Based the advanced "Lab on Fiber" technology and femtosecond (Fs) laser induced Two-Photon Polymerization (TPP) technology, polymer microstructures printed on fiber tip have great potential as high sensitivity micro-sensors. However, additional functionalization is usually required, the traditional treatments such as electron beam sputtering and chemical coating cannot achieve precise functionalization of local microstructure and require additional post-processing. In this work, we report a successive multi-material on-fiber TPP strategy for 4D-microstructure fabrication and prepare a fiber-tip polymer magnetic microsensor in one step. First, a cantilever is printed on the fiber tip to form a Fabry-Perot (F-P) interferometer. Then, using a self-made magnetic fluid photoresist, a magnetic cube is printed on the cantilever tip as a magnetically responsive element. This method achieves precise functionalization of local microstructure in one step, avoiding further post-processing. The prepared microcantilever magnetic sensor achieves a high sensitivity of 119 pm mT-1 , providing an ultra-compact optical solution for high-resolution measurements of weak magnetic fields. With the rapid development of advanced intelligent materials, the multi-material on-fiber TPP strategy can be extended to other stimulus-response materials, offering new guidance for manufacturing various stimulus-response micro-sensors and micro-actuators on fiber tip.
In this paper, a microcantilever fiber optical biosensor based on Fabry-Pérot interferometric (FPI) was invented and used for antibiotic sensitivity testing (AST). This biosensor combines a cantilever and the single mode fiber (SMF) to form an FPI. After bacteria attach to the cantilever, their movement causes cantilever vibration, which can be obtained by measuring the change in dip wavelength of the interference spectrum. We used this biosensor to detected Escherichia coli, indicating the vibration amplitude of the cantilever increases with the increase of the number of bacteria fixed on the cantilever. Obtained the minimum inhibitory and bactericidal concentration against E. coli within 30 minutes, validating the rapid AST ability of this biosensor. The microcantilever fiber optical biosensor developed in this paper provides a novel technology for AST.
A wide-range OFDR strain sensor based on UV-exposed-SMF and distance compensation method was demonstrated. A UV-exposed-SMF with Rayleigh backscattering (RBS) enhancement of 35.4 dB was successfully obtained to improve the signal-to-noise ratio. By combining distance compensation method, the strain, up to 9000 με, could be successfully demodulated under the spatial resolution of 1.5 mm.
A novel vector displacement sensor based on femtosecond laser direct writing gratings and waveguides in a seven-core fiber was proposed. Avoiding the use of fan-in and fan-out devices, such a vector displacement sensor realized a highly integrated structure. The displacement sensitivity, displacement resolution and directional accuracy of the proposed sensor were 0.28 nm/mm, 0.01 mm, and <0.1°, respectively.
Chirped and tilted fiber Bragg grating (CTFBG) was fabricated in SMF-28e fiber by using femtosecond laser line-by-line technology. The tilt angle and chirp rate of above-mentioned CTFBG were 8° and 10 nm/cm, the insertion loss, 3dB-bandwidth, filtering efficiency and central wavelength were 0.8 dB, 75 nm, 75% and 1511.38 nm, respectively. In addition, chirped FBG (CFBG) and tilted FBG (TFBG) were fabricated by using femtosecond laser line-by-line technology, and the spectral properties of CFBG, TFBG and CTFBG were compared and analyzed.
Fiber Bragg Grating (FBG) is an important type of fiber devices, which has been widely applied in optical filtering, fiber laser, and fiber sensor networks. Due to its uniform Refractive Index (RI) modulation, the conventional FBG usually behaves with prominent sidelobes in the reflection spectrum. In this paper, we propose a simplified dual-path approach utilizing femtosecond laser point-by-point direct writing method, to fabricate apodized FBGs with both high reflectivity and side mode rejection ratio. We adjusted the area of the femtosecond laser applying on the fiber core to achieve different overlapping integrals in different areas using a dual-path approach. By linearly translating the laser focus on the fiber core through two symmetrical paths, two identical Gaussian apodization functions was introduced to fabricate apodized FBG in YOFC single-mode fiber with target wavelengths in the range 1520–1570 nm using focused 515 nm femtosecond laser pulses and a fiber-guiding system with sub-micrometer transverse control. Following such simplified fabrication method, a new apodized grating with both enhanced reflectivity (⪆90%) and side mode rejection ratio (⪆ 13 dB) has been achieved. Such improved spectral quality allows the fabricated FBGs to fulfill the requirements of the applications in optical communication and sensing systems.
