Fig. 1. Fabrication and characteristics of the nanoridge HMM. (a) Schematic diagram of the gold nanoridge HMM sensor with a liquid flow channel and SEM image of the fabricated nanoridge array with a consistent period of 180 nm, length of 10 μm, and average width and height of 148 and 240 nm, respectively. (b) Photograph of the nanoridge HMM sensor integrated with a microfluidic system. (c) Isofrequency surface of nanoridge HMMs at the wavelength of 1200 nm using effective medium theory. (d) FEM-based numerical simulation results of the three-dimensional cross-sectional spatial distribution of the magnetic field for the q=1 mode at the incident angle of 45°. In the x–z plane, the black and white arrows represent the direction of the x component of the wavevector k and the Poynting vector S at the location, respectively. The results denote the presence of negative refraction of energy flow in the structural region of HMMs. The magnetic field distributions in the x–y and y–z planes correspond to the positions at half the height of the nanoridges and half the width of the grooves, respectively. (e) Real and imaginary parts of the effective permittivity of nanoridge HMMs with a width, period, and height of 150, 180, and 240 nm, respectively. It shows a hyperbolic dispersion in the visible to near-infrared region. The vertical dotted line indicates the epsilon-very-large regime. (f) Effective homogeneous three-layer waveguide structure, with the HMM slab between a semi-infinite superstrate and a substrate.

Fig. 2. Dispersion properties of the nanoridge HMM. (a), (b) Calculated reflection dispersion of the nanoridge HMM using the RCWA (a) and analytical model (b) with the same structural geometric parameters in Fig. 1(e) and a bottom gold film with a thickness of 25 nm. The black dashed and dash-dotted lines represent the light lines in the superstrate and substrate, respectively. The solid lines represent the analytical solutions of q-order guided modes (cavity and leaky modes), and the dotted lines represent the analytical solutions of cavity modes with modal orders of q−0.5. The area above the light line in superstrate represents the cavity-mode region, and the leaky-mode region is located between the substrate and superstrate light lines. (c), (d) For q=1 mode and the structural height of 240 nm, the dependence of the maximal bulk sensitivity Sq,max on εx and εz (c), and the variation of surface sensitivity Sq,surf of nanoridge HMMs as a function of different filling ratios (d). The black hemisphere marker in (c) represents the nanoridge HMM with a filling ratio of 5/6. (e) Analytical reflection dispersions of q=1 mode of nanoridge HMMs with different εx. The black solid and dotted lines correspond to that of (b), and the blue plane surface represents the condition of B=1.3338.

Fig. 3. Simulation of the cross-sectional spatial distributions of the magnetic field in the x–z plane at the resonance wavelength for the q=1,  2 modes with a bottom gold film of 25 nm. The results indicated by the black, red, blue, and purple markings correspond to the field distributions at incident angles of 0°, 45°, 61.5°, and 70°, respectively.

Fig. 4. Characterization of the bulk sensitivity of the nanoridge HMM sensor integrated with microfluidics. (a) Schematic diagram showing the setup used for reflectivity measurements. (b) Experimental reflection dispersion of the fabricated nanoridge HMM in DI water, where the black dash-dotted and dotted lines represent the q=1 and q=2 guided modes, respectively, and the black dashed line represents the light line in DI water. (c), (d) FEM-based simulated (c) and experimental (d) reflectance spectra of the nanoridge HMM sensor in DI water and 0.5% glycerol in DI water at the incident angle of 61.5°. (e) Variation of measured wavelength shift with DI water and 0.5% glycerol in DI water at different incident angles for the q=1 mode of nanoridge HMMs with a period of 180 nm and varying width w and height h. Error bars represent the standard deviation. (f) Variation of wavelength shift for the q=1,  2 modes with different concentrations of glycerol in DI water at the incident angle of 61.5°. The size of the data points represents the error bars.

Fig. 5. Evaluation of the biosensing performance of the sensor device. (a) Schematic diagram of bio-functionalization and specific immobilization on the HMM biosensor. (b) Real-time-detection reflectance spectra of streptavidin with concentration of 5 μg/mL in PBS. White dots represent the minimum reflectivity positions. (c) Real-time detection wavelength shifts of different concentrations of streptavidin in PBS with a spectrometer wavelength resolution of 0.5 nm. (d) Wavelength shift as a function of streptavidin concentration. The red curve was fitted using the Hill equation and error bars represent the standard deviation.

Fig. 6. Fabrication process and SEM pictures of the samples. (a) Schematic diagram of the steps of fabricating the nanoridge HMMs. (b), (c) Whole-scale and detailed SEM images of a fabricated gold nanoridge array with a period of 180 nm and average width and height of 148 and 240 nm, respectively. (d) Collapse of photoresist before electroplating.

Fig. 7. Calculated reflection spectra of nanoridge HMM with and without the Cr/Ti adhesion layer at the incident angle of 61.5°.

Fig. 8. Calculation of surface sensitivity. (a) Dependence of normalized surface sensitivity contributed from εx and εz on filling ratios of nanoridge HMM using EMT. (b) Dependence of the variation of εx and εz with the wavelength on filling ratios.

Fig. 9. Comparison between the calculated permittivity of nanoridge HMM and nanorod HMM using EMT. The parameters of nanoridge HMM are adopted from Fig. 1 in the main text. The parameters of nanorod HMM are as follows: the period, height, and radius are 210, 350, and 75 nm, respectively. These structural parameters are determined when these two types of HMMs possess the same center resonance wavelength, which is calculated using the finite element method.