Current sensing using bismuth rare-earth iron garnet films Michael Ko and Elsa Garmire Ferrimagnetic iron garnet films are investigated as current-sensing elements. The Faraday effect within the films permits measurement of the magnetic field or current by a simple polarimetric technique. Polarized diffraction patterns from the films have been observed that arise from the presence of magnetic domains in the films. A physical model for the diffraction is discussed, and results from a mathematical analysis are in good agreement with the experimental observations. A method of current sensing that uses this polarized diffraction is demonstrated. 1. Introduction Yttrium iron garnet has been shown to be a sensitive magnetic-field sensor by use of its Faraday effect along with polarization-sensitive optics. 1 This mate- rial is readily available because it is used in Faraday isolators, and new crystals with related compositions are rapidly being developed with larger Faraday rotations. The experiments reported here were used to investigate the possibility of current sensing by use of a bismuth rare-earth iron garnet film 3composition is 1TbBi2 3 1FeGa2 5 O 12 4, here called BIG, grown at AT&T Bell Laboratories 2 for optical isolator applications. Our motivation is to achieve a current sensor that can be used with multimode fibers. The BIG film was measured to exhibit a Faraday rotation of 0.2°@Oe at 1.152 μm. The minimum detectable field that used simple Ge detectors was determined experimentally to be ,0.2 Oe, which translates to a current-sensing sensitivity of 300 mA measured 3 mm from a straight wire. Twenty times improvement is expected if more sensitive detectors are used. In addition to the conventional Faraday effect, a diffraction ring was observed from the mag- netic domains occurring within the 300-μm-thick sample. This diffraction is uniquely polarized so that the spatial separation of the two polarizations can be utilized to sense current without the need for a polarization analyzer. The experiments were per- formed with the BIG samples inserted within a coil of wire. 2. Magnetic-Field Sensing Current passing around a coil of wire causes a mag- netic field that can be sensed by means of Faraday rotation. In the experiments reported here, a BIG sample that was originally designed as an optical isolator was placed in the center of a current coil. The magnetic field at the center of a solenoid of N turns and length L containing current I is H 5 NI@L, 112 where H is in units of ampere turns per meter. One can convert this to units of oersted by dividing by a conversion factor of 80. Several solenoids with vari- ous numbers of coil turns were used to obtain differ- ent ranges of magnetic field. For maximum sensitivity as an electric-field sensor, a polarization analyzer is set at 45° to the incident polarization. The fraction of light coming through the analyzer depends on the amount of Faraday rotation U through P@P 0 5 11@2231 6 sin12U24. 122 The Faraday rotation angles are determined by mea- surement of the output and input optical power. The measured rotation angle is shown in Fig. 1 as a function of calculated magnetic field. The figure shows a reasonably linear relationship between the Faraday rotation and magnetic field. The small deviations from linearity are due to either the differ- ence between the measured and calculated field or the When this research was performed, the authors were with the Center for Laser Studies, University of Southern California, Los Angeles, California 90089-1112. M. Ko’s permanent address is the Northrop Corporation, 8900 E. Washington Boulevard, Pico Rivera, California 90660-3737. Received 8 June 1994; revised manuscript received 30 August 1994. 0003-6935@95@101692-05$06.00@0. r 1995 Optical Society of America. 1692 APPLIED OPTICS @ Vol. 34, No. 10 @ 1 April 1995
Transcript
Current sensing usingbismuth rare-earth iron garnet films
Michael Ko and Elsa Garmire
Ferrimagnetic iron garnet films are investigated as current-sensing elements. The Faraday effectwithin the films permits measurement of the magnetic field or current by a simple polarimetric technique.Polarized diffraction patterns from the films have been observed that arise from the presence of magneticdomains in the films. A physical model for the diffraction is discussed, and results from a mathematicalanalysis are in good agreement with the experimental observations. A method of current sensing thatuses this polarized diffraction is demonstrated.
