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.