Utilization Of Faraday Mirror In Fiber Optic Current Sensors

RADIOENGINEERING, VOL. 17, NO. 4, DECEMBER 2008103polarization rotation angle in fiber-optic sensor withnumber of loops Nθ (t ) μV v B (t ) dl μ0VNi (t ) .(10)lFor a given rotator with Verdet constant V the polarization rotation in time θ(t) depends only on the measuredcurrent waveform i(t). The rate of the polarization rotationand the measured current value can be evaluated by meansof polarimetry.4. Linear Birefringence SuppressionConsidering the need for preservation of single polarization state during the propagation the application ofsingle mode fiber is demanded. The fiber core material(SiO2) has a relatively low Verdet constant valueV 3,67 rad T-1 m-1. However, it is possible to providesufficient sensitivity with an adequate fiber loops count.Winding a fiber in loops leads unfortunately to mechanicalstress and consecutively to linear birefringence formationin the fiber core. The linear polarization of coupled lightwave transforms into elliptical polarization and sensorsensitivity is decreased. Consider a single mode fiber withdiameter Dc which is wounded into a single loop with radius Rl. The specific phase shift δs which experience bothorthogonal wave components is [7]δs πλEc CcDc24 Rl2inner mechanical stress in the fiber coil and the linear birefringence rate is decreased. The temperature dependence ofresidual linear birefringence is also reduced [8].The sensors with back light propagation can be constructed for the birefringence compensation. This approachexploits the non-reciprocity of Faraday effect and the reciprocity of linear birefringence. The light wave is reflected on the far end and its polarization state is rotatedwith an angle θ 90 . Then, it is coupled back into thefiber. The light wave which travels the same path in theopposite direction experiences a double polarization rotation imposed by the Faraday effect, due to its non-reciprocity. The orthogonal wave components are swapped inrelation to the fast and slow fiber axis (as described in theIntroduction). The phase shift is equalized and the influence of linear birefringence disappears in the ideal case. Inthe real case the power losses in the fiber and by the lightreflection lead to the presence of residual linear birefringence, which can decrease the sensitivity. The orthoconjugate retroreflector (OCR) is exploited for the light reflection and polarization rotation. The common term for thiscomponent is Faraday mirror, Fig. 2.(11)where λ is the wavelength of the couple light wave, Ec isYoung’s modulus, Cc is the stress-optic coefficient. Forsilica fiber, Ec 7,45 109 Pa and Cc -3,34 10-11 Pa-1 atλ 633 nm [7].Some methods for linear birefringence suppressionbased on diverse principles have been published. The basicmethod utilizes a twisted single mode fiber [3]. The twisting imposes a circular birefringence into a fiber. The rateof circular birefringence exceeds the rate of linear birefringence. A similar approach employs Spun HiBi fibers (SpunHigh Birefringence) [4]. In this type of fibers a chiral stresscomponents are formed in the fiber cladding which imposea circular birefringence. In both approaches the linear birefringence can be neglected. The magneto-optic circularbirefringence is superimposed to the latent one and its rateof change can be evaluated. The disadvantage of thesemethods is strong temperature dependence of the latentcircular birefringence.Another approach is fiber annealing [8]. A fiber coilis fixed in a ceramic labyrinth. This setup is exposed toannealing with a slow temperature rise in the range10-1 100 C/min. After the temperature achieves 800 C,it is stabilized for several hours. Subsequently, the temperature is slowly decreased with steepness 0.1 C/min.The influence of high temperature treatment reduces theFig. 