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Abstract
Optofluidic sensors, which tightly bridge photonics and micro/nanofluidics, are superior candidates in point-of-care testing. A fiber-based interferometric optofluidic (FIO) sensor can detect molecular biomarkers by fusing an optical microfiber and a microfluidic tube in parallel. Light from the microfiber side coupled to the microtube leads to lateral localized light-fluid evanescent interaction with analytes, facilitating sensitive detection of biomolecules with good stability and excellent portability. The determination of the sensitivity with respect to the interplay between light and fluidics, however, still needs to be understood quantitatively. Here, we theoretically and experimentally investigate the relationship between refractive index (RI) sensitivity and individual geometrical parameters to determine the lateral localized light-fluid evanescent interaction. Theoretical analysis predicted a sensitive maximum, which could be realized by synergically tuning the fiber diameter d and the tube wall thickness t at an abrupt dispersion transition region. As a result, an extremely high RI sensitivity of 1.6×104 nm/RIU (σ=4074 nm/RIU), an order of magnitude higher than our previous results, with detection limit of 3.0×10−6 RIU, is recorded by precisely governing the transverse geometry of the setup. The scientific findings will guide future exploration of both new light-fluid interaction devices and biomedical sensors.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Optofluidic sensors, which combine micro/nanofluidics and optics in a very fascinating and valuable way, have arisen because of their high sensitivity with smaller sample consumption and miniaturized devices [1,2]. These sensors have found wide applications in the food and drug industries, environmental monitoring, and clinical diagnostics [3,4]. The fluidic part is exploited not only to efficiently handle the sample to be tested but also as an optical part to reconfigure the guided light, resulting in high interaction efficiency between light and fluids. For example, in Fabry-Pérot cavities [5,6], sensors fabricated from hollow-core [7] and microstructured optical fibers [6,8], fluid guides the light and enables maximal optical coupling across the entire photonic structure. This integrated approach exploits the inherent fluidic capability of photonic structures while preserving effective coupling between light and fluids. In addition, the microfluidic channels can suitably integrate along the optical path based on evanescent interaction. For example, a liquid-core optical ring resonator (LCORR) [9,10] transports and detects the fluid sample by using the microtube as an optical resonant sensor. Biomolecular binding can be detected by measuring the induced whispering gallery mode (WGM) resonance shift, which is induced by the evanescent interaction with analytes. The tubular structure can also be formed by rolling up a strained, functionalized nanomembrane [11–13] with a well-defined shape and size on versatile substrates [14–16], which could miniaturize the sensor size to the nanoscale with multifunction [17] and large-scale integration [18] and allow the detection of single-cell features and behaviors [13,19,20].
The underlying physics of a label-free optofluidic sensor involve the optical interaction in the form of evanescent waves with the target analyte. The detection capability is largely determined by how the sensor translates this evanescent interaction into a detectable optical signal. The high sensitivity of resonant sensors relies on a high-quality factor Q, which results in strict demands on the geometry of the resonant cavity. Alternatively, interferometric sensors are easily fabricated and have good stability [21–23]. To enhance the evanescent interaction, we have developed a fiber-based interferometric optofluidic (FIO) sensor for biomolecular detection [24,25]. The microfluidic tube is attached with an optical microfiber by its side to form a modal interferometer. The light from the optical fiber can effectively penetrate through the tube wall and into the target substance. The FIO sensor has presented a refractive index (RI) sensitivity of 1.2×103 nm/refractive index unit (RIU), which allows for the detection of molecular bindings at the inner tube surface. However, the influence of the transverse geometry on the RI sensitivity remains ambiguous. In this work, we theoretically and experimentally investigate the relationship between RI sensitivity and individual geometrical parameters to determine the lateral localized light-fluid evanescent interaction. We have revealed that certain combinations between the wall thickness t and microfiber diameter d could maximize the optical response. In the abrupt dispersion transition region, the RI sensitivity can be infinitely high. Following the theoretical guidance, we have significantly enhanced the RI sensitivity to 1.6×104 nm/RIU by finely controlling the transverse geometry.
