-waveguide length (L f ) on the spectral response of the coupled-SLR CROW device. Because the Sagnac-loop radius, coupling gap, and directional-coupler length are held constant, variation in L f becomes the dominant mechanism for modifying the overall round-trip optical length (L rt )​. An increase in L f introduces additional phase accumulation in each circulation cycle, resulting in a systematic shift of the resonance positions. This behavior stems from the fact that the resonance condition is determined by the total accumulated round-trip phase, so modifying only the feedback-path length changes the phase balance between the discrete SLR-mediated resonant pathway and the broadband transmission channel. A direct consequence of increasing L f is a reduction in the device’s FSR. Because the FSR is inversely proportional to the round-trip optical length, Δλ ≈ λ 2 /(ng​L rt ​), a longer feedback waveguide increases L rt ​and causes adjacent resonances to move closer together. This trend is clearly evidenced in Figs. 5 (a–d): as L f ​ increases from 52.6 µm to 64.6 µm, the resonances become progressively more closely packed, with the spacing between adjacent peaks shrinking from approximately 2.4 nm to 1.9 nm, reflecting the reduction in FSR associated with the increased round-trip optical path length. Importantly, although the resonance positions shift and the FSR contracts, the characteristic asymmetric (Fano-type) line shape is preserved throughout the sweep, demonstrating that Fano interference remains strong even as the round-trip phase is modulated. This phase sensitivity highlights the role of the feedback path as a tunable degree of freedom that enables fine spectral engineering without modifying the SLR geometry or coupling interfaces. Overall, varying L f provides a straightforward means of adjusting both the spectral period and the resonance bias of the coupled-SLR cavity. The ability to engineer the FSR by modifying only the feedback-path length is advantageous for applications requiring specific resonance spacing or wavelength targeting, while retaining steep asymmetric features ensures that high-resolution refractive-index sensing performance is maintained. Figure 6 (a) correlates the device transmission spectrum with the spatial field evolution inside the coupled-SLR CROW at selected excitation wavelengths. The positions at which the field distributions are extracted are marked on the spectral curve and displayed in Figs. 6 (b–f). At λ = 1548.7 nm, shown in Fig. 6 (b), the device operates off-resonance and the optical field predominantly follows the bus/feedback path, with only weak energy coupling into the SLR cavities. As the excitation wavelength approaches the asymmetric Fano feature, namely λ = 1549.6 nm, 1550.8 nm, and 1552.0 nm, corresponding to Figs. 6 (c), 6(d), and 6(e), respectively pronounced field localization is observed exclusively in the SLR-1. Across these three cases, negligible field buildup is seen in SLR-2, indicating that only a single resonant pathway contributes significantly to the scattering process. This asymmetric excitation condition, combined with the broadband transmission channel provided by the feedback waveguide, underpins the formation of the characteristic Fano lineshape. When the wavelength detunes further from resonance to λ = 1552.8 nm, illustrated in Fig. 5 (f), the optical field no longer remains confined within the SLR-1 and instead returns to the direct propagation path, resulting in high transmission. Collectively, these field maps verify that under the examined biasing conditions, the SLR-1 acts as the dominant resonant element, while SLR-2 plays only a minor role. The interaction between this single-cavity resonant channel and the continuum-like transmission through the bus/feedback path gives rise to the observed Fano interference and associated spectral asymmetry. Figure 7 (a) illustrates the transmission spectra of the coupled-SLR-based CROW sensor for refractive indices ranging from n = 1.33 to n = 1.36, while Fig. 7 (b) quantifies the corresponding resonance-wavelength shifts for eight characteristic dips (Dip-1 → Dip-8). A clear and systematic red shift of the resonance minima is observed with increasing ambient refractive index, confirming that the optical mode exhibits strong evanescent-field interaction with the external analyte. The preservation of the distinct Fano-type asymmetric lineshape throughout the refractive-index variation indicates stable interference between the discrete resonant channel supported primarily by one SLR and the broadband transmission channel through the feedback waveguide. This robustness under perturbation demonstrates that the coupled-SLR configuration maintains spectral integrity and high-Q resonance even when the surrounding refractive index changes, a key attribute for high-precision refractometric sensing. Quantitatively, the linear fits in Fig. 7 (b) yield sensitivities (S = Δλ/Δn) of 106.4, 113.6, 110, 116.4, 110, 120, 115.7, and 120 nm/RIU for Dips 1 to 8, respectively. These values indicate a narrow variation range, demonstrating stable and reproducible phase modulation across multiple resonance orders. The slight fluctuation in sensitivity among different dips can be attributed to localized dispersion effects and variations in effective confinement of the counter-propagating modes within the coupled loops. The nearly linear dependence of resonance wavelength on refractive index for all eight modes validates the device’s operation in the perturbative regime, where Δλ ∝ Δn. This linearity simplifies sensor calibration and ensures predictable performance over the operating range. Moreover, the comparable slopes among successive dips confirm uniform phase accumulation and negligible modal mismatch between the SLRs and the feedback path. To further validate the sensing performance of the proposed system, we determined the changes in relevant parameters, i.e., modulation depth, FWHM, and Q-factor, as the refractive index of the surrounding medium increases. To better illustrate overall performance, we calculated the arithmetic average and standard deviation (SD) of those values for all observable resonances in the considered spectral range (Fig. 8 ). The proposed system exhibits clear and monotonic changes in its spectral characteristics with increasing refractive index of the surrounding medium, confirming its suitability for refractive-index sensing. A gradual decrease in modulation depth suggests a weaker guiding of resonance wavelengths, while the simultaneous narrowing of the FWHM leads to a corresponding increase in the Q-factor. This combination indicates that although the signal contrast weakens slightly, the resonance itself becomes sharper and more spectrally well-defined, improving the precision with which wavelength shifts can be detected. Overall, the observed trends demonstrate a robust and consistent optical response, supporting the applicability of this structure for sensitive and reliable refractive-index sensing. 4. Sensitivity enhancement mechanism Figure 9 illustrates the CROW sensor incorporating SLRs with a modified feedback waveguide based on a subwavelength-grating (SWG) segment. In the 3-D view (Fig. 9 a) and corresponding planar schematic (Fig. 9 b), the two SLRs remain interconnected through the feedback path, but the conventional strip-waveguide section is replaced with a periodic SWG structure. This engineered segment provides an additional degree of refractive-index tunability through its enhanced modal interaction with the external medium while maintaining phase continuity within the coupled cavity. The SWG section comprises periodically arranged silicon segments with pitch Λ = 250 nm. This subwavelength periodicity enables the guided mode to experience an effective refractive index lower than that of a solid strip waveguide, increasing the accessible evanescent field. As a result, changes in the analyte refractive index induce larger modal-index perturbations in the feedback branch, providing improved sensitivity without altering the SLR geometry or coupler interfaces. Figure 9 (c) presents the simulated transverse electric-field distribution (E x ) within the SWG feedback segment at 1550 nm. Strong field penetration into the cladding is observed, confirming that the periodic structure supports high-fraction evanescent interaction. By embedding the SWG only within the feedback path, the device simultaneously preserves the sharp asymmetric spectral response originating from the SLR-based coupled cavity and enhances refractive-index responsivity through engineered phase accumulation. Figure 10 (a) shows the simulated transmission spectra of the coupled-SLR CROW sensor employing a subwavelength-grating (SWG) feedback waveguide for refractive indices from n = 1.33 to 1.36. The SWG section enhances the evanescent-field interaction in the feedback branch by lowering the core’s effective index and increasing