1. Introduction
Yttrium iron garnet has been shown to be a sensitivemagnetic-field sensor by use of its Faraday effectalong with polarization-sensitive optics.1 This mate-rial is readily available because it is used in Faradayisolators, and new crystals with related compositionsare rapidly being developed with larger Faradayrotations. The experiments reported here were usedto investigate the possibility of current sensing by useof a bismuth rare-earth iron garnet film 3compositionis 1TbBi231FeGa25O124, here called BIG, grown at AT&TBell Laboratories2 for optical isolator applications.Our motivation is to achieve a current sensor that canbe used with multimode fibers.The BIG film was measured to exhibit a Faraday
rotation of 0.2°@Oe at 1.152 µm. The minimumdetectable field that used simple Ge detectors wasdetermined experimentally to be ,0.2 Oe, whichtranslates to a current-sensing sensitivity of 300 mAmeasured 3 mm from a straight wire. Twenty timesimprovement is expected if more sensitive detectorsare used. In addition to the conventional Faradayeffect, a diffraction ring was observed from the mag-netic domains occurring within the 300-µm-thicksample. This diffraction is uniquely polarized sothat the spatial separation of the two polarizations
When this research was performed, the authors were with theCenter for Laser Studies, University of Southern California, LosAngeles, California 90089-1112. M. Ko’s permanent address is theNorthrop Corporation, 8900 E. Washington Boulevard, Pico Rivera,California 90660-3737.Received 8 June 1994; revised manuscript received 30 August
can be utilized to sense current without the need for apolarization analyzer. The experiments were per-formed with the BIG samples inserted within a coil ofwire.
2. Magnetic-Field Sensing
Current passing around a coil of wire causes a mag-netic field that can be sensed by means of Faradayrotation. In the experiments reported here, a BIGsample that was originally designed as an opticalisolator was placed in the center of a current coil.The magnetic field at the center of a solenoid of Nturns and length L containing current I is
H 5 NI@L, 112
where H is in units of ampere turns per meter. Onecan convert this to units of oersted by dividing by aconversion factor of 80. Several solenoids with vari-ous numbers of coil turns were used to obtain differ-ent ranges of magnetic field.For maximum sensitivity as an electric-field sensor,
a polarization analyzer is set at 45° to the incidentpolarization. The fraction of light coming throughthe analyzer depends on the amount of Faradayrotation U through
P@P0 5 11@2231 6 sin12U24. 122
The Faraday rotation angles are determined by mea-surement of the output and input optical power. Themeasured rotation angle is shown in Fig. 1 as afunction of calculated magnetic field. The figureshows a reasonably linear relationship between theFaraday rotation and magnetic field. The smalldeviations from linearity are due to either the differ-ence between themeasured and calculated field or the
presence of the diffraction effect discussed below.1A diaphragm was used to eliminate the higher-orderdiffraction ring during this measurement.2 Furtherresearch is needed to characterize these deviationsmore fully. At the available magnetic-field levels, weobserved no hysteresis within the sensitivity of ourmeasurements.The slope of the graph gives a sensitivity of 0.2°@Oe.
This is in excellent agreement with an expected valueof 0.18°@Oe based on the Faraday characteristics ofthe sample 1rotating 1.3-µm-wavelength light by 45°at 320 Oe2, assuming linear rotation with the field upto the saturation point and assuming that sensitivityvaries quadratically with inverse wavelength.
3. Minimum Detectable Current
The minimum detectable current can be determinedfrom the minimum detectable field 1MDF2. Thelatter was investigated by use of a differential detec-tion scheme1 consisting of a Glan polarization beamsplitter 1set at 45° to the vertically polarized beam2and two detectors. If the difference between the twooutputs is divided by their sum, the result is afunction of only the Faraday rotation angle 1for smallrotation2:
P1 2 P2
P1 1 P25 2U. 132
This procedure eliminates the effect of source powerfluctuations. In our experiments only P1 2 P2 wasevaluated 1by use of a differential amplifier2, whichwas acceptable since the total power did not fluctuateby more than 10%. The measured MDF was 0.2 Oe.When used as a current sensor the BIG sample will
most likely be used near a straight power line, for
Fig. 1. Measured Faraday rotation angle versus calculated mag-netic field within a solenoid. Sample was BIG film, AT&T wafer2311, 315 µm thick, designed to be a Faraday isolator at 1.3 µm1rotation of 130°@mm and magnetic saturation #320 Oe2. Thetwo sets of data points correspond to two different solenoids withdifferent numbers of turns.
which
H 5I
2pR, 142
where I is the current in the line and R is the distancefrom the conductor to the measurement point. As-suming that R 5 3 mm, we found that the minimumdetectable field, 0.2 Oe, translates into a minimumdetectable current of ,300 mA. Improvements inthe optics and detectors can be expected to lower theMDF. At low frequencies at least one paper 1usingbulk film2 has reported aMDF of 0.001 Oe@ŒHz at 100Hz,1 which is 20 times better than our preliminarymeasurements. This would result in a minimumdetectable current of less than 15 mA.