2. Sensing principle
Figure 1(a) shows the schematic of the FIO sensor, which consists of a microfiber and a microtube. The microtube acts as the microfluidic channel for the sample actuated by using a motorized pump. The proximal end of the microfiber connects to a broadband light source (Golight, OS-EB-S-D-1450-400-30-0-FA), and the distal end connects to an optical spectrum analyzer (OSA, Yokogawa, AQ6370C) to measure the transmission spectrum. The optical modes that transmit through the sensor are determined by the transverse geometry, characterized by the microfiber diameter d, tube wall thickness t, and outer tube diameter D, as shown in Fig. 1(a). The two optical modes, denoted as the fiber mode and the hybrid mode (Fig. 1(b)) with comparable powers Ifiber and Ihybrid, respectively, interfere with each other and propagate longitudinally along the waveguide, as shown in Fig. 1(c), resulting in a periodic transmission spectrum. The fiber mode is tightly confined in the silica fiber, while the hybrid mode resides in both the fiber and the wall with a double-lobed profile. The FIO sensor relies on the evanescent field of the hybrid mode to detect the refractive index change near the interior surface, which can be obtained by measuring the wavelength shifts of the transmission spectrum.
Fig. 1. (a) Schematic of the FIO sensor. (b) Calculated intensity profiles of the two guided optical modes, denoted as “fiber mode” and “hybrid mode” in the context. (c) Light intensity over the FIO sensor. (d) Calculated transmission spectrum of the FIO sensor.
3. Theoretical analysis
The transmission property of the FIO sensor can be expressed by
We assume that λ is approximately 1550 nm, the RI of the surrounding polymer is 1.37, and the RI of the fluid in the microtube is approximately 1.33. Figure 2(a) shows the calculated Ω as a function of the geometrical parameters d and t, which presents higher amplitudes in the lower-left corner. Since the microfiber and microtube have identical refractive indices, the absolute sizes of d and t determine the ability to confine light in the waveguide. Therefore, smaller d and t cause more fractions to spread out of the waveguide into the liquid sample, resulting in a higher Ω. In addition, we have found that the d/t contrast largely determines the central location of the two modes. A decreased d/t pushes the intensity profiles of the two modes, especially the hybrid mode, towards the inward direction. To demonstrate the effect of d/t, Fig. 3(a) depicts the radial distribution of the hybrid mode along the blue line shown in Fig. 1(a), with a fixed d at 6 µm. Figure 3(b) shows that the hybrid mode with an appropriately decreased d/t penetrates deeper into the liquid sample, leading to an extended sensing area and strengthened evanescent field. Note that excessively large t relative to d would move the inner wall surface away from the center of the hybrid mode, leading to a decreased evanescent field, as shown by the purple line with d/t=2 in Fig. 3(a). As a result, an optimal d/t amplitude at 2.4 µm was determined for a maximum Ω. In Fig. 2(a), the highest absolute value of Ω, corresponding to the strongest evanescent field, is obtained at a certain point of d=3 µm and t=1.1 µm (neither t=0.3 µm nor any value of t >1.1 µm), where are the best combinations of d and t within the range of 3 µm ≤ d≤8 µm and 0.3 µm ≤ t≤5 µm.
Fig. 2. Calculated results of Ω (a), G (b), and RI sensitivity S (c) as a function of the microfiber diameter d and capillary wall thickness t. The dashed lines in (b) and (c) mark the dispersion transition, corresponding to G=0 and S=∞.
Fig. 3. (a) Radial intensity distribution and (b) intensity profiles of the hybrid mode for different relative sizes of d and t (d/t=6, 4, 3, 2.4, and 2). Inset: radial intensity distribution at the interior surfaces of the microtube with the couples of (d, t) in (a). The dashed lines show the interior and exterior surfaces of the microtube. The microfiber diameter was kept at d=6 µm.
Figure 2(b) shows the relationship between the group RI difference G and the geometrical parameters d and t. The value of G (i) is generally negative, according to Eq. (3), resulting in a positive RI sensitivity S, (ii) equals to zero, corresponding to infinitely great RI sensitivity S, which is marked with the dotted line, and (iii) is positive leading to negative RI sensitivity S, which is enabled for the region circled with the dotted line. To reveal the underlying physics of the G map, we plot Δneff /λ and ∂Δneff /∂λ as a function of the microfiber diameter d and capillary wall thickness t in Figs. 4(a) and 4(b) with the same color scale. These two maps exhibit that both Δneff /λ and ∂Δneff /∂λ have higher amplitudes with smaller d and t. In comparison, ∂Δneff/∂λ is higher than Δneff /λ in most cases, corresponding to larger red and green regions. The dotted line in Fig. 2(b) corresponds to the case that these two factors have identical values. In the region circled with the dotted line, Δneff /λ is larger than ∂Δneff /∂λ, corresponding to G>0. Figure 4(c) shows the evolution of G with two selected wall thicknesses t along lines t=1.5 and 2 µm, respectively. Figure 4(d) demonstrate the corresponding sensitivities S, to show the effect of G on the RI sensitivity. For t=1.5 µm, G has a zero point at d=3.6 µm, which leads to an infinitely high sensitivity. For t=2 µm, G can only take negative values and the RI sensitivity have finite values. Notably, the maximum S values correspond to the minimal G amplitudes, suggesting the significant effect of the dispersion factor on RI sensitivity.
