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Abstract
Fiber-optic sensors are an indispensable element of modern sensing technologies by virtue of their low cost, excellent electromagnetic immunity, and remote sensing capability. Optical Vernier effect is widely used to enhance sensitivity of fiber-optic sensors but requires bulky and complex cascaded interferometers. Here we propose and experimentally demonstrate an ultracompact (∼2 mm by ∼2 mm) Vernier-effect-improved sensor by only using a single microfiber-knot resonator. With the Vernier effect achieved by controlling the optical beating with the spectral ripple of a super light emitting diode (SLED), we show ∼20x sensitivity enhancement for quantitative temperature monitoring. Our sensor creates a new practical method to realize Vernier effect in fiber-optic sensors and beyond.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Fiber-optic sensors are an indispensable element of modern sensing technologies by virtue of their low cost [1,2], excellent electromagnetic immunity [3,4], and remote sensing capability [5–7]. Various structures and configurations have been explored to achieve fiber-optic sensors with high reliability and sensitivity. Among them, fiber-optic sensors based on a single resonator or interferometer, such as fiber Bragg gratings [8–10], Fabry-Perot resonators [11–14], Mach-Zehnder interferometers [15–17], and microfiber knot resonators [18–22], attract great interest due to their low cost, small footprint, ease of fabrication, and quantitative sensing capability [23]. However, most of them suffer from moderate sensitivity partially resulting from their limited sensing mechanisms.
Optical Vernier effect originating from the optical beating of two interferometers with slightly shifted interferometric frequencies provides a promising mechanism to boost the sensitivity of fiber-optic sensors and beyond [24–26]. It has been applied to different interferometric configurations, including Fabry-Perot interferometers [27], Mach-Zehnder interferometers [28], and Sagnac interferometers [29]. However, since the optical beating of two interferometers is needed for implementation of the optical Vernier effect, it conventionally requires a bulky and complex configuration of cascaded interferometers. This sacrifices the merits of fiber-optic sensors based on a single resonator or interferometer mentioned above [30–32].
In this article, we propose and experimentally demonstrate an ultracompact (∼2 mm by ∼2 mm) Vernier-effect-improved sensor by only using a single microfiber-knot resonator. This is enabled by designing and experimentally optimizing the microfiber-knot resonator to realize optical beating with the spectral ripple of a SLED. Specifically, we experimentally vary the diameter of the tapered microfiber to approach the critical coupling condition to obtain the maximum extinction ratio of the microfiber-knot resonator. Moreover, to verify the optical Vernier effect, we experimentally tune the diameter of the microfiber-knot resonator to match its spatial frequency with that of the spectral ripple of the SLED. With the Vernier-effect-improved sensor, we show ∼20x sensitivity enhancement and use it for quantitative temperature monitoring, which verifies the practical utility of the demonstrated method for realizing Vernier effect in fiber-optic sensors and other types of single-resonator sensors.
2. Results and discussion
2.1 Design of the Vernier-effect-improved sensor
The design of the ultracompact Vernier-effect-improved sensor by a single microfiber-knot resonator for quantitative temperature monitoring is shown in Fig. 1. The sensor is mainly comprised of a microfiber-knot resonator with the microfiber diameter of d and the knot diameter of D. These geometric parameters are selected to match the spatial frequency of the microfiber-knot resonator with that of the intrinsic spectral ripple of the SLED (ZBOS 1200-1700-SLED) to realize optical Vernier effect. The hotplate with a temperature resolution of 0.1 °C is used to provide a controllable temperature environment for the application of quantitative temperature monitoring while the optical spectrum analyzer (OSA, Yokogawa AQ6370D) is used to observe the transmission spectrum of the Vernier-effect-improved sensor.
Fig. 1. Design of the ultracompact Vernier-effect-improved sensor by a single microfiber-knot resonator for quantitative temperature monitoring. The microfiber-knot resonator with the microfiber diameter of d and the knot diameter of D is tuned to match its spatial frequency with that of the intrinsic spectral ripple of the SLED to realize optical Vernier effect. The insets show the microscope images of the fabricated microfiber-knot resonator. The hotplate is used to provide a controllable temperature environment for the application of quantitative temperature monitoring while the optical spectrum analyzer is used to observe the transmission spectrum of the Vernier-effect-improved sensor.
