Metamaterials are artificially designed subwavelength-structure media that show unusual electromagnetic properties. They have attracted considerable attention for electromagnetic engineering and light control uses, including enantioselective sensing [1], light–matter coupling [2], optoelectronic multifunctional control [3], zero index [4], nonlinear photonics [5,6], enhanced imaging [7], and optical cryptography [8]. In particular, metamaterial-based plasmonic biosensors have great potential for medical research and clinical diagnostics due to their ability to rapidly detect biomolecular interactions in real time without the need for labels [9,10], as well as their potential to overcome the limitations of conventional plasmonic biosensors [11–15]. These metamaterials support particular electromagnetic modes based on surface plasmon resonance (SPR), which exhibits high sensitivity to subtle variations in the refractive index of the surrounding environment. This highly sensitive response, which can be accessed using measurable parameters such as wavelength [16,17], angle [18], and intensity [19], enables a strongly correlated quantified detection of the variation in refractive index induced by biomolecular binding at the sensing surface.

In recent years, hyperbolic metamaterials (HMMs), which exhibit extreme optical anisotropy, have promoted the development of many nanophotonic fields [20–28], particularly in sensing [29–33]. HMMs are artificially designed to feature hyperbolic dispersion, and these structural configurations lead to the highly sensitive bulk plasmon–polariton (BPP) guided modes that can be used for sensing. The guided modes of HMMs typically demonstrate a high quality factor and present a localized, intensified evanescent field, which can greatly enhance the resolution and sensitivity of sensors. Owing to these guided modes, biosensors based on HMMs, especially vertical-structure-type HMMs [29,32,33], exhibit higher extreme sensitivity compared to conventional plasmonic biosensors. Vertical-structure-type HMMs, represented by nanorod HMMs, possess a positive transverse permittivity and a negative vertical permittivity [34], which can support low- and high-k BPP guided modes. For this type of HMM, the BPP guided modes can behave as Fabry–Perot (F-P) cavity, leaky, or true-waveguide modes based on the different exciting conditions [35]. Among these, the leaky mode has been widely adopted in sensing research owing to its extremely high sensitivity, stable high mode-coupling efficiency, simplicity, and high flexibility in operation schemes such as the Kretschmann configuration. Leaky modes play a vital role in HMM sensing.

However, the phase-insensitive-reflection analytical model [35], which is widely adopted to describe the HMM sensing modal behaviors, still has difficulties in explaining some characteristics of leaky modes observed in experiments and numerical simulations such as the dispersion discontinuity between different modal regions. While some numerical-simulation-based studies analyze some phenomena that accompany the excitation of leaky modes, such as the strong spatial confinement of the electromagnetic field and the penetration-enhanced evanescent field [32,36,37], these non-analytical studies cannot deduce the eigenmode intrinsic factors that determine the plasmonic sensing and face challenges in predicting high-sensitivity sensing modal behaviors.

In this work, the plasmonic sensing intrinsic mechanisms of vertical-structure-type HMMs are investigated through both theoretical and experimental approaches. We determined that the high rate of change of the modal dispersion (the high modal group velocity) stemming from a large transverse permittivity of HMMs is directly responsible for high sensitivity. Correspondingly, we have developed a plasmonic sensing platform based on gold nanoridge HMMs by combining electron-beam lithography (EBL), oxygen plasma etching, and electroplating. This fabrication method can achieve an extremely high structural filling ratio while maintaining a high structural height, which is difficult to achieve through the conventional etching process. The ultrahigh filling ratio leads to a significantly large transverse permittivity of HMMs, which directly contributes to the extremely sensitive BPP guided modes. We experimentally achieved a sensitivity of 53,300 nm/RIU and a figure of merit (FOM) of 533 in the visible to near-infrared region using the developed nanoridge HMM sensor. To the best of our knowledge, this is the highest bulk sensitivity obtained in experiments for HMMs. Using the biotin–streptavidin standard affinity model, we performed label-free detection of streptavidin ranging from 20 to 0.05 μg/mL, and the developed plasmonic nanoridge HMM sensor achieved two orders of magnitude enhanced sensitivity compared with the same type of HMM sensor. This work not only provides direct theoretical guidance for the development of HMM plasmonic sensing but also broadens the horizon in new-generation plasmonic sensors.

