Electromagnetic skyrmions in a deep-subwavelength plasmonic resonator for vitro diabetic nephropathy diagnostic

Electromagnetic skyrmions in a deep-subwavelength plasmonic resonator for vitro diabetic nephropathy diagnostic | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 26 October 2025 V1 Latest version Share on Electromagnetic skyrmions in a deep-subwavelength plasmonic resonator for vitro diabetic nephropathy diagnostic Authors : Tian Shuo Bai , Meng Jia , Wan Zhu Wang , Xuanru Zhang 0000-0002-3179-9279 , Siqi Han , and T. J. Cui [email protected] Authors Info & Affiliations https://doi.org/10.22541/au.176150026.64108205/v1 Published Advanced Functional Materials Version of record Peer review timeline 234 views 178 downloads Contents Abstract Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract Microwave resonance sensors integrated in an ultra-compact planar circuit enable real-time and label-free biosensing, offering significant potentials for in-vitro diagnostics and home healthcare. However, the detection of weak biological signals at low concentrations has fundamental limitation due to large disparity between the microwave wavelength and molecular scale of biomolecules. Here, we realize an electromagnetic (EM) skyrmion mode in a microwave plasmonic resonator with an electrical size of 1/50 wavelength. The combination of strong EM field confinement and high quality factor of 185 yields markedly enhanced wave-matter interactions, resulting in a 105-fold sensitivity improvement over the traditional microstrip ring resonator operating at the same frequency. The sensing capability is experimentally validated through the detection of diabetic nephropathy (DN), with a reporting limit for DN-associated proteins down to 12.5 pmol in amount of substance and 125 nmol/L in concentration at an operating wavelength of 0.33m. These findings constitute a major advance in microwave resonance sensing, dramatically advancing its detection limits and paving a way for rapid and early diagnostic platforms in integrated systems. Introduction Electromagnetic (EM) resonance sensing technology enables real-time, label-free biosensing across a wide range of frequencies, from microwave to optical [1-5]. The fundamental principle depends on the strong interaction between EM waves and matter, converting microscopic dielectric variations caused by the biological events, such as antibody-antigen binding [6-8], exosome binding [9, 10], cell proliferation, apoptosis, and carcinogenesis [11-13], into macroscopic and detectable shifts or splits in resonance frequency. Among these sensors, microwave resonance sensors offer abundant potentials for miniaturized and functional sensing systems in the internet of things due to their high systematic integration, excellent environmental robustness, and low cost [14-16]. The configurations of conventional microwave resonance sensors encompass the split-ring resonators [17, 18], spiral resonators [19, 20], and interdigital resonators [21]. However, they face challenges in detecting minuscule biological signals, particularly in scenarios like early disease diagnosis. Conventional microwave resonance units with large electric sizes exhibit poor sensitivity due to the EM radiation into free space, which weakens the interaction between EM waves and matter, as well as reduces the quality factor (Q-factor). Additionally, compressing the physical size of the resonators for miniaturized integration increases the challenge of detecting minuscule biological signals amidst environmental noise due to the rise in operating frequency. The emergency of spoof localized surface plasmons (SLSP) provides an effective route to detect extremely weak sensing signals with ultra-compact circuit integration, and as experimentally verified in some scenarios such as sub-micromolar glucose sensing [22] and deep-subwavelength scatterer detection [23]. The classic SLSP patterns in microwaves include toroidal-shaped and spiral-shaped structures, which mimic the physical properties of optical localized surface plasmons, featuring strong EM enhancement, deep-subwavelength EM confinement, and high Q-factor resonance [24-26]. Driven by flexible tunability and diverse configurations of artificial metal structures [27], recent advances in constructing novel EM resonance modes have garnered significant interest for their enhanced sensing capabilities, including localized hotspots [28], quasi-bound states in the continuum [29, 30], and non-Hermitian exceptional points [23, 31]. Spiral-shaped SLSPs can also support EM skyrmions, which are topologically stable three-dimensional