Fiber Optic Magnetic Field Sensors

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KUNGL TEKNISKA HÖGSKOLANInstitutionen förSignaler, Sensorer & System

10044 STOCKHOLM

ROYAL INSTITUTEOF TECHNOLOGY

Instrumentation Laboratory Elektrisk mätteknik

Fibre Optic Magnetic Field SensorsUtilizing Iron Garnet Materials

by

Hans Sohlström

TRITA-ILA 93.01

S-10044 STOCKHOLM

Department ofSignals, Sensors & Systems



V

Descriptors

YIG, iron garnets, rare earth garnets, magneto-optics, optical waveguide,

fibre optic sensors, ma gnetic field measu rem ent , cur ren t m easu rem ent .

Abstract

This thesis deals with the subject of fibre optic magnetic field sensors

utilizing iron garnet materials . Such materials exhibit a large Faraday

rotation which make them advantageous for application in compact mag-

net ic field sensors.

After a n in tr oduction, in wh ich fibre optic sensors a nd optical meth ods t o

measure e lectr ic current are reviewed, the original research work is

summarized.

A system for th e measu remen t of the m agneto-optic properties of tr an s-

par ent ma terials is described. Measur ement results, showing th e influence

of temperature, magnetic field direction and sample treatment on thema gneto-optical propert ies of YIG-cryst als, ar e pr esent ed. The pr oper ties of

thin magneto-optical waveguiding films have also been studied using

different light coupling methods. Measurement results obtained for holo-

graphic grating, prism and edge (end-fire) light coupling to different

substitu ted YIG films a re pr esent ed. It is shown th at th e launching method

ma y affect t he propert ies to be measu red.

The design a nd perform an ce of several versions of extrin sic guided wa ve

fibre optic magnetic field sensors are then reported. The sensors employ

substituted YIG (Yttrium Iron Garnet, Y3Fe5O12) thin film waveguides as

sensing elements. Polarization maintaining fibres were used as feed andreturn to provide two signal channels. The signals were combined in a

balanced measu remen t system, providing insensitivity to both fluctu at ions

in optical power a nd loss. Sensors ha ve been ma de both with sepa ra te fibres

to guide the light to and from t he sensin g element an d with a single fibre for

both functions. The two fibre version, although less ”elegant”, is found to

ha ve a better perform an ce. This version a lso ma kes it possible to deter mine

both the magnitude and sign of the magnetic field. Measurement results

indicate a usable measurement range of at least several mT with a noise

equivalent magnetic field level of less than 8nT/ √ Hz.

The design and performance of multimode fibre optic magnetic fieldsensors ut i l iz ing the Faraday effect in an epitaxia l ly grown thick

(YbTbBi)IG film is also described. This type of sensor is found to be linear

over a ra nge from 27mT t o less th an 270nT. Sensor pr ototypes suit able for

current monitoring in high voltage transmission lines have also been

developed.



VI



VII

List of publications

This t hesis is based on th e work cont ained in th e following papers:

A: U. Holm, H. Sohls tröm and T. Brogårdh, ”Measurement sys tem for

magneto-optic sensor materials”, J . Phys. E: Sci . Instrum., vol. 17,

p. 885–889, 1984.

B: U. Holm, H. Sohlstr öm a nd T. Brogår dh, ”YIG-sensor design for fibre

optical magnetic field measurement”, OFS 84 , R. Th. Kersten and

R. Kist, p. 333–336, VDE-Verla g, Berlin, 1984.

C: U. Holm and H. Sohls t röm, Measurement of YIG crystal characteristics

for the design of optical magnetic field sensors , TR84.01, Instrumenta-

tion La borat ory; Royal In st itu te of Techn ology, Stockh olm, 1984.

D: H. Sohlstr öm, U. Holm an d K. Svantesson, ”A Polar izat ion Based Fibre

Optical Sensor System Using a YIG Optical Waveguide for Magnetic

Field Sensing”, S prin ger proceed in gs in Ph ysics 44: Opt ical Fiber

Sensors , H. J. Arditty, J. P. Dakin, and R. Th. Kersten, p. 273–278,

Springer-Verlag, Berlin, 1989.

E: H. Sohls tröm, U. Holm an d K. G. Svant esson, ”Chara cterization of

Magnetooptical Thin Films for Sensor Use”, S PIE Proc Electro-Optic

and Magneto-Optic Materials and Applications, J . P. Cast era , vol. 1126,

p. 77–84, 1989.