2. The principle of orthoconjugate retroreflector (OCR).In Fig. 2, after the orthogonal wave components E1xand E1y pass the optical fiber in forward direction, theyexperience a rotation θ 45 . When they are reflected bythe mirror, they pass the Faraday rotator again. The resultant rotation is θ 90 . Now the orthogonal componentspass the fiber back but in complementary fiber axis. Weobtain a linearly polarized light on the close end of thefiber with the rotation θ 90 . When a magnetic fieldinfluences the fiber, the polarization will be different fromthe value θ 90 . This can be evaluated by means ofpolarimetry.5. Theoretical Analysis of OCRThe Jones calculus can be exploited for theoreticalanalysis of fiber-optic sensor with OCR. The analyzedsetup is shown in Fig. 3. For the simplification, followinganalysis does not take into account power losses in a fiberand on the optical components. In a real sensor, powerlosses are always present and they decrease its sensitivity.The next simplification is the assumption that the singlemode fiber which is being analyzed is free from intrinsiclinear birefringence. The linear birefringence is induced by

104P. DREXLER, P. FIALA, UTILIZATION OF FARADAY MIRROR IN FIBER OPTIC CURRENT SENSORSthe fiber bending only. The experiments published in [9]show that this can be fulfilled for commercially availablefibers. This allows to match the eigenstates to the coordinate systems which simplifies the analysis as shown below.stances when only the linear or only the circular birefringence is present. The resultant polarization state is given bytheir superposition.Consider the presence of linear birefringence δ only(φ 0). It is possible to modify the relation (12) cos δ jsin δ1 22'J 2 TOF J1 2 0 Fig. 3. The Jones calculus description of fiber optic sensor setup.The light wave on the input of an optical fiber is describedby the Jones vector J1. Consider the polarization angleθ 45 compared to vertical. The light wave passes thefiber described by the matrix TOF and its polarization stateis changed. The resultant vector is γ 1 1 α jβ J 2 TOF J1 γα jβ 1 2 δ sin Δsin Δ φcos Δ j 1 (12)1 ΔΔ2 δ sin Δ 1 sin Δ2 φcos Δ jΔ2 Δ 1 α jβ γ ,2 α jβ γ 1 δδ 1 (16)cos jsin22 0 α ' jβ ' . '' 2 α jβ 1After the back propagation in the fiber the light waveis described by the vectorJ 4' TOF TOCR J 2' ''1 α jβ 2 α jβ 0'0'2 α ' jβ ' 1 α β ' '2'2' 2 α β α jβ '2( δ)' (17)δ 1 1 2 2 1 2 δ2 δ sin cos 22 1 cos 22 sin22(13)It is obvious that we obtain a linearly polarized waveat the close end of the fiber. The polarization state is rotated with an angle θ 90 . The influence of linear birefringence has disappeared.is a geometric mean of phase shifts φ and δ which areimposed by the circular and unwanted linear birefringence [10].In the second instance, consider the presence of circular birefringence φ only (δ 0) which is induced by themeasured magnetic field. The light wave at the far end offiber is described by the vectorwhere δ Δ φ2 2 2The light wave J2 has generally elliptical polarizationstate and enters the OCR described by the matrix TOCR. Onthe output we getJ 3 TOCR J 2 1 0 1 α jβ γ 2 1 0 α jβ γ (14)1 α jβ γ .2 α jβ γ The light wave passes the fiber in the back directionand on its close end is described by the vectorJ 4 TOF J 3 1 α jβ 2 γJ 2'' TOF J1 γ α jβ γ α jβ α jβ γ (15)2221 α β γ 2αγ j2 βγ 2 222 α β γ 2αγ j2βγ The resultant vector (15) is relatively difficult to analyze regarding to the investigation of birefringence. For thesolution of this challenge we can analyze the separate in-''1 α ''2 γ1 cos φ sin φ 1 sin φ cos φ 1 2 '''''' γ 1 1 α γ '' '' α '' 1 2 α γ (18)After the back propagation in the fiber the light waveis described by the vectorJ 4'' TOF TOCR J 2'' ''1 α 2 γ γ '' α '' γ '' α '' α '' γ '' ''''2''2'' ''1 α γ 2α γ ''2''2'' ''2 (α γ 2α γ ) cos φ sin φ 2 cos φ sin φ 222 ( cos φ sin φ 2 cos φ sin φ ) 1 cos φ sin φ sin 2φ .222 ( cos φ sin φ sin 2φ ) 12222(19)