vector field configurations. It has been reported that EM skyrmions can compress resonances into deep-subwavelength sizes smaller than 1/100 wavelength [32, 33], hence enhancing the interaction between EM waves and matter at extreme EM dimensions and boosting sensing sensitivity. Hence, EM skyrmions open the avenue for the multifunctional and miniaturized sensing explorations in microwaves, including complex permittivity measurement [34], micro-displacement sensing [35], and biological macromolecules detection [22]. Here, we investigate the use of microwave EM skyrmion for in vitro diagnosis. Figure 1. Conceptual illustration of the proposed vitro diagnostic sensor. (a) Photograph of the proposed sensor, highlighting its advantages such as miniaturized structure, label-free sensing, rapid and sensitive detection, and the potential for early disease diagnosis. (b) The sensing detection process involves converting biological binding signals into microwave frequency shift signals. (c) The structure of the EM skyrmion sensor consists of an excited microstrip line, SLSP resonance unit, and a hole on the ground plane. (d) The electric field vectors (E) and magnitude distributions (|E|) of the fundamental skyrmion mode. Early disease diagnosis is of significant medical importance, as it enables timely intervention, slows disease progression, and reduces the clinical and economic burden on patients [36]. Achieving early disease diagnosis faces two primary challenges: 1) develop non-invasive, label-free, and highly sensitive detection technologies for the rapid identification of disease markers; and 2) select appropriate disease markers that offer good specificity and can be easily extracted from human secretions, such as urine and sweat. Here, we take diabetic nephropathy (DN) as an example. For detection techniques, renal biopsy is considered the diagnostic gold standard and invaluable for precise diagnosis and prognosis in glomerular diseases. Its invasive nature, technical complexity, potential bleeding risk, and turnaround time of 1-3 days make it impractical for routine screening [37]. At present, the clinical assessment of DN primarily relies on the measurement of albumin excretion rate (AER) and estimated glomerular filtration rate (eGFR), both of which predominantly indicate glomerular injury [38]. However, AER, despite being a widely accepted diagnostic parameter, often becomes elevated only during the later stages of DN when substantial renal impairment has already occurred. Moreover, a subset of diabetic individuals may present with normal AER values despite having underlying renal dysfunction [38]. Likewise, eGFR estimations derived from serum creatinine (SCR) are subject to variability due to influencing factors such as individual muscle mass, dietary intake, and the specific estimation formula applied, which can reduce diagnostic accuracy, particularly in diverse patient populations, such as those with type 2 diabetes [38]. Hence, it is imperative to develop a reliable set of in vitro diagnostic tools for early disease diagnosis. Here, we propose an in vitro diagnostic sensor utilizing the EM skyrmion supported by the deep-subwavelength SLSP with an electrical size of λ 0 /50 (where λ 0 is the operating wavelength) in the microwave frequency, as shown in Figure 1 . The proposed sensor combines the real-time, label-free merits of microwave resonance sensing technology with the deep-wavelength confinement, enhanced wave-matter interaction properties of the EM skyrmion mode. Hence, the proposed sensor enables rapid and sensitive detection with the ultra-compact circuit integration, offering significant potential for early disease diagnosis, as shown in Figures 1a and b. The sensing capability of the proposed sensor is experimentally verified in defining DN. Cytoskeleton-Associated Protein 4 (CKAP4) is classified as a type II transmembrane protein, composed of an intracellular N-terminal domain, a single-span transmembrane segment, and a C-terminal domain located extracellularly. It is predominantly localized to the endoplasmic reticulum and participates in a variety of intracellular biological processes. Recent evidence has demonstrated that CKAP4 expression is markedly elevated in vascular smooth muscle cells under conditions of chronic kidney disease. This upregulation contributes to the progression of vascular calcification by regulating Yes-associated protein signaling pathways and facilitating calcium ion influx [39]. Notably, vascular calcification, defined by ectopic calcium accumulation within the vascular wall, has been identified as a