sensors Article
Adaptable Optical Fiber Displacement-Curvature Sensor Based on a Modal Michelson Interferometer with a Tapered Single Mode Fiber G. Salceda-Delgado 1, *, A. Martinez-Rios 2 , R. Selvas-Aguilar 1 , R. I. Álvarez-Tamayo 3 , A. Castillo-Guzman 1 , B. Ibarra-Escamilla 4 , V. M. Durán-Ramírez 5 and L. F. Enriquez-Gomez 2,6 1
2 3 4 5 6
*
Universidad Autónoma de Nuevo León, Pedro de Alba S/N, Ciudad Universitaria, 66455 San Nicolás de los Garza, Nuevo León, Mexico; [email protected] (R.S.-A.); [email protected] (A.C.-G.) Centro de Investigaciones en Óptica A. C., Loma del bosque 115, Col. Lomas del Campestre, 37150 León, Gto., Mexico; [email protected] (A.M.-R.); [email protected] (L.F.E.-G.) CONACYT – Universidad Autónoma de Nuevo León, Facultad de Ciencias Físico-Matemáticas, 66455 San Nicolás de los Garza, Nuevo León, Mexico; [email protected] Instituto Nacional de Astrofísica, Óptica y Electrónica (INAOE), L. E. Erro 1, Sta. Ma. Tonantzintla, Puebla 72824, Mexico; [email protected] Centro Universitario de los Lagos, Universidad de Guadalajara, Enrique Díaz de León 1144, paseos de la montaña, 47460 Lagos de Moreno, Jalisco, Mexico; [email protected] Instituto Tecnológico de Aguascalientes, Avenida Adolfo López Mateos 1801, 20256 Aguascalientes, Ags., Mexico Correspondence: [email protected]; Tel.: +52-818-329-4000 (ext. 7121)
Academic Editor: Vittorio M. N. Passaro Received: 26 April 2017; Accepted: 30 May 2017; Published: 2 June 2017
Abstract: A compact, highly sensitive optical fiber displacement and curvature radius sensor is presented. The device consists of an adiabatic bi-conical fused fiber taper spliced to a single-mode fiber (SMF) segment with a flat face end. The bi-conical taper structure acts as a modal coupling device between core and cladding modes for the SMF segment. When the bi-conical taper is bent by an axial displacement, the symmetrical bi-conical shape of the tapered structure is stressed, causing a change in the refractive index profile which becomes asymmetric. As a result, the taper adiabaticity is lost, and interference between modes appears. As the bending increases, a small change in the fringe visibility and a wavelength shift on the periodical reflection spectrum of the in-fiber interferometer is produced. The displacement sensitivity and the spectral periodicity of the device can be adjusted by the proper selection of the SMF length. Sensitivities from around 1.93 to 3.4 nm/mm were obtained for SMF length between 7.5 and 12.5 cm. Both sensor interrogations, wavelength shift and visibility contrast, can be used to measure displacement and curvature radius magnitudes. Keywords: fiber optic sensor; modal optical fiber Michelson interferometer; displacementcurvature measurement
1. Introduction Optical fiber sensors applied to the measurement of physical, chemical, and biological parameters have been a subject of great interest since they have special advantages such as simplicity, compactness, immunity to electromagnetic field, easy construction, fast response, resistance to hazard environments, and real time measurement, among others. Moreover, mechanical bending is an important physical parameter to be measured in order to determine deformations, displacements, and curvature radius for high resolution optical instrumentation processes. In recent years, several bending sensors
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bending sensors based on optical fiber structures have been reported [1–10]. Most of them are based Sensors 2017, 17, 1259 2 of 8 on the modal Mach-Zehnder interferometer (MZI), whose construction is by means of optical fiber devices which couples light propagation modes between core and cladding, such as tapered fibers based on opticalfiber fibergratings structures have[9], been reported [1–10]. Most them aremicro-fiber based on the modal [8], long-period (LPFG) fiber Bragg gratings (FBG)of[10], and lenses [3], Mach-Zehnder interferometer (MZI), whose construction is by means of optical fiber devices which among others. In the aforementioned in-fiber structures, the use of two mode coupler devices is couples light modes corethe andfabrication cladding, such as tapered fibersLPFGs, [8], long-period fiber necessary to propagation construct an MZI,between however, process for FBGs, and spliced gratings (LPFG) [9], fiber Bragg (FBG) [10], and micro-fiber lenses also [3], among others. Inone the spherical shape structures is not gratings quite as simple. In the case of fiber tapers, by means of just aforementioned in-fiber structures, the use of two mode coupler devices is necessary to construct an MZI, taper, an MZI can be constructed [11], but the taper needs to be abrupt, increasing the thinness and however,ofthe process for FBGs, LPFGs, and spliced spherical shape both structures fragility thefabrication tapered fiber. Furthermore, the use of special fibers to generate arms is ofnot the quite MZI as simple. In the of fiber tapers, also by means of justfiber one [2,12] taper, and an MZI can becrystal constructed [11], has been used forcase bending measurement, e.g., multicore photonic fiber [13]. but the taper needs to be abrupt, increasing the thinness fragility of due the tapered fiber. Furthermore, Nevertheless, the structure becomes more complex andand unrepeatable to the splice collapses, as the use of special fibers to generate arms the MZI hasthat beenare used bending measurement, e.g., well as more expensive because of both the use of of special fibers notfor readily accessible. A simpler multicore fiber [2,12] and photonic crystal fiber [13]. Nevertheless, the structure becomes more complex structure than the Mach-Zehnder interferometer is the optical fiber Michelson interferometer (OFMI), and unrepeatable to the splice collapses, well is asrequired more expensive because the use of special in which only one due optical fiber mode coupler as device to construct the of interferometer. The fibers that notsensing readily device accessible. simpler structure than therefractive Mach-Zehnder the OFMI as aare fiber has A been reported to measure indexinterferometer [14], pressure is[15], optical fiber Michelson interferometer (OFMI), in which only one optical fiber mode coupler device temperature [16], and strain [17] by using fiber structures based on tapered fiber, photonic crystal is required to construct thelarge interferometer. The OFMI as a fiber sensing device has been reported to fiber, multicore fiber, and core diameter fiber, respectively. measure refractive [14], pressure [15], temperature [16], and strain [17] by using and fiberadjustable structures In this work, index we propose and experimentally demonstrate a robust, simple, based on fiber,axial photonic crystal fiber, multicore fiber, and large core on diameter fiber, respectively. sensor fortapered mechanical displacement or bending measurements based an OFMI structure. The In this interferometer work, we propose and experimentally demonstratefiber a robust, simple, and adjustable Michelson is constructed by a single-mode (SMF) adiabatic bi-conical sensor taper for mechanical axialsegment. displacement bending measurements on an OFMI Michelson spliced to an SMF The or core and cladding of the based SMF segment act structure. as the twoThe paths of the interferometer is constructed by a single-mode (SMF) adiabaticnobi-conical taperbetween spliced to an SMF Michelson interferometer. When the bi-conicalfiber taper is straight, interference modes is segment. The and cladding SMF is segment the two paths of the Michelson interferometer. presented. Incore contrast, when of thethetaper bent, act an as interference pattern is produced by modal When the bi-conical straight, no interference betweencorresponds modes is presented. In contrast, when the interference which, taper withisthe interferometric structure, to an OFMI spectrum. By taper is bent, interference is produced byan modal which, with the interferometric increasing thean bending of thepattern bi-conical taper with axialinterference displacement, a wavelength spectral shift structure, corresponds to aninOFMI spectrum. By interference increasing the bending of the bi-conical taper with an and a small fringe contrast the notches of the pattern of the OFMI reflection spectrum axialproduced. displacement, a wavelength and a small fringe contrast in notches of the interference are Taking advantagespectral of theseshift characteristics, we construct anthe optical fiber displacementpattern of sensor. the OFMI spectrum are produced. advantage of these we curvature As reflection a special sensor characteristic, bothTaking the magnitude value of thecharacteristics, wavelength shift construct an optical fiber displacement-curvature sensor. As a special sensor characteristic, both the and the spectral shape of the device depend on the SMF segment length, which can be tailored. magnitude value the wavelength shift and the spectral shape of the device depend the SMF Sensitivities fromofaround 1.93 to 3.4 nm/mm and a fringe period spectrum rangingonfrom ~6.21segment to ~1.8 length, which can be tailored. Sensitivities from around 1.937.5 tocm 3.4 to nm/mm nm were experimentally obtained for SMF lengths from 15 cm. and a fringe period spectrum ranging from ~6.21 to ~1.8 nm were experimentally obtained for SMF lengths from 7.5 cm to 15 cm. 2. Structure and Working Principle of the Proposed Optical Fiber Michelson Interferometer 2. Structure and Working Principle of the Proposed Optical Fiber Michelson Interferometer (OFMI) (OFMI) The structure structure of of the the proposed proposed OFMI OFMI and and the the light light modes modes propagation propagation through through the the device device are are The shown in fiber taper spliced to antoSMF segment with length L comprise the sensing shown in Figure Figure1.1.An Anoptical optical fiber taper spliced an SMF segment with length L comprise the device. The light that is launched to the core fiber at the input is propagated through the tapered fiber sensing device. The light that is launched to the core fiber at the input is propagated through the (left pointing red arrows). thearrows). taper position, the fundamental of the core fiberofcouples of tapered fiber (left pointingInred In the taper position, themode fundamental mode the corepart fiber its energy to cladding modes. Then, both modes fromboth the core andfrom cladding travel thetravel SMF couples part of its energy to cladding modes. Then, modes the core andthrough cladding segment. In the normal cleaved end face of the SMF, the ~4% energy modes are reflected by Fresnel through the SMF segment. In the normal cleaved end face of the SMF, the ~4% energy modes are reflection by (right pointing blue arrows) and propagate in opposite the taper, where reflected Fresnel reflection (right pointing blue arrows) anddirections propagatethrough in opposite directions the cladding modewhere recouples part of the energy to the core through the taper, the cladding mode recouples partmode. of the energy to the core mode.
