Discussion

As shown in Figure 2 a, a distributed feedback (DFB) laser diode (FITEL, Furukawa Electric Co.) operating at 1550 nm with a 1.1 MHz linewidth was used as a light source, and two photodetectors (Thorlabs PDA50B-EC) were used as the output power meters. Here, the CR (the coupling ratio between the output light intensity \(I_{1}\) at the cross port and the input light intensity \(I_{0}\)) was set as the sensing parameter, which could be theoretically analyzed according to coupled mode theory\cite{Payne_1985}.
\(CR=\sin^2(\kappa l)\)                                                                                                                                                       (1)
where \(\kappa\) and \(l\) were the coupling coefficient and the coupling length, respectively. \(\kappa\) was determined by the microfiber radius r , the refractive index of silica glass\(n_{1}\) and the PDMS \(n_{2}\). When the external strain ε was applied on microfiber coupler, both \(\kappa\) and \(l\) would be changed. The coupling coefficient change \(\kappa\) was determined by the microfiber radius r , the refractive index of silica glass\(n_{1}+n_{1}\) and the PDMS \(n_{2}+n_{2}\) under the external strain ε . The change in refractive index was given by
\(∆n=-n^3\varepsilon\left[P_{12}-v\left(P_{11}+P_{12}\right)\right]\)                                                                                                             (2)
where v , \(P_{11}\), and \(P_{12}\) were the Poisson’s ratio and elastic coefficients, respectively\citet{Qi_2020},\citet{Dai_2008}. The elongation \(l\) was εl.
When ∆κ and \(l\) were small enough, the change in coupling ratio\(CR\) was given approximately by
\(∆CR=\frac{\partial\left[\text{CR}\right]}{\partial\kappa}\bullet∆\kappa+\frac{\partial\left[\text{CR}\right]}{\partial l}\bullet∆l\)                                                                                                                   (3)
Based on Equation (1-3), the external strainε could be calculated by analyzing the \(CR\ \)of the microfiber coupler. For example, Figure 2b showed the CR of the microfiber coupler (\(r=1\ \mu m\)) under 0-0.005% strain. When the coupling length was 18.125 mm (\(CR=0.5\)with \(\varepsilon=0\)), the CR decreased linearly with increasing strain.
The strain sensitivity was evaluated by the Gauge factor (GF). By substituting Equation (3), the GF was
\(GF=|∆CR/ε|=(κ+∆κ/ε)l∙|\sin⁡(2κl)|\)                                                                                     (4)
Based on Equation (4), the strain sensitivity GF had been expressed as the product of two terms: the envelope function\(\left(\kappa+\frac{\kappa}{\varepsilon}\right)l\) and the sinusoidal function \(\left|\sin\left(2\text{κl}\right)\right|\). To obtaining a higher sensitivity, both two terms should be considered. The first term was monotone increasing with increasing \(l\) and \(\kappa\). Considering that the \(\kappa\) decreased with the increase of the microfiber radius r\citet{Zhao_2018a}, the sensor would be more sensitive with a thinner microfiber and a longer coupling length. The second term was periodic and reached a maximum only when\(2\kappa l=\left(2m\pm\frac{1}{2}\right)\pi\), where \(m\) was an integer. This term indicated that there must be optimal operating point for the microfiber coupling sensor. By substituting\(2\kappa l=\left(2m\pm\frac{1}{2}\right)\pi\) into Equation (1),\(CR=0.5\) had been confirmed for the initial optimal operating point, which could be achieved by pre-stretching of the microfiber coupler. Figure 2c showed the calculations of the GF with different radii and coupling lengths under the 0.001% strain. When \(l>20\ mm\) and\(r<0.8\ \mu m\), the theoretical value of GF could be larger than 2000, which was higher than most reported flexible strain sensors.
The strain sensing performance of our proposed flexible microfiber coupler sensor was characterized with a tensile strain tester. The sensors with the microfiber coupler radii of 1.0 μm, 1.5 μm and 2.0 μm were stretched under 0-0.07% strain range. As shown in Figure 2d, the 1-μm-radius microfiber coupler sensor had a highest sensitivity and relatively good linearity. Due to the low refractive index contrast between the silica microfiber coupler and PDMS encapsulation material, the microfiber coupler sensor with radius less than 1 μm would suffer from high optical loss and low detectable signal. To investigate the weak strain sensing performance, the 1-μm-radius microfiber coupler sensor was further stretched and investigated with a step of 0.001% strain. Figure 2e showed an ultra-high sensitivity of GF=900 according to the calculated slope, which was consistent with our theoretical analysis as the red star marker position illustrated in Figure 2c. It was worth noting that the detection limit of our sensor was more than one order of magnitude larger than other exhibited flexible photonic devices\citet{Li_2018a}. Moreover, limited by the resolution of the tensile strain tester, minimum strain and strain step that applied on this sensor was only 0.001%, the excellent linearity and obvious separation of the experimental curve points shown in Figure 2e indicated that the actual detection limit of this microfiber coupler sensor would be much lower than 0.001%.