RADIOENGINEERING, VOL. 17, NO. 4, DECEMBER 2008The term sin 2φ in (19) represents the phase shift dueto the circular birefringence induced by the magnetic field.The light wave travels the fiber twice experiencing a double rotation 2φ. On the output of the fiber the polarizationstate can be evaluated by means of dual quadrature polarimetry. Both components of vector J4 can be detected inthe channels with orthogonal polarizers (polarizing beamsplitter). The components of Jones vector represent theelectric field intensities. Optical power of the waves andthe voltages on detector’s output are proportional to thesquare of electric field intensities in both channels. Thedependence of detected signal magnitudes on the rotationis shown in Fig. 4 for both orthogonal channels. We canfind the characteristics linear for a small rotation angles.105beam for OCR and couples it back into the fiber. After theback propagation, the divergent beam is collimated via C2and its part is deflected by means of NBS. The polarizingbeam splitter PBS splits the beam in two orthogonal channels which are equipped with photodetectors PD1 andPD2. PBS serves as a polarization analyzer. The wholesensor is designed for wavelength λ 633 nm since silicafiber exhibits adequate magneto-optic sensitivity at thispoint. Standard single mode FC connectors were chosen.Polarizer P avoids the coupling of reflected beam back intothe laser diode’s pigtail, the power stability of the laserdiode is not affected in this way.The proposed sensor was experimentally realized forthe pulsed current measurement in the range of kA. Thevalue of Verdet constant limits theoretical maximal currentvalue which is being measured. For the silica fiber with thecore material constant V 3.67 rad T-1 m-1 the maximalcurrent value for one fiber loop N 1 isI max Fig. 4. The dependence of detected signal magnitudes on thepolarization rotation.6. Experimental Realization of FiberOptic SensorOn the base of obtained results in previous chaptera fiber optic current sensor has been designed. The sensorutilizes OCR in order to linear birefringence compensation.The scheme of the sensor is depicted in Fig. 5.The source of the carrier optical signal is laser diodeL with a single mode fiber pigtail. By the help of matingsleeve S1 the fiber is connected to the second one withintegrated collimator C1. The collimated beam is generallyelliptically polarized. Polarizer P ensures initial linearpolarization. After passing the non-polarizing beam splitterNBS the beam is coupled into the fiber via collimator C2.θ maxπ 170 kA .μ0VN 4 4π 10 7 3, 67 1The period of analyzer PBS polarimetric functionends at this point. In the real sensor the residual linearbirefringence caused by the power losses decreases thesensor sensitivity and the maximal current value will behigher. However, the rate of this effect is difficult to estimate. It will depend on the way how the fiber is led to thesensing fiber coil. The bandwidth restriction is placed bythe magneto-optical as well as by the electronic part of thesensor. When we aim on the magneto-optical part we cansee that the bandwidth is limited by the time of lightpropagation in the sensing fiber coil. Consider one fiberloop with the radius Rl 5 cm, and the fiber refractiveindex nf 1.5. The maximum bandwidth of the magnetooptical part of the sensor isBW 0, 44c0, 44 3 108 280 MHz . (21)2πRl nf N 2π 5 10 2 1,5 1For sensitivity comparison, the current pulsemeasurement without and with the presence of OCR wereperformed. The identical conditions were kept for bothcases. Fig. 6 shows a scheme of the experimental setup forcurrent measurement without OCR. The sensor setup utilizing OCR is depicted in Fig. 7. By the reason of morecomplicated optical components adjustment only absolutepolarimetric method with single analyzer A and singlephotodetectors PD was realized for the OCR demonstrationpurposes.Fig. 5. The scheme of designed fiber optic current sensor.The mating sleeves S3, S2 join the sensing fiber part SF tothe part of the optical signal evaluation. C3 collimates the(20)Fig. 6. The experimental sensor setup without OCR.