Figure Figure 1. 1. Structure Structure of of the the modal modal Michelson Michelson interferometer interferometer with with the the light light modes modes propagation. propagation.
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Because the core and cladding modes have different propagation constants; an interference Because the core andthe cladding modes different phase propagation constants; an interference pattern is produced from reflected light. have The generated difference, which causes the mode pattern is produced from the reflected light. The generated phase difference, which causes the mode interference between core and cladding modes, can be approximated by the expression [14]: interference between core and cladding modes, can be approximated by the expression [14]: 4neff L (1) 4π∆nef f L ϕ= (1) λ n eff is the difference of effective refractive index of core and cladding modes, L is the optical where where ∆ne f f is theλdifference of wavelength effective refractive index of core and cladding modes, L is the optical path length, and is the input in vacuum. path length, and λ is the input wavelength in vacuum. The tapered optical fiber is adiabatic and has a bi-conical shape with transition lengths of 2.5 The tapered optical fiberand is adiabatic and has aofbi-conical shape lengths of 2.5 mm, mm, a waist length of 1 mm, a waist diameter 60 µm. The fiberwith wastransition tapered with the mentioned adimensions waist length of 1 mm, and a waist diameter of 60 µm. The fiber was tapered with the mentioned by using a glass processing machine Vytran model GPX-3400 manufactured by Vytran dimensions by using a glass processing machine Vytranofmodel GPX-3400 manufactured Vytran to LLC LLC at Morganville, NJ, USA. As the dimensions a bi-conical fused taper are by essential its at Morganville, NJ, USA. As the dimensions of a bi-conical fused taper are essential to its functioning functioning as an interferometric device [18], the taper dimensions were selected in order to have a as an interferometric device taper dimensions were selectedloses in order to have a taper is taper that is adiabatic, yet at[18], the the limit in which the taper gradually its adiabaticity by athat slight adiabatic, yet at the limit in which the taper gradually loses its adiabaticity by a slight deformation deformation such as bending. Considering other taper dimensions, such as waist size, waist length, such bending. length, Considering other taper dimensions, suchadiabaticity as waist size, waist length, and transitions and as transitions will result in differences in the and spectral properties of the length, will result in differences in the adiabaticity and spectral properties of the OFMI. Using a OFMI. Using a fiber circulator, the reflected output spectrum of the OFMI from the amplified fiber circulator, the reflected spectrum of the OFMI from the amplified spontaneous emission spontaneous emission (ASE)output of an Erbium-Ytterbium double cladding fiber (EYDCF) was measured (ASE) of an Erbium-Ytterbium double cladding fiber (EYDCF) was measured by an Optical Spectrum by an Optical Spectrum Analyzer (OSA) with a resolution of 0.07 nm, as seen in Figure 2. The spectra Analyzer (OSA) a resolution of 0.07 output nm, as seen 2. The spectra of the coupler ASE input signal of the ASE inputwith signal and the reflected signalinofFigure the OFMI when the mode is straight and reflected output signal of OFMI when mode coupler is straight andbe when it is bent to andthe when it is bent to a radius of the ~48,208.75 mm isthe also shown in Figure 2. As can observed, while athe radius of ~48,208.75 mm is also shown in Figure 2. As can be observed, while the tapered optical tapered optical fiber is fixed in a straight position, the output spectrum is just the ASE reflected fiber fixed inSMF a straight position, the taper output is just as thea ASE the SMF lightisfrom the segment, since the is spectrum not performing modereflected coupler light until from it is perturbed segment, since the taper is not performing as a mode coupler until it is perturbed by bending. by bending.
Figure 2. (a) Schematic of the OFMI measurement; (b) input spectrum intensity from an EYDCF to Figure 2. (a) Schematic of the OFMI measurement; (b) input spectrum intensity from an EYDCF to circulator port 1; (c) Output spectrum intensity from circulator port 3 to an OSA for measurement. circulator port 1; (c) Output spectrum intensity from circulator port 3 to an OSA for measurement.
The wavelength wavelength period period of length is depicted in Figure 3. As The of the the OFMI OFMIas asaafunction functionofofthe theSMF SMF length is depicted in Figure 3. can be observed, the wavelength period decreases as L increases. The experimental results can be As can be observed, the wavelength period decreases as L increases. The experimental results can be approximatelyfitted fittedto: to: approximately ∆λ =− 0.2176L 0.2176L+4.5616 4.5616
(2) (2)
where wavelength fringe fringeseparation separationasasa afunction function length of the SMF piece. Where∆λ Δλdenotes denotes the wavelength ofof thethe length of the SMF piece. For For proposed OFMI-based sensor, SMF length range varied from tocm, 15 cm, where the the proposed OFMI-based sensor, thethe SMF length range varied from 7.5 7.5 to 15 where the the datadata can be approximated to a linear fit maximum slope value of around −0.2176 nm/cm. The inset in Figure
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can be approximated to a linear fit maximum slope value of around −0.2176 nm/cm. The inset in Figure 3 shows the measured reflected interference pattern spectra for the OFMI with and 3 shows the measured reflected interference pattern spectra for the bentbent OFMI with 15,15, 11,11, and 7.5 7.5 L when they bent a curvature radius ~48,208 mm. cmcm of of L when they areare bent toto a curvature radius ~48,208 mm.
Figure3.3.Interference Interferencefringe fringeseparation separationofofthe theMichelson Michelsoninterference interferencepattern patternversus versuslength lengthofofsingle single Figure mode fiber piece. The inset shows the spectra for OFMIs with SMF lengths of 7.5, 11, and 15 cm. mode fiber piece. The inset shows the spectra for OFMIs with SMF lengths of 7.5, 11, and 15 cm.