As shown by the blue curve in Figure 2f, where the microfiber coupler sensor worked at 0.001% detection limit situation, the strain sensing range would be limited within a quarter cycle of strain-CR cosine curve, that was just 0.034%. If we wanted to expand the sensing range, then the detection limit would be sacrificed as shown in Figure 2d compared with the \(r=1.5\ um\) and \(r=2\ um\) situations, where the sensitivity GF would be deteriorated from 900 to 304 and 190, respectively. To solve the contradiction of low detection limit and large sensing range, the optical loss of the microfiber coupler under applied strain was adopted as the second measurand with CR simultaneously. Here, the optical loss referred to the ratio of the sum of the power \(I_{1}+I_{2}\) of the two output ports of the microfiber coupler to the input optical power \(I_{0}\) . As shown by the red curve in Figure 2f, the optical loss had a monotonically increasing trend until the applied strain up to 0.45%. Combining the cosine periodic functional strain-CR response and monotonically increasing strain-optical loss response simultaneously, we found that different optical loss values could mark the exact period of the strain-CR cosine periodic functional curve, the method of one-to-one corresponding optical loss and CR could clearly locate the strain state of the sensor. Due to the hysteresis effect of PDMS material, the optical loss values did not display strictly linear data state. Actually, it was precisely because these slight fluctuations in the strain-optical loss curve, these optical loss effect based flexible strain sensor\citet{Zhu_2021},\citet{Pan_2020},\citet{Guo_2019} could not achieve low detection limit and high sensitivity. However, these slight fluctuations in the strain-optical loss curve did not affect the practical expanding of the strain sensing range.
To further investigate the stability and repeatability of this optical microfiber coupler strain sensor, periodic stretching-releasing motion for more than 10 000 cycles was applied to the sensor with fixed 0.12% strain. As shown in Figure 2g, the CR variation amplitude was stable during the entire test. The detailed plots of the area outlined in red, green and blue (correspond to the earlier, middle and later stage of the cycle testing, respectively) were also shown in upper magnified inset of Figure 2g, where the strain-induced CR variation curves kept the same at different stages during the testing.
The response time of this flexible microfiber coupler sensor had been thoroughly investigated. Because the maximum stretching frequency of tensile strain tester was limited to be Hz-scale, which would be much lower than the frequency response bandwidth of this sensor. Here, we adopted a non-contact acoustic pressure testing method for the high speed and ultralow strain applying. A loudspeaker driven by a signal generator was used as a dynamic strain applying source and placed 10 cm away from the sensing film. The loudspeaker produced a 3 kHz sinusoidal sound wave with an acoustic pressure level of 83 dBC, as measured by a calibrated electronic microphone near the sensing film. Through the CR demodulation scheme, we obtained the CR change time-varying waveform, as shown in Figure 2h, where nearly undistorted sinusoidal shape could be clearly distinguished. The frequency spectrum of the \(CR\) change waveform had been analyzed as shown in Figure 2i, where the global SNR of the applied 3 kHz frequency component was estimated to be about 24 dB. According to Nyquist-Shannon sampling theorem\citet{Shannon_1949}, the response frequency of our flexible microfiber coupler sensor was reasonable to assume at least twice of the applied 3 kHz. So the response time could be calculated as:
\(∆t<\frac{1}{2f\max}=\frac{1}{2\times3000}=0.167ms\)                                                                                                                (5)
Compared with previously reported high sensitivity flexible strain sensors, the detection limit of our proposed microfiber coupler sensor had reached the top level, and the response speed had exceeded the highest level among flexible strain sensors, as shown in Table 1.
Owing to the superior mechanical property and excellent sensitivity, this proposed microfiber coupler sensor would have tremendous potential applications in wearable devices for monitoring ultraweak physiological signals, slight human motions and subtle environmental perturbations. By using PDMS as an encapsulation material, this microfiber coupler strain sensor had been developed to be a biocompatible, flexible and durable device, which could be easily and firmly attached to the human skin with comfortable wearability. As shown in Figure 3 a, this flexible microfiber coupler sensor could be directly attached to the skin of human face, neck, wrist, finger, and ankle etc., for real-timely detecting the breath, pulse, gesture, and speech. Breathing is one of the prime functions fulfilled by human, and it can have considerable effects on the morphology and on the craniofacial and cervical functions, and is also closely related to some respiratory diseases. This flexible microfiber coupler strain sensor was mounted on facial masks to monitor strain induced by respiratory motions, where inhalation and exhalation would bring about air pressure changes inside the mask and deform the mask. Three different respiration modes were detected and discriminated by virtues of the distinguishable response patterns as shown in Figure 3b, where 0.2 ΔCR and 38 times/min for deep breath, 0.07 ΔCR and 23 times/min for normal breath, 0.02 ΔCR and 17 times/min for shallow breath, respectively. By detecting the mask deformation, the respiration frequency, breathing depth and various breathing styles could be sensed and detected, which would be helpful to discover and diagnose some respiratory diseases.