4. Diffraction from Magnetic Domains
An important diffraction phenomenon emanating fromthe Faraday sample was identified during materialcharacterization. In the absence of an applied mag-netic field, a ring formed around the transmittedbeam, as shown in Fig. 2. It was found that the ringwas orthogonally polarized compared with the polar-ization of the central spot and of the incident beam.Similar ringlike diffraction was observed earlier inthe study of magneto-optic spatial light modulators.3,4The ring had a half-angle of 0.015 rad 10.86°2 and anangular spread of ,1@3 its radius. We have ana-lyzed this effect theoretically and then used it as apossible multimode and polarization-insensitive cur-rent sensor.The diffraction is a manifestation of the presence of
magnetic domains in the sample when viewed alongthe easy axis of the magnetization tensor. In thethin ferrimagnetic film used here, the domains haveinternal magnetizations either parallel or antiparal-lel to the direction of light propagation, showing up asstripes between crossed polarizers. Diffraction of
Fig. 2. Vidicon image of a diffraction pattern of the 1.15-µm laserbeam transmitted through BIG film. The scale permits measure-ment of the diffraction angle. The diffraction pattern was circu-lar; ellipticity is due to distortion when the pattern was recorded.
polarized light by these stripes has been used in thepast as a quick and reliable means of determining thestripe width by research groups investigating mag-netic bubble domains in bubble memory devices,without the need for microscopic inspection of themagnetic material. What we investigated here isthe use of this diffraction effect to measure a locallyapplied magnetic field 1current2.The zero external field-domain structure can be
inferred from the polarimeter photograph of similarmaterial 1grown by the same AT&T group that pre-pared our sample2, shown in Fig. 3 1taken from Ref. 52,which shows a characteristic domain width of 30–50µm. The crenellated structure of the domains in thismaterial is quite unusual; magnetic garnet domainsare usually smooth walled when viewed along theprincipal symmetry axis. The main effect of anapplied field in this material is to rearrange thedomains, causing stripes of one magnetization direc-tion to grow wider at the expense of stripes in theother direction. The stripes may move a great dealduring this rearrangement, unless the applied field isexactly along the symmetry axis. As the field in-creases the thinning stripes collapse into bubbles,which finally disappear as soon as the field is in-creased past the saturation magnetization.To understand how transmitted light forms the
ring shown in Fig. 2, consider any line through thedomain structure, such as that shown in Fig. 3. Theeffect of the domains is to form a diffraction gratingalong this line, where adjacent magnetic domainsrotate linearly polarized light in opposite directions,according to the Faraday effect, as shown in Fig. 4.This rotated polarization can be decomposed intoconstant components in the direction of the incidentpolarization 1vertical2, and into alternating compo-nents in the direction normal to the incident polariza-tion 1horizontal2. The vertical polarization compo-nent will be undeviated, forming the central spot.The horizontal polarization components define a bi-nary phase-only electric-field grating with a p phaseshift between adjacent domains. Because of this,the horizontal components are diffracted into anannular ring which is rather wide because of theuncertainty in domain width.
Fig. 3. Pattern of magnetic domains in a BIG film determined byphotographing through crossed polarizers 1from Ref. 52.