critical early pathological event in the development of DN. Therefore, we selected anti-cytoskeleton-associated protein 4 (Anti-CKAP4) as the antibody, while the antigen CKAP4 is extracted from the urinary extracellular vesicles (uEVs). The uEVs encapsulate various biomolecules that reflect the pathophysiological state of the kidneys and can be separated from patients’ urine using wheat germ agglutinin (WGA)- coupled magnetic beads. The reporting limit for antigen reaches 12.5 pmol in amount of substance and 125 nmol/L in concentration at an operating wavelength of 0.33 m, representing a significant advancement of microwave resonance sensing technology in early clinical disease screening. Meanwhile, the reporting limit is sensitive enough for various biomedical diagnostic markers. Our results offer valuable insights for the next generation of ultra-compact sensing systems, enabling sensitive and portable solutions for in vitro diagnostic and home healthcare. Deep-subwavelength EM skyrmion sensor Guided wave excitation of the EM skyrmion plays an important role in large-scale planar integration [33]. Unlike plasmonic skyrmion interference-based methods, which necessitate tailored external illuminations for momentum matching [40-42], our proposed EM skyrmion sensor integrates into planar circuits with an SLSP resonance unit and an excited microstrip line, as shown in Figure 1c. The electric field vectors (E) and magnitude (|E|) distributions of the fundamental EM skyrmion used for biosensing are demonstrated in Figure 1d. Figure 2 shows the basic properties of our proposed EM skyrmion sensor. The SLSP resonance unit is composed of a metal spiral arm and a central circular patch with a diameter of 0.6 mm, as shown in Figure 2a. The spiral arm is 0.15 mm wide and follows the Archimedes spiral equation x ( t ) = r∙t∙ cos( t ) and y ( t ) = r∙t∙ sin( t ). The parameter t determines the starting and ending positions of the spiral arm, and t ranges from 0 to 65. The SLSP resonance unit is excited by a 50 Ω microstrip line with a width of w = 1.34 mm from the side. A hole with a diameter of D = 8 mm placed on the ground plane results in a more symmetric field distribution and higher sensitivity [22]. The dielectric substrate is F4B with a thickness of 0.5 mm, a permittivity of 2.65, and a loss tangent of 0.001. The thickness of all metal patterns of the EM skyrmion sensor is 35 μm. Unlike plasmonic skyrmions in optics, which support only a single mode at a specific frequency [43,44], EM skyrmions in microwaves can support multiple resonance modes with nearly equidistant resonance frequencies [32, 33]. Figure 2b shows the simulated reflection (S 11 ) and transmission (S 21 ) spectra of the proposed EM skyrmion sensor, showing a train of deeply subwavelength resonances at equally-spaced frequencies, f 0 , f 0 + Δ f , f 0 + 2Δ f , f 0 + 3Δ f …, where, f 0 and Δ f are the fundamental resonance frequency and free spectral range, respectively. Figure 2c shows a linear relationship between the resonance frequencies and skyrmion modes, also demonstrating nearly equidistant skyrmion resonances. The insets in Figure 2b show the vector configurations of electric field distribution for different skyrmion modes ( m = 1, 2, 3, 4), along with the magnetic field (H), electric field (E), and surface current (J) distributions for the fundamental mode at the z = 0.5 mm plane. The EM skyrmions are rotationally symmetric and independent of azimuth. The vector distributions of the electric field indicate that the vector fields rotate in integer multiples of a π-twist from the center to the periphery along the radial direction, demonstrating multiple π-twist skyrmion configurations (For details, see Supplementary Note 1). For sensing applications in the detection of minuscule biological signals, two key indicators are primarily focused on: Q-factor and figure of merit (FoM). High Q-factor is expected to enhance sensing sensitivity, while the FoM dictates the ease of sensing and detection [45]. The Q-factor is defined as Q = f 0 /Δ f FWHM , where f 0 represents the resonance frequency and Δ f FWHM represents the full width at half maximum (FWHM). The FoM is defined as FoM = Q × δI, which evaluates the excitation, where δI represents the excitation efficiency, corresponding to the dip in S 21 , as shown in Figure 2a. Figure 2d shows the Q-factors and the FoMs of different skyrmion modes, with the fundamental mode resonance exhibiting the highest Q-factor of 184.6 and FoM of 134.8. We further investigate the electric field and magnetic field magnitude distributions for different skyrmion