Refractive-index sensors based on localized surface plasmonic resonances (LSPRs) have been considerably developed in the past decades. Due to the advantages of a coupler-free setup, remarkable enhancement of the local fields, and the comparable size with the targeting biomolecules [1–4], LSPRs significantly impact the fields of chemical and biological sensing. Recent research regarding LSPR sensors focused on characterizing the extinction cross section with respect to the excitation wavelengths (i.e., wavelength interrogation), which radically limits their possibility of being primed refractive-index sensors. Recently, there appeared a variety of methods to promote the sensitivity of the wavelength interrogation, for example, lifting the plasmonic nanostructure with a supporting dielectric layer or introducing Fano resonances with greater quality factors [5–9]. In addition to the wavelength interrogation, more recently the phase interrogation has been proposed to further enhance the sensitivity of LSPR sensors due to the nature of a rapid phase flip at resonances [10–15]. In this work we design an X-shaped plasmonic sensor (XPS) that supports plasmonic resonances of quadrupole modes at the near-infrared region, combining with our common-path optical system and phase-contrast algorithm to boost the sensing resolution of refractive-index plasmonic sensors. The measured sensing resolution shows two orders greater than that of the conventional plasmonic refractive-index sensors [5–7].

In fact, there exist two critical demands to optimize the sensitivity of a plasmonic sensor in phase-interrogation measurements. One is to break the symmetry of the plasmonic structure, such that the corresponding resonant wavelengths for s-polarized and p-polarized modes become different, elevating the phase contrast between the s-polarized and p-polarized modes (${\varphi }_{P-S}$) [16]. The other is to employ high-order resonance modes that allow better sensing capability due to their greater quality factors. The phase change of a resonance mode with a high quality factor is sharper than a resonance mode with a low quality factor, which helps to increase the sensitivities for phase interrogation. Therefore, high-order modes are certainly more sensitive, but their scattering cross section is typically too weak to provide a detectable signal level or a stable signal-to-noise ratio. To meet these two demands, herein we design an XPS with a quadrupole resonance, to optimize both of the sensitivity and signal intensity. The detailed structural dimensions of the XPS are shown in Fig. 1(a), where $L$ $(\text{the length of arms})=380\mathrm{nm}$, $W$ $(\text{the width of arms})=75\mathrm{nm}$, $\alpha$ $(\text{the angle between two arms})=60°$, and the periodicity of the XPS array of 600 nm. To fabricate the designed XPS, we employed an electron beam lithographic system (ELS-7800, Elionix) with the acceleration voltage of 80 kV and beam current of 50 pA to define the pattern as a mold. During the electron beam exposure, we spun polymethyl methacrylate (PMMA, 950 K) as the resist on an SF11 glass substrate, and further applied Espacer (Kokusai Eisei Co., Showa Denso Group, Japan) to ease the charging effect from the nonconductive substrate. Next, we deposited a bilayered film (3 nm titanium and 50 nm gold) by an electron beam evaporator, followed by a lift-off process. Finally, a $540\times 540{\mathrm{\mu m}}^2$ array of the repeated XPS unit cells was realized, and its secondary electron microscopic images are shown in Fig. 1(b).

 

Fig. 1. (a) Illustration of XPS made of gold on an SF11 glass substrate ($n=1.78$). Each dimension is shown in the following: $L=380\mathrm{nm}$, $W=75\mathrm{nm}$, $t=50\mathrm{nm}$, $\alpha =60°$, and periodicity of 600 nm. (b) SEM image of XPS. The scale bar is 600 nm. Inset shows a magnified SEM image with a scale bar of 200 nm.

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To demonstrate the ultrasensitivity of the fabricated XPS by the phase interrogation, it is essential to identify the resonant positions of the XPS first by characterizing its wavelength spectra of the multiple plasmonic modes. The corresponding transmittance analysis at normal incidence was measured by a micro-Fourier-transform infrared spectrometer (Vertex 70v, Bruker), equipped with an infrared microscope (Hyperion 2000 with a $15\times$ objective, $\mathrm{NA}=0.4$, an air-cooled tungsten source, and an InGaAs detector, Bruker). As shown in Fig. 2(a), the experimental result clearly pinpoints that the resonant wavelengths with respect to water are at 1312 nm for p-polarized excitation (TM mode), and at 1780 nm for s-polarized excitation (TE mode), respectively. Notice that we design the resonant wavelengths of XPS at 1312 nm in water under TE excitation on purpose, for matching the working wavelength of the infrared fiber laser we applied for phase-interrogation measurements later. In addition, we also employed a commercial software package, CST Microwave Studio (Computer Simulation Technology GmbH, Darmstadt, Germany), to confirm the resonant positions of the fabricated XPS, as shown in Fig. 2(b). Next, we further obtain the sensitivity of wavelength interrogation by differentiating the resonance positions between air and water in measurement, as shown in Fig. 2(a). By calculating the shift of resonant dips and applying the refractive index of air and water, we can estimate that the sensitivity is 303 nm/RIU, which is similar to the cases of conventional LSPR sensors [1,17]. Both the experimental measurement and the numerical simulation are in good agreement except a small dip of the experimental result at around 1400 nm due to imperfection of fabrication. In addition to spectra analysis, we also show the electric field distribution of the XPS for p-polarized excitation at 1312 nm. Evidenced in Fig. 2(c), we reveal that the plasmonic resonance at 1312 nm stems from the quadrupole mode.