2.2 Experimental realization and tuning of the Vernier-effect-improved sensor
To ensure a high signal-to-noise ratio in sensing applications, we experimentally optimize the extinction ratio of the microfiber-knot resonator by varying the coupling condition as show in Fig. 2. As the extinction ration of the resonator is mainly determined by the coupling efficiency between the microfiber and the knot, we experimentally vary the diameter of the tapered microfiber to control the coupling efficiency. The microfiber diameter is controlled by an adiabatic tapering process of a commercial single mode optical fiber (Corning F-SMF-28) via using an oxyhydrogen flame as the heating source [33,34]. The microfiber knot is obtained by assembling one end of the microfiber into a loop and tightening it under a microscope to control the knot diameter as shown in Fig. 2(a)-(c). The transmission spectra of the resonators with a knot diameter of 1.8 mm and different microfiber diameters are shown in Fig. 2(d). The transmittance equation for the microfiber-knot resonator can be described by the equation [35]:
where a is the optical loss coefficient of the microfiber knot, t is the coupling coefficient from the straight microfiber to the microfiber knot. With the microfiber diameter of 3.0 µm shown by the inset in Fig. 2(a), the coupling efficiency is smaller than the optical loss in the resonator, which results in a relatively small extinction ratio due to this undercoupling. When the microfiber diameter is decreased to 2.1 µm as shown by the inset in Fig. 2(b), the coupling efficiency is close to the optical loss of the resonator, which leads to a large extinction ratio due to approximating the critical coupling. When the microfiber diameter is further decreased to 1.2 µm as shown by the inset in Fig. 2(c), the coupling efficiency is larger than the optical loss of the resonator, which also results in a relatively small extinction ratio due to this overcoupling. Moreover, the large coupling efficiency decreases the quality (Q) factor of the resonator from ∼20,000 to ∼10,000, which is not demanded for sensing application. Therefore, the microfiber diameter of 2.1 µm is selected for fabricating our Vernier-effect-improved sensor.Fig. 2. Experimental tuning of the extinction ratio of the microfiber-knot resonator by varying the coupling condition. The corresponding microscope images of the microfiber-knot resonators are shown in (a) - (c), respectively. (d) The transmission spectra of the microfiber-knot resonators at undercoupled (black line), overcoupled (magenta line), and critically coupled (red line) conditions, respectively.
To experimentally realize the optical Vernier effect in the sensor, we need to match the spatial frequency of the microfiber-knot resonator with that of the intrinsic spectral ripple of the SLED. The emission spectrum of the SLED is firstly characterized as shown in Fig. 3(a). The free spectral range of the intrinsic spectral ripple is ∼0.308 nm. By conducting Fourier transformation of the spectrum, its spatial frequency spectrum is obtained in Fig. 3(d) with a peak at ∼3.2 nm-1 which corresponds to the free spectral range of the spectral ripple. With knowing this spatial frequency, we fabricated a microfiber-knot resonator with a microfiber diameter of 2.1 µm and a knot diameter of 1.8 mm. Its free spectral range is ∼0.324 nm as shown in Fig. 3(b) while the corresponding spatial frequency is ∼3.1 nm-1 as shown in Fig. 3(e). Theoretically, the free spectral range of a microfiber-knot resonator $FS{R_\textrm{s}}$ can be estimated by using the following equation [1]:
Where $\lambda $ is the wavelength in the vacuum and ${n_{\textrm{eff}}}$ is the effective refractive index. At the wavelength of 1620 nm, the calculated free spectral range of our resonator is 0.32 nm with which our experimental result agrees well. The small detuning between the spatial frequencies of the spectral ripple and the resonator enables the optical beating for realization of optical Vernier effect as shown in Figs. 3(c) and 3(f). The measured free spectral range of the Vernier envelop $FS{R_\textrm{v}}$ is 6.81 nm, which agrees well with the theoretical value 6.24 nm obtained by using the following equation [36]:Fig. 3. Experimental realization of optical Vernier effect by optical beating (a) The emission spectrum of the SLED. The free spectral range is 0.308 nm. (b) The transmission spectrum of the microfiber-knot resonator. The free spectral range is 0.324 nm. (c) The transmission spectrum of the Vernier-effect-improved sensor. The free spectral range of the Vernier envelop is 6.81 nm. Their corresponding spatial frequency spectra are shown in (d)-(f), respectively.
To further verify the above conclusion, we experimentally tune the optical Vernier effect by varying the detuning between the spatial frequencies of the spectral ripple and the resonator. Specifically, we experimentally tune the spatial frequency of the resonator by changing the knot diameter from 2.35 mm to 1.57 mm while maintaining the microfiber diameter of 2.1 µm as shown in Figs. 4(a)-(e). Correspondingly, the free spectral range of the resonator $FS{R_\textrm{s}}$ varies from 0.264 nm to 0.373 nm as shown in Figs. 4(f)-(j) while the Vernier envelope variations are shown in Figs. 4(k)-(o). The maximum free spectral range of the Vernier envelop $FS{R_\textrm{v}}$ is obtained with $FS{R_\textrm{s}}$ = 0.30 nm as this value is closest to $FS{R_\textrm{r}}$= 0.308 nm, which agrees with the prediction of Eq. (2).