modes along the radial direction, as shown in Figures 2e and f. Compared to the higher-order modes ( m ≥ 2), the fundamental mode exhibits a larger maximum field magnitude, as shown in Figure 2g, which is expected to enhance wave-matter interactions and sensing sensitivity. Figure 2. Mode analysis of the proposed EM skyrmion sensor. (a) Structure of the proposed EM skyrmion sensor. (b) Simulated reflection (S 11 ) and transmission (S 21 ) spectra of the proposed EM skyrmion sensor. The insets show the vector configurations of electric field distribution for different skyrmion modes ( m = 1, 2, 3, 4), along with the magnetic field (H), electric field (E), and surface current (J) distributions for the fundamental mode at the z = 0.5 mm plane. (c) Multiple skyrmion modes with near-equidistant resonance frequencies. (d) Comparison of Q-factor and FoM for different skyrmion modes. (e, f) Comparison of the electric field (e) and magnetic field (f) magnitude distributions for different skyrmion modes along the radial direction. (g) The maximum electric field and magnetic field magnitudes for different skyrmion modes along the radial direction. Sensitivity analysis of the fundamental EM skyrmion mode The proposed EM skyrmion sensor is significant for its high sensitivity to trace-amount biosensing quantities and the benefits of ultra-compact integration. The excellent sensing performance is attributed to the strong plasmonic wavelength compression, enhanced wave-matter interactions, and high Q-factor. Figure 3 compares the resonance properties and sensing performance of the proposed EM skyrmion sensor with a complementary microstrip ring resonator (MRR) resonating at the same frequency. The transmission (S 21 ) spectra of the EM skyrmion sensor and MRR sensor are shown in Figure 3a. The resonance frequency is around 900 MHz, corresponding to an operating wavelength (λ 0 ) of approximately 0.33 m. The diameter of the EM skyrmion sensor is 6.6 mm, hence its electrical size features λ 0 /50 at an extremely deep-subwavelength scale. However, the diameter of the MRR sensor is 36 mm with an electrical size of λ 0 /4.6, which is only constrained to the subwavelength scale. Furthermore, the EM skyrmion sensor demonstrates a narrower FWHM and superior excitation efficiency compared to the conventional MRR sensor, as shown in Figure 3a. The insets in Figure 3a show the Lorentz fitting curves for defining the FWHM. Hence, the EM skyrmion sensor exhibits Q-factor of 184.6, which is higher than the value of 119.1 of the MRR sensor. Figure 3b shows the simulated electric field magnitudes (|E|) of both the proposed EM skyrmion sensor and the conventional MRR sensor, with an identical colorbar for comparison. The greater brightness of the former reflects a stronger electric field and enhanced wave-matter interaction. To quantitatively analyze the sensing-enhanced effect, we compare the dielectric sensing sensitivity of the proposed EM skyrmion sensor with that of the conventional MRR sensor, as shown in Figure 3c and d. The dielectric under test is assigned a thickness of 0.1 mm and a loss tangent of 0.025 to mimic the loss characteristics of surface-linked bio-analytes. The lossy dielectric is placed on top of the SLSP resonance unit with a diameter of 6.8 mm, completely covering the SLSP surface, as shown in Figure 3c. Hence, the volume under test (VUT) of the sensing dielectric features only 3.63 μL with an electric size of 9.84 × 10 −8 λ 0 3 . For comparison with the conventional MRR sensor, a lossy dielectric with an identical VUT is placed at the position with the highest electric field magnitude in the MRR sensor, as shown in Figure 3d. The proposed EM skyrmion sensor exhibits a superior frequency shift, approximately 105-fold greater than that of the conventional MRR sensor. To clearly highlight the sensitivity advantage of the EM skyrmion sensor, the resonance frequency is normalized. A larger VUT can enhance sensing sensitivity, for instance, when the sensing dielectric covers the entire surface of the MRR. The proposed EM skyrmion sensor still exhibits a superior frequency shift, approximately 4.3-fold greater than that of the conventional MRR sensor, as shown in Supplementary Note 2. Defining a local sensitivity as S L = sensitivity/area [22], which synthetically judges the sensitivity and sensing footprint, then S L of the proposed EM skyrmion sensor is 483-fold that of the conventional MRR sensor. Hence, the proposed EM skyrmion sensor can achieve higher sensing sensitivity with ultra-compact circuit integration. Figure 3. Sensing performance comparisons of the proposed