field penetration into the cladding. As the surrounding refractive index rises, the resonance dips exhibit pronounced red shifts, larger than those in the ridge-feedback design, confirming improved modal sensitivity. The characteristic Fano-type asymmetry is retained across the sensing range, indicating that the periodic SWG does not disrupt the discrete–continuum interference but rather amplifies the refractive-index–induced phase modulation within the cavity. Figure 10 (b) further quantifies this enhancement. The extracted sensitivities range from 185.8 to 212.2 nm/RIU, nearly twice those of the ridge-feedback device (106–120 nm/RIU). This improvement arises from the increased effective-index contrast and higher overlap factor (Γ) provided by the SWG segment, which boosts the phase-modulation efficiency. The parallel slopes of the linear fits confirm uniform field confinement and consistent phase accumulation across all resonances. The linear λ–n dependence demonstrates that the device remains within the perturbative regime, ensuring accurate and repeatable refractive-index tracking. Overall, the SWG-assisted feedback configuration achieves substantial sensitivity enhancement through passive structural engineering while preserving the compact footprint and sharp Fano lineshape of the coupled-SLR cavity. This design nearly doubles the refractive-index responsivity, validating the SWG-integrated CROW as a promising platform for high-resolution, low-LoD photonic sensing on SOI. To fully investigate the sensing performance, we analyze the average and standard deviation of modulation depth, FWHM, and Q-factor of all resonances in the considered spectral range in the Figure. 11, similarly to the previous sensor configuration. The SWG-based system exhibits consistent and monotonic variations in its key spectral parameters with changes in the surrounding refractive index, indicating enhanced suitability for refractive-index sensing. Compared to the earlier configuration, the modulation depth is lower, but remains more stable across the investigated RI range, indicating better retention of signal contrast. Similarly to the previous case, the FWHM exhibits a gradual narrowing trend, which in turn contributes to an overall increase in the Q-factor, yielding sharper and more spectrally defined resonances. Importantly, this design also achieves a higher sensitivity, expressed in nm/RIU, enabling more pronounced resonance shifts in response to small variations in refractive index. Together, these changes demonstrate that the modified system may provide a more responsive and precise platform for refractive-index sensing. To contextualize the performance of the proposed coupled-SLR CROW sensor, Table 2 summarizes recent refractive-index sensors reported across different photonic platforms, including Si₃N₄, SOI, and hybrid plasmonic waveguides. The comparison highlights key performance metrics such as wavelength sensitivity, Q-factor, fabrication complexity, and limit of detection (LoD). Conventional microring and SWG-based resonators can achieve high sensitivity but often require stringent fabrication tolerances or complex geometries. In contrast, the coupled-SLR CROW devices introduced in this work offer competitive sensitivity with significantly reduced structural complexity and improved tolerance to fabrication variations. This comparison underscores the advantage of the proposed architecture in balancing sensitivity, robustness, and design simplicity. Table 2 Performance comparison of refractive-index sensors based on various integrated photonic platforms and resonator architectures. Material platform Device structure Sensitivity (nm/RIU) Q-factor Numerical/ Experimental Fabrication challenges Ref. Si 3 N 4 Ring resonator with slot waveguide 70 750 Numerical High [ 28 ] SOI Hybrid dual slot SWG ring resonator 1005 22,429 Numerical High [ 29 ] SOI SWG ring resonator 1012 1219 Numerical High [ 30 ] SOI Ring resonator 120 10 5 Numerical Low [ 6 ] Hybrid plasmonic SWG Racetrack resonator 377.1 to 477.7 312.8 to 346.5 Numerical High [ 31 ] Hybrid plasmonic MZI 160 - Experimental High [ 32 ] Si 3 N 4 Resonant cavity 201.5 to 341.5 3.9×10 4 Experimental Moderate [ 15 ] SOI CROW 106.4 to 120 3835.8 to 7842.1 Numerical Low This work SOI CROW 185.8 to 212.2 1910.8 to 3790.2 Numerical Moderate This work 5. Conclusion A compact and highly sensitive refractive index sensor based on a coupled-resonator optical waveguide (CROW) employing Sagnac loop reflectors (SLRs) on a silicon-on-insulator (SOI) platform has been designed and numerically analyzed. The coupled-SLR configuration, enhanced with a feedback loop, provides strong phase control and supports Fano-type asymmetric resonances with steep spectral slopes, thereby enabling precise detection of refractive index variations. A systematic investigation of structural parameters, including loop radius, coupling length, and feedback-path length, demonstrated their distinct influence on resonance asymmetry, free spectral range, and overall spectral performance. The sensor achieves stable operation with sensitivities exceeding 100 nm/RIU and average Quality factor above 5000 in the ridge-feedback configuration while maintaining excellent fabrication tolerance and reproducibility. Incorporation of a subwavelength-grating (SWG) feedback segment further enhances evanescent-field interaction, achieving sensitivities up to ~ 212 nm/RIU and an average Quality factor exceeding 2500 without increasing the device footprint or complexity. The SWG-assisted CROW architecture therefore combines high sensitivity, tunability, and structural robustness within a simple, monolithic layout. These findings confirm the potential of coupled-SLR CROW devices as an efficient and scalable solution for high-resolution refractometric sensing. The demonstrated phase engineering approach and Fano-resonance control can be further extended to multi-parameter biosensing, temperature-compensated detection, and integrated photonic systems requiring compact, high-performance spectral filtering. Declarations Acknowledgement The authors acknowledge the constant support of Warsaw University of Technology in the completion of this work. Disclosures The authors declare no conflicts of interest. Ethical Approval This study did not involve human participants, live vertebrates, or any biological material requiring ethical approval. Therefore, ethical approval was not applicable. Consent to Participate Not applicable, as this study did not involve human participants. Competing interests N/A Authors’ Contributions: Conceptualization – M.A.B; Methodology – M.A.B; Validation – M.A.B. and B.J.; Formal Analysis – M.A.B; Investigation – M.A.B. and B.J.; Writing – Original Draft – M.A.B; Writing – Review & Editing – M.A.B. and B.J; Supervision – M.A.B. Acknowledgement The authors acknowledge the constant support of Warsaw University of Technology in the completion of this work. Funding N/A Availability of data and materials The data supporting the findings in this work are available from the corresponding author with a reasonable request. Consent to Publish Not applicable, as this study did not involve human participants or identifiable data. References Ariannejad, M.M.; Akbari, E.; Hanafi, E. Silicon Sub-Wavelength Grating Resonator Structures for Gas Sensor. Superlattices and Microstructures 2020 , 142 , 106506, doi:10.1016/j.spmi.2020.106506. 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Micromachines 2024 , 15 , 610, doi:10.3390/mi15050610. Sun, X.; Thylén, L.; Wosinski, L. Hollow Hybrid Plasmonic Mach–Zehnder Sensor. Opt. Lett., OL 2017 , 42 , 807–810, doi:10.1364/OL.42.000807. Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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1","display":"","copyAsset":false,"role":"figure","size":147903,"visible":true,"origin":"","legend":"\u003cp\u003e(a) 3D representation, (b) 2D representation, of CROW-based sensor employing SLRs.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-8253816/v1/0b076de58c34711cc0304878.png"},{"id":97506342,"identity":"c18ffd40-80c7-43b1-b5dc-a6bdb256ed1f","added_by":"auto","created_at":"2025-12-05 08:21:02","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":136082,"visible":true,"origin":"","legend":"\u003cp\u003eTransmission spectrum of the coupled-SLRs, (a) R=2 µm, L\u003csub\u003ef\u003c/sub\u003e = 46.32 µm, (b) R=3 µm, L\u003csub\u003ef\u003c/sub\u003e =62.02 µm, (c) R=4 µm, L\u003csub\u003ef\u003c/sub\u003e =77.72 µm, (d) R=5 µm, L\u003csub\u003ef\u003c/sub\u003e =93.42 µm.\u0026nbsp; Note: L\u003csub\u003eDC\u003c/sub\u003e=5 µm, g=150 nm.