Arterial pulse is a significant physiological signal for the clinical diagnosis of cardiovascular diseases. The arterial pulse is evaluated for the contour of the pulse wave and its volume, rate, and rhythm, the intensity of arterial pulse signal is often too weak to be palpated or detected, especially at the fingertip and ankle sites. This flexible microfiber coupler strain sensor was attached to different body’s sites, such as the neck, wrist, fingertip and ankle. By virtues of high sensitivity and low detection limit of this flexible strain sensor, the pulse waveforms at all body’s sites were precisely detected and recorded as shown in Figure 3c. The pulse waveform details could be captured and recovered without distortion, for example, the pulse signals at neck, wrist, and finger exhibited three peak characteristics, and the ankle only had two peaks, which was exact in agreement with the pulse signal characteristics at body’s different sites\cite{Fang_2021}.
The weak motions of human body could be effectively monitored by this flexible microfiber coupler sensor, which would have broad application prospects in human-machine interaction and phonation rehabilitation training. Firstly, this flexible microfiber coupler sensor was attached on the wrist site for the gesture recognition demonstration, where the bending of fingers would drive the wrist to produce weak movements. As shown in Figure 3d, bending and straightening of different fingers could be clearly recognized and distinguished. Then, this flexible microfiber coupler sensor was attached on the neck to monitor the tiny epidermis and muscle movements during speech for phonation recognition. As shown in Figure 3e. this sensor captured distinguishable and repeatable signal patterns when the volunteer spoke some alphabet letters, S-C-U-T. It could be found that the three enlarged detail view of letter “T” waveforms were nearly the same, which indicated that this flexible sensor would be more powerful for in situ real-time monitoring based on further pattern recognition technique.
To demonstrate the fast response, high sensitivity and continuous monitoring characteristics of this flexible sensor, an experiment was designed and conducted to monitor the ant-crawling induced dynamic weak strains. The flexible microfiber coupler sensor was fixed on a stage with stretched form, and an ant with 1.1mg weight could freely craw from left to right on the sensor film surface (Figure 4 a). During the crawling movements, the sensor had captured the ant-crawling induced weak strain signals in real time (Movie 1 in Supporting Information). The recorded parabolic shape curve as shown in Figure 4b indicated that this sensor completely had the ability for ultralight ant movement recognition. However, the non-flat response curve also revealed that the sensitivities were not distributed homogeneously on the sensor film, thereby causing difficulty in quantitative dynamic measurement.
To further explore the dynamic weak strain sensing ability, this flexible microfiber coupler sensor was tested as a non-contact acoustic microphone. As shown in Figure 4c, the sensor was stretched and suspended above a loudspeaker driven by a signal generator. The loudspeaker produced single frequency sinusoidal sound waves from 20 Hz to 20 kHz, with an increment of 10 Hz, 100 Hz and 10 kHz, respectively. At all these acoustic-strain frequency levels, the acoustic pressure level was set, as measured by a calibrated electronic microphone, to be about 96 dBC. As illustrated in Figure 4d, the measured \(CR\) under logarithm function obviously response the acoustic pressure induced strain, where the 3 dB frequency response bandwidth was mainly located within 50 Hz to 3 kHz. And the \(CR\) decayed rapidly at frequencies lower than 50 Hz and higher than 3 kHz, the main reason was that the stiffness of PDMS film greatly affected the frequency response range, especially the high-frequency part. As illustrated in Supporting Information (Figure 1S), the measured CR at the 300 Hz and 3 kHz frequency testing points could be clearly captured and distinguished with nearly undistorted sinusoidal shape. According to amplitude of CR change, it could be deduced that the strain induced by the acoustic wave pressure on the sensor was just about 0.000011%, which was much lower than above measured detection limit 0.001%. Unlike the single frequency sinusoidal acoustic strain applied in the above experiments, the real human voice was a complex signal composed of acoustic waves of different frequencies and intensities, and it changed rapidly with time. To verify the microphone function of this flexible sensor, an audio clips (music “You raise me up”, 15s duration) was applied to the loudspeaker and broadcasted to sensor. Figure 4e represented the demodulated \(CR\)change frequency spectrum under the music audio clip source, which was mainly concentrated in the range from 100 Hz to 3 kHz, and the inset showed the CR change time-varying waveform. This demodulated CR change time-varying waveform was converted into an audio file (Audio 1 in Supporting Information). Listening to this demodulated audio file, the music could be clearly recognized with little noise, which showed the fidelity of flexible microphone application.
The broadband response of this sensor also provided a new mechanism for multi-parameter sensing based on the frequency division multiplex technology. As shown in Figure 4g, the flexible sensor was fixed and attached to the skin of the wrist, so the arterial pulse signals from the attached wrist and the human voice signals broadcasted from the loudspeaker could apply simultaneously on the sensor. Arterial pulse signals mainly located within the frequency range about 0.3-2 Hz, and the human voice signals were in the range from 100 Hz to 3 kHz, so there two signals could be monitored and demodulated simultaneously by this flexible sensor (Figure 4f). As shown in the Figure 4g, the record signals were enveloping curves of low frequency pulse modulated with high frequency sound. Employing frequency domain filter algorithms, the pulse (75 times per minute) and the voice signals were separately filtered and displayed. Audio 2 in Supporting Information showed that the restored sound was similar with the original audio, which further validated the high fidelity of the sensor.