 

Fig. 2. (a) Measurement and (b) simulation of transmittance spectra of XPS. (c) Simulation of electrical field distribution under p-polarized mode excitation at 1312 nm with water. The result shows a quadrupole-mode resonance. The symbols plus and minus mean the charge density distribution.

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To conduct the phase interrogation, we developed an in-house common-path phase detection system illustrated in Fig. 3. We applied total internal reflection configuration at a fixed incident angle to probe the optical phase of XPS by evanescent waves because the XPS responds a greater cross section of scattering and extinction to the TM evanescent waves, so that in this case the signal-to-noise ratio will be better than that of the far-field excitation [18]. Note that the resolution of our common-path phase-interrogation system is $2\times {10}^{-5}\mathrm{rad}$, and other details are listed in [19]. Once the XPS is excited through evanescent waves, the reflected beam passes through a quarter-wave plate and a rotating linear polarizer for the extraction of the optical phase information. After passing through a quarter-wave plate, the traveling s- and p-polarized waves then became left- and right-circular waves, respectively, due to a $\pi /2$ phase retardation. Next, a linear polarizer was selectively rotated to record the optical intensity at different rotation angles. With the measured intensity at $\theta =0$, $\pi /4$, $\pi /2$, and $3\pi /4$, the optical phase difference between p- (${\varphi }_P$) and s-polarized (${\varphi }_S$) waves, ${\varphi }_{P-S}$, can be finally extracted through Eq. (1) [16]:

 

Fig. 3. Illustration of optical setup of our in-house phase interrogation system. The common-path setup is designed to increase S/N ratio by reducing the signal fluctuations between two photodiodes.

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Once the refractive index of the analyte varied, there corresponded a shift in ${\varphi }_{P-S}$ through the excitation of XPS for the phase interrogation. It is worth mentioning that the measured ${\varphi }_{P-S}$ is independent of the intensity of s- and p-polarized waves based on Eq. (1), so that the signal can be well distinguished from noise. Finally, the sensitivity of the XPS probed by phase interrogation was determined by measuring the sucrose solutions with different concentrations of 0.1, 0.25, 0.5, 0.75, and 1.0 wt. %. The corresponding refractive indices of the sucrose solutions are obtained from [20]. Between each test of different concentration, we washed out the sample surface with deionized water for 2 min to ensure there is no residual sucrose. Through linear fitting of the measurement data, the sensitivity reaches 17.46 rad/RIU and each datum point was the average result of 10 measurements, as shown in Fig. 4 (blue square and blue dashed line). We also verify the result by simulation (red triangle), which agrees with our measurement well, and by linear fitting the sensitivity of numerical simulation is 33.44 rad/RIU (red dashed line). In addition, to fairly compare the performances of the wavelength- and phase-interrogation, we cannot directly consider their sensitivities due to different units but their sensing resolution (i.e., the same units). The sensing resolution is the ratio between system resolution and sensitivity, so that its unit turns to RIU only. The system resolutions for the FTIR (Fourier transform infrared) spectrometer and our in-house common-path phase-interrogation system are $3\times {10}^{-2}\mathrm{nm}$ and $2\times {10}^{-5}\mathrm{rad}$, respectively. Therefore, the corresponding sensing resolutions for the wavelength- and phase-interrogation methods are $9.90\times {10}^{-5}\mathrm{RIU}$ and $1.15\times {10}^{-6}\mathrm{RIU}$, clearly evidencing that based on the same nanostructures, our common-path phase-interrogation system indeed provides better sensing performance of 86 times higher than the extinction spectra. In addition to outperforming the conventional wavelength-interrogation method, to our knowledge, such a sensing resolution is also much higher than other reported LSPR sensors [5–9,16].

 

Fig. 4. Experimental analysis (blue square) and theoretical (red triangle) analysis of the sensitivity of the XPS by the phase-interrogation method. The target is sucrose aqueous solution with different concentrations corresponding to different refractive index. By linear fitting, we obtained the sensitivities of 17.46 rad/RIU and 33.44 rad/RIU for measurement (blue dashed line) and simulation (red dashed line), respectively.

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In conclusion, we design an XPS to detect the refractive index change and experimentally compare its sensitivities and sensing resolution between wavelength- and phase-interrogation methods. For the wavelength-interrogation method, we apply an FTIR spectrometer to examine the extinction spectra of XPS, observing a sensitivity of 303 nm/RIU. For the phase-interrogation method, we use an in-house common-path phase-interrogation system, detecting a sensitivity of 17.46 rad/RIU. With the combination of the designed XPS and our phase-interrogation method, we obtain a remarkable sensing resolution of $1.15\times {10}^{-6}\mathrm{RIU}$. Such a result is almost two-orders of magnitude greater than the controlled extinction measurement (i.e., $9.90\times {10}^{-5}\mathrm{RIU}$), and also superior to other reported LSPR sensors.