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-8253816/v1/8fd0ae55ea594baa312eebc5.png"},{"id":97670700,"identity":"1828390d-2668-4ae5-b004-c4a8f1f4d199","added_by":"auto","created_at":"2025-12-08 09:31:11","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":214175,"visible":true,"origin":"","legend":"\u003cp\u003eTransmission spectrum of the coupled-SLRs, (a) L\u003csub\u003eDC\u003c/sub\u003e=9 µm, L\u003csub\u003ef\u003c/sub\u003e = 74.6 µm, (b) L\u003csub\u003eDC\u003c/sub\u003e=8 µm, L\u003csub\u003ef\u003c/sub\u003e =71.4 µm, (c) L\u003csub\u003eDC\u003c/sub\u003e=6 µm, L\u003csub\u003ef\u003c/sub\u003e =65.2 µm, (d) L\u003csub\u003eDC\u003c/sub\u003e=5 µm, L\u003csub\u003ef\u003c/sub\u003e =62 µm, (e) L\u003csub\u003eDC\u003c/sub\u003e=3 µm, L\u003csub\u003ef\u003c/sub\u003e =55.74 µm (f) L\u003csub\u003eDC\u003c/sub\u003e=2 µm, L\u003csub\u003ef\u003c/sub\u003e =52.6 µm. Note: R=3 µm, g=150 nm.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-8253816/v1/683bb7e761c5119fc193d015.png"},{"id":97506347,"identity":"420a2ba6-e807-408b-a6c7-2aa276432e25","added_by":"auto","created_at":"2025-12-05 08:21:02","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":144299,"visible":true,"origin":"","legend":"\u003cp\u003eTransmission spectrum of the coupled-SLRs, (a) g=125 nm, (b) g=150 nm, (c) g=175 nm, (d) g=200 nm. Note: R=3 µm, L\u003csub\u003eDC\u003c/sub\u003e=2 µm and L\u003csub\u003ef\u003c/sub\u003e=52.6 µm.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-8253816/v1/2dd9994488e04d6e02539789.png"},{"id":97670699,"identity":"8485ac6a-bad1-46d6-bd28-68ccbde88400","added_by":"auto","created_at":"2025-12-08 09:31:11","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":200706,"visible":true,"origin":"","legend":"\u003cp\u003eTransmission spectrum of the coupled-SLRs, (a) L\u003csub\u003ef\u003c/sub\u003e=52.6 µm, (b) L\u003csub\u003ef\u003c/sub\u003e=56.6 µm, (c) L\u003csub\u003ef\u003c/sub\u003e=60.6 µm, (d) L\u003csub\u003ef\u003c/sub\u003e=64.6 µm. Note: R=3 µm, L\u003csub\u003eDC\u003c/sub\u003e=2 µm and g=150 nm.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-8253816/v1/ce2e7776771cc859db7bb831.png"},{"id":97506351,"identity":"9c3b8b74-24db-43c5-9775-a01ece66b1c2","added_by":"auto","created_at":"2025-12-05 08:21:02","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":195022,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Transmission spectrum of the coupled-SLRs. Norm. E-field distribution in the device for operational wavelength of, (b) 1548.7 nm, (c) 1549.6 nm, (d) 1550.8 nm, (e) 1552 nm, (f) 1552.8 nm.\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-8253816/v1/95db2846df16bed48ad1f69a.png"},{"id":97671438,"identity":"80defd2a-b097-4350-b77d-54f6f9f9264e","added_by":"auto","created_at":"2025-12-08 09:32:37","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":71673,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Transmission spectrum of the coupled SLRs with ridge feedback waveguide for n=1.33 to 1.36, (b) Resonance wavelength versus refractive index plot for Dip-1 to Dip-8.\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-8253816/v1/c8f0bc8696fc6a76657ca6bd.png"},{"id":97506353,"identity":"cddec4a1-2f94-46b0-bb24-ae3fae7c7e28","added_by":"auto","created_at":"2025-12-05 08:21:02","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":62637,"visible":true,"origin":"","legend":"\u003cp\u003eAverage (dots) and standard deviation (vertical lines) values of modulation depth (a), FWHM (b), and Q-factor (c) plotted vs. refractive index for all considered resonances in the coupled SLRs with ridge feedback waveguide.\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-8253816/v1/2eaa06f725e2997b20ce87fa.png"},{"id":97506356,"identity":"47d15f3b-10e7-4842-b11f-9b47cb4c3236","added_by":"auto","created_at":"2025-12-05 08:21:02","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":184218,"visible":true,"origin":"","legend":"\u003cp\u003e(a) 3D representation, (b) 2D representation, of CROW-based sensor employing SLRs with feedback SWG waveguide, (c) E\u003csub\u003ex\u003c/sub\u003e-field distribution in the SWG waveguide segment (Λ = 250 nm) at 1550 nm, illustrating the optimized configuration employed in the feedback waveguide.\u003c/p\u003e","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-8253816/v1/8ec23499d68c08ab1788ec97.png"},{"id":97506357,"identity":"aa3b4f08-3cc0-45b9-9c85-435898156f96","added_by":"auto","created_at":"2025-12-05 08:21:02","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":63353,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Transmission spectrum of the coupled SLRs with SWG feedback waveguide for n=1.33 to 1.36, (b) Resonance wavelength versus refractive index plot for Dip-1 to Dip-8.\u003c/p\u003e","description":"","filename":"10.png","url":"https://assets-eu.researchsquare.com/files/rs-8253816/v1/512a7d1c75e9b2dc9026607b.png"},{"id":97506359,"identity":"8a5ccb46-7e54-4470-8271-2232327b45df","added_by":"auto","created_at":"2025-12-05 08:21:02","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":63810,"visible":true,"origin":"","legend":"\u003cp\u003eAverage (dots) and standard deviation (vertical lines) values of modulation depth (a), FWHM (b), and Q-factor (c) plotted vs. refractive index for all considered resonances in the coupled SLRs with SWG feedback waveguide.\u003c/p\u003e","description":"","filename":"11.png","url":"https://assets-eu.researchsquare.com/files/rs-8253816/v1/2906a50e89415e9e1bc4e335.png"},{"id":99315590,"identity":"16a30f0a-36fe-4435-a84a-e14138f0927e","added_by":"auto","created_at":"2025-12-31 16:27:06","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2031229,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8253816/v1/569ea29a-497d-441e-907c-aed38aa7f8cf.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A Coupled Resonator Optical Waveguide-Based Refractive Index Sensor Employing Sagnac Loop Reflectors","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eSilicon (Si) photonics has emerged as a leading platform for on-chip refractive index sensing due to its CMOS compatibility, high index contrast, and ability to support compact interferometric and resonant structures with strong light\u0026ndash;matter interaction[\u003cspan additionalcitationids=\"CR2 CR3\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. Among the various integrated sensing approaches, resonator-based devices such as microring resonators[\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e], Sagnac interferometers[\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e], and cascaded resonant networks[\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e] have received significant attention owing to their high spectral resolution and suitability for label-free biochemical detection. However, many of these architectures suffer from sensitivity limitations, fabrication-induced phase errors, or restricted tunability, which can limit their performance in practical applications requiring high resolution, robustness, and compactness. As sensing requirements continue to advance, there is a growing need for architectures that combine structural simplicity with enhanced field confinement and improved control over spectral response[\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eCoupled-resonator optical waveguides (CROWs) have recently gained interest as promising candidates for high-performance refractive index sensing because they leverage multi-cavity interference to achieve sharp resonances and flexible spectral engineering within a small footprint[\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. When properly configured, CROW structures can exhibit steep transmission slopes and strong phase sensitivity, attributes that are particularly advantageous for wavelength-interrogated sensors[\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. Integrating Sagnac loop reflectors (SLRs) into CROW networks further expands their capabilities by enabling bidirectional propagation and discrete-continuum interference, giving rise to Fano-type resonances that enhance detection accuracy[\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. These features motivate the exploration of coupled-SLR-based CROW topologies to achieve robust, highly sensitive, and fabrication-tolerant refractive index sensors on the SOI platform[\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eAn important motivation for adopting coupled-SLR with a feedback-loop configuration for refractive-index sensing lies in its inherent fabrication robustness[\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. Because the resonant cavity is formed through a single, continuous waveguide rather than several fully isolated resonators, random dimensional variations in either SLR section or in the feedback path primarily induce a uniform spectral shift. This behavior avoids distortion of the resonance lineshape. As a result, the distinct spectral characteristics of the device, including the Fano-type asymmetry, remain largely preserved even under typical silicon-on-insulator (SOI) fabrication tolerances. This stability is highly beneficial for sensing applications, as it reduces the need for post-fabrication adjustments and ensures more consistent performance between devices. By contrast, multi-resonator platforms are vulnerable to relative phase errors that can distort the spectral response and lower sensing accuracy[\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. Furthermore, the high refractive-index contrast (Δn) of the SOI platform facilitates strong optical confinement and compact loop dimensions, while also enabling enhanced evanescent-field interaction through narrow or refractive index-engineered waveguides to increase the overlap factor (Γ) and thereby enhance the wavelength sensitivity [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. Taken together, the compact footprint, tunable lineshape characteristics, and strong tolerance to fabrication variations make this coupled-SLR and feedback-loop architecture an excellent candidate for high-performance refractive-index sensing, especially in wavelength-interrogated operation.