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Abstract
This work proposes and demonstrates a novel interferometric sensor based on a zigzag-shaped tapered optical microfiber (Z-OMF) working at the dispersion turning point (DTP). The Z-OMF can be fabricated in a controllable manner through a modified fiber tapering method. Our study shows that the bending taper can transfer a portion of the fundamental HE11 mode to higher-order modes, and when the bending angle of the Z-OMF reaches 1.61°, high contrast interference fringes can be formed between the HE11 and the HE21 modes. More importantly, we find that by optimizing the diameter of the OMF, the group effective refractive index (RI) difference between HE11 and HE21 mode equals zero, and the refractive index sensing performance can be dramatically improved. To validate our proposed sensing mechanism, we experimentally demonstrate an ultrahigh sensitivity of 1.46×105 ± 0.09×105 nm/RIU. The proposed Z-OMF interferometer has the advantage of high sensitivity and low cost and shows excellent potential in chemical and biological detection.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In the past few decades, optical microfiber sensors have witnessed vigorous development. Due to their high evanescent field ratio and small geometry size, there is a wide range of applications, including biological detection, environmental monitoring, food security, etc. Notably, microfiber-based biochemical sensors have garnered tremendous attention nowadays and show potential applications in chemical analysis and biological assay [1–7]. The majority of the microfiber-based biochemical sensors rely on the surrounding refractive index (SRI) sensing mechanism. By now, various novel microfiber-based RI sensing schemes have been proposed and investigated. These sensing devices include tapered optical microfiber [8,9], optical microfiber couplers [10–12], non-circular cross-section microfibers [13,14], microfiber resonators [15–17], and microfiber gratings [18,19].
On the other hand, improving the sensitivity of existing microfiber sensors has long been a common target for researchers. Optical microfiber sensors with outstanding sensitivity are highly desired in trace bio-analyte detection, which could boost potential applications in acute myocardial infarction diagnosis and even molecular characterization on the single-molecule level. During the past years, an enormous amount of studies that aim to enhance the sensing performance of optical microfiber sensors have been reported. Generally, these proposed strategies can be divided into three categories: nanomaterial decoration [6–8], Vernier effect [4,16,20], and the dispersion turning point (DTP) [9,12,21,22]. Particularly, the DTP in microfibers has proven to be an effective exceptional phenomenon for sensitivity improvement. DTP corresponds to the point where the group effective RI difference of guided modes in coupling equals zero. By carefully tailoring the geometry and optical parameters of a microfiber device, the DTP can be readily achieved in microfiber couplers [10–12], tapered optical fibers [21,22], and highly birefringent microfiber Sagnac interferometers [23–25], and show potentially superior properties that can be exploited to achieve ultrahigh sensitivities of tens of thousands nm/RIU in liquids and gas medium.
The tapered optical microfiber is simpler in configuration than other device schemes, significantly facilitating practical implementation. However, the transition segments should be abrupt to break the adiabaticity condition and excite higher-order modes effectively. The fabrication of abrupt tapers usually relies on the small heating spots from arc discharge or CO2 lasers [26], unavailable in most commercial fiber tapering apparatuses that utilize oxyhydrogen flame or electrical ceramic heating elements. In order to overcome this limitation, specialty fibers such as double cladding optical fibers [23] and two-mode optical fibers [27] are employed by splicing between two sections of single-mode fibers and tapering by commercial fiber tapering apparatuses. The core mismatch between the single-mode fiber and the specialty fiber can improve the excitation ratio of higher-order modes and results in high contrast interference fringes.
This study proposes and demonstrates a zigzag-shaped OMF (Z-OMF) interferometer fabricated from standard single-mode optical fibers via a modified flame brushing tapering method with a high degree of controllability. We first studied the necessary bending angle of the taper to achieve a high-quality interference spectrum between the HE11 and the HE21 modes. Then we numerically investigated the dispersion characteristics of the sensor and found that the DTP can be achieved only when the diameter of the waist region lies in a specific range. Finally, we experimentally demonstrated the DTP and obtained an ultrahigh sensitivity of 1.46×105 ± 0.09×105 nm/RIU.