Ultrasensitive nanomechanical instruments, e.g., atomic force microscopy (AFM), can be used to perform delicate biomechanical measurements and reveal the complex mechanical environment of biological processes. However, these instruments are limited because of their size and complex feedback system. Here, we demonstrate a miniature fiber optical nanomechanical probe (FONP) that can be used to detect the mechanical properties of single cells. The stiffness matching of the FONP and sample can be realized by customizing the microcantilever’s spring constant. As a proof-of concept, three FONPs with spring constants varying from 0.421 N/m to 52.6 N/m by more than two orders of magnitude were prepared. The Young's modulus of heterogeneous soft materials, such as polydimethylsiloxane, onion cells and MCF-7 cells, were successfully measured. FONP has made substantial progress in realizing basic biological discoveries, and our strategy provides a universal protocol for directly programming fiber-optic AFMs.
A probe-type all-fiber ultraviolet photodetector is proposed in this paper. A ZnO microwire is fixed on the end facet of a single-mode fiber through a glass tube with specific diameter to form a Fabry-Pérot interferometer. With this all-fiber structure, fast-response ultraviolet detection can be realized in an all-optical scheme. Since the refractive index of ZnO microwire increases under the illumination of ultraviolet, interference wavelengths of abovementioned device redshifts with the increase of ultraviolet light intensity. By employing a continuous 266-nm laser beam and chopping method, the sensitivity is obtained to be 0.268 nm/(W·cm-2 ) and the response time is only 0.56 ms. To be more specifically, the response speed of the device is further explored by a 266-nm pulsed laser, and the response time of the device is measured to be only 13 μs. The proposed device provides a new idea for the next generation of high-performance ultraviolet photodetectors and may find potential applications in the future.
Due to the exponential growth of data in the information society, there is a growing number of optical fibers as the main channels for data transmission. How to label the fiber channels clearly is one of the most critical issues to maintain the normal flow of work in communication systems. Conventional fiber channel labeling relies on physical numbering, which significantly increases the routine maintenance cost when dealing with numerous optical transmission links. This means that the existing methods can no longer meet the growing marking function of optical fiber transmission networks. As an important fiber device, fiber Bragg grating has shown great potential in optical fiber communication systems because of its good stability, anti-electromagnetic interference, and so on. In this work, we propose a fiber tag based on a fiber Bragg grating array fabricated by a highly efficient femtosecond-laser point-by-point inscription. Each Bragg grating in the fiber tag can be recognized by demodulating the time domain reflection signal characteristics of the fiber. By analyzing the spatial distribution information of the Bragg grating segment and demodulating the information carried by the fiber tag with the preset grating segment length, the feasibility of the information carried by the fiber tag is proved. Combined with the characteristics of Bragg grating with specific wavelength response, using different wavelengths of detection light to read the time-domain reflection signal of fiber tags, provides a method to improve the information storage capacity of fiber tags. This also implies that the wavelength range of the detection light will affect the acquired label information, which will bring interferences to the correct acquisition of the information carried by the tag. The proposed optical fiber tag is fully compatible with the existing fiber-optic communication network without additional physical labeling by using the physical characteristics as the basis of the coding mark, providing an innovative solution for the efficient labeling of numerous fiber transmission channels.
Two types of FBG were fabricated in the 20/400μm passive Double-Clad Fiber (DCF) without coating (w/o-coating) and with coating (w-coating) by femtosecond laser plane-by-plane technology. The w/o-coating FBG with a central wavelength of 1060.62 nm, a reflectivity greater than 99.5% and a 3dB-bandwidth of 3.52 nm, the w-coating FBG with a central wavelength of 1080.10 nm, a reflectivity greater than 99.9% and a 3dB-bandwidth of 2.87 nm, respectively. To the best of our knowledge, this is the first report of fabricating high quality fiber Bragg grating in 20/400μm DCF using femtosecond laser direct writing method.