\u003c/p\u003e\u003cp\u003eIn this paper, we proposed a compact sensing platform composed of two inversely coupled Sagnac loop reflectors linked through a feedback waveguide, and we analyze its spectral behavior using finite element method in COMSOL Multiphysics software. We identify the mechanisms governing its Fano-type resonance formation and quantify how key structural parameters influence the free-spectral range, lineshape asymmetry, and extinction characteristics. We further demonstrate that incorporating a subwavelength-grating (SWG) feedback section markedly enhances the refractive-index sensitivity. Together, these results establish a tunable and fabrication-tolerant architecture for high-performance integrated refractive-index sensing.\u003c/p\u003e"},{"header":"2. Design and numerical analysis","content":"\u003cp\u003eThe sensing device is designed on the SOI platform and is based on two inversely coupled Sagnac loop reflectors (denoted as, SLR-1 and SLR-2) connected through a self-coupled feedback waveguide. Each SLR consists of a directional coupler (DC) and a waveguide loop that supports counter-propagating waves. When light enters an SLR, it splits into clockwise and counterclockwise components, which accumulate phase in the loop and then recombine at the same coupler. Their recombination produces wavelength-dependent constructive or destructive interference. By placing two such SLRs in proximity and coupling them through a central DC, the structure creates coherent mixing between the optical fields of the two loops. The resonance itself follows:\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:m\\lambda\\:={n}_{eff}{L}_{rt},$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003ewhere L\u003csub\u003ert\u003c/sub\u003e is the effective round-trip length including contributions from both SLR loops and the feedback path. Because the cavity behaves as a standing-wave resonator, its free spectral range (FSR) is determined by:\u003cdiv id=\"Equb\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equb\" name=\"EquationSource\"\u003e\n$$\\:\\text{F}\\text{S}\\text{R}\\approx\\:\\frac{{\\lambda\\:}^{2}}{{n}_{g}{L}_{rt}},$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003ewhere n\u003csub\u003eg\u003c/sub\u003e is the group index.\u003c/p\u003e\u003cp\u003eIn the sensing operation, the SLR loops and the feedback waveguide are exposed to the external analyte. A change in the analyte refractive index modifies the modal effective index (n\u003csub\u003eeff\u003c/sub\u003e) through evanescent-field interaction, and thus changes the total round-trip phase accumulated in the coupled cavity. This results in a spectral shift of the resonance, which forms the basis of refractive-index sensing. The wavelength sensitivity is expressed as\u003cdiv id=\"Equc\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equc\" name=\"EquationSource\"\u003e\n$$\\:{S}_{\\lambda\\:}=\\frac{\\varDelta\\:\\lambda\\:}{\\varDelta\\:n};$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eWhere​​ Δλ and Δn denote the change in resonance wavelength and the change in ambient refractive index, respectively. Although a Fano resonance exhibits an asymmetric lineshape due to interference between a discrete state and a continuum, the quality factor (Q-factor) is still defined using the standard resonance-width relation. The Q-factor is expressed as\u003cdiv id=\"Equd\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equd\" name=\"EquationSource\"\u003e\n$$\\:Q-factor=\\frac{{\\lambda\\:}_{res}}{FWHM}$$\u003c/div\u003e\u003c/div\u003e;\u003c/p\u003e\u003cp\u003eWhere λ\u003csub\u003eres\u003c/sub\u003e​ is the resonance wavelength and FWHM​ is the full width at half maximum of the Fano resonance. It is noteworthy that Fano resonances exhibit intrinsically asymmetric line shapes arising from interference between discrete and continuum modes, and, thus, the conventional symmetric Lorentzian FWHM is not directly applicable. Therefore, following the approach demonstrated in [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e], we define the FWHM as the absolute spectral separation between the dip/resonance \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\lambda\\:}_{d}\\)\u003c/span\u003e\u003c/span\u003e and the peak \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\lambda\\:}_{p}\\)\u003c/span\u003e\u003c/span\u003e of the given resonance, i.e., \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:FWHM=\\:\\left|{\\lambda\\:}_{d}-{\\lambda\\:}_{p}\\right|\\)\u003c/span\u003e\u003c/span\u003e, which provides a robust and physically meaningful measure of the effective resonance width for strongly asymmetric profiles.\u003c/p\u003e\u003cp\u003eThe architecture presented in this work is particularly advantageous for refractive-index sensing because it combines high spectral sharpness with low loss. Unlike conventional microring resonators where the standard bus\u0026ndash;ring coupling geometry excites predominantly a single propagation direction, the SLR structure inherently generates counter-propagating waves and therefore supports richer bidirectional interference. When two SLRs are coupled, the resulting interference produces strong asymmetric resonances with very steep spectral slopes. These sharp Fano features can significantly enhance practical sensitivity, since even a small resonance shift produces a large transmission change. Furthermore, the feedback waveguide introduces an additional phase parameter that enables flexible resonance tuning without the need of complicated multi-stage structures. Compared with other higher-order filtering architectures, such as cascaded microrings[\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e, \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e], ring-assisted Mach\u0026ndash;Zehnder interferometers[\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e], or multi SLR chains[\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e], this structure achieves comparable spectral control with a significantly smaller footprint and fewer constituent resonators. This reduction in complexity not only simplifies fabrication but also enhances sensing reliability by reducing phase-matching requirements and minimizing cumulative optical loss.\u003c/p\u003e\u003cp\u003eTo ensure consistent evaluation of the device behavior under variations of loop radius, coupling length, and feedback-path configuration, the geometrical parameters of the coupled-SLR CROW sensor are summarized in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. These parameters define the fundamental physical layout of the two SLRs, the inter-SLR coupling region, and the feedback waveguide. By systematically adjusting only one parameter at a time while keeping the others fixed within the ranges listed, the study isolates the individual influence of each structural component on resonance asymmetry, free spectral range, and overall spectral performance. This parameterization provides the baseline for all numerical simulations and enables a clear interpretation of the device\u0026rsquo;s spectral and sensing characteristics.\u003c/p\u003e\u003cp\u003eAll simulations in this work were carried out using the COMSOL Multiphysics\u0026reg; software package. The electromagnetic response of the device was modeled using the Electromagnetic Waves, Frequency Domain physics interface, which solves Maxwell\u0026rsquo;s equations in the steady-state frequency regime. A triangular finite-element mesh with a minimum element size of 50 nm was employed to accurately resolve subwavelength features and coupling regions. Scattering boundary conditions were applied at the outer domain to prevent nonphysical reflections and to emulate open-boundaries. A wavelength sweep was performed across the C-band (1530 nm to 1565 nm) to evaluate the transmission characteristics and extract the resonance behavior of the structure. The Si waveguide core and SiO\u003csub\u003e2\u003c/sub\u003e substrate were assigned refractive index values obtained directly from the COMSOL material library.