Analysisand andExperimental ExperimentalResults Results 3.3.Analysis Theschematic schematic stage to characterize the by OFMI by mechanical displacement The of of thethe stage usedused to characterize the OFMI mechanical displacement or bendingor is shown 4. The OFMI was mounted in a fabricated V groove in a flexible metal isbending shown in Figure in 4. Figure The OFMI was mounted in a fabricated V groove in a flexible metal sheet sheet ensuring that the bi-conical taper was positioned in the middle of the sheet whose total length ensuring that the bi-conical taper was positioned in the middle of the sheet whose total length was wascm. 29.1The cm. OFMI The OFMI glued on one metal sheet end avoid the fiberbeing beinglongitudinally longitudinally 29.1 was was glued onlyonly on one metal sheet end to to avoid the fiber stressedwhen whenbending bendingand andprevent preventthe thefiber fiberfrom frombreaking. breaking.The Themetal metalsheet sheetwas wascompressed compressedby bythe the stressed axial displacement of a micrometric linear translation stage. The corresponding bending for every axial displacement of a micrometric linear translation stage. The corresponding bending for every displacementposition positionwas wascalculated calculatedby byusing usingthe theformula formula[12]: [12]: displacement rd2
d2 s2
(3) +2d s2 r= (3) 2d where 2s is the distance between the two ends of the metal sheet, and d is the maximum deflection where is thesheet distance between of the2s metal (see Figure 4).the two ends of the metal sheet, and d is the maximum deflection of the metal sheet (see Figure 4). When the linear translation stage compresses the metal sheet, the device is bent and its curvature When the linear compresses sheet, the toward device isshorter bent and its curvature radius decreases. Astranslation a result, thestage spectral responsethe of metal the OFMI shifts wavelengths and radius decreases. a result, the spectral response of the OFMI shifts shorteras wavelengths and a small visibility As increase is also caused in the interference pattern oftoward the spectrum, can be observed ain small visibility is also caused theµm interference pattern of the as can which be observed Figure 5, fromincrease zero displacement to in 3300 of a device with ~10 cmspectrum, of SMF length, are the instraight Figure position 5, from zero to 3300 of a device with ~10 cm In of Figure SMF length, theis and displacement a curvature radius of µm 55,448.53 mm, respectively. 5, the which upper are curve straight position and a curvature radius of 55,448.53 mm, respectively. In Figure 5, the upper curve is the measurement output spectrum when the device is straight, i.e., without modal interference. As the the measurement output spectrum when the device is straight, i.e., without modal interference. As the displacement is applied, the device is bent, modal interference takes place, and the fringe contrast of displacement applied, the device is bent, modal takesincreases place, and the fringe contrastshift of the notches inisthe interference pattern increases as interference the displacement while a wavelength the notches in the interference pattern increases as the displacement increases while a wavelength shift is also caused. Figure 6 shows the spectral visibility sensor response for a device with 7.5 mm of SMF issegment also caused. Figure 6 showsinthe spectral visibility sensor for a device with(ρ 7.5increases mm of SMF length. An increase visibility was observed as theresponse inverse curvature radius from 1.5 × 10−6 to 7 × 10−6 mm−1 with an approximate linear factor of around 10,687 (a.u.)/(1/mm). Different sensor lengths were tested and they show similar visibility increase.
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segment length. An increase in visibility was observed as the inverse curvature radius (ρ) increases from 1.5 × 10−6 to 7 × 10−6 mm−1 with an approximate linear factor of around 10,687 (a.u.)/(1/mm). Different sensor lengths were tested and they show similar visibility increase. Sensors 2017, 17, 1259 5 of 8 Sensors 2017, 17, 1259 Sensors 2017, 17, 1259
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Figure 4. Schematic of the mechanical stage for the displacement and curvature radius
Figure 4. Schematic ofofthe stage for the displacement and curvature radius characterization characterization themechanical Michelson interferometer. Figure4. 4.interferometer. Schematic ofof the the mechanical mechanical stage radius of the Michelson Figure Schematic stage for for the the displacement displacementand andcurvature curvature radius characterizationofofthe theMichelson Michelson interferometer. interferometer. characterization
Figure 5. OFMI output spectra for several mechanical displacement positions separated by 100 µm Figure 5. OFMI output spectra for several mechanical displacement positions separated by 100 µm for a device with L ~ 10 cm.
a device with Lspectra ~ 10 cm.for several mechanical displacement positions separated by 100 µm for Figure 5. for OFMI output Figure 5. OFMI output spectra for several mechanical displacement positions separated by 100 µm a deviceforwith L ~10 cm. a device with L ~ 10 cm.
Figure 6. Spectral visibility response for a device with 7.5 mm length of SMF.
Figure 6. Spectral visibility response for a device with 7.5 mm length of SMF. Figure 6. Spectral visibility response for a device with 7.5 mm length of SMF.
Figure 6. Spectral visibility response for a device with 7.5 mm length of SMF.
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For L values of 7.5, 10, and 12.5 cm, the wavelength shift of the OFMI output spectrum as a function of the mechanical displacement and curvature radius (m) is shown in Figure 7. The corresponding For L values of 7.5, 10, and 12.5 cm, the wavelength shift of the OFMI output spectrum as a curvature radius for each displacement position is indicated at the top of the graphic. The response function of the mechanical displacement and curvature radius (m) is shown in Figure 7. The of the three different SMF lengths exhibits an approximately linear behavior. The linear fitting of the corresponding curvature radius for each displacement position is indicated at the top of the graphic. experimental data can be fitted by the following equations: The response of the three different SMF lengths exhibits an approximately linear behavior. The linear fitting of the experimental data can be fitted by the following equations: ∆λ L=7.5 = 3.4d + 2.03 L 7.5 3.4d 2.03 (4) ∆λ L= 10 = 2.77d + 1.64 2.77d + 1.64 (4) L 10= 1.93d ∆λ L=12.5 1.75 L 12.5 1.93d 1.75
where ∆λ is the wavelength shift of the OFMI output spectrum and d is the value of the mechanical where Δλ is the wavelength shift of the OFMI output spectrum and d is the value of the mechanical axial displacement of the linear translation stage. As can be observed, the slope increases from 1.93 to axial displacement of the linear translation stage. As can be observed, the slope increases from 1.93 3.4 nm/mm as the L value decreases. to 3.4 nm/mm as the L value decreases.
Figure Figure 7. 7. Comparison Comparison of of the the wavelength wavelength shift shift response response caused caused by by mechanical mechanical displacement displacement and and bending for devices with 7.5, 10, and 12.5 cm length values of SMF lengths segments. bending for devices with 7.5, 10, and 12.5 cm length values of SMF lengths segments.
As the effect effect of oftemperature temperatureisisan animportant importantparameter parameter considered in sensor performance, toto bebe considered in sensor performance, the the OFMI exposed to temperature changes. An with OFMI an SMF ofwas 12.5positioned mm was OFMI was was exposed to temperature changes. An OFMI an with SMF length of length 12.5 mm positioned on when a hot it plate it awas bent to a bending radius of around 48,208 mm, and on a hot plate waswhen bent to bending radius of around 48,208 mm, and a spectral shiftaofspectral 3.7 nm shift of 3.7 nm to larger with negligible visibility change observed as the to larger wavelengths with wavelengths negligible visibility change was observed as the was temperature increases ◦ C. temperature increases from room temperature to 100the °C.wavelength Figure 8 shows wavelength shift versus from room temperature to 100 Figure 8 shows shiftthe versus the temperature of the this OFMI with a length of 12.5 mm;shift the wavelength increases in a linear way thistemperature OFMI with aoflength of 12.5 mm; the wavelength increases inshift a linear way with a factor of with a factor nm/°C. As the OFMI is sensible to temperature changes, temperature ~0.05658 nm/◦of C.~0.05658 As the OFMI is sensible to temperature changes, temperature perturbations can perturbations alter measurement. the sensor bending measurement. However, this can betheavoided alter the sensorcan bending However, this can be avoided by maintaining sensor inbya maintaining the sensor in a temperature-controlled environment. temperature-controlled environment. A special special characteristic characteristic to to add add to to our our sensor sensor is that the straight position position of the sensor sensor can be designed as the zero initial condition; for this case, the output is the reflected spectrum without zero initial condition; this case, the output is the reflected spectrum without modal modal interference interference (see (see upper upper spectrum spectrum in Figure 5). The The tapering tapering fabrication fabrication for for the the construction construction of of the sensor is simple, fast, and repeatable. The The manufacturing manufacturing process process for for the the sensor sensor construction construction simply simply employs a splicer machine to splice standard fiber to a bi-conical tapered tapered fiber. fiber. When the thesensor sensor is used to measure the displacement related to the bending, spectral is used to measure the displacement related to bending, spectralthe wavelength wavelength sensor response can be theanlength an SMF, can done shift sensor shift response can be adjusted byadjusted varying by thevarying length of SMF, of which can which be done bybe simply by simply splicingfiber. standard Also, theshape spectral shape of response of the can be cutting or cutting splicingor standard Also,fiber. the spectral response the sensor cansensor be modified modified by changing the SMF length, and the sensor interrogation can be done by either wavelength shift or spectral visibility change. These characteristics are very useful to adapt the sensor to special conditions for a particular measurement application.