The measurement of ultra-high temperatures is crucial for making meaningful advancements in the aerospace and power industries. Single-crystal sapphire fibers are desirable for the fabrication of ultra-high temperature sensors due to its high melting temperature of 2045 °C. Sapphire fiber Bragg gratings (SFBGs) suffer from a significant deterioration in their spectra following an ultra-high temperature exposure due to high-temperature oxidation. Here, an ultra-high-temperature sensor based on SFBG created by femtosecond laser inscription and inert gas-sealed packaging is proposed and demonstrated. The SFBG high-temperature sensor consists of a sapphire tube infiltrated with argon gas and an SFBG inscribed with a femtosecond laser line-by-line technique. Moreover, a standard FC/APC connector was set up at the end of the sapphire tube. The ultra-high temperature sensor was isothermally annealed for 55 hours at 1600 °C. Furthermore, the long-term thermal stability and temperature response of the sensors was evaluated, and then Savitzky-Golay smoothing and interpolation of the reflection spectrum were utilized to increase the accuracy in detecting the peak wavelength. It has been found that the stabilized ultra-high-temperature sensor can withstand temperatures up to 1600 °C for up to 20 hours. Furthermore, a third-order polynomial fitted to the response was used for calibrating the sensor from room temperature to 1800 °C. Additionally, its temperature sensitivity at 1800°C was 41.9 pm/°C. These results make it eminently suitable for utilization for ultra-high temperature measurements in power, smelting, and aviation industries.
Highly birefringent fiber Bragg grating have been widely used for multi-parameter measurements such as torsion and strain. Here, we propose and demonstrate a novel highly birefringent cladding fiber Bragg grating (Hi-Bi CFBG) fabricated for simultaneous measurement of torsion and strain at high temperature. After optimization of fabrication parameters, the Hi-Bi CFBG with a high birefringence of 2.2 × 10-4 and a low reflection less than 1% was successfully fabricated in a conventional single-mode fiber by using a femtosecond laser direct writing technology. This Hi-Bi CFBG consists of sawtooth periodic refractive index modulation fabricated in the fiber cladding. The significant polarization splitting of the reflection peak of the Hi-Bi CFBG is 233 pm induced by strong birefringence. And then, a simultaneous measurement of torsion and strain at high temperature of 700 °C was carry out, and the results show that the fiber torsion angle and direction can be deduced by monitoring the variation of the reflection difference between the two polarizationpeaks and the fiber strain can be detected by monitoring the wavelength shift of one of the polarization-peaks. The Hi-Bi CFBG exhibited a high torsion sensitivity of up to 80.02 dB/(deg/mm) and a strain sensitivity of 1.06 pm/με at high temperature of 700 °C. As such, the proposed femtosecond-laser-inscribed Hi-Bi CFBG can be used as a mechanical sensor in many areas, especially in intelligent health monitoring at extreme environments
Semiconductor-based photodetectors have received wide attention. Traditional photodetectors are based on electrical test methods, which inevitably disturbed by dark current noise. In order to overcome this problem, this paper proposes an all-optical photodetection scheme based on a microfiber/SiC-nanowire directional coupling structure, which directly utilizes the refractive index change of SiC nanowire caused by photogenerated carriers instead of the change of photocurrent. The device is fabricated by transferring a single SiC nanowire to a microfiber with diameter of about 1 μm by microscopic operating system. When the device is irradiated by a 266 nm deep ultraviolet laser, its light detection sensitivity reaches up to 103 pm/(W/cm2).
Negative-index fiber Bragg gratings (FBGs) were fabricated using 800 nm femtosecond laser overexposure and thermal regeneration. A positive-index type I-IR FBG was first inscribed in H2-free fiber with a uniform phase mask, and then a highly polarization dependent phase-shifted FBG (PSFBG) was created from the type I-IR FBG by overexposure. Subsequently, the PSFBG was annealed at 800 °C for 12 hours. A negative-index FBG was obtained with a reflectivity of 99.22%, an insertion loss of 0.08 dB, a blue-shift of 0.83 nm, and an operating temperature of up to 1000 °C.
Gas pressure sensor based on an antiresonant reflecting guidance mechanism in a hollow-core fiber (HCF) with an open microchannel is experimentally demonstrated. The microchannel is created on the ring cladding of the HCF by femtosecond laser to provide an aircore pressure equivalent to the external pressure. The HCF cladding functions as an antiresonant reflecting waveguide, which induces sharp periodic losses in its transmission spectrum. The proposed sensor is miniature, robust, and exhibits a high pressure sensitivity of 3.592 nm/MPa, a low temperature cross-sensitivity of 7.5 kPa/°C.