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eGeometric parameters of the device used in this study\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"3\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eParameter\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eExpression\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eValue\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eR\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eRadius of Sagnac loop\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e2 \u0026micro;m to 5 \u0026micro;m\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eg\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eThe gap between the waveguides, and also the gap between the two SLRs\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e125 nm to 200 nm\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eL\u003csub\u003eDC\u003c/sub\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eLength of the directional coupler\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e2 \u0026micro;m to 9 \u0026micro;m\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eW\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eWidth of the waveguide\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e400 nm\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eL\u003csub\u003ef\u003c/sub\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eLength of the feedback waveguide\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eπ\u0026times;(R\u0026times;5\u0026thinsp;+\u0026thinsp;L\u003csub\u003eDC\u003c/sub\u003e + g \u0026ndash; W)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eC-band\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eOperational wavelength range\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e1530 nm to 1565 nm\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e"},{"header":"3. Device optimization","content":"\u003cp\u003eFigure \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e (a-d) presents the simulated transmission spectra of the coupled-SLR CROW structure for different SLR radii (R), while maintaining a fixed directional-coupler length L\u003csub\u003eDC\u003c/sub\u003e=5 \u0026micro;m and a uniform coupling gap of g\u0026thinsp;=\u0026thinsp;150 nm. Four cases are examined, corresponding to R\u0026thinsp;=\u0026thinsp;2, 3, 4, and 5 \u0026micro;m, with the feedback-waveguide length L\u003csub\u003ef\u003c/sub\u003e appropriately adjusted in each configuration to ensure efficient phase interaction within the composite cavity. As the loop radius increases, the overall round-trip optical length (L\u003csub\u003ert\u003c/sub\u003e) of the device which includes contributions from both SLR loops, the feedback path, and the directional couplers, also increases. The longer round-trip path leads to a systematic reduction in the free spectral range (FSR), resulting in a denser distribution of spectral resonances within the wavelength window. In the simulated structures, the FSR decreases from approximately 4.3 nm to 2.1 nm as R increases from 2 \u0026micro;m to 5 \u0026micro;m. The corresponding analytical predictions range from 4.67 nm to 2.14 nm. These results indicate percentage deviations of about 7.9% at R\u0026thinsp;=\u0026thinsp;2 \u0026micro;m and 1.9% at R\u0026thinsp;=\u0026thinsp;5 \u0026micro;m between the numerical and analytical calculations.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eIn all four cases, the device preserves a high-contrast Fano-type lineshape in the vicinity of each resonance. This asymmetric spectral response originates from the interference between discrete resonance pathways supported by the Sagnac loops and the quasi-broadband pathway enabled through the central coupling section and the feedback waveguide. Because L\u003csub\u003eDC\u003c/sub\u003e and g are kept constant for all configurations, the coupling strength between waveguides remains nearly identical, isolating the effect of increased loop perimeter as the dominant mechanism governing changes in spectral characteristics. The observed increase in resonance density with larger R therefore directly reflects the longer accumulated phase per round-trip rather than variations in coupling efficiency.\u003c/p\u003e\u003cp\u003eFurthermore, the persistence of the Fano asymmetry across all loop radii highlights the structural robustness of the coupled-SLR configuration. Even as the cavity size grows, constructive and destructive interference among counter-propagating fields within each SLR, together with the feedback-mediated mixing between the loops, yields similarly sharp spectral features. These steep resonance slopes are advantageous for refractive-index sensing, as they enhance wavelength-shift detectability and enable high-resolution measurements.\u003c/p\u003e\u003cp\u003eFigure \u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e (a-f) shows the simulated transmission spectra of the coupled-SLR CROW structure for different directional-coupler lengths (L\u003csub\u003eDC\u003c/sub\u003e)​, while keeping the loop radius fixed at R\u0026thinsp;=\u0026thinsp;3 \u0026micro;m and the coupling gap at g\u0026thinsp;=\u0026thinsp;150 nm. Six values of L\u003csub\u003eDC\u003c/sub\u003e ​ are investigated: 9, 8, 6, 5, 3, and 2 \u0026micro;m, with corresponding feedback-waveguide lengths L\u003csub\u003ef​\u003c/sub\u003e adjusted to maintain phase matching within the composite cavity. A clear evolution of the spectral response is observed as L\u003csub\u003eDC\u003c/sub\u003e ​ is varied. When L\u003csub\u003eDC\u003c/sub\u003e is relatively long, as in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e(a), the resonance profile becomes more symmetric and the characteristic Fano asymmetry is significantly diminished. This indicates that the extended coupling region suppresses the phase imbalance between the discrete resonant path and the broadband background pathway. As L\u003csub\u003eDC\u003c/sub\u003e ​ decreases, the interference between these pathways strengthens, leading to increasingly asymmetric Fano resonances. The most pronounced Fano lineshape appears when L\u003csub\u003eDC\u003c/sub\u003e​=2 \u0026micro;m to 6 \u0026micro;m, as seen in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e (c)-(f), where the transmission exhibits sharp asymmetric dips with steep slopes.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThroughout Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, the free spectral range (FSR) remains nearly unchanged, since the total round-trip length is dominated by the fixed loop perimeter and the feedback-waveguide section, while variations in L\u003csub\u003eDC\u003c/sub\u003e contribute only marginally to L\u003csub\u003ert\u003c/sub\u003e​. Thus, the primary effect of changing L\u003csub\u003eDC\u003c/sub\u003e is not resonance-spacing modification but lineshape control. These results demonstrate that L\u003csub\u003eDC\u003c/sub\u003e acts as an effective tuning parameter for engineering spectral asymmetry and resonance sharpness. In particular, shorter coupler lengths enable stronger Fano interference, offering steeper resonance slopes advantageous for high-resolution refractive-index sensing.\u003c/p\u003e\u003cp\u003eFigure \u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e investigates how a uniform change of the coupling gap (g) across all three coupling regions (the two SLR directional couplers and the inter-SLR coupling section) modifies the transmission response of the coupled-SLR CROW. For the smallest gaps, g\u0026thinsp;=\u0026thinsp;125 nm in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e(a) and g\u0026thinsp;=\u0026thinsp;150 nm in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e(b), the evanescent overlap is strong, enabling efficient loading of the resonant pathway and appreciable mixing with the broadband transmission channel. Under these conditions, the spectrum displays pronounced Fano resonances: asymmetric line profiles with steep slopes and high extinction (13 dB to 25.5 dB), including the characteristic double-dip structure that arises from two interference solutions (two hybridized resonant conditions) within one free-spectral interval. The asymmetry and depth here indicate that both the discrete (cavity) and continuum (bus/feedback) pathways contribute comparably, maximizing the interference contrast.\u003c/p\u003e\u003cp\u003eAs the gap (g) increases to 175 nm (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e(c)) and further to 200 nm (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e(d)), the coupling weakens across all sections, which suppresses the discrete\u0026ndash;continuum interference responsible for Fano lineshapes. Consequently, the spectral response transitions to more symmetric, weakly modulated features (and eventually to near-flat transmission), with the earlier double-dip behavior disappearing. In this weak-coupling regime, only a small fraction of the field is coupled into the resonant loop and inter-SLR mixing is minimal; the response is therefore dominated by the broadband path rather than by interference between comparable channels.