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by changing the SMF length, and the sensor interrogation can be done by either wavelength shift or spectral visibility change. These characteristics are very useful to adapt the sensor to special conditions Sensors 2017, 17, 1259 7 of 8 for a particular measurement application.
Figure 8. Wavelength shift versus temperature of an OFMI with an SMF length of 12.5 mm. Figure 8. Wavelength shift versus temperature of an OFMI with an SMF length of 12.5 mm.
4. Conclusions 4. Conclusions In conclusion, a robust, simple, and highly sensitive optical fiber mechanical axial displacement In conclusion, a robust, simple, and highly sensitive optical fiber mechanical axial displacement or curvature radius sensor based on a Michelson interferometer using an adiabatic bi-conical taper, or curvature radius sensor based on a Michelson interferometer using an adiabatic bi-conical taper, which can be interrogated by spectral wavelength shift or visibility change, has been demonstrated which can be interrogated by spectral wavelength shift or visibility change, has been demonstrated for the first time to our knowledge. The tapered optical fiber, which is compact, is spliced with an for the first time to our knowledge. The tapered optical fiber, which is compact, is spliced with an SMF segment to conform the sensor. When the sensor is bent by applying an axial displacement, the SMF segment to conform the sensor. When the sensor is bent by applying an axial displacement, the symmetry of the taper is modified, which causes a variation in the taper refractive index profile and symmetry of the taper is modified, which causes a variation in the taper refractive index profile and a breaking down of the tapered adiabaticity to couple modes and interference between them. As a a breaking down of the tapered adiabaticity to couple modes and interference between them. As a consequence of such a perturbation, a phase delay between modes causes a wavelength shift of the consequence of such a perturbation, a phase delay between modes causes a wavelength shift of the output spectrum device to smaller wavelength values as well as an increase of visibility in the fringes output spectrum device to smaller wavelength values as well as an increase of visibility in the fringes of the sensor interference pattern, due to the loss of the tapered adiabaticity which enables mode of the sensor interference pattern, due to the loss of the tapered adiabaticity which enables mode coupling. As an additional advantage, for the need of a specific application, the mechanical axial coupling. As an additional advantage, for the need of a specific application, the mechanical axial displacement sensitivity by wavelength shift and the fringe separation sensor spectrum can be displacement sensitivity by wavelength shift and the fringe separation sensor spectrum can be tailored tailored or adjusted by changing the length of the single-mode segment spliced to the taper by simple or adjusted by changing the length of the single-mode segment spliced to the taper by simple splicing splicing or cutting an SMF. The proposed optical fiber displacement sensor based on a Michelson or cutting an SMF. The proposed optical fiber displacement sensor based on a Michelson interferometer interferometer is shown to be a reliable optical fiber device for high resolution optical instrumentation is shown to be a reliable optical fiber device for high resolution optical instrumentation applications. applications. Acknowledgments: This work was funding in part by the Secretary of Public Education for the Teacher Acknowledgments: This work was funding in part by the Secretary of Public Educationand for the theSupport Teacher Improvement Program in Mexico (SEP-PROMEP) (103.5/15/11043, DSA/103.5/16/10510), program for scientific and technological research by Autonomous University of Nuevo Leon (IT439-15, CE332-15). Improvement Program in Mexico (SEP-PROMEP) (103.5/15/11043, DSA/103.5/16/10510), and the Support R. I. Álvarez-Tamayo to thanks to Cátedras program. program for scientificwants and technological researchCONACyT by Autonomous University of Nuevo Leon (IT439-15, CE33215). R. I. Álvarez-Tamayo wants to thanks to Cátedras CONACyT program. Author Contributions: G. Salceda-Delgado and A. Martinez-Rios conceived the main idea; G. Salceda-Delgado, R. I. Álvarez-Tamayo, L. F. Enriquez-Gomez the conceived experiments; G. Salceda-Delgado analyzed Author Contributions:and G. Salceda-Delgado and A.performed Martinez-Rios the main idea; G. Salceda-Delgado, the results and drafted the paper; performed R. Selvas-Aguilar, A. Martinez-Rios, R. I. Álvarez-Tamayo, R. I.experimental Álvarez-Tamayo, and L. F. Enriquez-Gomez the experiments; G. Salceda-Delgado analyzed the A. A. Castillo-Guzmán, B. Ibarra-Escamilla, and V. M. Durán-Ramírez contributed to the revision of the paper and experimental results and drafted the paper; R. Selvas-Aguilar, A. Martinez-Rios, R. I. Álvarez-Tamayo, A. A. gave pertinent comments. Castillo-Guzmán, B. Ibarra-Escamilla, and V. M. Durán-Ramírez contributed to the revision of the paper and Conflicts of Interest: The authors declare no conflict of interest. gave pertinent comments.
Conflicts of Interest: The authors declare no conflict of interest.
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Zhang, Z.Z.; Yu-Ming, G.; Shin-Tson, W.; Shug-June, H. Ultra-sensitive curvature sensor based on liquid crystal-infiltrated fiber interferometer. J. Appl. Phys. 2016, 50, 1–6. [CrossRef] Wang, X.; Chen, D.; Li, H.; Feng, G.; Yang, J. In line Mach-Zehnder interferometric sensor based on a seven-core optical fiber. IEEE Sens. J. 2017, 17, 100–104. [CrossRef] Xiong, M.; Gong, H.; Wang, Z.; Zhao, C.-L.; Dong, X. Fiber curvature sensor based on spherical-shape structures and long-period grating. Opt. Lasers Eng. 2016, 86, 356–359. [CrossRef] Zhao, Y.; Cai, L.; Li, X.-G. Temperature-Insensitive optical fiber curvature sensor based on SMF-MMFTCSMF-MMF-SMF Structure. IEEE Trans. Instrum. Meas. 2017, 66, 141–147. [CrossRef] Raji, Y.M.; Lin, H.S.; Ibrahim, S.A.; Mokhtar, M.R.; Yusoff, Z. Intensity-modulated abrupt tapered fiber Mach-Zehnder Interferometer for the simultaneous sensing of temperature and curvature. Opt. Laser Technol. 2016, 86, 8–13. [CrossRef] Hu, H.-F.; Sun, S.-J.; Lv, R.-Q.; Zhao, Y. Design and experiment of an optical micro bend sensor for respiration monitoring. Sens. Actuators A Phys. 2016, 251, 126–133. [CrossRef] Monteiro, C.S.; Ferreira, M.S.; Silvia, S.O.; Kobelke, J.; Schuster, K.; Bierlich, J.; Frazao, O. Fiber Fabry-Perot interferometer for curvature sensing. Photonic Sens. 2016, 6, 339–344. [CrossRef] Monzon-Hernandez, D.; Martinez-Rios, A.; Torres-Gomez, I.; Salceda-Delgado, G. Compact optical fiber curvature sensor based on concatenating two tapers. Opt. Lett. 2011, 36, 4380–4382. [CrossRef] [PubMed] Zhang, S.; Gong, H.; Qian, Z.; Jin, Y.; Dong, X. Fiber curvature sensor based on Mach-Zehnder interferometer using up-taper cascaded long-period grating. Microw. Opt. Technol. Lett. 2015, 58, 246–248. [CrossRef] Feng, D.; Qiao, X.; Albert, J. Off-axis ultraviolet-written fiber Bragg gratings for directional bending measurements. Opt. Lett. 2016, 41, 1201–1204. [CrossRef] [PubMed] Salceda-Delgado, G.; Monzon-Hernandez, D.; Martinez-Rios, A.; Cardenas-Sevilla, G.A.; Villatoro, J. Optical microfiber mode interferometer for temperature-independent refractometric sensing. Opt. Lett. 2012, 37, 1974–1976. [CrossRef] [PubMed] Salceda-Delgado, G.; van Newkirk, A.; Antonio-Lopez, J.E.; Martinez-Rios, A.; Schulzgen, A.; Amezcua-Correa, R. Compact fiber-optic curvature sensor based on super-mode interference in a seven-core fiber. Opt. Lett. 2015, 40, 1468–1471. [CrossRef] [PubMed] Villatoro, J.; Minkovich, V.P.; Zubia, J. Photonic crystal fiber interferometric vector bending sensor. Opt. Lett. 2015, 40, 3113–3116. [CrossRef] [PubMed] Tian, Z.; Yam, S.; Loock, H.P. Refractive index sensor based on an abrupt taper Michelson interferometer in a single-mode fiber. Opt. Lett. 2008, 33, 1105–1107. [CrossRef] [PubMed] Tan, X.; Geng, Y.; Li, X. High-birefringence photonic crystal fiber Michelson interferometer with cascaded fiber Bragg grating for pressure and temperature discrimination. Opt. Eng. 2016, 55, 090508. [CrossRef] Duan, L.; Zhang, P.; Tang, M.; Wang, R.; Zhao, Z.; Fu, S.; Gan, L.; Zhu, B.; Tong, W.; Liu, D.; et al. Heterogeneous all-solid multicore fiber based multipath Michelson interferometer for high temperature sensing. Opt. Exp. 2016, 24, 20210–20218. [CrossRef] [PubMed] Hua, L.; Song, Y.; Huang, J.; Lan, X.; Li, Y.; Xiao, H. Microwave interrogated large core fused silica fiber Michelson interferometer for strain sensing. Appl. Opt. 2015, 54, 7181–7187. [CrossRef] [PubMed] Salceda-Delgado, G.; Martinez-Rios, A.; Monzon-Hernandez, D. Tailoring Mach–Zehnder Comb-Filters Based on Concatenated Tapers. J. Lightwave Technol. 2013, 31, 761. [CrossRef] © 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