Fig. 4. Experimental tuning of optical Vernier effect by varying the detuning between the spatial frequencies of the spectral ripple and the resonator. (a) - (e) The microscope images and (f) - (j) transmission spectra of the microfiber-knot resonators with various diameters. (k) - (o) The transmission spectra of the corresponding Vernier-effect-improved sensors show the tunable free spectral range of the Vernier envelop.
2.3 Sensitivity-enhanced quantitative temperature monitoring
With the Vernier-effect-improved effect, we apply it for sensitivity-enhanced quantitative temperature monitoring. As the sensitivity enhancement factor M of our Vernier-effect-improved sensor is determined by the following equation [37]:
we fabricated the resonator with a knot diameter of 1.8 mm to obtain a $FS{R_\textrm{s}}$ value of 0.324 nm to be close to the $FS{R_\textrm{r}}$ value of 0.308 nm. This ensures a high sensitivity enhancement factor of ∼20. The two ends of the microfiber knot resonator are fixed on a glass slide by using epoxy resin adhesive to prevent external disturb. A dehumidifier is used to ensure a stable humidity of the experimental environment. The influence of the relative humidity on our temperature monitoring is almost negligible. We conducted quantitative temperature monitoring by using this Vernier-effect-improved sensor and compared its performance with that of the single microfiber-knot resonator without optical Vernier effect. The interferogram of the sensor without optical Vernier effect experiences a small linear red shift when the environment temperature increases from 30 °C to 40 °C as shown in Fig. 5(a). The red shift originates from the increased optical path length of the microfiber-knot resonator due to thermal expansion. In comparison, the Vernier envelope experiences a large blue shift as shown in Fig. 5(b). This is because the value of $FS{R_\textrm{r}}$ (0.308 $\textrm{nm}$) is smaller than the value of $FS{R_\textrm{s}}$ (0.324 $\textrm{nm}$) in the sensitivity equation of Vernier effect $S\sim FS{R_\textrm{r}}/({FS{R_\textrm{r}} - FS{R_\textrm{s}}} )$ [36,38]. The sensitivity of the Vernier-effect-improved sensor is 155.67 pm/°C while the sensitivity of the sensor without optical Vernier effect is 8.81 pm/°C as shown in Fig. 5(c). A ∼20x sensitivity enhancement is experimentally observed which agrees well with our theoretical prediction. To evaluate the practical utility of the Vernier-effect-improved sensor for quantitative temperature monitoring, we test its measurement reproducibility in three independent temperature monitoring experiments. The sensor demonstrates excellent reproducibility and stability with an average coefficient of variation of 4.11 × 10−4%. Compared with the previously reported Vernier effect-based fiber sensors [39,40], our sensor exhibits comparable sensing performances but with a much smaller footprint and a simpler configuration.Fig. 5. Sensitivity-enhanced quantitative temperature monitoring by using the Vernier-effect-improved sensor. (a) The transmission spectra of the sensor without optical Vernier effect for quantitative temperature monitoring. (b) The transmission spectra of the sensor with optical Vernier effect for quantitative temperature monitoring. (c) Comparison of the measurement sensitivity with and without optical Vernier effect. The sensitivity is enhanced from 8.81 pm/°C to 155.67 pm/°C, with an enhancement factor of ∼20. (d) Reproducibility of the quantitative temperature monitoring by using the Vernier-effect-improved sensor. The error bars show the standard deviations of the measured wavelengths in three independent measurements. The coefficients of variation are 3.06 × 10−4%, 3.35 × 10−4%, 4.11 × 10−4%, 3.69 × 10−4%, 5.62 × 10−4% and 4.81 × 10−4%, respectively. And the average coefficient of variation is 4.11 × 10−4%.
3. Conclusion
In conclusion, we propose and experimentally demonstrate an ultracompact Vernier-effect-improved sensor by only using a single microfiber-knot resonator. This is achieved by manipulating the detuning between the spatial frequencies of the microfiber-knot resonator and the intrinsic spectral ripple of the SLED. With the implementation of optical Vernier effect, we show ∼20x sensitivity enhancement for quantitative temperature monitoring. Our sensor creates a new method to realize Vernier effect in fiber-optic sensors and other types of single-resonator sensors, which provides a simple, reliable, low-cost, high-sensitivity strategy for various sensing applications such as biochemical sensing and environmental monitoring.
Funding
National Natural Science Foundation of China (11804254); Japan Society for the Promotion of Science (JP20K14785); Murata Science Foundation; Natural Science Foundation of Guangdong Province (No.2021A1515011935); Innovation and Strong School Engineering Fund of Guangdong Province (No.2020ZDZX2022); Innovation and Strong School Engineering Fund of Guangdong Province (No.2021ZDJS094); Guangdong Engineering Technology Research Center (No. 2021J020).
Disclosures
The authors declare no conflicts of interest.
Data availability
The 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.
Supplemental document
See Supplement 1 for supporting content.
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