2. Sensor geometry and operation mechanism
Figure 1 shows the schematic diagram of the proposed Z-OMF sensor structure, which consists of two bent tapers that connect with the single-mode fibers and a section of uniform microfiber. When guided light in the fundamental core mode enters the bent taper region, it can excite both the HE11 mode and HE21 mode due to the break of the adiabatic condition. These two modes propagate through the waist region and recombine in the up-taper region, which forms the basic Mach-Zehnder interferometer configuration. The phase difference can be caused and accumulated between these two modes when they travel along the optical path due to the different effective refractive indexes. Thus, an interference spectrum can be formed at the output port.
It should be noted that, in a cylindrically symmetric nonadiabatic optical tapered microfiber, the LP01 mode can excite the HE11 and HE21 modes, and interference occurs between these two modes. However, for a Z-OMF, the asymmetric taper structure favors the excitation of the HE11 and HE21 modes. Although other higher-order modes can also be excited in the asymmetric taper, the ratio is small enough to be negligent. The beating between HE11 and HE21 modes occurs when they travel along the Z-OMF optical path. The guided modes can seep into the surrounding medium through the evanescent wave and interact with the surrounding medium. Different modes possess different ratios of the evanescent wave, and hence, experience different degrees of light-medium interaction. Consequently, the variation in the ambient liquid medium could change the optical path differences between the two modes and the interferometer wavelength shifts.
The evolution of the transmission spectra obeys the cosine function of the phase difference between the HE11 and HE21 modes. According to the two-mode interferometric theory, with a phase difference $\phi $, the output spectrum can be expressed as:
where $\phi = 2\pi \Delta {n_{\textrm{eff}}}L/{\lambda _N}$ is the phase difference between the HE11 and HE21 modes, and $\Delta {n_{eff}} = {n_1} - {n_2}$, where n1 and n2 are the effective refractive indexes of the HE11 and HE21 modes, respectively. L is the effective coupling length, and I1 and I2 are the intensities of the two modes, respectively. λN denotes the wavelength of Nth dip on the interference spectrum. By taking a minor variation, the RI sensitivity of λN can be calculated as [9]:3. Theoretical simulations and optimization procedure
We first numerically optimize the parameters of the Z-OMF sensor to achieve high-quality interference spectra and ultra-high sensitivities. The bending angle of the taper and the waist diameter are the two most parameters of the Z-OMF. The bending angle of the taper plays a dominant role in the excitation of the higher-order modes, and an appropriate bending angle is crucial for achieving high-contrast interference fringes. The diameter of the uniform waist region determines the spectral position of the DTP.
3.1 Bending angle
We adopted the beam propagation method to investigate the mode excitation property of the bent taper. As the down taper plays the primary role in the mode conversion, the up taper only functions as the optical power combiner, so our study mainly focuses on the down taper. A 3D model was built to simulate the bent taper. As shown in Fig. 2(a), the bent taper can be divided into three sections: the thick straight taper, the bent section, and the thin straight section. We set the length of the bent section to be 600 µm, the starting diameter and ending diameter to be 45 µm and 40 µm, respectively. These parameters are consistent with those of experimentally fabricated Z-OMFs. We set the initial length of the whole taper to be 7.1 mm and the diameter of the uniform waist to be 10 µm. Such a long and gentle taper can effectively suppress the mode conversion caused by abrupt diameter shrinkages. The wavelength was set to be 1550 nm. The fundamental LP01 mode was launched into the SMF, and the evolution of the HE11 mode, HE21 mode, and HE12 mode were monitored. In our study, we varied the bending angle α from 0° to 2.26°.
Fig. 2. (a) Schematic drawing of the bent taper. (b) Simulated light beam propagation trajectory in the bent taper. (c) monitored power evolution of the excited modes along the bent taper. (d) Actual mode excitation ratio versus bending angle for HE11, HE21, and HE12 modes.
The typical simulated light beam propagation trajectory in the bent taper is displayed in Fig. 2(b). It clearly shows that when light travels through the bent region, beating patterns form in the thin straight section and the uniform waist section. The monitored optical power evolution tendency in Fig. 2(c) indicates that the interference is mainly contributed by the HE11 mode and the HE21 mode. As the sinusoidal oscillation of the monitored modal power in the waist region is caused by the optical power exchange between the interferential modes, we can use the central point value between the oscillation dips and peaks to represent the actual power value of the modes. The evolution of the actual power of HE11 mode, HE21 mode, and HE12 mode as the bending angle gradually increases from 0° to 2.26° are shown in Fig. 2(d). It shows that when the bending angle is small, the excitation ratios of HE21 mode and HE12 mode are below 0.1, and the HE11 mode dominates. However, when the bending angle increases, the excitation ratio of the HE11 mode decreases steadily, and the excitation ratio of the HE21 mode grows continuously, whereas the excitation ratio of the HE12 mode keeps below 0.1. The excitation ratio of HE11 mode and HE21 mode is equal to 0.41 when the bending angle reaches 1.61°, the power ratio of the HE11 mode keeps decreasing, and the HE21 mode keeps increasing. Thus, the optimum bending angle to achieve high contrast interference fringes is 1.61°. However, if we regard an interference fringe with a depth of 6 dB as high-quality interference fringes that are easy for data processing, then the optimal bending angle can be extended to 1.39°∼1.85°.