EM skyrmion sensor and the conventional MRR sensor. (a) Simulated transmission (S 21 ) spectra of the proposed EM skyrmion sensor and the conventional MRR sensor resonating at the same frequency. (b) Simulated electric field distributions of both the proposed EM skyrmion sensor and the conventional MRR sensor, with an identical colorbar for comparison. (c, d) Sensitivity comparisons between the EM skyrmion sensor (c) and the MRR conventional sensor (d). Sensor fabrication, surface functionalization, and antigen preparation The photograph of the fabricated EM skyrmion sensor is shown in Figure 4 a. Figure 4b shows the flowchart of real-time and label-free biosensing using the fabricated EM skyrmion sensor, including surface functionalization, antibody-antigen binding, and microwave biosensing experiment. The detailed experimental steps for surface functionalization are shown in Supplementary Note 3. To verify the successful modification of antibodies on the sensor surface, scanning electron microscopy (SEM) is performed on the EM skyrmion sensor. The SEM images are acquired using a scanning electron microscope (QUANTA 200, FEI, USA) at an accelerating voltage of 20 kV. The modification of antibodies on the sensor surface is observed at magnifications of 100 × and 500 ×, respectively, as shown in Figure 4c. Compared to the control group, both experimental groups exhibit successful antibody immobilization on the sensor surface. Furthermore, between the two experimental groups, a higher amount of antibody is immobilized on the sensor surface when the antibody concentration in the modification reaction is 50 ng/μL, which is significantly superior to the group with an antibody concentration of 150 ng/μL. Therefore, the optimal concentration of antibody modification has been determined. The transmission spectra of 20 pieces of sensors are measured, demonstrating a slight variation of the resonance frequency before surface functionalization, as shown in Figure 4d. After surface functionalization, the resonance frequencies of all sensors shift towards higher frequencies. This may result from surface modification chemicals reducing the sensor substrate’s effective permittivity. Figure 4. Sensor fabrication, surface functionalization, and antigen preparation. (a) Photograph of the fabricated EM skyrmion sensor. (b) Flowchart of real-time and label-free biosensing using the fabricated EM skyrmion sensor. (c) Scanning electron microscope (SEM) images of the surface-functionalized sensor. (d) Uniformity analysis of resonance frequency for 20 pieces of EM skyrmion sensors before and after surface modification. (e) Flowchart for extracting specific and concentrated antigens from the urine of patients with DN. (f) Characterization of EVs isolated by NTA. (g) Quantification of concentration levels in cell lysate and EVs by WB. Figure 4e shows the flowchart for extracting specific and concentrated antigens from the urine of patients with DN, using WGA-coupled magnetic beads [46, 47]. The detailed experimental steps for antigen extraction are shown in Supplementary Note 4. The extracellular vesicles (EVs) are characterized using the NanoSight NS300 system (Malvern, UK). The detailed experimental steps for nanoparticle tracking analysis (NTA) are shown in Supplementary Note 5. Figure 4f shows the characterization of EVs isolated by WGA-coupled magnetic beads by NTA. The results of NTA reveal that the isolated vesicles had a size distribution with a peak at approximately 140 nm and a particle concentration reaching 7.36 × 10⁶ particles/mL, indicating the typical size and abundance of EVs. The cells and EVs were lysed using radioimmunoprecipitation assay (RIPA) buffer for western blot (WB) analysis. The detailed experimental steps for WB analysis are shown in Supplementary Note 6. WB analysis confirms the presence of canonical exosomal markers ALIX, CD63, and TSG101 in the isolated vesicles. In addition, CKAP4, a known marker of DN, is detected in both the cell lysate and uEVs, confirming that the isolated vesicles originated from urine samples of DN patients. Clinical sample collection for antigen extraction is shown in Supplementary Note 7. Microwave biosensing experiments The microwave biosensing experiments by detecting the resonance frequency shift of the proposed EM skyrmion sensor for tracking specific antigen-antibody binding events are shown in Figure 5 . The photograph of the sensing experimental configuration is shown in Figure 5a. The photograph of the near-field mapping measurement is shown in Figure 5b. The measured near-field distributions (|E z |) of the