Adaptable Optical Fiber Displacement-Curvature Sensor Based on a Modal Michelson Interferometer with a Tapered Single Mode Fiber G. Salceda-Delgado 1, *, A. Martinez-Rios 2 , R. Selvas-Aguilar 1 , R. I. Álvarez-Tamayo 3 , A. Castillo-Guzman 1 , B. Ibarra-Escamilla 4 , V. M. Durán-Ramírez 5 and L. F. Enriquez-Gomez 2,6 1
2 3 4 5 6
*
Universidad Autónoma de Nuevo León, Pedro de Alba S/N, Ciudad Universitaria, 66455 San Nicolás de los Garza, Nuevo León, Mexico; [email protected] (R.S.-A.); [email protected] (A.C.-G.) Centro de Investigaciones en Óptica A. C., Loma del bosque 115, Col. Lomas del Campestre, 37150 León, Gto., Mexico; [email protected] (A.M.-R.); [email protected] (L.F.E.-G.) CONACYT – Universidad Autónoma de Nuevo León, Facultad de Ciencias Físico-Matemáticas, 66455 San Nicolás de los Garza, Nuevo León, Mexico; [email protected] Instituto Nacional de Astrofísica, Óptica y Electrónica (INAOE), L. E. Erro 1, Sta. Ma. Tonantzintla, Puebla 72824, Mexico; [email protected] Centro Universitario de los Lagos, Universidad de Guadalajara, Enrique Díaz de León 1144, paseos de la montaña, 47460 Lagos de Moreno, Jalisco, Mexico; [email protected] Instituto Tecnológico de Aguascalientes, Avenida Adolfo López Mateos 1801, 20256 Aguascalientes, Ags., Mexico Correspondence: [email protected]; Tel.: +52-818-329-4000 (ext. 7121)
Academic Editor: Vittorio M. N. Passaro Received: 26 April 2017; Accepted: 30 May 2017; Published: 2 June 2017
Abstract: A compact, highly sensitive optical fiber displacement and curvature radius sensor is presented. The device consists of an adiabatic bi-conical fused fiber taper spliced to a single-mode fiber (SMF) segment with a flat face end. The bi-conical taper structure acts as a modal coupling device between core and cladding modes for the SMF segment. When the bi-conical taper is bent by an axial displacement, the symmetrical bi-conical shape of the tapered structure is stressed, causing a change in the refractive index profile which becomes asymmetric. As a result, the taper adiabaticity is lost, and interference between modes appears. As the bending increases, a small change in the fringe visibility and a wavelength shift on the periodical reflection spectrum of the in-fiber interferometer is produced. The displacement sensitivity and the spectral periodicity of the device can be adjusted by the proper selection of the SMF length. Sensitivities from around 1.93 to 3.4 nm/mm were obtained for SMF length between 7.5 and 12.5 cm. Both sensor interrogations, wavelength shift and visibility contrast, can be used to measure displacement and curvature radius magnitudes. Keywords: fiber optic sensor; modal optical fiber Michelson interferometer; displacementcurvature measurement
1. Introduction Optical fiber sensors applied to the measurement of physical, chemical, and biological parameters have been a subject of great interest since they have special advantages such as simplicity, compactness, immunity to electromagnetic field, easy construction, fast response, resistance to hazard environments, and real time measurement, among others. Moreover, mechanical bending is an important physical parameter to be measured in order to determine deformations, displacements, and curvature radius for high resolution optical instrumentation processes. In recent years, several bending sensors
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bending sensors based on optical fiber structures have been reported [1–10]. Most of them are based Sensors 2017, 17, 1259 2 of 8 on the modal Mach-Zehnder interferometer (MZI), whose construction is by means of optical fiber devices which couples light propagation modes between core and cladding, such as tapered fibers based on opticalfiber fibergratings structures have[9], been reported [1–10]. Most them aremicro-fiber based on the modal [8], long-period (LPFG) fiber Bragg gratings (FBG)of[10], and lenses [3], Mach-Zehnder interferometer (MZI), whose construction is by means of optical fiber devices which among others. In the aforementioned in-fiber structures, the use of two mode coupler devices is couples light modes corethe andfabrication cladding, such as tapered fibersLPFGs, [8], long-period fiber necessary to propagation construct an MZI,between however, process for FBGs, and spliced gratings (LPFG) [9], fiber Bragg (FBG) [10], and micro-fiber lenses also [3], among others. Inone the spherical shape structures is not gratings quite as simple. In the case of fiber tapers, by means of just aforementioned in-fiber structures, the use of two mode coupler devices is necessary to construct an MZI, taper, an MZI can be constructed [11], but the taper needs to be abrupt, increasing the thinness and however,ofthe process for FBGs, LPFGs, and spliced spherical shape both structures fragility thefabrication tapered fiber. Furthermore, the use of special fibers to generate arms is ofnot the quite MZI as simple. In the of fiber tapers, also by means of justfiber one [2,12] taper, and an MZI can becrystal constructed [11], has been used forcase bending measurement, e.g., multicore photonic fiber [13]. but the taper needs to be abrupt, increasing the thinness fragility of due the tapered fiber. Furthermore, Nevertheless, the structure becomes more complex andand unrepeatable to the splice collapses, as the use of special fibers to generate arms the MZI hasthat beenare used bending measurement, e.g., well as more expensive because of both the use of of special fibers notfor readily accessible. A simpler multicore fiber [2,12] and photonic crystal fiber [13]. Nevertheless, the structure becomes more complex structure than the Mach-Zehnder interferometer is the optical fiber Michelson interferometer (OFMI), and unrepeatable to the splice collapses, well is asrequired more expensive because the use of special in which only one due optical fiber mode coupler as device to construct the of interferometer. The fibers that notsensing readily device accessible. simpler structure than therefractive Mach-Zehnder the OFMI as aare fiber has A been reported to measure indexinterferometer [14], pressure is[15], optical fiber Michelson interferometer (OFMI), in which only one optical fiber mode coupler device temperature [16], and strain [17] by using fiber structures based on tapered fiber, photonic crystal is required to construct thelarge interferometer. The OFMI as a fiber sensing device has been reported to fiber, multicore fiber, and core diameter fiber, respectively. measure refractive [14], pressure [15], temperature [16], and strain [17] by using and fiberadjustable structures In this work, index we propose and experimentally demonstrate a robust, simple, based on fiber,axial photonic crystal fiber, multicore fiber, and large core on diameter fiber, respectively. sensor fortapered mechanical displacement or bending measurements based an OFMI structure. The In this interferometer work, we propose and experimentally demonstratefiber a robust, simple, and adjustable Michelson is constructed by a single-mode (SMF) adiabatic bi-conical sensor taper