F: K. Svant esson, H. Sohlstr öm an d U. Holm, ”Magneto-optical garnet

ma ter ials in fibre optic sensor systems for ma gnetic field sen sing”, SPIE

Proc Electro-Optic and Magneto-Optic Materials and Applications II ,

H. Damm an n, vol. 1274, p.260–269, 1990.

G: H. Sohls tr öm a nd K. Svant esson, ”A waveguide based fibre optic

magnetic field sensor with directional sensitivity”, SPIE Proc Fiber

Optic S ensors: En gineering an d A pplications , A. J . Bruinsma and

B. Culshaw, vol. 1511, p. 142–148, 1991.

H: H. Sohlstr öm a nd K. Svan tesson, ”The perform an ce of a fibre optic

magnetic field sensor utilizing a magneto-optical garnet”, Fiber and

Integrated Optics, vol. 11, p.137–141, 1992, also pres ent ed at th e OFS8

conference in Mont erey, J an . 92.



VIII



IX

Contents

Abst ract .............................................................................................................V

List of pu blicat ions ......................................................................................... VII

Cont en ts ........................................................................................................... IX

1. The a im a nd organizat ion of the t hesis ........................................................ 1

2. Int roduction ................................................................................................... 3

Fibr e opt ic sen sors .................................................................................. 3

Magnet ic field measu rement .................................................................. 7

Measu rement of elect r ic cur ren t ............................................................ 9

Opt ical methods for magn et ic field a nd ................................................. 9

YIG ........................................................................................................ 183. Sta r tin g point s for th e sensor development work ..................................... 22

4. Mat eria l cha ra cteriza tion mea su rem ent s .................................................. 24

Bu lk mater ia ls ...................................................................................... 24

Wavegu ides ........................................................................................... 30

5. Sen sors. ........................................................................................................ 35

Sin gle-mode systems ............................................................................. 35

Mu lt imode systems ............................................................................... 41

6. Conclusions .................................................................................................. 45

7. Ackn owledgem en ts ...................................................................................... 46

Refer ences ........................................................................................................ 47Comm ents on th e au thorsh ip of the paper s ................................................... 55

Paper abst racts ................................................................................................ 56

Paper repr in t s .................................................................................................. 59

Paper A

Paper B

Paper C

Paper D

Paper E

Paper F

Paper GPaper H



X



Fibre Optic Magn etic Field S ensors Utilizin g Iron Garn et Materials

1

1. The a im and organ iza t ion of the th esis

The industrial development has created a growing demand for new types of

measu remen t a nd t herefore n ew types of sensors, to enha nce the qua lity of

different processes. The physical environment for the sensors has, at the

sam e tim e, become t ougher an d more electr oma gnetically polluted.

To overcome the electromagnetic pollution and also to achieve other

advantages , there has , s tart ing in the mid seventies , been a s teadily

growing int erest in fibre optic sensors. Opt ical m eth ods h ave long been u sed

for mea sur ement pur poses, but th e t echn ological ba se developed for fibre

optic comm un icat ion applicat ions ha s widened th e scope considera bly. Fibre

optic remote sensing system s, providing imm un ity to electr oma gnetic int er -feren ce, electr ical isolat ion an d a nu mber of oth er a dvant ages, could n ow be

developed.

The mea sur ement of magnetic field or cur ren t in electr ical power system s

ar e applicat ions in wh ich t hese advan ta ges are very significan t.

This th esis is to a lar ge extent based on work ma de as par t of th e ”Single

Mode Sensor P roject” th at was st ar ted in 1981 as a co-opera tive effort by the

Instrumentation Laboratory of the Royal Institute of Technology, the

Inst itu te of Microelectronics (IM) and the Institute of Optical Research (IOF).

The project was financed by the National Swedish Board for Technical

Development (STU).The aim of the project was to study the applicability of single mode

optical fibre technology for sensor use. ASEA AB (now ABB), one of the

proponents of the project , had a t that t ime developed a number of

multimode fibre optic sensors. Partly because of their interest the develop-

ment of a magnetic field or electric current sensor was chosen as the

working goal.

Most of the electric current sensors developed at that time utilized the

Faraday effect in long lengths of fibre, coiled around the conductor. The

difficulties encountered with such sensors led us to study sensors based on

localized sensing elements made from materials having a large Faradayrotation, e.g. YIG (Y3Fe5O12).

During the early stages of the project work, polarization maintaining

fibres became available. We then recognized the possibility of a system in

which polarisation maintaining fibres were used to carry the light to and

from a sensing element in t he form of a YIG waveguide.

Stu dies of mult imode sensors u sing bulk YIG or th ick films of substitu ted

YIG , were also carried out. A number of such sensors were developed for

different applicat ions.

The a im of th is th esis is to stu dy th e feasibility of ma gnetic field sens ors

based on ir on gar net ma ter ials. As both single-mode and m ult imode sensors



Hans Sohlström

2

Fig.1. A m agnetic field sensor in th e form of a waveguid ing ”chip” – the idea

as envisioned d urin g th e initial stages of the project.

are treated, the thesis can also be said to form a comparison of the two

types.