The gold nanoridge array was fabricated using a combination of EBL, oxygen plasma etching, and electroplating (see Appendix A for more fabrication details). Figure 1(a) shows a schematic diagram of the liquid-flow-channel-based nanoridge HMM sensing platform and a scanning electron microscope image of the fabricated gold nanoridge array sample. Figure 1(b) shows a photograph of the microfluidic-system-integrated nanoridge HMM sensor under the Kretschmann configuration. Because fabricating patterned templates with widths below 40 nm, heights above 400 nm, and lengths of tens of micrometers using only EBL is challenging due to the lack of structural rigidity of photoresist, the adoption of oxygen plasma etching between EBL and electroplating is indispensable in the fabrication of nanoridge HMMs with high filling ratios and heights. Moreover, owing to the closure effect [38], the deposition process can only fabricate ladders without high verticality of sidewalls, making electroplating an appropriate approach. On the other hand, the traditional etching process cannot fabricate extremely narrow and deep nanogroove arrays with a large structural area on noble metals that are chemically inactive. Compared with conventional focused-ion-beam-based shallow nanogroove structures, gold nanoridges fabricated using the combination of EBL, oxygen plasma etching, and electroplating can achieve a high structural height beyond the traditional fabrication processes while maintaining a high filling ratio.

HMMs are identified as anisotropic media owing to their hyperbolic isofrequency surface for TM polarized waves [39], which can be classified as type I (εx=εy≡ε∥>0,εz≡ε⊥<0) and type II (εx=εy≡ε∥<0,εz≡ε⊥>0) using the well-known effective medium theory (EMT). For type I HMMs, represented by the nanorod array (one of the vertical-structure-type HMMs), the propagating wave can exceed the high-wavevector limit of the elliptical dispersion media without a low vector limitation, because the open-form isofrequency surface is continuous along the direction of wave propagation (x–y plane). Hence, these types of HMMs can support both low- and high-k modes. Likewise, conventional type II HMMs, such as the metal–dielectric multilayer (one of the horizontal-structure-type HMMs), can only support high-k modes. The gold nanoridge HMM is a special and vertical version of a type II HMM, and the permittivity perpendicular to the nanoridges (εx≡ε⊥) and parallel to the nanoridges (εy=εz≡ε∥) can be calculated using the Maxwell–Garnet approximation as follows [40]: ε⊥=(PεAu+1−Pεh)−1,(1)ε∥=PεAu+(1−P)εh,(2)where P, εAu, and εh represent the filling ratio of nanoridges, the permittivity of Au, and the permittivity of dielectric between nanoridges, respectively. The isofrequency surface of the nanoridge HMM is demonstrated in Fig. 1(c), and Fig. 1(d) shows the negative refraction of the energy flow based on a finite element method (FEM) simulation (see Appendix A); this phenomenon can confirm hyperbolic dispersion [41]. Notably, even though nanoridge HMMs are categorized as type II, they exhibit a similar partial permittivity (εx>0,εz<0) to that of type I HMMs. This trend is shown in Fig. 1(e), where the permittivity values of gold and surrounding dielectric were adopted from experimental data [42] and deionized (DI) water (n=1.3332), respectively. This indicates that nanoridge HMMs, whose significant structural height allows them to be distinguishable from the nanogroove structure of a 1D nanowire array [43], can support BPP guided modes similar to those of type I HMMs (e.g., the plasmonic nanorod HMMs). These vertical-structure-type HMMs can be considered as 1D planar waveguides that are infinitely extended along the y-direction, with waves propagating along the x-direction and a finite thickness along the z-direction, as shown in Fig. 1(f). Without losing generality, the wavevector k could be taken as k=βx^+kzz^, where β=Bk0. When momentum matching conditions are satisfied (such as B=nprismsinθ under the method of attenuated total reflection), BPP guided modes can be directly excited by the incident light in free space. Among them, the electromagnetic wave enters the HMM layer, undergoes a total reflection on the side of the detection environment (superstrate), and then penetrates out to the same side (substrate) of the incident light to form the leaky modes. At this instance, the electromagnetic field in the waveguide and the evanescent field in the superstrate are used in sensing by virtue of their extreme sensitivity to the variation of the refractive index of the surrounding environment.