for mechanical axialsegment. displacement bending measurements on an OFMI Michelson spliced to an SMF The or core and cladding of the based SMF segment act structure. as the twoThe paths of the interferometer is constructed by a single-mode (SMF) adiabaticnobi-conical taperbetween spliced to an SMF Michelson interferometer. When the bi-conicalfiber taper is straight, interference modes is segment. The and cladding SMF is segment the two paths of the Michelson interferometer. presented. Incore contrast, when of thethetaper bent, act an as interference pattern is produced by modal When the bi-conical straight, no interference betweencorresponds modes is presented. In contrast, when the interference which, taper withisthe interferometric structure, to an OFMI spectrum. By taper is bent, interference is produced byan modal which, with the interferometric increasing thean bending of thepattern bi-conical taper with axialinterference displacement, a wavelength spectral shift structure, corresponds to aninOFMI spectrum. By interference increasing the bending of the bi-conical taper with an and a small fringe contrast the notches of the pattern of the OFMI reflection spectrum axialproduced. displacement, a wavelength and a small fringe contrast in notches of the interference are Taking advantagespectral of theseshift characteristics, we construct anthe optical fiber displacementpattern of sensor. the OFMI spectrum are produced. advantage of these we curvature As reflection a special sensor characteristic, bothTaking the magnitude value of thecharacteristics, wavelength shift construct an optical fiber displacement-curvature sensor. As a special sensor characteristic, both the and the spectral shape of the device depend on the SMF segment length, which can be tailored. magnitude value the wavelength shift and the spectral shape of the device depend the SMF Sensitivities fromofaround 1.93 to 3.4 nm/mm and a fringe period spectrum rangingonfrom ~6.21segment to ~1.8 length, which can be tailored. Sensitivities from around 1.937.5 tocm 3.4 to nm/mm nm were experimentally obtained for SMF lengths from 15 cm. and a fringe period spectrum ranging from ~6.21 to ~1.8 nm were experimentally obtained for SMF lengths from 7.5 cm to 15 cm. 2. Structure and Working Principle of the Proposed Optical Fiber Michelson Interferometer 2. Structure and Working Principle of the Proposed Optical Fiber Michelson Interferometer (OFMI) (OFMI) The structure structure of of the the proposed proposed OFMI OFMI and and the the light light modes modes propagation propagation through through the the device device are are The shown in fiber taper spliced to antoSMF segment with length L comprise the sensing shown in Figure Figure1.1.An Anoptical optical fiber taper spliced an SMF segment with length L comprise the device. The light that is launched to the core fiber at the input is propagated through the tapered fiber sensing device. The light that is launched to the core fiber at the input is propagated through the (left pointing red arrows). thearrows). taper position, the fundamental of the core fiberofcouples of tapered fiber (left pointingInred In the taper position, themode fundamental mode the corepart fiber its energy to cladding modes. Then, both modes fromboth the core andfrom cladding travel thetravel SMF couples part of its energy to cladding modes. Then, modes the core andthrough cladding segment. In the normal cleaved end face of the SMF, the ~4% energy modes are reflected by Fresnel through the SMF segment. In the normal cleaved end face of the SMF, the ~4% energy modes are reflection by (right pointing blue arrows) and propagate in opposite the taper, where reflected Fresnel reflection (right pointing blue arrows) anddirections propagatethrough in opposite directions the cladding modewhere recouples part of the energy to the core through the taper, the cladding mode recouples partmode. of the energy to the core mode.
Figure Figure 1. 1. Structure Structure of of the the modal modal Michelson Michelson interferometer interferometer with with the the light light modes modes propagation. propagation.
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Because the core and cladding modes have different propagation constants; an interference Because the core andthe cladding modes different phase propagation constants; an interference pattern is produced from reflected light. have The generated difference, which causes the mode pattern is produced from the reflected light. The generated phase difference, which causes the mode interference between core and cladding modes, can be approximated by the expression [14]: interference between core and cladding modes, can be approximated by the expression [14]: 4neff L (1) 4π∆nef f L ϕ= (1) λ n eff is the difference of effective refractive index of core and cladding modes, L is the optical where where ∆ne f f is theλdifference of wavelength effective refractive index of core and cladding modes, L is the optical path length, and is the input in vacuum. path length, and λ is the input wavelength in vacuum. The tapered optical fiber is adiabatic and has a bi-conical shape with transition lengths of 2.5 The tapered optical fiberand is adiabatic and has aofbi-conical shape lengths of 2.5 mm, mm, a waist length of 1 mm, a waist diameter 60 µm. The fiberwith wastransition tapered with the mentioned adimensions waist length of 1 mm, and a waist diameter of 60 µm. The fiber was tapered with the mentioned by using a glass processing machine Vytran model GPX-3400 manufactured by Vytran dimensions by using a glass processing machine Vytranofmodel GPX-3400 manufactured Vytran to LLC LLC at Morganville, NJ, USA. As the dimensions a bi-conical fused taper are by essential its at Morganville, NJ, USA. As the dimensions of a bi-conical fused taper are essential to its functioning functioning as an interferometric device [18], the taper dimensions were selected in order to have a as an interferometric device taper dimensions were selectedloses in order to have a taper is taper that is adiabatic, yet at[18], the the limit in which the taper gradually its adiabaticity by athat slight adiabatic, yet at the limit in which the taper gradually loses its adiabaticity by a slight deformation deformation such as bending. Considering other taper dimensions, such as waist size, waist length, such bending. length, Considering other taper dimensions, suchadiabaticity as waist size, waist length, and transitions and as transitions will result in differences in the and spectral properties of the length, will result in differences in the adiabaticity and spectral properties of the OFMI. Using a OFMI. Using a fiber circulator, the reflected output spectrum of the OFMI from the amplified fiber circulator, the reflected spectrum of the OFMI from the amplified spontaneous emission spontaneous emission (ASE)output of an Erbium-Ytterbium double cladding fiber (EYDCF) was measured (ASE) of an Erbium-Ytterbium double cladding fiber (EYDCF) was measured by an Optical Spectrum by an Optical Spectrum Analyzer (OSA) with a resolution of 0.07 nm, as seen in Figure 2. The spectra Analyzer (OSA) a resolution of 0.07 output nm, as seen 2. The spectra of the coupler ASE input signal of the ASE inputwith signal and the reflected signalinofFigure the OFMI when the mode is straight and reflected output signal of OFMI when mode coupler is straight andbe when it is bent to andthe when it is bent to a radius of the ~48,208.75 mm isthe also shown in Figure 2. As can observed, while athe radius of ~48,208.75 mm is also shown in Figure 2. As can be observed, while the tapered optical tapered optical fiber is fixed in a straight position, the output spectrum is just the ASE reflected fiber fixed inSMF a straight position, the taper output is just as thea ASE the SMF lightisfrom the segment, since the is spectrum not performing modereflected coupler light until from it is perturbed segment, since the taper is not performing as a mode coupler until it is perturbed by bending. by bending.