The total electric field on the observation screencaused bymultiple-slit Fraunhofer diffraction is givenby the summation of all contributions from each slit1domain2 having the appropriate phase shift 10 or p2.Assuming a Gaussian beam of width w0 illuminates asample that is divided into alternating domains ofwidthW, the Fraunhofer diffraction pattern is
I@I0 5sin2 F
F2exp5223w01F 6 p2@W426, 152
where F 5 1kW sin f2@2. In our experiment theradius of incident laser beam w0 was ,1 mm, and Wwas 50 µm. The Gaussian term is a maximum when
kW sin f 6 p 5 0 or sin f 5 6l@12W 2. 162
At zero angle the Gaussian term is essentially zero,which agreed with our experimental observation thatno x-polarized light appeared in the forward-goingbeam at zero field. At higher magnetic fields 1largecurrents2, when the Faraday rotation is stronger, thestrength of the diffracted ring increases. When thefield is large enough that a substantial fraction of thelight is diffracted, it then begins to couple back intothe zero-order mode 1central spot2 and also into asecond-order ring, twice the size of the first ring, asexpected from coupled-mode theory. This was seenin our experiments at solenoid currents .800 mA.Domain variations of the order of 30% cause an
expected spread in the diffraction orders of compa-rable amount. One can take this into account byintegrating Eq. 152 over a Gaussian distribution ofpossible domain widthsW. Figure 5 shows the theo-retical diffraction pattern expected, assuming a 40 610 µm domain width, which agrees well with thezero-current experimental results.
6. Current Sensing by Use of the Diffraction Effect
As the applied current 1i.e., magnetic field2 increases,increased magnetization in the magnetic domains
Fig. 4. Conceptualization of the process by which magneticdomains create diffraction: 1a2 domains are either up or down; 1b2polarization rotation is 6U, depending on whether the domain isup or down; 1c2, 1d2, projections of the polarization vertically andhorizontally, showing that the vertical component keeps its initialpolarization and is undeviated by the domains whereas thehorizontal component experiences a p phase grating with a periodtwo domains in width.
will result in more Faraday rotation of linearly polar-ized light. This in turn will change the optical powerratio between the ring and the central bright spot.Thus it is possible for one to measure current ormagnetic field by measuring power transfer betweenthe ring and central spot rather than by analyzingpolarization. When light is initially polarized alongy, there will be more light in the x component 1ring2and less in the y component 1central spot2 as thepolarization rotation increases with increased mag-netic field.We used an infrared-sensitive Ge detector attached
to a powermeter tomeasure the relative powers of thecentral spot and the diffraction ring. Apolarizer wasused to eliminate the signal rediffracted into thecentral spot at high currents. In the absence of anapplied field, the power ratio was approximately 6:41spot to ring2. Without applied current the fractionalpower in the ring is expected to be Pr102 5 C sin2 U,and the fractional power in the central spot is Ps102 5C cos2 U, where U is the initial Faraday rotationangle caused by internal magnetization andC is someconstant that depends on transmission. As an exter-nal magnetic field is applied 1or current is sentthrough the coil2, the optical power in the ring andcentral spot are, respectively,
Pr ; Pr102 1 dPr 5 C sin2 U 1 2C cos U sin U dU,
17a2
Ps ; Ps102 1 dPs 5 C cos2 U 2 2C cos U sin U dU.
17b2
Because the powers in the central spot and ring atzero current are comparable, it makes sense to mea-sure their difference. If this difference is ratioed totheir sum,
Pr 2 Ps
Pr 1 Ps; R 5 sin2 U 2 cos2 U 1 4 sin U cos U dU,
182
Fig. 5. Theoretical calculation of the expected diffraction patternusing a width of 40 6 10 µm and a Gaussian beam of 1 mm.
and the current-induced Faraday rotation is foundfrom
dU1I2 5R1I2 2 R102
4 sin U cos U. 192
Equation 192 can be written in terms of only R and R102by use of the fact that R102 5 sin2 U 2 cos2 U 5 1 2
2 cos2 U, so that cos2 U 5 31 2 R1024@2 and sin2 U 5
31 1 R1024@2. Then
dU1I2 5R1I2 2 R102
231 2 R102241@2. 1102
The Faraday rotation angle was calculated frommeasurements of R1I2 and R102. The results aregraphed in Fig. 6, clearly demonstrating the possibil-ity of a current sensor based on the spatial separationof polarization components. It is interesting to notethat the nonlinear shape of Fig. 6 is similar to that ofFig. 2. More careful experiments are required todetermine if this nonlinearity is connected with therelation of magnetic field to current or to the materialitself.It should be noted that the above analysis neglected
rediffraction back into the central spot or to thehigher-order ring. It also assumed that the domainstructure is relatively intact. Change in the diffrac-tion pattern with applied field was visually inspectedwith the aid of an infrared vidicon. It was foundthat, when the current in the solenoid was,0.8A, thex polarization contained not only the first-order diffrac-tion ring but also a weak zero order 1central spotcomponent polarized along x instead of y2, and asecond x-polarized ring of diffraction weakly startedto appear. The diameter of the second ring wasalways twice as large as that of the first ring. Thering size decreased a small amount 1,10%2 as thecurrent was increased further, which indicated asmall increase in average domain size.