Measurement technology is an application oriented research area, and

the stress in this thesis is on the sensor development and the material

cha ra cterizat ion. The paper s on wh ich t he t hesis is based describe differen taspects of the sensor development work, from the initial ideas to working

sensor prototypes. In this summary I will primarily motivate and discuss

the work in order to give a context to the different papers. For this purpose

the summary includes an introduction in which the theory is outlined and

also some illustr at ive results , tha t were omitt ed in th e papers due t o the

limitations of the conference contribution format. The introduction also

contains an overview of fibre optic sensors and current measurement in

general. In section 3, I then outline the sensor development and the role of

th e ma ter ial cha ra cter ization. The sum ma ry of my work is given in sections

4 an d 5. At th e end of each of these t wo sections r eferen ces ar e given t o th edifferent papers. Finally, in the conclusion, I summarize and speculate

somewha t a bout th e implicat ions of th e results.




3

2. In t roduct ion

Fibre opt ic s ensors

Definit ions

A fibre optic sensor consists of an optical sensing element which under the

influen ce of th e quan tit y to be measu red m odula tes light, an d optical fibres

to guide th e light t o and from t he sensing element. When a lso th e sensing

elemen t cons ists of optical fibres, th e sensor is intrinsic, and when t he fibres

ar e only ut ilized to guide the light t o an d from t he sensin g element , which is

itself external to the fibre, the sensor is extrinsic. In literature, the term

fibre optic sensor is somet imes r eserved for th e int rinsic sensors only.

This definition does not include pyrometers that use an optical fibre

between t he collectin g optics an d t he det ector. Form ally it a lso excludes t he

pyrometr ic devices tha t m easur e the t empera tu re of a m etallic film on th e

fibre end and similar devices where the sensing element ”emits light”,

alt hough t hey a re often considered to be fibre optic sensors.

Another class of sensors th at should be men tioned in this cont ext ar e th e

optically powered electronic sensors or hybrid sensors. As all th eir conn ec-

tions with th e out side world ar e optical, they shar e ma ny of the advan ta ges

of the fibre optic sensors, while at th e sam e time t hey allow th e use of esta b-

lished electronic sensing principles. They may also provide a way for

convent iona l sensors to be integra ted int o optical sensor net work s.

His torical notes

Optical measurement methods have long been used: optical telephone

transmission was patented in 1880, and patents from 1927 (Marconi Co.)

and 1934 (American Telephone & Telegraph Co.)1 show the principles of

optical fibres, wavelength multiplexing, etc. Without usable optical fibresan d laser light sour ces, however, litt le progress wa s ma de. In t he 1960’s t he

laser was invented and optical fibres became available, figure2. The rapid

development in the optical communications field has since then made

opt ical and electr o-opt ical component s ava ilable at r easona ble prices also for

measur ement applicat ions.

In the first fibre optic sensors that were developed, bundles of optical

fibres were u sed2, but similar sen sors with single fibres soon a ppear ed 3.

Dur ing th e ear ly 70’s ma ny of th e comm only used sen sing prin ciples where

developed 4,5,6,7,8. Since then, the technological advances of the fibre optic

communications research and development have immediately been takenadvan ta ge of in th e sensor comm un ity.



Hans Sohlström

4

Limit for thesilica fibre

1968 1970 1972 1974 1976 1978 1980 1982 1984

10 4

10 3

10 2

10 1

10 0

10 –1

10 –2

10 –3

Year

F i b r e l o s s [ d B / k m ]

Fig.2. Th e m inim um losses of fibres d eveloped for optical com m un ications.

The truly unique features of the fibre optic sensors, their immunity to

electromagnetic interference and their electrical isolation, were recognized

from t he very sta rt , and scenar ios from th e sevent ies indicat ed a complete

switch to optical measurement technologies. What was not, however,

th oroughly recognized was th at indust ry rea lly needed reliable sta nda rdized

equipment with proven performance, not laboratory prototypes. After a

general disa ppointm ent at th e end of th e 80’s, ther e is now in t he 90’s a

renewed optimism, th ough on a more realistic scale, as th e first indust rial

prototypes of fibre optic sensors are being introduced. One of the leading

applicat ion ar eas for th is is th e electr ical power indu str y, one of th e ar eas

where the original interest first s tirred, indicating the important role of

tim e an d a pioneerin g applicat ion in t he accepta nce of new t echn ologies.

Principles

J ust as with th e convent iona l electr ic sensors th e nu mber of combina tions of

measurement quantity, sensing principle and output parameter is large.

The output parameter, the type of modulation that carries the information

from th e sensin g elemen t is a possible pr inciple of class ificat ion.The optical power or th e intensity of the returned light is a fundamental

par am eter. In fact, int ensity is the only quan tity we can measu re. All oth er

quantities must in some way be converted to intensities at one or more

detectors a nd possibly with a varia tion with t ime.