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eFigure \u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e illustrates the influence of the feedback-waveguide length (L\u003csub\u003ef\u003c/sub\u003e) on the spectral response of the coupled-SLR CROW device. Because the Sagnac-loop radius, coupling gap, and directional-coupler length are held constant, variation in L\u003csub\u003ef\u003c/sub\u003e becomes the dominant mechanism for modifying the overall round-trip optical length (L\u003csub\u003ert\u003c/sub\u003e)​. An increase in L\u003csub\u003ef\u003c/sub\u003e introduces additional phase accumulation in each circulation cycle, resulting in a systematic shift of the resonance positions. This behavior stems from the fact that the resonance condition is determined by the total accumulated round-trip phase, so modifying only the feedback-path length changes the phase balance between the discrete SLR-mediated resonant pathway and the broadband transmission channel.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eA direct consequence of increasing L\u003csub\u003ef\u003c/sub\u003e is a reduction in the device\u0026rsquo;s FSR. Because the FSR is inversely proportional to the round-trip optical length, Δλ\u0026thinsp;\u0026asymp;\u0026thinsp;λ\u003csup\u003e2\u003c/sup\u003e/(ng​L\u003csub\u003ert\u003c/sub\u003e​), a longer feedback waveguide increases L\u003csub\u003ert\u003c/sub\u003e ​and causes adjacent resonances to move closer together. This trend is clearly evidenced in Figs.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e(a\u0026ndash;d): as L\u003csub\u003ef\u003c/sub\u003e​ increases from 52.6 \u0026micro;m to 64.6 \u0026micro;m, the resonances become progressively more closely packed, with the spacing between adjacent peaks shrinking from approximately 2.4 nm to 1.9 nm, reflecting the reduction in FSR associated with the increased round-trip optical path length. Importantly, although the resonance positions shift and the FSR contracts, the characteristic asymmetric (Fano-type) line shape is preserved throughout the sweep, demonstrating that Fano interference remains strong even as the round-trip phase is modulated. This phase sensitivity highlights the role of the feedback path as a tunable degree of freedom that enables fine spectral engineering without modifying the SLR geometry or coupling interfaces. Overall, varying L\u003csub\u003ef\u003c/sub\u003e provides a straightforward means of adjusting both the spectral period and the resonance bias of the coupled-SLR cavity. The ability to engineer the FSR by modifying only the feedback-path length is advantageous for applications requiring specific resonance spacing or wavelength targeting, while retaining steep asymmetric features ensures that high-resolution refractive-index sensing performance is maintained.\u003c/p\u003e\u003cp\u003eFigure \u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e(a) correlates the device transmission spectrum with the spatial field evolution inside the coupled-SLR CROW at selected excitation wavelengths. The positions at which the field distributions are extracted are marked on the spectral curve and displayed in Figs.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e(b\u0026ndash;f). At \u003cb\u003eλ\u003c/b\u003e\u0026thinsp;=\u0026thinsp;1548.7 nm, shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e(b), the device operates off-resonance and the optical field predominantly follows the bus/feedback path, with only weak energy coupling into the SLR cavities. As the excitation wavelength approaches the asymmetric Fano feature, namely λ\u0026thinsp;=\u0026thinsp;1549.6 nm, 1550.8 nm, and 1552.0 nm, corresponding to Figs.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e(c), 6(d), and 6(e), respectively pronounced field localization is observed exclusively in the SLR-1. Across these three cases, negligible field buildup is seen in SLR-2, indicating that only a single resonant pathway contributes significantly to the scattering process. This asymmetric excitation condition, combined with the broadband transmission channel provided by the feedback waveguide, underpins the formation of the characteristic Fano lineshape. When the wavelength detunes further from resonance to λ\u0026thinsp;=\u0026thinsp;1552.8 nm, illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e(f), the optical field no longer remains confined within the SLR-1 and instead returns to the direct propagation path, resulting in high transmission. Collectively, these field maps verify that under the examined biasing conditions, the SLR-1 acts as the dominant resonant element, while SLR-2 plays only a minor role. The interaction between this single-cavity resonant channel and the continuum-like transmission through the bus/feedback path gives rise to the observed Fano interference and associated spectral asymmetry.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eFigure \u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e(a) illustrates the transmission spectra of the coupled-SLR-based CROW sensor for refractive indices ranging from n\u0026thinsp;=\u0026thinsp;1.33 to n\u0026thinsp;=\u0026thinsp;1.36, while Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e(b) quantifies the corresponding resonance-wavelength shifts for eight characteristic dips (Dip-1 \u0026rarr; Dip-8). A clear and systematic red shift of the resonance minima is observed with increasing ambient refractive index, confirming that the optical mode exhibits strong evanescent-field interaction with the external analyte. The preservation of the distinct Fano-type asymmetric lineshape throughout the refractive-index variation indicates stable interference between the discrete resonant channel supported primarily by one SLR and the broadband transmission channel through the feedback waveguide. This robustness under perturbation demonstrates that the coupled-SLR configuration maintains spectral integrity and high-Q resonance even when the surrounding refractive index changes, a key attribute for high-precision refractometric sensing.\u003c/p\u003e\u003cp\u003eQuantitatively, the linear fits in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e(b) yield sensitivities (S\u0026thinsp;=\u0026thinsp;Δλ/Δn) of 106.4, 113.6, 110, 116.4, 110, 120, 115.7, and 120 nm/RIU for Dips 1 to 8, respectively. These values indicate a narrow variation range, demonstrating stable and reproducible phase modulation across multiple resonance orders. The slight fluctuation in sensitivity among different dips can be attributed to localized dispersion effects and variations in effective confinement of the counter-propagating modes within the coupled loops. The nearly linear dependence of resonance wavelength on refractive index for all eight modes validates the device\u0026rsquo;s operation in the perturbative regime, where Δλ \u0026prop; Δn. This linearity simplifies sensor calibration and ensures predictable performance over the operating range. Moreover, the comparable slopes among successive dips confirm uniform phase accumulation and negligible modal mismatch between the SLRs and the feedback path.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eTo further validate the sensing performance of the proposed system, we determined the changes in relevant parameters, i.e., modulation depth, FWHM, and Q-factor, as the refractive index of the surrounding medium increases. To better illustrate overall performance, we calculated the arithmetic average and standard deviation (SD) of those values for all observable resonances in the considered spectral range (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e). The proposed system exhibits clear and monotonic changes in its spectral characteristics with increasing refractive index of the surrounding medium, confirming its suitability for refractive-index sensing. A gradual decrease in modulation depth suggests a weaker guiding of resonance wavelengths, while the simultaneous narrowing of the FWHM leads to a corresponding increase in the Q-factor. This combination indicates that although the signal contrast weakens slightly, the resonance itself becomes sharper and more spectrally well-defined, improving the precision with which wavelength shifts can be detected. Overall, the observed trends demonstrate a robust and consistent optical response, supporting the applicability of this structure for sensitive and reliable refractive-index sensing.