For leaky modes, the z-component of the wavevector is quantized based on the finite waveguide geometry, which is determined by the modal order, waveguide thickness, and reflected phase shift. The leaky-mode dispersion can be written as tan(kzh−φ)=−εxεzεsupB2−εsupB2−εz,(3)where h, εsup, and φ represent the height of the HMMs, the superstrate permittivity, and the phase shift originating from the interface between the HMM and the substrate, respectively. The arctangent value arctan(−εxεz(B2−εsup)/(B2−εz)/εsup) on the right side of the equal sign represents the total reflection phase shift provided by the interface between the HMM slab and the superstrate. The calculated cavity-mode and leaky-mode reflection dispersion of the nanoridge HMM using rigorous coupled-wave analysis (RCWA) [44] and the analytical model are shown in Figs. 2(a) and 2(b). The analytical dispersion reproduced the RCWA simulation with excellent agreement in the leaky-mode-dispersion region. This indicates that the leaky modes are strongly correlated with the reflected phase shift at the boundaries of the HMM waveguide, and the permittivities directly determine the value of the total reflection phase shift. This is distinct from the cavity modes with phase-insensitive reflections [35], for which the analytical model indicates modal continuity and negative group velocity throughout the entire dispersion region.

Notably, a highly reflective film (such as a gold film) with a thickness of tens of nanometers is generally deposited between the HMMs and the substrate. This film not only plays the role of a seed layer of fabricating HMMs but also supports multiple round-trip reflections of electromagnetic waves in the hyperbolic waveguide, which enhance the coupling efficiency and lead to the highly confined BPP guided modes. Thus, the φ considered here is related to the electromagnetic frequency and the thickness of the highly reflective film. In the visible to near-infrared region, we considered φ as a constant with a value of 0.32π based on a gold film with thickness of 25 nm. We neglected the extended discussion of φ (of the dependence on electromagnetic frequency and thickness of the gold film) because of its triviality in the eigenmode analysis. Notably, in reflection dispersion, TM guided modes undergo a phase shift of −0.5π before the constantly increasing β exceeds the critical angle condition (light lines in superstrate); therefore, the q-order modes (where q is a positive integer) move to states of q−0.5 (a half integer) derived from the analytical solutions, which contributes to the discontinuity of cavity modes and leaky modes in the dispersion illustration.

Figure 3 illustrates the distinct field distributions of bulk resonance modes, characterized by pronounced maxima and minima typical of standing wave patterns within the waveguide. For incident angles of 0° and 45°, the corresponding q=1,2 cavity modes are formed due to the dissatisfaction of the total internal reflection condition (critical angle 61.45°). Without the phase shift associated with total internal reflection, the field distributions are nearly identical except for their intensities. Notably, compared to the case without a bottom gold film [Fig. 1(d)], the phase shift introduced by the gold film is clearly reflected in the spatial distribution of the field, resulting in the appearance of incomplete field distribution nodes near the gold film. For incident angles of 61.5° and 70°, the evanescent field, which has a high penetration depth in the superstrate, exhibits typical leaky-mode behavior. When the angle exceeds the critical angle, the evanescent field shows attenuation characteristics that increase with both the angle and the modal order, indicating a reduction in modal sensitivity.