Figure 2. (a) Schematic of the OFMI measurement; (b) input spectrum intensity from an EYDCF to Figure 2. (a) Schematic of the OFMI measurement; (b) input spectrum intensity from an EYDCF to circulator port 1; (c) Output spectrum intensity from circulator port 3 to an OSA for measurement. circulator port 1; (c) Output spectrum intensity from circulator port 3 to an OSA for measurement.
The wavelength wavelength period period of length is depicted in Figure 3. As The of the the OFMI OFMIas asaafunction functionofofthe theSMF SMF length is depicted in Figure 3. can be observed, the wavelength period decreases as L increases. The experimental results can be As can be observed, the wavelength period decreases as L increases. The experimental results can be approximatelyfitted fittedto: to: approximately ∆λ =− 0.2176L 0.2176L+4.5616 4.5616
(2) (2)
where wavelength fringe fringeseparation separationasasa afunction function length of the SMF piece. Where∆λ Δλdenotes denotes the wavelength ofof thethe length of the SMF piece. For For proposed OFMI-based sensor, SMF length range varied from tocm, 15 cm, where the the proposed OFMI-based sensor, thethe SMF length range varied from 7.5 7.5 to 15 where the the datadata can be approximated to a linear fit maximum slope value of around −0.2176 nm/cm. The inset in Figure
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can be approximated to a linear fit maximum slope value of around −0.2176 nm/cm. The inset in Figure 3 shows the measured reflected interference pattern spectra for the OFMI with and 3 shows the measured reflected interference pattern spectra for the bentbent OFMI with 15,15, 11,11, and 7.5 7.5 L when they bent a curvature radius ~48,208 mm. cmcm of of L when they areare bent toto a curvature radius ~48,208 mm.
Figure3.3.Interference Interferencefringe fringeseparation separationofofthe theMichelson Michelsoninterference interferencepattern patternversus versuslength lengthofofsingle single Figure mode fiber piece. The inset shows the spectra for OFMIs with SMF lengths of 7.5, 11, and 15 cm. mode fiber piece. The inset shows the spectra for OFMIs with SMF lengths of 7.5, 11, and 15 cm.
Analysisand andExperimental ExperimentalResults Results 3.3.Analysis Theschematic schematic stage to characterize the by OFMI by mechanical displacement The of of thethe stage usedused to characterize the OFMI mechanical displacement or bendingor is shown 4. The OFMI was mounted in a fabricated V groove in a flexible metal isbending shown in Figure in 4. Figure The OFMI was mounted in a fabricated V groove in a flexible metal sheet sheet ensuring that the bi-conical taper was positioned in the middle of the sheet whose total length ensuring that the bi-conical taper was positioned in the middle of the sheet whose total length was wascm. 29.1The cm. OFMI The OFMI glued on one metal sheet end avoid the fiberbeing beinglongitudinally longitudinally 29.1 was was glued onlyonly on one metal sheet end to to avoid the fiber stressedwhen whenbending bendingand andprevent preventthe thefiber fiberfrom frombreaking. breaking.The Themetal metalsheet sheetwas wascompressed compressedby bythe the stressed axial displacement of a micrometric linear translation stage. The corresponding bending for every axial displacement of a micrometric linear translation stage. The corresponding bending for every displacementposition positionwas wascalculated calculatedby byusing usingthe theformula formula[12]: [12]: displacement rd2
d2 s2
(3) +2d s2 r= (3) 2d where 2s is the distance between the two ends of the metal sheet, and d is the maximum deflection where is thesheet distance between of the2s metal (see Figure 4).the two ends of the metal sheet, and d is the maximum deflection of the metal sheet (see Figure 4). When the linear translation stage compresses the metal sheet, the device is bent and its curvature When the linear compresses sheet, the toward device isshorter bent and its curvature radius decreases. Astranslation a result, thestage spectral responsethe of metal the OFMI shifts wavelengths and radius decreases. a result, the spectral response of the OFMI shifts shorteras wavelengths and a small visibility As increase is also caused in the interference pattern oftoward the spectrum, can be observed ain small visibility is also caused theµm interference pattern of the as can which be observed Figure 5, fromincrease zero displacement to in 3300 of a device with ~10 cmspectrum, of SMF length, are the instraight Figure position 5, from zero to 3300 of a device with ~10 cm In of Figure SMF length, theis and displacement a curvature radius of µm 55,448.53 mm, respectively. 5, the which upper are curve straight position and a curvature radius of 55,448.53 mm, respectively. In Figure 5, the upper curve is the measurement output spectrum when the device is straight, i.e., without modal interference. As the the measurement output spectrum when the device is straight, i.e., without modal interference. As the displacement is applied, the device is bent, modal interference takes place, and the fringe contrast of displacement applied, the device is bent, modal takesincreases place, and the fringe contrastshift of the notches inisthe interference pattern increases as interference the displacement while a wavelength the notches in the interference pattern increases as the displacement increases while a wavelength shift is also caused. Figure 6 shows the spectral visibility sensor response for a device with 7.5 mm of SMF issegment also caused. Figure 6 showsinthe spectral visibility sensor for a device with(ρ 7.5increases mm of SMF length. An increase visibility was observed as theresponse inverse curvature radius from 1.5 × 10−6 to 7 × 10−6 mm−1 with an approximate linear factor of around 10,687 (a.u.)/(1/mm). Different sensor lengths were tested and they show similar visibility increase.
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segment length. An increase in visibility was observed as the inverse curvature radius (ρ) increases from 1.5 × 10−6 to 7 × 10−6 mm−1 with an approximate linear factor of around 10,687 (a.u.)/(1/mm). Different sensor lengths were tested and they show similar visibility increase. Sensors 2017, 17, 1259 5 of 8 Sensors 2017, 17, 1259 Sensors 2017, 17, 1259
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Figure 4. Schematic of the mechanical stage for the displacement and curvature radius
Figure 4. Schematic ofofthe stage for the displacement and curvature radius characterization characterization themechanical Michelson interferometer. Figure4. 4.interferometer. Schematic ofof the the mechanical mechanical stage radius of the Michelson Figure Schematic stage for for the the displacement displacementand andcurvature curvature radius characterizationofofthe theMichelson Michelson interferometer. interferometer. characterization
Figure 5. OFMI output spectra for several mechanical displacement positions separated by 100 µm Figure 5. OFMI output spectra for several mechanical displacement positions separated by 100 µm for a device with L ~ 10 cm.
a device with Lspectra ~ 10 cm.for several mechanical displacement positions separated by 100 µm for Figure 5. for OFMI output Figure 5. OFMI output spectra for several mechanical displacement positions separated by 100 µm a deviceforwith L ~10 cm. a device with L ~ 10 cm.
Figure 6. Spectral visibility response for a device with 7.5 mm length of SMF.
Figure 6. Spectral visibility response for a device with 7.5 mm length of SMF. Figure 6. Spectral visibility response for a device with 7.5 mm length of SMF.
Figure 6. Spectral visibility response for a device with 7.5 mm length of SMF.
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For L values of 7.5, 10, and 12.5 cm, the wavelength shift of the OFMI output spectrum as a function of the mechanical displacement and curvature radius (m) is shown in Figure 7. The corresponding For L values of 7.5, 10, and 12.5 cm, the wavelength shift of the OFMI output spectrum as a curvature radius for each displacement position is indicated at the top of the graphic. The response function of the mechanical displacement and curvature radius (m) is shown in Figure 7. The of the three different SMF lengths exhibits an approximately linear behavior. The linear fitting of the corresponding curvature radius for each displacement position is indicated at the top of the graphic. experimental data can be fitted by the following equations: The response of the three different SMF lengths exhibits an approximately linear behavior. The linear fitting of the experimental data can be fitted by the following equations: ∆λ L=7.5 = 3.4d + 2.03 L 7.5 3.4d 2.03 (4) ∆λ L= 10 = 2.77d + 1.64 2.77d + 1.64 (4) L 10= 1.93d ∆λ L=12.5 1.75 L 12.5 1.93d 1.75
where ∆λ is the wavelength shift of the OFMI output spectrum and d is the value of the mechanical where Δλ is the wavelength shift of the OFMI output spectrum and d is the value of the mechanical axial displacement of the linear translation stage. As can be observed, the slope increases from 1.93 to axial displacement of the linear translation stage. As can be observed, the slope increases from 1.93 3.4 nm/mm as the L value decreases. to 3.4 nm/mm as the L value decreases.