The use of the term intensity here is somewhat unclear. Intensity or

radiant intensity is, according to international standards, defined as power

per solid angle. Although t his qua nt ity is modulat ed when t he t ota l power is

modulated, it would in principle be more correct to speak of optical power

and power modulation. The use of th e ter m intensity as a relative measure

of power is, however, established in literature and will also be followed inth is text.




5

In an extrinsic intensity sensor the modulation can take place in an

optical system with moving parts9, a piece of material with an environ-

mentally dependent optical loss10 , etc. In an intrinsic sensor the modula-

tion is caused by a variation in the optical properties of the fibre itself.

Several loss mechanisms can be exploited, microbending11 ,12 , reflections

from gratings in the fibre13 , temperature dependent scattering in thefibre14 , losses cau sed by dopan ts in t he fibre a nd light decoupling from th e

fibre15 ar e some examples.

Several of th ese are loss mechanisms t ha t a re a lways present in a fibre

optic system . This indicates a ma jor weak ness of an int ensity based sen sor:

th ere is in pr inciple always a loss varia tion in th e optical system a nd t his

could not directly be discrim inat ed from var iat ions in t he mea sur an d. Often

however, some known properties of the measurand signal can be used to

separ at e it from th e loss var iat ion.

To completely remove the uncertainty that is created by the loss varia-

tion, a system with a reference cha nn el can be used. In such a system twolight int ensities are m easur ed. If th e relation between t he influence of the

loss and the influence of the measurand is different for the two channels,

the influence of the loss can be removed. One realization of this is the

balanced system in which t he su m of th e two detected in ten sities is affected

by the sys tem loss and the dis tr ibution between them only by the

measu ra nd. A similar approach is to use the int ensity var iations with t ime

to achieve a system t ha t is independen t of th e absolut e inten sity. The use of

fluorescence decay for t empera tu re sensin g has been st udied16.

Th e wavelength of the light can be used to car ry inform at ion in severa l

ways. The sensing element can cause a wavelength dependent loss and

tr an smit only cert ain wa velengths of th ose emitt ed from a broadban d light

source17 . The sensing element can also receive light with one wavelength

and emit light with another. The information can then lie in the spectral

content of the emitted light18 , in which case it is a tr ue wavelength modu-

lation, or in t he int ensity of th e convert ed light , in which case it is better

described as an in ten sity based system , perh aps with a reference cha nn el.

The phase of the light is used in the very sensitive interferometric

sensors19. In such a sensor the free-path arms of a conventional inter-

ferometer a re r eplaced by optical fibres t ha t ma ke t he int erferometer m uch

more rugged and at the same time very sensitive to any change in the

effective refractive indices or lengths of the fibres. The changes can for

example be caused by an absolute rotation, making the device a rotation

sensor; th e environment al pr essure, mak ing it a very sensitive hydrophone

or a magnetostrictive perturbation, making it a very sensitive magneto-

meter.

Th e polarization state of the light can also be utilized in the sensing

element. The most usu al examples of this ar e sensors u sing the Fa ra day

effect, as will be further discussed below, but extrinsic electro-optic electric

field sensors20 an d pressu re sensors ba sed on ph otoelastic effects in extr in-

sic sensors21 or in fibres2 2 ,2 3 can a lso be found in l i tera ture . The



Hans Sohlström

6

polarization state can, however, not be used as the information carrying

para meter in t he fibre.

Most of the sensors that use polarization modulation in the sensing

element internally convert it to an intensity modulation. Alternatively, it

could be converted to two different intensities creating a balanced system,

cf. above. The use of a polarization maintaining optical fibre makes itpossible to tr an smit th ese two cha nn els in one fibre core.

Single-mode or m ul t im ode

Out of the above ment ioned par am eters, only the wavelength an d th e inten -

sity can be maint ained when t he light propagates along a multimode fibre.

The optical loss variation always present in a practical system, however,

limits the applicability of intensity as the information carrier. The many

different propagation modes allowed in the multimode fibre, give rise to a

dispersion that destroys the phase information and causes a bandwidth

limitat ion for t he int ensity inform at ion.The core of a single-mode fibre is so thin, normally 5–10µm, that only

one mode is allowed. For monochromatic light it has no dispersion. The

sma ll dispersion a ssociated with th e spectr al width of th e light can, in ma ny

inst an ces, be ignored. The pha se inform at ion is ret ain ed in th e single-mode

fibre. The pha se drift a ssociat ed with cha nges of th e optical length of th e

fibre mu st, however, be taken into accoun t. The polar isat ion st at e can not be

maintained for any longer lengths of fibre because the almost perfect

circular symmet ry of th e fibre ma kes th e two ort hogona l polar ization m odes

degenerat e, allowing the polar ization sta te t o cha nge un der t he influence of

the fibre birefringence.