3.2 Fiber diameter
In this section, we investigate how the diameter of the Z-OMF influences the DTP and sensitivity. Considering that the phase difference is mainly induced by the uniform waist region and the taper's influence is negligible, we focus on the uniform waist region in the following numerical study.
Numerical analysis has been carried out to study how fiber diameter and wavelength influence the DTP and RI sensitivity. Figure 3(a) shows the calculated group effective RI difference G between HE11 mode, HE21 mode for a Z-OMF as a function of fiber diameter. The ambient refractive index is set to be 1.333 (water). It is clear that for a specific operation wavelength, the curve for G can be divided into two sections by a zero point (i.e., G = 0). According to Eq. (2), the RI sensitivity can reach infinity when G = 0, and this critical diameter value gradually increases from 1.7 to 2.6 µm as the operation wavelength increases from 1000 nm to 1500 nm.
Fig. 3. (a) Group effective RI difference versus fiber diameter with different wavelengths of 1000 nm, 1100 nm, 1200 nm, 1300 nm, 1400 nm, and 1500 nm (SRI = 1.333). (b) Calculated RI sensitivities as a function of fiber diameter with different wavelengths with RI of 1.333.
In order to elucidate how the sensing performance is influenced by fiber diameter more clearly, we calculated the RI sensitivities of the Z-OMF RI sensors as a function of fiber diameter for different operation wavelengths. As depicted in Fig. 3(b), when the fiber diameter is smaller than the turning point diameter, the sensitivity dramatically increases towards -∞ as the diameter increases. In contrast, when the diameter is larger than the turning point diameter, the sensitivity is significantly enhanced towards +∞ as the diameter approaches the turning point. Therefore, the sensitivity will drop away from DTP. These simulation results provide helpful guidelines for the fabrication of high-performance Z-OMFs.
4. Experimental demonstration
4.1 Fabrication of the Z-OMF
The Z-OMF is prepared by using a modified flame brushing method. Unlike the conventional fiber tapering strategy in which the optical fiber is aligned with the pulling direction, we exerted a slightly tilted angle to the optical fiber when mounted it on the fiber tapering setup. Thus, an included angle is formed between the axial of the optical fiber and the pulling direction. As shown in Fig. 4(a), when the optical fiber is heated and pulled by the translation stages, bent tapers form, and the resultant uniform waist region is nearly parallel to the pulling direction. In this way, by tuning the initial inclusion angle between the optical fiber and pulling direction, the bending angle of the taper can be precisely controlled. In order to obtain good control over the diameter and optical properties of the fabricated Z-OMF, we connected the two ends of the optical fiber to a 1550 nm laser source and a detector, respectively. Thus the optical loss and the output spectra can be measured in real-time, and the fabrication process can be terminated once the desired parameter is reached.
Fig. 4. (a) Schematic diagram of the modified fiber tapering method for fabrication of Z-OMF. (b) The normalized transmission spectrum of 1550 nm laser versus lengthening the time during the tapering process. (c) Normalized frequency versus length of the microfiber.
Figure 4(b) shows a typical recording of the transmission during the tapering process of a Z-OMF, which is pulled about 3 centimeters. In the pulling process, the fundamental mode begins to convert to high-order mode from point A, and further, its energy dissipates to the surrounding because of a sharp drop in the core radius from point B. The reduction of the fiber diameter can increase the interference frequency. Consequently, spectrum oscillation appears subsequently after pulling, which means that higher-order modes can be excited. Then all the excited higher modes reached their cut-off point C, and the interference signal disappeared where the diameter meets the single mode condition again. In order to identify the excited modes, the short-time Fourier Transform analysis has been carried out. This analysis method known in acoustics as a sonogram or spectrogram is an effective tool to investigate the observed oscillations originating from the beating of different modes [28]. As Fig. 4(c) shows, curves from top to bottom represent the beating of fundamental HE11 mode with HE12 mode, HE21 mode, and TE01 mode, respectively. Excitation of different modes enables the modal interference for the Z-OMF.