Fig. 6. Current-induced Faraday rotation angle, determined bymeasurement of the ratio between light in the diffraction ringcompared with light transmitted in the central spot, as a functionof applied current, using Eq. 1102. The sample was BIG film,AT&T wafer 2532, 470 µm thick, designed for Faraday isolation at1.5 µm 1rotation of 90°@mm and magnetic saturation at #320 Oe2.
Current-sensing applications of ferrimagnetic irongarnets have been investigated. It has been shownthat bismuth iron garnet films exhibit a Faradayrotation of 0.2°@Oe at 1.152 µm. The measuredminimum detectable field of ,0.2 Oe means a mini-mum detectable current of approximately 300 mA.This is expected to improve significantly with moresensitive detectors. The limit, however, will be givenby the coercivity of the garnet. More accurate mea-surements may also exhibit hysteresis, not observedin the present experiments, which must be taken intoaccount in any applications requiring high accuracy.In addition to the conventional Faraday effect, it
has been shown that polarization-sensitive diffractionfrom the samples can be utilized to sense the current.This provides a polarization-insensitive, multimode-fiber sensor. The unique diffraction pattern from thesamples was explained with both physical and math-ematical models. The physical model was based onmagnetic domains with alternating phase shifts, pre-dicting the polarization separation between the ringand central spot, as observed in the experiments.The physical model was used to provide a mathemati-cal analysis that showed that only the first diffractedorder would be visible at zero applied field in thegeometry we used.Amethod of current sensing by measurement of the
power ratio between the undiffracted and the firstdiffracted orders has been demonstrated. For sens-ing higher currents, more accurate analysis shouldtake account of the domain structure change whenthe sample is under the influence of high appliedmagnetic field. This diffraction method of determin-
ing the magnetic field breaks down, however, as soonas bubble domains form, implying that this method ofreading out the magneto-optic response of the garnethas an upper limit of detectable magnetic field that islower than the more conventional methods based ondirect observation along the magnetization axisthrough crossed polarizers. Future systems wouldutilize optical fibers or micro-optics and semiconduc-tor lasers for compact sources.
The authors gratefully acknowledge funding fromNorthrop Corporation and provision of the BIG sampleby AT&T Bell Laboratories, as well as comments onmagnetic bubble films from an anonymous reviewer.
References and Notes1. M. N. Deeter, A. H. Rose, and G. W. Day, ‘‘Fast, sensitive
magnetic-field sensors based on the Faraday effect in YIG’’IEEE J. Lightwave Technol. 8, 1838–1842 119902.
2. The samples were kindly supplied by S. Licht of AT&T BellLaboratories, Murray Hill, NJ 07974.
3. J. A. Davis and J. M. Waas, ‘‘Current status of the magneto-optic spatial light modulator,’’ in Spatial Light Modulators andApplications III, U. Efron, ed., Proc. Soc. Photo-Opt. Instrum.Eng. 1150, 334–345 119892.
4. M. Waring, ‘‘Polarized beam splitting effect in heterogeneouslymagnetizedmagneto-optic films,’’ inOptical Information Process-ing Systems and Architecture, B. Javidi, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 1151, 567–576 119892.
5. R. Wolfe, E. M. Gyorgy, R. A. Lieberman, V. J. Fratello, S. J.Licht, M. N. Deeter, and G. W. Day, ‘‘High frequency magneticfield sensors based on the Faraday effect in garnet thick films,’’in Proceedings of the IEEE 8th Optical Fiber Sensors Confer-ence 1Institute of Electrical and Electronics Engineers, NewYork, 19922, pp. 390–392.