By definition, the sensitivity for bulk refractive index changes in the environment (which is defined as bulk sensitivity) is expressed as Sq=[λq(εd1)−λq(εd)]/(εd1−εd), where λq(εd) is the center resonant wavelength of q-order modes with the surrounding environmental permittivity of εd. The bulk sensitivity achieves the maximum when εd1=B, which is derived as Sq,max=2πh−εxεz(B2−εz)arctanξ(qπ+φ)(qπ+φ+arctanξ)(B−εd),(4)where ξ=−εxεz(B2−εd)/(B2−εz)/εd. The dependence of calculated Sq,max on εx and εz for q=1 mode is shown in Fig. 2(c). Owing to the large value of −Re(εz) of nanoridge HMMs [shown in Fig. 1(e)], Eq. (4) could be simplified to Sq,max=[2πhεxarctan(εx(B2−εd)/εd)]/[(qπ+φ)2·(B−εd)] when Δn=εd1−εd≪εd. This indicates that the lower-order modes would achieve a higher bulk sensitivity under a larger value of transverse permittivity and a higher structural height. Precisely speaking, a large transverse permittivity leads to a high group velocity of leaky modes close to the critical angle, which is directly responsible for the high bulk sensitivity. By adopting different structural heights and filling ratios, the dependence of the modal group velocity of q=1 mode on the different transverse permittivity is shown in Fig. 2(e). The Δλ shown in Fig. 2(e) represents the shifted value of the center resonance wavelength when n changes from 1.3332 to 1.3338. For the same environmental refractive index change, the closer to the boundary between the cavity-mode and leaky-mode regions, the greater the wavelength shift of leaky-mode sensing. At the same time, the greater the group velocity [inversely proportional to the slope of the leaky-mode curve in Fig. 2(e)] of the leaky modes closer to the boundary between the cavity-mode and leaky-mode regions (the closer it is to the light line in the superstrate), the higher the bulk sensitivity of leaky-mode sensing. Considering Eqs. (3) and (4), one can analyze that the structural height only modulates the bulk sensitivity by manipulating the center resonance wavelength as a result of the satisfaction of the wavevector quantized condition. The non-wavelength-dependent modal bulk sensitivity Sq,mode can be defined as Sq,mode=Sq,max/λq, which is derived as Sq,mode=arctanεx(B2−εd)εd(qπ+φ)(B−εd).(5)This more clearly reveals that the transverse permittivity directly determines the modal bulk sensitivity. Considering Eq. (1), the positive correlation between εx and P suggests that a high filling ratio is critical for achieving high-sensitivity sensing.

Notably, the high-frequency bound for BPP guided modes depends on the lower value between the cut-off frequency ωcut−off of guided modes and the effective plasma frequency ωpeff of HMMs. The cut-off frequency is derived as ωcut−off=c0(qπ/h)/εx by solving the cavity-mode dispersion equation β2/εz+(qπ/h)2/εx=k02 when β2=0, and the effective plasma frequency ωpeff obeys the condition of Re[εx,z(ωpeff)]=0. Owing to a high structural filling ratio, the low-order modes all adopt ωcut−off as the high-frequency bound [35]. As the modal order increases, cut-off frequency is close to the high frequency, yielding to the epsilon-very-large (EVL) regime of transverse permittivity that occurs at the condition of −εAu/εh=P/(1−P). In this situation, the large imaginary part of transverse permittivity and the frequency approaching the Au interband absorption result in a high optical loss together. At the same time, the converging modal density with the increase of modal orders leads to a smaller frequency bandwidth of high-order guided modes, which accelerates the decrease of high-order-leaky-mode group velocity. This trend has also been revealed in Figs. 2(a) and 2(b), so that the high-order leaky modes achieve relatively lower bulk sensitivity despite their larger transverse permittivity in the high-frequency region.

In biosensing, surface sensitivity is defined as the sensitivity of variations in the refractive index in the nanoscale range around the sensing surface, which is attributed to the specific adsorption of small biomolecules on the surface. This slight dielectric perturbation can hardly be sensitively detected by the evanescent field with the long penetration depth above the surface. However, the modal resonance conditions significantly change when the small biomolecules fall into the slits between nanoridges, thereby causing a modification in εh. Here, we delivered a rational definition of the surface sensitivity, written as Sq,surf=∂λq/∂εh (see Appendix A for more details). Figure 2(d) shows the dependence of analytical-theory-based calculated surface sensitivity on the filling ratio. The increase in filling ratios contributes to a larger transverse permittivity and a higher surface sensitivity. From the perspective of the spatial distribution of the sensing electromagnetic field, the smaller slit contains a larger proportion of the effective space volume of the sensing modal field. Thus, the dielectric change in the volume of the same space due to the adsorption of small biomolecules will result in a greater transition of the electromagnetic modal resonance condition in HMMs with smaller slits. Notably, the surface sensitivity shows a direct and positive correlation with transverse permittivity. Owing to the similarity of modal dispersions, the presented analytical theory can also apply to all type I HMMs. This indicates that for all plasmonic HMM sensors with such hyperbolic dispersion properties, a particular artificial design to achieve a large transverse permittivity and structure height is the key to achieving the desired high sensitivity.