In this paper, an egg-shaped microbubble is proposed and analyzed firstly, which is fabricated by the pressure-assisted arc discharge technique. By tailoring the arc parameters and the position of glass tube during the fabrication process, the thinnest wall of the fabricated microbubble could reach to the level of 873nm. Then, the fiber Fabry–Perot interference technique is used to analyze the deformation of microbubble that under different filling pressures. It is found that the endface of micro-bubble occurs compression when the inner pressure increasing from 4Kpa to 1400KPa. And the pressure sensitivity of such egg-shaped microbubble sample is14.3pm/Kpa. Results of this study could be good reference for developing new pressure sensors, etc.
A Graphene Oxide (GO) modified surface plasmon resonance (SPR) sensor based on the silver-coated side-polished fiber was demonstrated. Stable GO aqueous dispersion was prepared through sonication, confirmed by UV-vis absorption spectrum and Tyndall effect. GO nanosheets were decorated on the Octadecanethiol (ODT)-silver sensor surface, where ODT act as a link between the silver and GO nano-films. The GO decoration process was in-situ monitored by SPR wavelength interrogation method. The proposed SPR fiber sensor show a refractive index sensitivity up to 2252.0 nm/RIU in the range of 1.30 ∼ 1.40 RIU and can be used as promising candidate in biosensing.
A fiber in-line Mach-Zehnder interferometer based on an inner air-cavity is presented for high-pressure measurement.
The inner air-cavity is fabricated by use of femtosecond laser micromachining together with fusion splicing technique.
A micro-channel is created on the top of the inner air-cavity to allow the high pressure gas to flow in. The fiber in-line
device is featured with miniature size, good robustness and excellent operation stability while exhibiting a high pressure
sensitivity of 8,239 pm/MPa.
This paper reports a new silica fiber-tip Fabry-Perot interferometer with thin film and large surface area characteristic for high pressure and vacuum degree detection simultaneously, which is fabricated by etching a flat fiber tip into concave surface firstly, with subsequent arc jointing the concave fiber into a inline Fabry-Perot cavity, then drawing one surface of the F-P cavity into several micrometers scale by arc discharge and finally etching the surface into sub-micrometer scale integrally. As the silica fiber-tip Fabry-Perot interferometer film thickness could be tailored very thinly by HF acid solution, plus the surface area of thin film could be expanded during the chemical etching process, the variation of the bubble cavity length is very sensitive to the inner/outer pressure difference of the fiber-tip Fabry-Perot interferometer. Experimental result shows an high sensitivity of 780nm/MPa is feasible. Such configuration has the advantages of lowcost, ease of fabrication and compact size, which make it a promising candidate for pressure and vacuum measurement.
We investigated experimentally liquid crystal (LC) filled photonic crystal fiber’s temperature responses at different temperature ranging from 30 to 80°C. Experimental evidences presented that the LC’s clearing point temperature was 58°C, which is consistent with the theoretical given value. The bandgap transmission was found to have opposite temperature responses lower and higher than the LC’s clearing point temperature owing to its phase transition property. A high bandgap tuning sensitivity of 105 nm/°C was achieved around LC’s clearing point temperature.
We reported a few high-sensitivity optical strain sensors based on different types of in-fiber FPIs with air bubble cavities those were fabricated by use of a commercial fusion splicer. The cavity length and the shape of air bubbles were investigated to enhance its tensile strain sensitivity. A FPI based on a spherical air bubble was demonstrated by splicing together two sections of standard single-mode fibers, and the spherical air bubble was reshaped into an elliptical air bubble by mean of repeating arc discharge, so the strain sensitivity of the FPI based on an elliptical air bubble was enhanced to 6.0 pm⁄με owe to the decrease of the air cavity length. Moreover, a unique FPI based on a rectangular air bubble was demonstrated by use of an improved technique for splicing two sections of standard single mode fibers together and tapering the splicing joint. The sensitivity of the rectangular-bubble-based strain sensor was enhanced to be up to 43.0 pm/με and is the highest strain sensitivity among the in-fiber FPI-based strain sensors with air bubble cavities reported so far. The reason for this is that the rectangular air bubble has a sharply taper and a thin wall with a thickness of about 1 μm. Moreover, those strain sensors above have a very low temperature sensitivity of about 2.0 pm/oC. Thus, the temperature-induced strain measurement error is less than 0.046 με/oC.