proposed EM skyrmion sensor coincide well with the simulated one, as demonstrated in Figure 5c. The measured S 21 spectrum and Lorentz fitting for defining FWHM are shown in Figure 5d. The measured resonance frequency of the proposed EM skyrmion sensor is 920.4 MHz, which is slightly higher than the simulated one. The measured excitation efficiency is lower than the simulated one (Figure 3a), accompanied by a significant FWHM broadening, resulting in a lower Q-factor of 70.8 compared to simulated value. This could be attributed to the losses in the coaxial cables and SMA connectors during the experiment. Figure 5. Microwave biosensing experiments for tracking specific antigen-antibody binding events. (a) Photograph of the sensing experimental configuration. (b) Photograph of near-field mapping measurement. (c) Simulated and measured |E z | distributions of the fundamental skyrmion mode at z = 2 mm plane. (d) Measured S 21 spectrum and Lorentz fitting for defining the FWHM. (e, f) Quantitatively analyze the impact of PBS solution rinsing. (e) Measured S 21 spectra for rinsing four times repeatedly. (f) Variation in resonance frequency for rinsing four times repeatedly. (g) Measured S 21 spectra after SF and AB. (h) Variation in resonance frequency after SF and AB. (i) The calibration curve for graded antigen concentrations using an extreme peak function. Before conducting microwave biosensing experiments, the residues on the sensor surface need to be rinsed off with the PBS solution. The effect of the PBS solution on the resonance frequency of the sensor without surface functionalization is quantitatively analyzed, as shown in Figures 5e and f. Figure 5e shows the transmission spectra after four repeated rinses, with the sensor surface dried using a rubber bulb after each rinse, and each rinse consuming 200 μL PBS solution. Figure 5f shows the variation in resonance frequency, indicating that the salt ions in the PBS solution adhering to the sensor surface cause a shift to lower frequencies. Additionally, the resonance frequency tends to saturate after shifting by 0.6 MHz, indicating that the salt ion content on the sensor surface remains invariable. Hence, a resonance frequency shift obviously exceeding 0.6 MHz can be considered a positive signal for antibody-antigen binding. Figures 5g and h show the results of microwave biosensing experiments for tracking specific antigen-antibody binding events. The concentration of the surface-modified antibodies is 50 ng/μL, and the concentration of the antigens is 11 ng/μL. The 100 μL antigen concentration is applied on the sensor surface, and incubated for 2 hours at room temperature. Next, the sensor is rinsed with PBS solution, then dried using a rubber bulb, and the S-parameters are measured. Figure 5g shows the measured S 21 spectra after surface functionalization (SF) and antigen-antibody binding (AB). The variation in resonance frequency is demonstrated in Figure 5h. When the antigen successfully binds to the antibody, it induces a significant frequency shift of 3 MHz towards a lower value. Furthermore, the antigens are set at graded concentrations of 0, 5.5, 11, 33, and 49.5 ng/μL, corresponding to 0, 12.5, 25, 75, and 112.5 pmol in the VUT of 100 μL to determine the optimal interval of AB. Five biological replicate groups are set for each concentration. Figure 5i shows the relationship between the resonance frequency shifts and graded antigen concentrations, along with the fitted calibration curve using an extreme peak function, which aligns with the classic lattice theory [48]. Hence, the optimal interval for AB is identified at an antigen concentration of approximately 11 ng/μL. The reporting limit for antigen reaches 12.5 pmol in moles and 125 nmol/L in concentration, representing a significant advancement of microwave resonance sensing technology in early clinical disease screening. Table 1 shows the comparison with existing detection methods for diagnosing DN. Routine screening methods such as urine dipstick tests, blood urea nitrogen (BUN), and SCR tests exhibit limited sensitivity and typically detect changes only in advanced stages of DN. For instance, the urine dipstick test shows a sensitivity of approximately 68-76% for detecting significant albuminuria or renal insufficiency in diabetic patients. Notably, false-negative rates can reach 20-50%, rendering dipsticks unreliable as a standalone screening tool [49]. BUN and SCR tests primarily reflect glomerular function at later stages and lack adequate sensitivity for early-stage detection. Renal ultrasound, although non-invasive, is limited to anatomical