Th e polarization maintaining (p. preserving) fibre is a special type of

single-mode fibre with a core t ha t is elliptical or h as an an isotr opic index of

refraction. This removes the degeneracy of the fibre polarization modes,

allowing th em t o exist indepen dent ly of each oth er. Polar ized light coupled

into th e fibre will, th us, be distribut ed into th e two polarization modes a nd

will then travel along the fibre without mode coupling. The polarization

sta te is in fact not generally maintained as the phase relation between the

two ort hogona l component s present at th e input is lost du e to the differen ce

in propagation const an t for t he t wo modes. The intensity ra tio between th e

light in the two modes is however maintained. Only for the special case

wher e only one polar ization m ode is excited t he fibre is r eally polar ization

maintaining.

P lana r wa vegu ides

J ust as light can be guided in a n optical fibre which is a circular waveguide,

it can be guided in a planar waveguide. The simplest st ru ctu re is th e planar

slab guide, figure3, wher e a plana r film of refra ctive index n f is san dwiched

between a substrate and a cover material with lower refractive indices

(nf >n

s, n

c). Often the cover material is air (n

c=1). In the slab guide there is

no confinement of the light in t he pla ne of the film.




7

Substrate, n s

Cover, nc

Film, n f h

Fig.3. T he planar slab waveguid e.

The light is guided in the same way as in an optical fibre, though con-

fined only in one dimension. Just as with the fibre, there are single-mode

an d m ultimode guides. Some of th e ma ter ial combinat ions u sed for plana r

guides have much larger index differences than normally used in fibres.Because of this, waveguide thicknesses, h, of 1µm or less are often

necessary to achieve strict single-mode guiding.

In analyzing the guide one has to treat the case of TE (Electric field

transverse to the propagation d irection) an d TM (Magnetic field transverse to

the propagation direction) state of polarization separately. Due to the

different phase shifts on total reflection, the propagation constants will be

different for the two cases. For small index differences and with thick

guides, the difference in pr opagat ion const an t between t he TE an d t he TM

mode, ∆β , is sma ll,

∆β=βTE –βTM

In m an y practical cases h owever, th e magnit ude of ∆β is noticeable.

Below, I will describe how the Faraday effect in a planar waveguide can

be trea ted as a coupling between t he TE a nd TM modes of the sam e order.

This coupling cannot effectively take place if the two modes do not run in

synchr onism , i. e. if ∆β is far from zero.

As in a slab waveguide ther e is no confinement of the light in th e plane of

the waveguide, one must use the planar equivalent of conventional ”bulk

optical” methods to control the light in the transverse direction. The

alternative is to confine the light in both dimensions with a channelwaveguide.

Magnet ic f ie ld measureme nt

Before dealing with the optical magnetic field measurement methods, a

short description of ma gnetic field mea sur ement in general is relevant .

Magnetic field measur ements a re n ot only made to measur e th e ma gnetic

field itself, but also to provide indirect information about other quantities.

Measurement of electric current, rotation speed measurement using apermanent magnet and a pick-up coil, acoustic pressure sensing using



Hans Sohlström

8

Sear ch-Coil Magnet ometer

Flux-Gate MagnetometerOptically Pumped Magnetometer

Nuclear Precession Magnetometer

SQUID Magnetometer

Hall-Effect Sensor

Magnetoresistive Magnetometer

Magnetodiode

Magnetotransistor

Fibre-Optic Magnetometer

Magnet o-Optical Sen sor

Magnetic Sen sor Techn ology

10–12 10–9 10–6 10–3 1 10+3

Detecta ble Field [T]

From Lenz From this thesis

Fig.4. Magnetic field sensor com parison, adapted from 26 . In ad dition to the

da ta t aken from the reference, the m agnetic field range for the sensors

dem onstra ted in th is thesis is given.

dynamic mic rophones , and s ubmar ine de tec t ion u s ing SQUID:s

(Supercondu cting Qu an tu m Int erference Device) to detect pertu rba tions of

the earth’s magnetic field are some examples. In addition to the large

practical differences, the ranges of magnetic field encountered are verydifferen t. Th e mea sur emen t of electr ic cur ren t ma y involve fields exceeding

1T, while sub ma rine det ection deman ds a noise level ar oun d 10-11T 24 ,25.

The required ban dwidth s r an ge from a bout 1Hz for subma rine detection to

GHz for E MC measurem ents.

An overview of some different measurement technologies is given in

figure4. The magnetic field range for the fibre optic sensors demonstrated

in this thesis is indicated in addition to the data from the reference.

Eviden t ly, sens ors ut ilizing ma gnet o-optical effects cover a la rge field ra nge.