106P. DREXLER, P. FIALA, UTILIZATION OF FARADAY MIRROR IN FIBER OPTIC CURRENT SENSORSFig. 7. The experimental sensor setup with OCR.The experimental sensor setup employing OCR is shown inFig. 8. For current generation a pulsed source with an inductive load was used [11]. The high voltage capacitor wasdischarged into a system of coils. The circuit was switchedby the power thyristor module equipped with a controlcircuitry and fly-back diode. Two sensing fiber loops encircled two wire loops of the inductive load. A doublecurrent value was indicated then. The waveform of thecurrent pulse was measured by the Rogowski coil sensortoo. Since the output voltage of the Rogowski coil is proportional to the derivation of the current, it was integratedby means of the mathematical function of the oscilloscope.A pigtailed laser diode with operating wavelengthλ 633 nm and the power P 10 mW was used as a lasersource. The whole fiber optic part of the sensor employeda single mode fiber SM600 with cladding diameterDc 125 μm and core diameter dc 4,3 μm. Fig. 9 showsa detailed view of the OCR and the beam splitter with integrated fiber optic collimators.Resonant discharge circuit produced harmonicdamped current waveform with oscillating frequencyf 59 kHz and first peak’s value in the range ofIp 1300 1600 A. The current value was obtained by thehelp of a calibrated Rogowski coil sensor. Fig. 10 presentswaveforms which were captured by the measurement without the OCR. Dual quadrature polarimetry using polarizingbeam splitter and couple of photodetectors was used foroptical signal evaluation [12]. The first waveform (fromthe top) in Fig. 10 is the Rogowski coil voltage and thesecond its integral, which indicates the real current waveform in the load with the top value Ip 1550 A. The thirdand fourth waveforms are the voltages on thephotodetector’s outputs.The waveforms which were captured by the currentpulse measurement with OCR are shown in Fig. 11. Thefirst waveform considered from the top is the Rogowskicoil voltage. The second waveform is its integral, whichrepresents the current waveform. The third waveform is thephotodetector’s output voltage. The duration of the currentpulse, which is represented by the sinus half wave, wastd 8.5 μs and it reached the value up to Ip 1600 A. Ithasn’t been able to achieve shorter pulses with this simplecurrent generator. But the main goal of this experiment wasto show the sensitivity improvement, not the bandwidthpossibilities.Fig. 10. The waveforms capturedmeasurement without OCR.bythecurrentpulseFig. 11. The waveforms capturedmeasurement with OCR.bythecurrentpulseFig. 8. The experimental setup of the magneto-optic currentfiber sensor with OCR.Fig. 9. The beam splitter assembly with polarizer and integratedcollimators (left) and orthoconjugate retroreflector(right).

RADIOENGINEERING, VOL. 17, NO. 4, DECEMBER 2008107When we compare the photodetector’s output voltages in Fig. 10 and Fig. 11 it is obvious that only very lowsensitivity was achieved with the sensor without OCR. InFig. 10, the voltage value does not exceed 5 mV in themoment of the current top Ip 1550 A.[3] ROSE, A., REN, Z. F., DAY, G. W. Twisting and annealing opticalfiber for current sensors. Journal of Lightwave Technology, 1996,vol. 14, no. 11, p. 2492 - 2498.The estimated voltage top value is Up 1.4 mV. Astrong photodiode’s shoot noise and thermal noise of thetransimpedance amplifier dominates in the output signal.When the sensor with OCR was used for the current pulsemeasurement a much larger sensitivity was achieved, Fig.11. The sensors output voltage Up 214 mV correspondswith the current top Ip 1365 A. The sensitivity has improved by a factor AS 174. Interference is observable inthe waveforms in Fig. 11. It is probably caused by the steepcurrent rise by the thyristor switching.