imaging and lacks the capability to detect molecular-level markers or early pathological changes [50]. While renal biopsy is considered the diagnostic gold standard and invaluable for precise diagnosis and prognosis in glomerular diseases, its invasive nature, technical complexity, potential bleeding risk, and turnaround time of 1-3 days make it impractical for routine screening [37]. Table 1. Comparison with existing detection methods for diagnosing DN. A: This Work Real-time; Label-free; Non-invasive; Low VUT; Rapid and Sensitive Initial development stage 100 μL ~2 h 125 nmol/L 12.5 pmol B: Urine Dipstick Test [53] Rapid; Cheap; Point-of-care High false-negative rate; 1-5 mL ~5 min ~150 μM C: SCR Test and BUN [54] Stable indicator of kidney function Late-stage diagnosis 2-5 mL 2-4 h SCR Test: ~45 μM [55]; BUN: ~1.8 mM [56] D: Kidney Ultrasound [50] Non-invasive; Anatomical imaging Late-stage diagnosis; No molecular quantification capability Not Applicable ~30 min Not Applicable E: Renal Biopsy [37] Gold standard for pathology Invasive; High technical complexity; Potential bleeding risk; Time-consuming Not Applicable (Tissue Samples) 1-3 days Not Applicable A: Our proposed method involves incubation antigen and microwave signal acquisition, with a total time of ~2 h. C: Creatinine and BUN detection time includes sample preparation, enzymatic reaction, and analysis via spectro- photometry or dry chemistry methods. D: Kidney ultrasound provides immediate imaging but lacks molecular quantification capability. E: Renal biopsy includes clinical scheduling, sample processing, and microscopic examination, requiring 1-3 days. In addition to horizontal comparisons with conventional clinical methods, it is also essential to assess vertical benchmarks across mainstream protein detection platforms, namely enzyme-linked immunosorbent assay (ELISA) and mass spectrometry (MS), both widely employed in biomarker discovery and disease monitoring. While ELISA offers a relatively standardized and widely adopted method for detecting disease-associated proteins, its detection limit generally ranges from 7 to 30 nmol/L, and the assay typically requires 3-6 hours to complete [51]. Moreover, ELISA is often limited by antibody availability, potential cross-reactivity, and the need for multiple incubation and washing steps, which can impede high-throughput or point-of-care applications. MS provides exceptional sensitivity and the ability to perform multiplexed analysis with detection limits reaching as low as 0.1-1 nmol/L. However, MS-based workflows demand substantial infrastructure, complex sample preprocessing, specialized personnel, and prolonged turnaround times (8-24 hours) [52], making it more suitable for centralized laboratories rather than bedside or decentralized diagnostics. Additionally, batch-to-batch variability and data normalization challenges further constrain its routine clinical deployment. Compared to conventional platforms such as ELISA and MS, our EM skyrmion biosensor offers a compelling balance between analytical performance and operational simplicity. The reporting limit of 125 nmol/L remains within the clinically relevant concentration range for medium-abundance to high-abundance disease-associated proteins, hence meeting the requirement of clinical DN diagnosis. Furthermore, the assay requires only 1 mL of urine and delivers quantitative, real-time, label-free results within approximately 2 hours, without the need for complex sample preparation or signal amplification. These characteristics enable practical deployment in resource-limited or decentralized settings where high-throughput and minimal-infrastructure testing is essential. Importantly, our platform addresses several key limitations of ELISA and MS-based approaches, including the need for labeling, time-consuming protocols, and high instrumentation costs. The ultra-compact EM skyrmion sensor makes it well-suited for portable diagnostic applications, potentially facilitating early-stage disease screening and real-time monitoring at the point of care. While future iterations of the platform will focus on enhancing detection sensitivity—potentially through signal amplification strategies or surface optimization—the current system already demonstrates strong potential as a translational diagnostic tool that bridges the gap between laboratory-based assays and real-world clinical needs. Conclusion We realized an EM skyrmion mode in a microwave plasmonic resonator in an electrical size of 1/50 wavelength. The resulting extreme wave-matter interaction enables a 105-fold improvement of the sensitivity