Together with the ”Fibre-Optic Magnetometer”, they cover the entire range

given in figure4 except the very low fields that can only be detected bySQUID Magnetometers.

Measurement of electric current has been the main application con-

sidered in th is work . It is, th erefore, appr opria te t o widen th e view and a lso

have a brief look at cur rent measur ement in general.

Measureme nt o f e lectr ic current

Current and perhaps voltage are the only quantities that can really be

measured with conventional electrical methods. All other quantities areconvert ed to a cur ren t or a volta ge tha t can in t ur n be mea sur ed, e.g., by an




9

indicating instrument. It may therefore seem somewhat surprising to find

th at th ere is a considerable int erest in u nconventiona l methods to measu re

current in high voltage power systems. A cause for this is that even though

the measurement is in principle a simple one, it is in practice complicated

for t wo reasons: the power dissipat ion in t he mea sur ement circuit a nd t he

need to keep th e display unit a t ground potential.The conventional way to solve this is to use a current transformer tha t

transforms the current down to a reasonable level and provides an isolation

barr ier between t he prima ry winding at line potent ial and t he secondar y

winding at ground potential. The size and cost of such a current trans-

former, however, increase with the line voltage. Also, current transformers

can only be used for AC measurements. For DC measurements, more

complex devices with Ha ll element s a re often used.

The increasingly complex cont rol system s used in t he power tr an smission

networks a lso crea tes a need for m ore point s of measur ement an d a wider

ra nge of measur ement situa tions. Curr ent meter ing for billing pur poses isusu ally done with equipment ha ving an accur acy in t he order of 0.2% an d

with a relatively low bandwidth, typically less than 1 kHz. For control and

protection purposes, however, errors of 1% or even more are usually

accepted. Ther e is even a n eed for on/off devices th at indicate t he pr esence

of cur ren t over a cert ain level.

Curr ent tr ansform ers with optical downlinks a s well as systems u sing

the Faraday effect at microwave frequencies have been investigated 27 . In

recent year s t he int erest ha s, however, been focused on fibre optic systems.

Optical me thods for magnetic f ield and

electr ic current measuremen t

Two main m e thods

Most of the work that has been published on optical methods to measure

magnetic fields concern either the Faraday effect or magnetos t r ic t i ve

perturbation of optical fibres. The Faraday effect, which is a change of the

polarization state of propagating light under the influence of a magnetic

field, is the ph enomenon ut ilized in t his work .Before we further describe the Faraday effect, a short description of the

oth er pr inciple is appr opriat e. In cont ra st t o the F ar ada y effect, which can

be ut ilized in both bulk optical element s, planar waveguides an d in fibres,

the magnetostrictive principle requires the use of fibres. The magnetostric-

tive principle was first suggested in 198028. It uses a magnetostrictive

material which is mechanically linked to the fibre, for example in the form

of a m agnet ostr ictive jacket on t he fibre or a bulk m agnet ostr ictive elemen t

onto which the fibre is wound. When subjected to a magnetic field the

ma gnetostr ictive element will chan ge its form , th ereby cau sing a st ra in a nd

a cha nge of th e length of the fibre. This cha nge of th e opt ical lengt h can be

detected if the fibre is placed in one a rm of a Mach-Zehnder interferometer.



Hans Sohlström

10

The fibre can be long an d as th e pha se sensitivity of th e inter ferometer is

high, t his device can poten tia lly be very sensit ive29 . However, it is u nfort u -

nately also sensitive to all other parameters that influence the optical

length of the fibre, e. g. temperature30. Although the measurement of

electr ic cur ren t wa s men tioned as a possible applicat ion31, th e driving force

of the development was the potential possibility of detecting the smallcha nges in th e eart h’s ma gnetic field cau sed by passing subma rines. At first

nickel was used for the magnetostrictive element, and later met a l l i c

glasses32 ,33. Different biasing34 an d feedback 35 ,36 ar ra ngements have been

investigated.

Many of the problems with temperature and vibration sensitivity have

been overcome with proper jacketing of th e fibre a nd with th e use of all fibre

optical systems. This type of sensor offers extremely high sensitivity, with

noise levels down to 10–1 5T/ √ Hz37 , but it is n ot su ited for electr ic cur ren t

measur ement and oth er large-signal applicat ions.

Other sensing principles that have been studied are: interferometric

detection of th e movement of a met al coat ed fibre in a m agnet ic field when a

current is sent through the coating38 ,39 ,40 , sur face plasmon r esona nce41 ,

liquid crystals42 and resistor heat ing43 . The use of a current transformer

that is in turn interrogated by a fibre optic interferometer has also been

tried44.