The experimental measurement setup, based on the Kretschmann configuration, is shown in Fig. 4(a). The system mainly consists of a wide-spectrum tungsten light source, phase lock-in amplifier, microfluidics-integrated sensor, reflected light imaging module, and spectrometer. The experiment employed the Thorlabs SLS201L small stable broadband light source, which operates within a spectral range of 500–2600 nm and delivers an optical output power of 10 mW, utilizing fiber jumpers for connection. During the collimation phase, the emitted light initially passed through the small aperture diaphragm 1, which served to diminish the light spot and eliminate stray light. Subsequently, the light was processed through a polarizer to obtain TM-polarized light. Ultimately, it was collimated by means of a collimating lens, effectively reducing the divergence angle of the incoming light.

The microfluidics-integrated sensor mainly consisted of microfluidic channels made of polydimethylsiloxane (PDMS), the sensing chip, a K9 Dove prism (which enhances the stability of microfluidic system and optimizes the operation), and a stainless-steel base. The nanoridge HMM sample was affixed to the K9 Dove prism using a refractive index matching liquid (MYCRO Cargille BK7) and encapsulated within a microfluidic setup. Next, the entire microfluidic setup was secured to a multi-dimensional adjustable sample stage. The angle of incidence could be finely controlled at 0.02° by rotating the sample stage.

In the imaging process, the incident light illuminated the surface of the metamaterial and was subsequently magnified by the imaging lens. A clear image at 4× magnification was visible on aperture diaphragm 2. Only the light reflected from the metamaterial was permitted to pass through diaphragm 2 and enter the fiber receiver. The spectrometer utilized was the HORIBA iHR320, which has a minimum resolution of 0.2 nm (0.5 nm set in our experiments), and is equipped with an InGaAs detector covering a spectral range of 900–2100 nm. Due to the low intensity of the incident light following collimation, a lock-in amplifier was employed to enhance the signal-to-noise ratio and ensure reliable measurement results. If higher-power broadband light sources are available, or if the entire measurement system can be integrated into a dark box in the future, the lock-in amplifier and related elements could theoretically be omitted to simplify the measurement configuration and reduce costs.

The reflection dispersion measured in DI water is shown in Fig. 4(b). The distinct dips observed (the continuous minimum reflectance) in the visible and NIR ranges in the experimental reflection dispersion correspond to the excited BPP modes in the nanoridge HMM. The dip above the light line in the superstrate (DI water) represents the excited cavity mode, while the dips below correspond to the leaky modes. The background spectrum was gained by the total reflection of incoming light as it passed through the prism in air, excluding the HMM sensor. In the experiment, the acquired reflection spectrum was normalized by dividing it by the background spectrum. The results of the experiment validated the presence of the BPP modes. By adjusting the incident angle within the ranges below and above the critical angle, cavity modes and leaky modes with different group velocities can be obtained. The incident angles range from 50° to 70°, and the refractive index of the prism used is nprism=1.5163. Because the filling ratio is above 0.5, the experimental measurements of the center resonance wavelength of guided modes are blueshifted compared to the calculated results based on EMT [45]. Nevertheless, it can be observed that the q=1 cavity mode had a very-close-to-zero negative group velocity vg=−0.024c0, where c0 is the speed of light in vacuum, indicating that the nanoridge array possesses hyperbolic characteristics, and the prediction of the guided-mode behaviors using EMT is still reliable away from the EVL regime. Moreover, the observed phase shift of the q=1 guided mode was consistent with the simulation prediction when the incident light exceeds the critical angle in experiments. q≥2 modes in the cavity-mode region and q≥3 modes in the leaky-mode region are not observed in experiments owing to the high modal density and high optical loss at high frequencies.