Fig. 4. Calculated Δneff /λ (a) and ∂Δneff /∂λ (b) as a function of the microfiber diameter d and capillary wall thickness t. Calculated group effective RI difference G (c) and RI sensitivity S (d) with microfiber diameter d variation at wall thickness t = 1.5, 2, and 2.6 µm.
Figure 2(c) shows the RI sensitivity S as a function of d and t, which can be also divided into three regions regarding the dispersion term G. Extremely high sensitivity can be achieved in the case of G∼0. The triangular G>0 region presents higher sensitivity amplitudes at higher wall thicknesses. Over the G<0 region, there is a banded region with high sensitivity, denoted by the darker orange area shown in Fig. 2(c), as a result of the contribution of Ω. We have extracted the (d, t) pairs with the top 50 sensitivities at the region d>5 µm, and the optimal (d, t) combinations can be expressed as
The outer diameter D of the tube imposes little on Ω, G, and RI sensitivity S from the calculated results. Taking our sensor described in [25] as an example, it is fabricated with the parameters d=6.9 µm and t=2.2 µm, which is marked by using a star in Fig. 2(c). The measured RI sensitivity was 1297 nm/RIU at approximately 1550 nm. To improve the sensitivity S, we should push the couples of (d, t) to the dispersion transition lines or the darker orange banded region.
4. Experimental verification
Figure 5 shows the experimental process to verify the above theory. The fabrication of an FIO sensor has been described in our previous reports [24,25]. Briefly, an uncoated singlemode optical fiber and a silica tube (Polymicro Technologies, TSP530660) are placed in lateral contact and thermally tapered down to a transverse diameter of tens of microns. The tapering was performed by using an oxyhydrogen flame as the heat source and stretching them with two linear stages. The tube has an outer diameter of 660 µm and a wall thickness of 65 µm. The fiber is 125 µm in diameter. To finely control the transverse structure, two additive processes have been introduced (as shown in Fig. 5):
- a. Prior fiber tapering. The singlemode fiber was downsized by performing a tapering process before paring with the tube. FIO sensors with varying microfiber diameters d have been achieved, as exhibited in Fig. 6(a).
- b. Internal pressure control. The microfluidic tube was sealed at its distal end with a UV-curable polymer. Its proximal end was connected to a nitrogen chamber to pump the tapered structure with controllable pressure. As a result, we are capable of fabricating FIO sensors with different wall thicknesses t, as shown in Fig. 6(b).
Fig. 5. Fabrication of an FIO sensor. Prior fiber tapering and additive internal pressure control have been introduced to finely control the critical geometrical parameters d and t. Microfiber diameter d and tube wall thickness t measurement by SEM. RI sensitivity obtainment by recording the wavelength shift caused by the fluid changing from water to the mixture of water and alcohol.
Fig. 6. SEM images of the transverse geometries with (a) different microfiber diameters d and (b) different wall thicknesses t. (c) Extended heating durations.
In addition, an extension of heating time allows the molten tube to shrink as a result of the surface tension. Consequently, the tube wall can be slightly thickened. However, this process would also induce the deformation of the optically waveguiding structure, as shown in Fig. 6(c), which results in a significant optical loss.