Figure Figure 7. 7. Comparison Comparison of of the the wavelength wavelength shift shift response response caused caused by by mechanical mechanical displacement displacement and and bending for devices with 7.5, 10, and 12.5 cm length values of SMF lengths segments. bending for devices with 7.5, 10, and 12.5 cm length values of SMF lengths segments.
As the effect effect of oftemperature temperatureisisan animportant importantparameter parameter considered in sensor performance, toto bebe considered in sensor performance, the the OFMI exposed to temperature changes. An with OFMI an SMF ofwas 12.5positioned mm was OFMI was was exposed to temperature changes. An OFMI an with SMF length of length 12.5 mm positioned on when a hot it plate it awas bent to a bending radius of around 48,208 mm, and on a hot plate waswhen bent to bending radius of around 48,208 mm, and a spectral shiftaofspectral 3.7 nm shift of 3.7 nm to larger with negligible visibility change observed as the to larger wavelengths with wavelengths negligible visibility change was observed as the was temperature increases ◦ C. temperature increases from room temperature to 100the °C.wavelength Figure 8 shows wavelength shift versus from room temperature to 100 Figure 8 shows shiftthe versus the temperature of the this OFMI with a length of 12.5 mm;shift the wavelength increases in a linear way thistemperature OFMI with aoflength of 12.5 mm; the wavelength increases inshift a linear way with a factor of with a factor nm/°C. As the OFMI is sensible to temperature changes, temperature ~0.05658 nm/◦of C.~0.05658 As the OFMI is sensible to temperature changes, temperature perturbations can perturbations alter measurement. the sensor bending measurement. However, this can betheavoided alter the sensorcan bending However, this can be avoided by maintaining sensor inbya maintaining the sensor in a temperature-controlled environment. temperature-controlled environment. A special special characteristic characteristic to to add add to to our our sensor sensor is that the straight position position of the sensor sensor can be designed as the zero initial condition; for this case, the output is the reflected spectrum without zero initial condition; this case, the output is the reflected spectrum without modal modal interference interference (see (see upper upper spectrum spectrum in Figure 5). The The tapering tapering fabrication fabrication for for the the construction construction of of the sensor is simple, fast, and repeatable. The The manufacturing manufacturing process process for for the the sensor sensor construction construction simply simply employs a splicer machine to splice standard fiber to a bi-conical tapered tapered fiber. fiber. When the thesensor sensor is used to measure the displacement related to the bending, spectral is used to measure the displacement related to bending, spectralthe wavelength wavelength sensor response can be theanlength an SMF, can done shift sensor shift response can be adjusted byadjusted varying by thevarying length of SMF, of which can which be done bybe simply by simply splicingfiber. standard Also, theshape spectral shape of response of the can be cutting or cutting splicingor standard Also,fiber. the spectral response the sensor cansensor be modified modified by changing the SMF length, and the sensor interrogation can be done by either wavelength shift or spectral visibility change. These characteristics are very useful to adapt the sensor to special conditions for a particular measurement application.
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by changing the SMF length, and the sensor interrogation can be done by either wavelength shift or spectral visibility change. These characteristics are very useful to adapt the sensor to special conditions Sensors 2017, 17, 1259 7 of 8 for a particular measurement application.
Figure 8. Wavelength shift versus temperature of an OFMI with an SMF length of 12.5 mm. Figure 8. Wavelength shift versus temperature of an OFMI with an SMF length of 12.5 mm.
4. Conclusions 4. Conclusions In conclusion, a robust, simple, and highly sensitive optical fiber mechanical axial displacement In conclusion, a robust, simple, and highly sensitive optical fiber mechanical axial displacement or curvature radius sensor based on a Michelson interferometer using an adiabatic bi-conical taper, or curvature radius sensor based on a Michelson interferometer using an adiabatic bi-conical taper, which can be interrogated by spectral wavelength shift or visibility change, has been demonstrated which can be interrogated by spectral wavelength shift or visibility change, has been demonstrated for the first time to our knowledge. The tapered optical fiber, which is compact, is spliced with an for the first time to our knowledge. The tapered optical fiber, which is compact, is spliced with an SMF segment to conform the sensor. When the sensor is bent by applying an axial displacement, the SMF segment to conform the sensor. When the sensor is bent by applying an axial displacement, the symmetry of the taper is modified, which causes a variation in the taper refractive index profile and symmetry of the taper is modified, which causes a variation in the taper refractive index profile and a breaking down of the tapered adiabaticity to couple modes and interference between them. As a a breaking down of the tapered adiabaticity to couple modes and interference between them. As a consequence of such a perturbation, a phase delay between modes causes a wavelength shift of the consequence of such a perturbation, a phase delay between modes causes a wavelength shift of the output spectrum device to smaller wavelength values as well as an increase of visibility in the fringes output spectrum device to smaller wavelength values as well as an increase of visibility in the fringes of the sensor interference pattern, due to the loss of the tapered adiabaticity which enables mode of the sensor interference pattern, due to the loss of the tapered adiabaticity which enables mode coupling. As an additional advantage, for the need of a specific application, the mechanical axial coupling. As an additional advantage, for the need of a specific application, the mechanical axial displacement sensitivity by wavelength shift and the fringe separation sensor spectrum can be displacement sensitivity by wavelength shift and the fringe separation sensor spectrum can be tailored tailored or adjusted by changing the length of the single-mode segment spliced to the taper by simple or adjusted by changing the length of the single-mode segment spliced to the taper by simple splicing splicing or cutting an SMF. The proposed optical fiber displacement sensor based on a Michelson or cutting an SMF. The proposed optical fiber displacement sensor based on a Michelson interferometer interferometer is shown to be a reliable optical fiber device for high resolution optical instrumentation is shown to be a reliable optical fiber device for high resolution optical instrumentation applications. applications. Acknowledgments: This work was funding in part by the Secretary of Public Education for the Teacher Acknowledgments: This work was funding in part by the Secretary of Public Educationand for the theSupport Teacher Improvement Program in Mexico (SEP-PROMEP) (103.5/15/11043, DSA/103.5/16/10510), program for scientific and technological research by Autonomous University of Nuevo Leon (IT439-15, CE332-15). Improvement Program in Mexico (SEP-PROMEP) (103.5/15/11043, DSA/103.5/16/10510), and the Support R. I. Álvarez-Tamayo to thanks to Cátedras program. program for scientificwants and technological researchCONACyT by Autonomous University of Nuevo Leon (IT439-15, CE33215). R. I. Álvarez-Tamayo wants to thanks to Cátedras CONACyT program. Author Contributions: G. Salceda-Delgado and A. Martinez-Rios conceived the main idea; G. Salceda-Delgado, R. I. Álvarez-Tamayo, L. F. Enriquez-Gomez the conceived experiments; G. Salceda-Delgado analyzed Author Contributions:and G. Salceda-Delgado and A.performed Martinez-Rios the main idea; G. Salceda-Delgado, the results and drafted the paper; performed R. Selvas-Aguilar, A. Martinez-Rios, R. I. Álvarez-Tamayo, R. I.experimental Álvarez-Tamayo, and L. F. Enriquez-Gomez the experiments; G. Salceda-Delgado analyzed the A. A. Castillo-Guzmán, B. Ibarra-Escamilla, and V. M. Durán-Ramírez contributed to the revision of the paper and experimental results and drafted the paper; R. Selvas-Aguilar, A. Martinez-Rios, R. I. Álvarez-Tamayo, A. A. gave pertinent comments. Castillo-Guzmán, B. Ibarra-Escamilla, and V. M. Durán-Ramírez contributed to the revision of the paper and Conflicts of Interest: The authors declare no conflict of interest. gave pertinent comments.
Conflicts of Interest: The authors declare no conflict of interest.
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