We demonstrated an ultrasensitive temperature sensor based on a unique fiber Fabry-Perot interferometer (FPI). The FPI was created by means of splicing a mercury-filled silica tube with a single-mode fiber (SMF). The FPI had an air cavity, which was formed by the end face of the SMF and that of the mercury column. Experimental results showed that the FPI had an ultrahigh temperature-sensitivity of up to -41 nm/°C, which was about one order of magnitude higher than those of the reported FPI-based fiber tip sensors. Such a FPI temperature sensor is expected to have potential applications for highly-sensitive ambient temperature sensing.
We proposed and experimentally demonstrated four kinds of high-sensitivity gas pressure sensors based on in-fiber devices, including a sub-micron silica diaphragm-based fiber-tip, a polymer-capped Fabry-Perot interferometer, an inflated long period fiber grating and a twin core fiber-based Mach-Zehnder interferometer, which have sensitivities of 1036, 1130, 1680, 9600 pm/MPa, respectively.
An improved arc discharge technique was demonstrated to inscribe high-quality LPFGs with a resonant attenuation of - 28 dB and an insertion loss of 0.2 dB by use of a commercial fusion splicer. Such a technique avoids the influence of the mass which is prerequisite for traditional technique. Moreover, no physical deformation was observed on the LPFG surface. Compared with more than 86 grating periods required by traditional arc discharge technique, only 27 grating periods were required to inscribe a compact LPFG by our improved arc discharge technique.
We demonstrated a high-sensitivity strain sensor based on an in-line Fabry-Perot interferometer with an air cavity whose was created by splicing together two sections of standard single mode fibers. The sensitivity of this strain sensor was enhanced to 6.02 pm/με by improving the cavity length of the Fabry-Perot interferometer by means of repeating arc discharges for reshaping the air cavity. Moreover, such a strain sensor has a very low temperature sensitivity of 1.06 pm/°C, which reduces the cross-sensitivity problem between tensile strain and temperature.
We present a new type of phase-shifted FBGs based on an in-grating bubble fabricated by femtosecond laser ablation together with fusion splicing technique. A micro-channel vertically crossing the bubble is drilled by femtosecond laser to allow liquid to flow in or out. By filling different refractive index liquid into the bubble, the phase-shift peak is found to experience a linear red shift with the increase of refractive index. Such a PS-FBG could be used to develop a promising tunable optical filter and sensor.
A novel intensity-modulated strain sensor based on a fiber in-line Mach-Zehnder interferometer is proposed and demonstrated, which is constructed by splicing a thin core fiber between two single mode fibers with a core offset. Such an interferometer exhibits a large fringe visibility of more than 15 dB. When used in axial strain sensing from 0 to 400 με, the interferometer operates at intensity mode of detection with a high sensitivity of -0.023 dB/μεwithout the cross sensitivity between temperature and strain. Its ease of fabrication, high strain sensitivity and intensity mode of detection makes it a low-cost alternative to existing sensing applications.
We demonstrate a miniaturized fiber in-line Mach–Zehnder interferometer high-temperature sensor based on inner aircavity adjacent to the fiber core, fabricated by femto-second laser micromachining and fusion splicing technique. Such a device is robust and insensitive to ambient refractive index change, with high temperature sensitivity of ~43.2 pm/°C, up to 1000°C,while exhibiting low cross-sensitivity to strain.
Microstructured optical fibers are usually divided into two different types of fibers: solid-core photonic crystal fibers and air-core photonic bandgaps fibers. This paper presents long period fiber gratings written in both solid-core PCFs and aircore PBGs by use of a CO2 laser. A sensitive stain sensor was demonstrated by use of a CO2-laser-written long period fiber grating in a solid-core photonic crystal fiber. An in-fiber polarizer based on a long period fiber grating was written by use of a focused CO2 laser beam to notch periodically on a solid-core photonic crystal fiber. Moreover, a novel long period fiber grating was written in air-core photonic bandgap fibers by use of a CO2 laser periodically collapse air holes in the fiber cladding.
