Fiber-optic extrinsic OL Fabry–Perot dc magnetic field sensor
September 15,2004/Vol.29,No.18/OPTICS LETTERS 2115
Fiber-optic extrinsic Fabry–Perot dc magnetic field sensor
Ki D.Oh
Unicess Networks,Inc.,Canada,Calgary,Alberta T3A 2E5,Canada
Anbo Wang and Richard O.Claus
Department of Electrical and Computer Engineering,Virginia Polytechnic Institute and State University,Blacksburg,Virginia 24061
Received April 9,2004
We demonstrate a compact extrinsic Fabry –Perot interferometer-based fiber-optic sensor that uses magneto-strictive amorphous metallic wire Unitika AF-10(Fe 77.5B 15Si 7.5)as a sensor gauge for measuring dc magnetic fields.We present a theoretical model based on a Gaussian electric field distribution to analyze the sensor operation as a function of longitudinal air-gap separation.The model shows good agreement with the ex-perimental results.A resolution of 50nT over a range of 50–40,000nT with a simple passive temperature-compensation method is obtained.?2004Optical Society of America OCIS codes:060.2370,120.3180.
Fiber-optic sensors based on the extrinsic Fabry–Perot interferometer demonstrate advantages with regard to compactness and polarization problems compared with the intrinsic interferometric sensors.1The con-ventional Mach–Zehnder or magnetostrictive metallic film-based magnetic field sensors show the limitations on polarization fading,temperature,and mechanical vibration.2,3
In this Letter we demonstrate the measurement of dc magnetic f lux with a compact extrinsic Fabry–Perot interferometer-based fiber-optic sensor.We present a theoretical model for radiation from a fiber end face with a Gaussian electric field distribution and a simple passive temperature-compensation method to enhance the sensor system stability for the measurement.
As shown in Fig.1,a single-mode fiber and a mag-netostrictive transducer (diameter 125m m)are used for the input–sensing waveguide and the magnetic field sensing gauge,respectively.After the gauge was treated with field annealing,we inserted it into a small hollow borosilicate tube that we fabricated (inner di-ameter 140m m).The gauge performs as a tempera-ture compensator and aligner so that the sensor is simple and compact.The light from a source (l ?1310nm)propagates along the fiber to a low-finesse Fabry–Perot (FP)cavity formed by an air gap between the fiber and the sensor gauge end faces.We adjusted the air-gap separation to well within one tenth of the coherence length of the source to utilize the tempera-ture compensation and the optimal operation.An optical phase difference occurs between the first ref lection I 1at the fiber–air interface and the second ref lection I 2at the air–gauge end face because of the change in the length of the air gap,which modulates the intensity at the detector for the interference.The source laser beam profile can be approximated by a Gaussian distribution as a function of the transverse components and the field radius at a given longitu-dinal distance of the wave vector.4The electric field intensity through the optical system is given by
E ?E 0exp ∑
2r 2
g 2
∏exp ?2jkz ?,(1)
where r 2?x 21y 2and k ?2p ?l .We assume that g ?z ??g 01z tan ?sin 21?NA ?n 0??,where g 0is the mode field radius of the fiber,the numerical aperture (NA)is ?n 122n 22?1?2?sin u ,n 0?1for the air gap,E 0is the field at zero radius,and n 1and n 2are the refractive indices of core and cladding of the fiber,re-spectively.The radiation from the fiber end face into the cavity produces light spreading that is confined in a cone determined by the NA of the fiber.For a single-mode fiber,mode field radius g 0is obtained by g 0?a ?0.6511.619V 23?212.879V 26?,5where a is the fiber core radius,and V ?2p a 3NA ?l .Intensity I ??E 2??I 0exp ?22r 2?g 2?z ??,where I 0is the intensity at the center of the transverse plane at distance z .The total power of the wave is the integral of the intensity over the plane and is a constant at any distance of z .Hence P 0?R 2p 0R `
0I 0exp ?22r 2?g 2?z ??r d r d w ?p g 2?z ?I 0?2.The circle of radius r ?g ?z ?gives 1?e 2?0.135of the total power level.We use simple two-beam interference to analyze the output power of the in-terferometer for the low-finesse cavity,where the multiple ref lections are negligible compared with the first two ref lections.If the input ref lectance is R 1at the interface between the fiber end face and air
gap
Fig.1.Schematic of an extrinsic Fabry–Perot interferometry-based dc magnetic field sensor.0146-9592/04/182115-03$15.00/0
?2004Optical Society of America
2116OPTICS LETTERS /Vol.29,No.18/September 15,2004
and the sensing ref lectance at the sensor gauge end face is R 2,the resulting intensity of the interfering waves in the fiber as a function of z is given by I ?2P 0R 1p g 02exp μ22r 2g 02?12P 0R A p g 2?z ?exp ∑
22r 2
g 2
?z ?
∏1P 0R B p g 0g ?z ?exp ∑
2r 2g 022r 2g 2
?z ?
∏cos ?Dw ?,(2)
where R A ??12R 1?2R 2,R B ?4?12R 1?p
R 1R 2,Dw ?z ?2p ?l ?1p ,and the longitudinal air-gap distance z is doubled as the wave ref lects back into the fiber.Since the gauge is based on a conducting amorphous metal,the ref lected electric field that is incident upon the conducting interface experiences a p phase change,as the total electric field intensity must vanish when we apply the continuity of the tangential component of the field at the boundary of the gauge end face.From Eq.(2),we obtain the
power of interfering waves inside the fiber,P ?R 2p 0R g 00I r d r d w .Thus we have
P ?P 0√
R 1?12exp ?22??1R A
?