[5] WAYNANT, R. Electro-Optics Handbook. New York: McGraw-HillProfessional, 2000.7. ConclusionThe fiber optic sensors which have been described inthis paper represents an advantageous way for DC and ACcurrents and magnetic fields measurement. Their advantages become significant by the measurement of pulsedquantities of very high level and very short time duration.The galvanic isolation is important in high voltage systemsand prevents ground loops further. The carrier signal is alight wave which can be transmitted for a long distancewithout bandwidth limitation. The bandwidth is then determined mainly by the electronic part of the sensor.The drawback of the single mode fiber optic sensorsis the presence of latent and induced linear birefringence. Itsignificantly reduces the sensor sensitivity due to the polarization state degeneration. However, some methods offerthe suppression or compensation of the linear birefringence. In this work, the compensation method which utilizes orthogonal polarization conjugation has been chosenas a promising approach. It has been theoretically analyzedby means of Jones calculus. The ability of linear birefringence compensation has been proved together with doublesensitivity improvement. The results of the analysis havebeen experimentally demonstrated by the measurement ofthe pulse current waveform.AcknowledgementsThe paper was prepared within the framework of theresearch plan No. MSM 0021630513 of the Ministry ofEducation, Youth and Sports of the Czech Republic.References[1] GAUGITSCH, M., HAUSER, H. Optimization of a magneto-opticallight modulator. Journal of Lightwave Technology, 1999, vol. 17,no. 12, p. 2633 - 2644.[2] CRAIG, A. E., CHANG, K. Handbook of Optical Components andEngineering. New Jersey: John Wiley & Sons, Inc., 2003.[4] LAMING, R. I., PAYNE, D. N. Electric current sensors employingspun highly birefringent optical fibers. Journal of LightwaveTechnology, 1989, vol. 7, no. 12, p. 2084 - 2094.[6] BORN, M., WOLF, E. Principles of Optics. Cambridge: CambridgeUniversity Press, 1999.[7] ULRICH, R., RASHLEIGH, S. C., EICKHOFF, W. Bendinginduced birefringence in single-mode fibers. Optical Letters, 1980,vol. 5, p. 273 - 275.[8] TANG, D., ROSE, A. H., DAY, G. W., ETZEL, S. M. Annealing oflinear birefringence in single-mode fiber coils: Applications tooptical fiber current sensors. Journal of Lightwave Technology,1991, vol. 9, no. 8, p. 1031 - 1037.[9] PAVLŮ, M. The Suppression of Mechanical Stress Impacts in FiberOptic Transmission Systems. Bachelor’s thesis. Brno: FEEC, BrnoUniversity of Technology, 2008.[10] RIPKA, P. Magnetic Sensors and Magnetometers. London: IEEE;Artech House, 2001.[11] DREXLER, P., FIALA, P. Methods for high-power EM pulsemeasurement. IEEE Sensors J., 2007, vol. 7, no. 7, p. 1006 – 1011.[12] DREXLER, P., FIALA, P. Identifying of the special purposegenerator pulses. In Proceedings of Progress in ElectromagneticsInternational Conference PIERS 2007. Beijing (China), 2007,p. 561 – 565.About Authors.Petr DREXLER graduated from the Faculty of ElectricalEngineering and Communication, Brno University ofTechnology. Since 2004 he has been with the Departmentof Theoretical and Experimental Electrical Engineering,Brno University of Technology. He received Ph.D. degreein Electrical Engineering in 2007. He is interested in thedomain of the electro/magnetooptical methods for electromagnetic field measurement, in the design of optoelectronic circuits and properties of electro/magnetoopticalsensors. He is a member of the IEEE.Pavel FIALA received Ph.D. in Electrical Engineeringfrom the Brno University of Technology, Faculty of Electrical Engineering and Communication in 1998. He joinedthe Department of Theoretical and Experimental ElectricalEngineering in 1990 as a research assistant. Since 2003 hehas been Associate professor and head of the Department.Dr. Fiala is interested in modeling and analysis of coupledfield problems by numerical method formulated with partial differential equations using the finite element method(FEM), the boundary element method and the finite difference method. In modeling and optimization, he introducedcoupled electromagnetic-thermal-mechanical deformationof lumped parameters models. He is a co-director of theEuropean project WISE – wireless sensing of the 6thframework dealing with sensor research for aeronauticsand cosmonautics (participant consortium EADS,DASSAULT, AVIATION, etc.) and a member of theIEEE, IEE, OSA, APS, SPIE.

which is called Faraday rotator. The basic setup is shown in Fig. 1. Fig. 1. The principle of integral fiber-optic current sensor. The sensor principle is based on the Ampere’s law l v Bl dIμ (9) where μ is the permeability of Faraday rotator material. For diamagnetic and paramagnetic materials holds μ μ0