Here, we fabricated a large number of sensors (approximately 100) with t≈2.2 µm and varying microfiber diameters d. As shown in Fig. 5, a group of sensors with a specific d were fabricated with the same hydrogen flow, stretching velocity and length. Some of them (more than 3) are imaged by using a scanning electron microscope (SEM) to measure the fiber diameter d and wall thickness t. The other sensors (more than 3) were encapsulated in a UV curable polymer to form a stable sensor package to test their refractive index responses. The transmissions spectra were recorded, with fluid indices n1=1.3325 (deionized water) and n2=1.334 (water/alcohol mixture) to measure the spectral shift Δλ. The refractive indices of the fluids have been calibrated by using a refractometer (ATAGO, PAL-RI). Each RI sensitivity can be obtained calculating S=Δλ/(n2-n1). Such processes have been repeated with a number of sensor groups with different d, by using different pre-tapered fibers. Figure 7(a) shows the measured RI sensitivities as a function of d, which are consistent with the calculated result. Figures 7(b)∼7(m) show the measured spectral responses of all the groups shown in Fig. 7(a). The maximum sensitivity can achieve at d=4.4 µm, with an average sensitivity of 1.6×104 nm/RIU and mean square error σ=4074 nm/RIU.
Fig. 7. (a) Experimental results of RI sensitivities as a function of microfiber diameter d. (b) to (m) Recorded spectral shifts of the individual groups.
According to the theoretical guidance, further reducing d would further boost the sensitivity. However, experiment shows that further downsizing d can induce high losses and reduce the contrast of the interference spectrum as a result of the unbalanced intensity distribution over the two optical modes. Therefore, the effect of the dispersion transition was not experimentally observed. There is room to exploit a more precise fabrication method to push the couples (d, t) towards the turning point to obtain higher sensitivity. However, note that an infinite sensitivity cannot be achieved, considering a finite spectral width over an interferometric dip. We have measured the fluctuation in the spectral shift for the FIO sensor with the maximal sensitivity; its standard deviation is 47.6 pm in 100 min at room temperature. Therefore, a sensor with a very low detection limit of 3.0×10−6 RIU can be obtained. Note that the transmission spectra in Fig. 7 may somewhat deviate from the ideal one plotted in Fig. 1(d), as a result of the involvement of the higher-order modes (HOMs). The HOMs are excited simultaneously at the transition region. These unwanted mode fractions can contribute to the transmission spectrum and the sensor response [26,27]. The HOM fraction may vary with wavelength, which may even induce a blue wavelength shift. However, we found that the HOM effect is relatively weak and most spectral components have almost identical or close RI responses. When the fluid refractive index changes, the mode fractions between the core, hybrid and higher-order modes may also vary, resulting in a change in fringe contrast. The individual sensors in the same group may present a difference in the spectral range (FSRs) (dip spacing), which is inversely proportional to the length of the interferometer. In contrast, the RI sensitivity is not relevant with the sensor length, and we did not strictly control the sensor length..
Table 1 presents the measured sensitivities experimentally obtained with microfiber evanescent-wave sensors in the literature for comparison. The sensitivity of the FIO sensor has been enhanced by an order of magnitude on the basis of our previous work. The current sensitivity is on the same level with the Sagnac and Mach-Zehnder sensors.
Table 1. Measured RI sensitivities of the microfiber evanescent-wave sensors.
5. Conclusion
The FIO sensors are promising for biomedical assays and analysis, owing to the integration of a fiber-optic evanescent-wave sensor and a microfluidic channel. Here, we have detailed the relationship of the RI sensitivity S of the FIO sensor with the fiber diameter d and microtube wall thickness t. Theoretical analysis shows that the sensitivity of an FIO sensor can be remarkably enhanced by pushing the combinations of fiber diameter d and wall thickness t to approach the turning point line. With the theoretical guidance, we have finely controlled the sensor geometry by introducing two additive process, namely the prior tapering and the internal pressure control. As a result, the RI sensitivity can achieve 1.6×104 nm/RIU (σ=4074 nm/RIU), corresponding to an LOD of 3.0×10−6 RIU. Further tuning of couples of (d, t) by combining tapered fiber with tapered silica tube or another material tube may promote the RI sensitivity of the FIO sensor to an extremely high level. Our studies offer an in-depth probe into lateral localized light-fluid evanescent interactions, open up new avenues for biomolecule detection at very low levels, and inspire the future development of FIO sensors in point-of-care testing.
Funding
National Natural Science Foundation of China (NSFC) (61705083, 61775082, 61805106, U1701268); Natural Science Foundation of Guangdong Province (GNSF) (2018A030313677, 2019A1515011144); The Local Innovative and Research Teams Project of Guangdong Pearl River Talents Program (2019BT02X105); Fundamental Research Funds for the Central Universities (21617305).
Disclosures
The authors declare no conflicts of interest.
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