12exp ∑
22g 02
g 2
?z ?
∏?
1R B g 0g ?z ?
?f ?z ??21?12exp ?2f ?z ?g 02??cos ?Dw ?!
,(3)
where f ?z ??g 0221g ?z ?22.In Fig.2(a)we show the power output obtained using Eq.(3).The fringe visi-bility is slightly increased as the separation is in-creased,since the larger second ref lection intensity is reduced by increasing the gap.A dimension change of the gauge that is due to the magnetic field 6is given by e ?CH 2,where C ?3l s ?2H A 2,H is the applied magnetic field intensity,l s is saturation magnetostriction,and H A is an anisotropy field.The average measured magnetostriction coefficient C for the gauges was approximately 1.531026Oe 22.We obtain the air-gap change by the field,D z ?L 1CH 2,at a distance z ,where L 1is the length of the gauge.In Fig.2(b)we show sensor output change obtained with an oscilloscope as we reduce the air-gap separation approximately from 4.9to 0m m and then increase it to 3.1m m.During the air-gap variation,the output is reduced to the minimum level because of the p phase change when the separation is reduced to zero.In Fig.2(c)we show a fringe visibility comparison obtained by applying Eq.(3)to the signal in Fig.2(b).The negative air-gap separation represents an air-gap reduction from a given position to zero air-gap https://www.wendangku.net/doc/0813414933.html,pared with the plane-wave approach,7which assumes a constant intensity distribution throughout the core region that leads a sharp increase in fringe visibility,the Gaussian model shows a good correlation with the experimental results,which explains a moderate power drop as the intensity varies with the Gaussian profile.The fiber used in
the sensor system is a step-index single-mode fiber
with a core diameter of 8.3m m,an index difference of 0.36%,and a NA of 0.13at 1%power angle.
The
Fig.2.(a)V ariation of output power using Eq.(3)with increasing gap separation:R 1?0.04and R 2?0.1.(b)Time-domain trace with varying gap separation:reducing to zero and then increasing from zero.Addi-tional phase change p of second reflection gives zero power at z ?0.(c)Fringe visibility comparison as a function of gap separation for (b).
September 15,2004/Vol.29,No.18/OPTICS LETTERS
2117
Fig.3.Temperature-compensated outputs (a)using coef-ficients from solutions of Eq.(5)and (b)applying compen-sator length adjustment L adj in addition to (a),resulting in compensation .99%
.
Fig.4.System calibration curve for dc magnetic field measurement.
temperature-compensation concept 8was introduced and we demonstrate an improved method.A passive temperature compensation equation based on the dif-ferences of the linear coefficients of thermal expansion of each material in this sensor is expressed as
?C m 2C f ?L 12?C t 2C f ?L 2?D L ?D T ,
(4)
where C m ,C f ,and C t are the coefficients of ther-mal expansion of the gauge,fiber,and compen-sator tube,respectively,and D L ?D T ?0.5l 3?fringe counts ?temperature changes ?.We fabricated a number of pairs of sensors with different gauge lengths and the corresponding compensator tube lengths to obtain the coefficients for this sensor config-uration,since the nominal coefficient values from the manufacturers are generic to bulk materials,which are not accurate enough to yield good temperature stability.We assume that C f ?0.5parts in 106?±C.For the two different sensors,Eq.(4)yields ∑A 12B 1A 22B 2
∏∑C m C t
∏
?
∑
?D L ?D T ?12?B 12A 1?C f ?D L ?D T ?22?B 22A 2?C f
∏
,(5)
where A 1,2,B 1,2,and ?D L ?D T ?1,2are the different
gauge lengths,compensator tube lengths,and sen-sor outputs,respectively.Once the coefficients are obtained from Eq.(5),we can fabricate the sensor with moderate temperature compensation as shown in Fig.3(a),where the output change is ?0.4fringes (?0.262m m in air-gap change)compared with the uncompensated sensor that gives a calculated air-gap change (D L ?C m L 1D T )of 4.393m m (?6.71fringes)for C m ?9.276parts in 106?±C,L 1?3.2cm,and D T ?14.8±C.To achieve good compensation we introduce an additional method of reducing the effect of mechanical cutting errors in length on the gauge,compensator tube,and epoxy spreading so that the right-hand side of Eq.(4)is zero,with exact com-pensation achieved by assuming L exact ?L 26L adj ,where L adj is a small adjustment length to adjust L 2to L exact .Inserting L exact into L 2in Eq.(4)gives the right-hand side zero,so the adjustment L adj ??D L ?D T ???C t 2C f ?is obtained.We typically achieved temperature compensation of better than 99%by use of this method as shown in Fig.3(b),where the tabs check the temperature readings and the gap change is ?0.0268fringes.In Fig.4we show the sensor system response for dc magnetic f lux for a range of 50–1000nT with a resolution of 50nT and obtained a similar response to 40,000nT.The lower range shows f luctuation in readings as the noise is predominant in the output.The signal-to-noise ratios were 1.58and 41.28dB at 50and 40,000nT,respec-tively.We used two small permanent magnets to bias the gauge in the range 3–4G and to determine the direction of the magnetic fields to be measured.Typi-cal sensor dimension is approximately 150m m 37cm (outer diameter 3length).
We have demonstrated a compact dc magnetic field sensor with a resolution of 50nT over a range of 50–40,000nT.The sensor can be used in vector magnetic field sensing,such as sensing of the Earth ’s magnetic field f luctuation and ambient magnetic field variation by ferromagnetic objects.
This work was supported financially by the U.S.Air Force under project PR FY71219503483.K.D.Oh ’s e-mail address is kdoh@https://www.wendangku.net/doc/0813414933.html,.References
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