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e"},{"header":"4. Sensitivity enhancement mechanism","content":"\u003cp\u003eFigure \u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e illustrates the CROW sensor incorporating SLRs with a modified feedback waveguide based on a subwavelength-grating (SWG) segment. In the 3-D view (Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003ea) and corresponding planar schematic (Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003eb), the two SLRs remain interconnected through the feedback path, but the conventional strip-waveguide section is replaced with a periodic SWG structure. This engineered segment provides an additional degree of refractive-index tunability through its enhanced modal interaction with the external medium while maintaining phase continuity within the coupled cavity.\u003c/p\u003e\u003cp\u003eThe SWG section comprises periodically arranged silicon segments with pitch Λ\u0026thinsp;=\u0026thinsp;250 nm. This subwavelength periodicity enables the guided mode to experience an effective refractive index lower than that of a solid strip waveguide, increasing the accessible evanescent field. As a result, changes in the analyte refractive index induce larger modal-index perturbations in the feedback branch, providing improved sensitivity without altering the SLR geometry or coupler interfaces. Figure\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e(c) presents the simulated transverse electric-field distribution (E\u003csub\u003ex\u003c/sub\u003e) within the SWG feedback segment at 1550 nm. Strong field penetration into the cladding is observed, confirming that the periodic structure supports high-fraction evanescent interaction. By embedding the SWG only within the feedback path, the device simultaneously preserves the sharp asymmetric spectral response originating from the SLR-based coupled cavity and enhances refractive-index responsivity through engineered phase accumulation.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eFigure \u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e(a) shows the simulated transmission spectra of the coupled-SLR CROW sensor employing a subwavelength-grating (SWG) feedback waveguide for refractive indices from n\u0026thinsp;=\u0026thinsp;1.33 to 1.36. The SWG section enhances the evanescent-field interaction in the feedback branch by lowering the core\u0026rsquo;s effective index and increasing field penetration into the cladding. As the surrounding refractive index rises, the resonance dips exhibit pronounced red shifts, larger than those in the ridge-feedback design, confirming improved modal sensitivity. The characteristic Fano-type asymmetry is retained across the sensing range, indicating that the periodic SWG does not disrupt the discrete\u0026ndash;continuum interference but rather amplifies the refractive-index\u0026ndash;induced phase modulation within the cavity.\u003c/p\u003e\u003cp\u003eFigure \u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e(b) further quantifies this enhancement. The extracted sensitivities range from 185.8 to 212.2 nm/RIU, nearly twice those of the ridge-feedback device (106\u0026ndash;120 nm/RIU). This improvement arises from the increased effective-index contrast and higher overlap factor (Γ) provided by the SWG segment, which boosts the phase-modulation efficiency. The parallel slopes of the linear fits confirm uniform field confinement and consistent phase accumulation across all resonances. The linear λ\u0026ndash;n dependence demonstrates that the device remains within the perturbative regime, ensuring accurate and repeatable refractive-index tracking. Overall, the SWG-assisted feedback configuration achieves substantial sensitivity enhancement through passive structural engineering while preserving the compact footprint and sharp Fano lineshape of the coupled-SLR cavity. This design nearly doubles the refractive-index responsivity, validating the SWG-integrated CROW as a promising platform for high-resolution, low-LoD photonic sensing on SOI.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eTo fully investigate the sensing performance, we analyze the average and standard deviation of modulation depth, FWHM, and Q-factor of all resonances in the considered spectral range in the Figure. 11, similarly to the previous sensor configuration. The SWG-based system exhibits consistent and monotonic variations in its key spectral parameters with changes in the surrounding refractive index, indicating enhanced suitability for refractive-index sensing. Compared to the earlier configuration, the modulation depth is lower, but remains more stable across the investigated RI range, indicating better retention of signal contrast. Similarly to the previous case, the FWHM exhibits a gradual narrowing trend, which in turn contributes to an overall increase in the Q-factor, yielding sharper and more spectrally defined resonances. Importantly, this design also achieves a higher sensitivity, expressed in nm/RIU, enabling more pronounced resonance shifts in response to small variations in refractive index. Together, these changes demonstrate that the modified system may provide a more responsive and precise platform for refractive-index sensing.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eTo contextualize the performance of the proposed coupled-SLR CROW sensor, Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e summarizes recent refractive-index sensors reported across different photonic platforms, including Si₃N₄, SOI, and hybrid plasmonic waveguides. The comparison highlights key performance metrics such as wavelength sensitivity, Q-factor, fabrication complexity, and limit of detection (LoD). Conventional microring and SWG-based resonators can achieve high sensitivity but often require stringent fabrication tolerances or complex geometries. In contrast, the coupled-SLR CROW devices introduced in this work offer competitive sensitivity with significantly reduced structural complexity and improved tolerance to fabrication variations. This comparison underscores the advantage of the proposed architecture in balancing sensitivity, robustness, and design simplicity.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003ePerformance comparison of refractive-index sensors based on various integrated photonic platforms and resonator architectures.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"7\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMaterial platform\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eDevice structure\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eSensitivity (nm/RIU)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eQ-factor\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eNumerical/\u003c/p\u003e\u003cp\u003eExperimental\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003eFabrication challenges\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c7\"\u003e\u003cp\u003eRef.\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSi\u003csub\u003e3\u003c/sub\u003eN\u003csub\u003e4\u003c/sub\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eRing resonator with slot waveguide\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e70\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e750\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eNumerical\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eHigh\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e[\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSOI\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eHybrid dual slot SWG ring resonator\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e1005\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e22,429\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eNumerical\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eHigh\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e[\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSOI\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eSWG ring resonator\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e1012\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e1219\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eNumerical\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eHigh\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e[\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSOI\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eRing resonator\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e120\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e10\u003csup\u003e5\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eNumerical\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eLow\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e[\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eHybrid plasmonic\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eSWG Racetrack resonator\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e377.1 to 477.7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e312.8 to 346.