The simulated and experimental reflectances of the nanoridge HMM sensor in DI water and 0.5% glycerol in DI water are shown in Figs. 4(c) and 4(d), of which the refractive index was 1.3319 and 1.3325 at the temperature of 30.2°C, respectively. The measured center resonance wavelength of reflectance spectra shows a redshift of 32 nm with an increase of 0.0006 in the refractive index of the surrounding environment and a corresponding bulk sensitivity of 53,300 nm/RIU, which, to the best of our knowledge, is the highest bulk sensitivity experimentally obtained for HMMs (see Appendix A, Table 1). Moreover, another significant parameter of a sensor is the FOM, defined as (Δλ/Δn)/FWHM, where the FWHM is the full-width of the resonant dip at half-maximum. The FOM determines the sensitivity of the sensor by considering the sharpness of the resonance. The experimental FWHM was 100 nm, yielding an FOM of 533.Table 1.

Comparison between the Nanoridge HMM Sensor and Advanced HMM Sensors

Figure 4(e) shows the variation of the wavelength shift with different incident angles for the q=1 mode with different structural geometric parameters. The experimentally observed higher wavelength shift of the nanoridge HMMs with a higher width and height confirms the prediction of the theoretical analysis. Owing to the larger transverse permittivity attributed to the higher filling ratio, the higher modal group velocity leads to a higher wavelength shift for the same bulk refractive index change at the smaller incident angle close to the critical angle. The variation in the wavelength shift for q=1,2 modes with different concentrations of glycerol in DI water is shown in Fig. 4(f). Each of the guided modes exhibits a high linear response of wavelength for concentrations in the range of 0%–0.5% and an abrupt singular response in the range of 0.5%–1%, which is due to the dissatisfaction of the ATR condition as a result of the excessively high refractive index of the superstrate. Compared to our earlier reported plasmonic nanorod HMM sensor [32] with 41,600 nm/RIU in the same resonance region (∼1200nm), the nanoridge HMM, which exhibits a larger transverse permittivity (Fig. 9) due to its higher filling ratio, has achieved the higher bulk sensitivity, which is also consistent with the prediction of the analytical model.

We used the biotin–streptavidin standard affinity model to demonstrate the ability of the plasmonic nanoridge HMM sensor to detect biomolecules. The nanoridge HMM biosensor was functionalized with thiolated biotin for the detection of streptavidin, as shown in Fig. 5(a). Initially, the nanoridge HMM chip was immersed in a 10 mmol/L Biotin-PEG2000-SH solution (in DI water) at 40°C for 24 h to form a self-assembled biotin monolayer on the sensor surface. After drying, the functionalized nanoridge HMM chip was integrated into the microfluid, which was prepared for detection. The measured real-time reflectance spectra of streptavidin are shown in Fig. 5(b). Different concentrations of streptavidin (SA) were injected into the biotin-functionalized sensor, and the sensing performance was monitored by measuring the shift in wavelength of the reflectance spectra, as shown in Fig. 5(c). First, the reflectance spectra of the sensor device were recorded by injecting phosphate-buffered saline (PBS), and after the spectral lines were stabilized, streptavidin (0.05–20 μg/mL) in PBS was continuously injected at 10 μL/min for approximately 45 min of real-time reflectance spectral recording. Finally, PBS was reintroduced to stabilize the liquid environment in the sensor. The resonance wavelength showed a different redshift with the concentration over time, which was due to the different numbers of molecular binding events that occurred at different concentrations. Notably, the nanoridge HMM sensor enhanced the sensitivity of detection by two orders of magnitude compared to that of the nanorod HMM sensor [32] because the nanoridge HMMs have a significantly higher filling ratio than the nanorod HMMs, which leads to a larger proportion of the effective space volume of the sensing modal field in slits and hence greatly enhances the surface sensitivity. This enhanced surface sensitivity holds the promise of revolutionizing the detection and monitoring of diseases at early stages.