Then the Z-OMF is packaged inside the microchannel of a poly(methylmethacrylate) (PMMA) chip and fixed in a fluid cell using the glue. Finally, it was integrated with a PDMS cover for the delivery of sample solutions. A digital microscope (KEYENCE VHX-1000) is employed to measure the profile of the fabricated Z-OMF. The microscopic image of a fabricated Z-OMF is displayed in Fig. 5. The overall length of the Z-tapered microfiber is about 21.9 mm, and the waist diameter is about 2.3 µm, which corresponds to the dispersion turning point of 1300nm. The bending angle of the taper is measured to be 1.73°, which lies within the numerically optimized bending angle range of 1.39°∼1.85°.
4.2 Sensing performance of the Z-OMF
Finally, we tested the RI sensing performance of the fabricated Z-OMF. In the experiment, light from a broadband source (BBS, YSL Photonics, SC-5) is launched into one end of the Z-OMF, and the output spectrum from the other end is collected by an optical spectrum analyzer (OSA, Yokogawa AQ6370D). The overall sensing experiments are carried out in a clean room with a temperature of 22 ± 0.5°C to eliminate the influence of temperature fluctuation.
Sensing experiments in a low RI region around 1.333 were investigated since it is a typical RI of the water-based biochemical analyte. Glycerol aqueous solutions with RIs from 1.33300 to 1.33320 with small increments are added into the flow cell sequentially. The RIs of the solutions were measured using an Abbe refractometer, which works at the visible range. Although there may be a slight discrepancy between the values measured in the visible range and the near-infrared range, the RI values measured by an Abbe refractometer can provide a reference to evaluate the performance of the Z-OMF sensor. To ensure the measuring accuracy, we replace the solution in the fluid cell with the same RI solution six times until the spectra become stable before each measurement.
Ultrahigh sensitivity usually can be achieved when the interferometer operates near the DTP. Therefore, several dips closest to the DTP have been selected to explore the RI sensing properties of Z-OMF. When the SRI gradually increases from 1.33300 to 1.33320, as shown in Fig. 6(a), the interference dips shift towards the DTP. The DTP gradually shifts to shorter wavelengths, which are in good accordance with our previous numerical results. The sensitivities of the dips that are near the DTP are presented in Fig. 6(b). The average sensitivity is calculated by taking into account all the measured points. It is found that the RI sensitivity increases dramatically as the dips get close to the DTP. Namely, the closer the dips/peaks are to the DTP, the greater the shifts are. An ultrahigh positive sensitivity of 1.46×105±0.09×105 nm/RIU has been achieved (Dip G). In addition, the polarization response of Z-OMF has also been verified in experiment, and it is found that the sensing characteristic of Z-OMF is polarization-independent, which is in that the birefringence caused by the asymmetrical structure originating from the slight bending angle can be ignored.
Fig. 6. (a) Transmission spectral response to SRI range from 1.33300 to 1.33320. (b) Wavelength shifts of interference dips versus SRI.
5. Conclusion
In conclusion, an ultrasensitive RI sensor based on a zigzag-shaped tapered optical fiber has been proposed and experimentally demonstrated. The Z-OMF is fabricated through a modified brushing flame tapering method. The higher-order modes excitation property of the bent taper has been numerically investigated, and the results indicate that an optimal value exists to achieve high purity interference between HE11 and HE21 modes. Then, the modal interference between HE11 mode and HE21 mode has been investigated, where an ultrahigh sensitivity can be obtained at the dispersion turning point. As a proof of concept, a RI sensitivity of 1.46×105 ± 0.09×105 nm/RIU has been achieved at the fiber diameter of 2.3 µm. The property of ultra-high RI sensitivity in the biologically relevant RI range makes the Z-OMF a promising platform for chemical and biological sensing applications.
Funding
National Natural Science Foundation of China (61974143, 61727813, 62005101, 61805241); Youth Innovation Promotion Association of the Chinese Academy of Sciences (2020223).
Disclosures
The authors declare that there are no conflicts of interest related to this paper.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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