A fiber in-line Michelson interferometer based on open micro-cavity is demonstrated, which is fabricated by femtosecond laser micromachining and thin film coating technique. In refractive index sensing, this interferometer operates in a reflection mode of detection, exhibits compact sensor head, good mechanical reliability, wide operation range and high sensitivity of 975nm/RIU (refractive index unit) at the refractive index value of 1.484.
A novel bio-detecting chip configuration based on the fiber surface plasmon enhancement mechanism is proposed and analyzed. Our improvement is proposing to couple the specialized shell-isolated gold nanoparticles into the sensing region of the opened fiber-integrated microfluidic chip, and achieving drastic surface plasmon enhancement by employing the guided optical mode. Simulation shows that the optical intensity distribution near the surface of exposed fiber hole is enhanced drastically, which could be beneficial to the fluorescence or Raman enhancement. Our work could contribute to searching novel microfluidic chip based bio-detecting methods such as for tracing poisonous and harmful substances detection.
A selective-filling technique was demonstrated to improve the optical properties of photonic crystal fibres (PCFs). Such a technique can be used to fill one or more fluid samples selectively into desired air holes. The technique is based on drilling a hole or carving a groove on the surface of a PCF to expose selected air holes to atmosphere by the use of a micromachining system comprising of a femtosecond infrared laser and a microscope. The exposed section was immersed into a fluid and the air holes are then filled through the well-known capillarity action. Provided two or more grooves are fabricated on different locations and different orientation along the fibre surface, different fluids may be filled into different airholes to form a hybrid fibre. As an example, we filled half of a pure-silica PCF by a fluid with n=1.480 by carving a rectangular groove on the fibre. Consequently, the half-filled PCF became a bandgap-guiding structure (upper half), resulted from a higher refractive index in the fluid rods than in the fibre core, and three bandgaps were observed within the wavelength range from 600 to 1700 nm. Whereas, the lower half (unfilled holes) of the fibre remains an air/silica index-guiding structure. When the hybrid PCF is bent, its bandgaps gradually narrowed, resulted from the shifts of the bandgap edges. The bandgap edges had distinct bend-sensitivities when the hybrid PCF was bent toward different directions. Especially, the bandgaps are hardly affected when the half-filled PCF was bent toward the fluid-filled region. Such unique bend properties could be used to monitor simultaneously the bend directions and the curvature of the engineering structures.
In this paper, a simple, compact and robust refractive index sensor has been developed, which is constructed by
twisting a pair of silica microfiber to form a coupling device. The transmission spectrum of the device is highly sensitive
to the surrounding refractive index and the highest sensitivity of -1665nm/RIU (refractive index unit) can be obtained at
the refractive index value of 1.3605 for the fibers with diameter of 2.1μm. The developed sensor device is easy to
construct, of low cost and compatible with optical fiber system.
By use of femtosecond laser assisted micro-machining, a novel kind of fiber in-line Mach-Zehnder interferometer is
fabricated through selective infiltrating of the solid core photonic crystal fiber. Two adjacent air holes of the innermost
layer are infiltrated of liquid with refractive index higher than that of the background silica. Theoretical analysis shows
that fundamental and higher order rod modes can be excited and interference can occur between the rod modes and the
fiber core mode. The temperature sensitivity of the device is measured to be -10.9 nm/ºC, which corresponds to a
refractive index sensitivity of 2.7x104 nm/RIU.
Fiber Bragg grating (FBG) is fabricated in the microfiber by use of femtosecond laser pulse irradiation. Such a grating
can be directly exposed to the surrounding medium without etching or thinning treatment of the fiber, thus possessing
high refractive index sensitivity while maintaining superior reliability. The FBG was successfully inscribed on the
tapered fiber with diameters ringing from 2 to 10 μm. Such a grating has high potential in various types of optical fiber
sensor applications.
We propose an ultra compact optical fiber sensor integrating a Mach-Zehnder interferometer (MZI) in fiber Bragg
grating (FBG) for simultaneous refractive index (RI) and temperature measurement. By use of the resonant wavelength
of the FBG and the interference dip of the MZI, the RI and temperature of the surrounding medium can be
unambiguously determined. The interesting properties of the sensor include good operation linearity, extremely high RI
sensitivity up to ~9148 nm/RIU (RI unit) in the RI range between 1.30 and 1.325 and precise sensing location,
determined by the MZI cavity created.
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