Introducing a uniform standard to evaluate the limit of detection (LOD) can reduce the influence of experimental conditions, including materials, equipment, and modification methods, leading to unbiased conclusions. We used the Hill equation to model the streptavidin adsorption process on the surface of the nanoridge HMM biosensor. The wavelength shift Δλ is proportional to the concentration of streptavidin and can be quantitatively given as [46] Δλ=Δλmaxc/(k+c), where c, Δλ, k, and Δλmax represent the concentration of streptavidin, wavelength shift of the resonance dip, Hill constant of biotin/streptavidin, and saturated wavelength shift of the sensor response, respectively. Based on the recorded data of different streptavidin concentrations, the gradient descent method was used to optimize the parameters k and Δλmax and thereby minimize the mean square error in the fitting. We obtained k=4.2μg/mL and Δλmax=42.69nm based on the best fitting, as shown in Fig. 5(d). Considering these two parameters and the minimum wavelength shift with a noise level of 0.05 nm as the detectable limit, the LOD of the developed plasmonic nanoridge HMM sensor for streptavidin was estimated to be 4.9 ng/mL (84 pmol/L).

An essential step for ensuring the reproducibility of biosensing experiments is the thorough removal of the biological layer after each test, allowing for remodification for subsequent concentration tests. In our experiment, to ensure the reproducibility of biosensing experiments, the sensing chip was immersed in 1 mol/L NaBH4 in 1:1 H2O/EtOH for 60 min after experiments for the removal of the biological layer and the remodification. After the surface of the sensor was coated with streptavidin, clear hydrophilicity was observed when the sensor was rinsed with DI water due to the presence of a large number of hydrophilic groups. However, after treatment with sodium borohydride, the hydrophilicity disappeared. This demonstrates that our reproducibility method is effective. At the same time, our previous work has validated [32], through energy dispersive spectrometry (EDS), the effectiveness of an ethanol–water solution of NaBH4 in removing self-assembled monolayers (SAMs) from the surface of gold metamaterials.

In conclusion, we have studied the intrinsic mechanisms of vertical-structure-type HMM plasmonic sensing and developed gold nanoridge HMMs. The theoretical analyses and experimental demonstrations indicate that the reflected phase shift at the boundaries of the hyperbolic waveguide is strongly correlated with the sensitivity of the BPP guided modes in HMMs. The additional total reflection phase shift decided by the resonance conditions of guided modes dominates the sensing properties of the sensor device, where a high rate of change of the modal dispersion (a high modal group velocity) stemming from a large transverse permittivity of HMMs directly determines the high sensitivity. This can be applied to all type I HMMs and to HMMs with similar dispersion characteristics. By combining EBL, oxygen plasma etching, and electroplating, we fabricated the nanoridge HMMs with extremely high-sensitivity BPP guided modes. By exciting these modes in the visible to near-infrared region, we achieved an bulk sensitivity of 53,300 nm/RIU and an FOM of 533. The adopted sample fabrication methods achieved a high structural filling ratio, leading to a significantly large transverse permittivity while maintaining a high structural height, which resulted in extremely high sensitivity. Notably, the potential methods for improving transverse permittivity also include filling the grooves with materials that have a high refractive index, which may allow for a lower required structural height through simpler etching processes. In the label-free experimental detection of biomolecules, the plasmonic nanoridge HMM sensor achieved enhanced sensitivity by two orders of magnitude compared to the same type of HMM sensor. Our work determines the key factors of HMM plasmonic sensing through theoretical analyses and experiments, demonstrating the distinguished sensing properties of HMMs and their great potential development in chemistry and biomedical sensing. At the same time, the developed HMM sensor offers a great potential integration into commercial sensors due to its stable, high mode-coupling efficiency and high flexibility in operation schemes. We believe that the efficient implementation and control of high-sensitivity electromagnetic modes of HMMs will have a wide range of applications in sensing and plasmon-based nanophotonics.

Acknowledgment. The authors thank support from engineers P. Li, J. Su, W. Xu, C. Shang, and Z. Li in the Center of Optoelectronic Micro and Nano Fabrication and Characterizing Facility of WNLO for fabrication and SEM tests. X. Yue thanks L. Chen and W. Zhao for their suggestions on the manuscript writing.