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eNumerical\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eHigh\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e[\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e]\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eHybrid plasmonic\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eMZI\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e160\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eExperimental\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eHigh\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e[\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e]\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSi\u003csub\u003e3\u003c/sub\u003eN\u003csub\u003e4\u003c/sub\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eResonant cavity\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e201.5 to 341.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e3.9\u0026times;10\u003csup\u003e4\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eExperimental\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eModerate\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e[\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSOI\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eCROW\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e106.4 to 120\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e3835.8 to 7842.1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eNumerical\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eLow\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003eThis work\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSOI\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eCROW\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e185.8 to 212.2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e1910.8 to 3790.2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eNumerical\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eModerate\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003eThis work\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e"},{"header":"5. Conclusion","content":"\u003cp\u003eA compact and highly sensitive refractive index sensor based on a coupled-resonator optical waveguide (CROW) employing Sagnac loop reflectors (SLRs) on a silicon-on-insulator (SOI) platform has been designed and numerically analyzed. The coupled-SLR configuration, enhanced with a feedback loop, provides strong phase control and supports Fano-type asymmetric resonances with steep spectral slopes, thereby enabling precise detection of refractive index variations. A systematic investigation of structural parameters, including loop radius, coupling length, and feedback-path length, demonstrated their distinct influence on resonance asymmetry, free spectral range, and overall spectral performance.\u003c/p\u003e\u003cp\u003eThe sensor achieves stable operation with sensitivities exceeding 100 nm/RIU and average Quality factor above 5000 in the ridge-feedback configuration while maintaining excellent fabrication tolerance and reproducibility. Incorporation of a subwavelength-grating (SWG) feedback segment further enhances evanescent-field interaction, achieving sensitivities up to ~\u0026thinsp;212 nm/RIU and an average Quality factor exceeding 2500 without increasing the device footprint or complexity. The SWG-assisted CROW architecture therefore combines high sensitivity, tunability, and structural robustness within a simple, monolithic layout.\u003c/p\u003e\u003cp\u003eThese findings confirm the potential of coupled-SLR CROW devices as an efficient and scalable solution for high-resolution refractometric sensing. The demonstrated phase engineering approach and Fano-resonance control can be further extended to multi-parameter biosensing, temperature-compensated detection, and integrated photonic systems requiring compact, high-performance spectral filtering.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAcknowledgement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors acknowledge the constant support of Warsaw University of Technology in the completion of this work.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eDisclosures\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare no conflicts of interest.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEthical Approval\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis study did not involve human participants, live vertebrates, or any biological material requiring ethical approval. Therefore, ethical approval was not applicable.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent to Participate\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable, as this study did not involve human participants.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eN/A\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthors\u0026rsquo; Contributions:\u003c/strong\u003e\u003cbr\u003eConceptualization \u0026ndash; M.A.B; Methodology \u0026ndash; M.A.B; Validation \u0026ndash; M.A.B. and B.J.; Formal Analysis \u0026ndash; M.A.B; Investigation \u0026ndash; M.A.B. and B.J.; Writing \u0026ndash; Original Draft \u0026ndash; M.A.B; Writing \u0026ndash; Review \u0026amp; Editing \u0026ndash; M.A.B. and B.J; Supervision \u0026ndash; M.A.B.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors acknowledge the constant support of Warsaw University of Technology in the completion of this work.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eN/A\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAvailability of data and materials\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe data supporting the findings in this work are available from the corresponding author with a reasonable request.\u003c/p\u003e\n\u003cp\u003e\u003cu\u003e\u003cstrong\u003eConsent to Publish\u003c/strong\u003e\u003c/u\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable, as this study did not involve human participants or identifiable data.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eAriannejad, M.M.; Akbari, E.; Hanafi, E. 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Lett., OL\u003c/em\u003e \u003cstrong\u003e2017\u003c/strong\u003e, \u003cem\u003e42\u003c/em\u003e, 807\u0026ndash;810, doi:10.1364/OL.42.000807.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Sagnac loop reflector, refractive index sensor, subwavelength grating, silicon-on-insulator, coupled resonator optical waveguide","lastPublishedDoi":"10.21203/rs.3.rs-8253816/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8253816/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis work presents a silicon-on-insulator (SOI) refractive index sensor based on a coupled resonator optical waveguide (CROW) architecture employing two inversely coupled Sagnac loop reflectors (SLRs) connected through a self-coupled feedback waveguide. The structure exploits bidirectional propagation and discrete\u0026ndash;continuum interference to produce sharp Fano-type asymmetric resonances with steep spectral slopes, enabling enhanced wavelength sensitivity. Numerical analysis demonstrates that tuning the loop radius, directional-coupler length, coupling gap, and feedback-path length provides precise control over free spectral range (FSR), resonance asymmetry, and spectral sharpness. The sensor exhibits stable and reproducible resonance shifts for refractive index variations from 1.33 to 1.36, achieving sensitivities between 106 and 120 nm/RIU for the ridge-feedback configuration. Sensitivity is further improved by introducing a subwavelength-grating (SWG) segment into the feedback waveguide, which enhances evanescent-field interaction and increases the overlap factor without compromising compactness or Fano asymmetry. The SWG-assisted design attains sensitivities of 185.8\u0026ndash;212.2 nm/RIU, nearly doubling responsivity. The proposed coupled-SLR CROW exhibits strong fabrication tolerance, high Q-factor, and compact footprint, outperforming conventional microring and cascaded resonator sensors in robustness and tunability. These characteristics establish the coupled-SLR and SWG-enhanced CROW as a promising platform for high-resolution, low-limit-of-detection photonic refractive index sensing applications on SOI.\u003c/p\u003e","manuscriptTitle":"A Coupled Resonator Optical Waveguide-Based Refractive Index Sensor Employing Sagnac Loop Reflectors","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-12-05 08:20:57","doi":"10.21203/rs.3.rs-8253816/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"9ef3b62f-40f4-4866-821a-82860eebb194","owner":[],"postedDate":"December 5th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":59111878,"name":"Physical sciences/Optics and photonics"},{"id":59111879,"name":"Physical sciences/Physics"}],"tags":[],"updatedAt":"2025-12-29T10:24:30+00:00","versionOfRecord":[],"versionCreatedAt":"2025-12-05 08:20:57","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8253816","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8253816","identity":"rs-8253816","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}