In t his cont ext, the possibilities to use convent iona l cur ren t t ra nsform ers

together with an optical dat a link for curr ent m easurem ents in h igh voltage

systems should be ment ioned. The equipment at high poten tial could th en

be powered by pick-off from the power line45 , or be a hybrid sensor,

optically powered t hr ough th e fibre46.

The Fa ra d ay effect

When a ma terial exhibiting the Farad ay effect is placed in a ma gnetic field

an d a beam of linearly polarized light is sent th rough it in th e direction of

the field, a rotation of the plane of polarization of the light will occur,

figure5.

The phenomenon was discovered in 1845 by Michael Faraday. Other

nam es for th e same effect ar e th e m agneto-optical rotation (MOR ), magnetic

circular birefringence (MCB ) or t he m agn eto-opt ical effect . The last t erm is,however, more genera l an d m ay a lso include other effects.

The effect is non-reciprocal in nature. This means that when the direc-

tion of light propagat ion is r eversed, the dir ection of rota tion as s een from a

fixed reference system, is not reversed. A light beam that passes twice

th rough th e medium in opposite directions will thus acquire a net rotat ion

which is t wice th at of a single pass.

The Faraday rota t ion is proport ional to the magnetization of the

material,

θ =

∫ L

k M.dl




11

EH

l

θ

Fig.5. T he Farad ay effect

where θ is th e polarizat ion r ota tion, M is the m agnetization, L is th e light

path and k is a constan t t hat is dependent on t he mat erial in question, the

wavelength a nd th e tem pera tu re. (Bold letter s denote vector quan tit ies.)

In par am agnetic and diama gnetic ma terials the magnetization an d, th us,also the polarization rotation is practically proportional to the magnetic

field str ength, H . One can th en describe the r ota tion in t erms of the Verdet

constan t, V ,

θ = ∫ L

V.H .dl={ }accordin gtoth egeomet ryoffigure5 = V.H.l

where H is the component of th e magnet ic field str ength par allel to th e light

propagation direction. (The Verdet constant is sometimes expressed in

terms of the magnetic flux density, B , which for th ese mat erials is linearly

related t o the ma gnetic field str ength, B=µH .)In ferri- and ferro-magnetic materials the magnetization is not linearly

related to the magnetic field strength, and a Verdet constant cannot be

used.

In addition to the magnetic circular birefringence, a linear birefringence

can be induced by a magnetization perpendicular to the light propagation

direction. This is called MLB (magnetic linear birefringence), Voigt or

Cotton-Mouton effect, though the last name originally denoted a similar

effect in fluids due t o molecule orienta tion in t he m agnet ic field. Ther e ma y

also be a m agnet ic field dependent differen ce in optical absorpt ion between

th e linear or t he circular polar izat ion st at es, MLD (magnetic linear dichro-

ism) and MCD (magnetic circular dichroism)47 ,48 . One should, however,

keep in min d th at th ere seems t o be a considera ble confusion concerning t he

na mes for t hese effects in litera tu re.

Besides m agnet ic field sensin g, the ma in a pplicat ion of the Fa ra day effect

is in isolators and circulators for microwave or optical frequencies though in

these applications , the effect is used in a s ta t ic ra ther than dynamic

manner.

The isolator is a device t ha t allows power t o flow in one d irection, wh ile

the other direction is blocked. The basic design consists of a polarizer

followed by a 45° Fa ra day rotat or a nd a second polar izer with it s polariza-

tion dir ection 45° from that of the first one. The 45° angle, however, makes



Hans Sohlström

12

High-frequency field h x

Precession

m x

m y

Steady m agnet ic field

Fig.6. Electron precession: The h igh-frequency field h x creates m agnetiza-tion both in the x- and the y-direction. A fter 50 .

the basic isolator design unsuitable for optical waveguide implementation,

an d a n um ber of varia tions of th e principle have been tr ied49.

A circulator is a similar device but with three ports, in which power

incident on one port will emerge at t he next port .

The origin of the Fara d a y effectThe Fa ra day effect a rises from t he int era ction of th e electr on orbit an d spin

with a ma gnetic field. The electr on orbit form s a m agnet ic dipole tha t t ends

to align in an applied constant field. As it, from a classical viewpoint, is a

spinning part icle, it will react to a pertu rbing moment um at right a ngles to

th e spin axis by precessing about the original spin axis, just as a spinning

top would do. The electr on spin beha ves similar ly, though t his is not obvious

from a classical viewpoint. The perturbing momentum can be caused by an

electromagnetic wave of ”optical” or microwave frequency. The closer this

frequency is to the precess ional frequency the more marked is the

interaction. If they coincide there is a resonance, called paramagneticresonance or ferromagnetic resonance, depending on the actual material

properties.

Macroscopically, the precession has the effect of creating a magnetization

at right a ngles to both th e applied consta nt magnetic field and t o th e pertur -

bation, cf. figure6.