over a microstrip ring resonator operating at the same frequency. Leveraging this effect, we developed a label-free, non-invasive diagnostic technique based on EM skyrmion resonance to identify diabetic nephropathy (DN), thereby bridging the gap between laboratory-based assays and practical clinical applications. The reporting limit for DN-associated proteins is down to 12.5 pmol in amount of substance and 125 nmol/L in concentration at an operating wavelength of 0.33 m. The large disparity between microwave wavelengths and the molecular scale of biomolecules highlights the sensitivity advantages of the proposed scheme. Furthermore, the technique combines real-time detection and high integration advantages inherent to microwave resonance sensing, paving the way for intelligent and portable health monitoring within the Internet of Things. Methods EM simulations. EM simulations were calculated using the time domain solver of the CST Microwave Studio with an accuracy of −60 dB and a maximum solver duration of 1000 pulses. The frequency range was set from 0 to 6 GHz, with a total sample point of 10,001. The Hexahedral mesh was employed with a maximum cell of 50 cells per wavelength near to model and a minimum cell of 50 fraction of maximum cell near to model. All boundaries were set to be open boundaries. Materials and fabrications. The PCB substrate was F4B with a dielectric constant of 2.65 and a loss tangent of 0.001. The printed metal patterns consisted of 35-μm thick copper, with a 2-μm thick gold layer electroplated on the copper surface for surface functionalization. Measurement setup. Keysight vector network analyzer E5063A was used to measure the transmission spectra of the EM skyrmion sensor. A sweeping range from 0.82 to 1.02 GHz with 2,001 sweep points was set during microwave biosensing experiments. The IF bandwidth was set at 15 kHz to lower the noises and jitters. Ethics approval statement All procedures involving human participants were approved by the Ethics Committee of the National Clinical Research Center for Kidney Disease Biobank and the Ethics Committee of the First Affiliated Hospital of Nanjing Medical University (Approval No. 2022-SR-295; Biobank Project Code: JSRB2021-03). Written informed consent was obtained from all participants in accordance with the Declaration of Helsinki. Acknowledgement This work was supported by the National Natural Science Foundation of China (62371132 and 62288101), the National Key Research and Development Program of China (2022YFA1404903), the Natural Science Foundation of Jiangsu Province (BK20231414, BK20212002), and the 111 Project (111-2-05). References [1] B. S. Miller et al. Spin-enhanced nanodiamond biosensing for ultrasensitive diagnostics. Nature, 587 , 588-593 (2020). [2] Y. Zhu et al. Optical conductivity-based ultrasensitive mid-infrared biosensing on a hybrid metasurface. Light Sci. Appl. 7 , 67 (2018). [3] K. V. Sreekanth et al. Extreme sensitivity biosensing platform based on hyperbolic metamaterials. Nat. Mater. 15 , 621-627 (2016). [4] X. Jiang, A. J. Qavi, S. H. Huang, and L. Yang. Whispering-Gallery Sensors. Matter 3 , 371-392 (2020). [5] X. Zhang, W. Y. Cui, Y. Lei, X. Zheng, J. Zhang, and T. J. Cui. 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Information & Authors Information Version history V1 Version 1 26 October 2025 Peer review timeline Published Advanced Functional Materials Version of Record 5 Apr 2026 Published Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords deep subwavelength electromagnetic skyrmions microwave sensing Authors Affiliations Tian Shuo Bai State Key Laboratory of Millimeter Waves View all articles by this author Meng Jia State Key Laboratory of Pharmaceutical Biotechnology View all articles by this author Wan Zhu Wang State Key Laboratory of Millimeter Waves View all articles by this author Xuanru Zhang 0000-0002-3179-9279 State Key Laboratory of Millimeter Waves View all articles by this author Siqi Han Affiliated Hospital of Medical School Nanjing University View all articles by this author T. J. Cui [email protected] State Key Laboratory of Millimeter Waves View all articles by this author Metrics & Citations Metrics Article Usage 234 views 178 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Tian Shuo Bai, Meng Jia, Wan Zhu Wang, et al. Electromagnetic skyrmions in a deep-subwavelength plasmonic resonator for vitro diabetic nephropathy diagnostic. Authorea . 26 October 2025. DOI: https://doi.org/10.22541/au.176150026.64108205/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu . 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