The m agnetic susceptibility of the ma ter ial will, under th e influence of

the steady magnetic field (in the z-direction), become a tensor with off-

diagona l component s of th e form,




13

χyx =–iωMω

ω20–ω2

χxy =+iωMω

ω2

0

–ω2

where ω is the angular frequency of the applied high-frequency field, ω0 is

the precession angular frequency and ωM is a factor that depends on the

material and the magnetization. The expressions become somewhat simpler

if we consider instead the magnetic susceptibility for a left or right circu-

lar ly polar ized pert ur bing high frequen cy field,

χR=ωM

ω0–ω

χL=ωM

ω0+ω

µR=µ0

1+ωM

ω0–ω

µL=µ0

1+ωM

ω0+ω

In these expressions we recognize the resonances discussed above. If loss

terms are included, the resonances will be damped and the permeabilities

will have ima gina ry pa rt s, cau sing loss an d dichr oism.

The strong interaction between neighbouring atoms in ferri- and ferro-

magnetic mat erials causes t hese mat erials to have several r esonan ces atdifferent frequencies and with different strengths, creating rather compli-

cat ed frequ ency (wavelength) dependencies for both t he r eal an d th e imagi-

nary terms.

L ight propa gat ion in magn eto-opt ica l m at er ia l s

To un dersta nd how the F ar aday effect influences th e light propagat ion, t he

wave equat ion is a su itable star ting point. For an infinite medium with no

extern al electr ical polar ization, th e wave equat ion can be writt en,

∇2E(r, t )=µε∂2

E(r ,t)∂t 2

The solut ion t o this is a plane wa ve with th e pha se velocity given by,

u=1

√ µε

Waves with different circular polarization states will have different µ:s,

and th us t ra vel with different speeds.

A linearly polarized wave can be seen as the sum of two circularly

polar ized waves with equal a mplitu de but opposite dir ections of rota tion. As

these two waves propagate with different speeds, they will acquire a phase

difference proportional to the travelled distance. In terms of their sum, the



Hans Sohlström

14

pha se differen ce ha s t he effect of rota tin g th e linear sta te of polar ization by

an an gle which is equal t o ha lf th e phase chan ge.

If we want to study the influence of the Faraday effect on the light

propagat ion in a waveguide with differen t pr opagat ion const an ts for t he TE

an d TM modes, this simple r easoning is not a pplicable. Instea d one can u se

the coupled-mode formalism51 . In t his form alism one studies how a sma llperturbation causes a coupling between the orthogonal eigenmodes of the

unpertu rbed medium. In the literatu re th is pertu rbation is normally in the

electrical permittivity ε, causing an electric polarization P . As only the

pr oduct of µ and ε appear in the wave equation, the Faraday effect can be

treated as a pertu rbation in ε of the following form,

∆ε =

0 –iδ 0

iδ 0 00 0 0

.ε0

δ=ωωM

ω20–ω2

With this approach, one finds for the case with only one of the modes

exited, th at th e power in th e oth er mode can be repr esented by,

F=1

1+

∆β

2θ2

sin2

√ θ2+

∆β

2

2 .z

where ∆β is the difference between the propagation constants of the twomodes, θ is the polarization rotation per unit length in a homogeneous

medium, a nd z is t he dista nce along t he pr opagation direction. If ∆β=0 this

simp lifies to,

F= sin 2 (θ.z)

From the above, it is evident that ∆β should be smaller than θ if any

appr eciable am oun t of power is to be coupled between th e modes.

Electr ic cur rent sensing u sing th e Fa ra da y effect

Glass sensing elem ent s

The first optical curr ent tr an sducers ut ilizing th e Fa ra day effect used bulk

optical glass element s int err ogated by an open pa th light beam, figure7.

Using two detectors, an d a polar izat ion separ at ing prism, a system which

is not a ffected by var iat ions in th e opt ical loss, can be achieved, figur e852.




15

I

θ

B

E

Polarizer

Polarizer

P0

P=P 0 cos2(θ–π /4)

Fig.7. The simp lest form of an optical current sensor utilizin g the Faraday

effect.

Polarizer

Det.

Det.

Laser

I

B

Polarizationsplitter

Fig.8. A bu lk optic current m easurem ent system with polarization stat e

detection. As the Faraday effect is non-reciprocal the two-way pass through

the sensing element effectively doubles the rotation.

The sensor is sensitive to the total magnetic field, thus, also to the

contributions from other conductors nearby. Also, the distance between the

condu ctor a nd t he sensin g element will influen ce th e scale factor. With t wo

sensing elemen ts, one on each side of th e condu ctor, a differen tia l system is

achieved, reducing th e influence from condu ctors a t large dist an ces.53

An iron core reduces the position dependence and the influence of exter-

na l fields, but a s th e iron core m ust ha ve a relat ively lar ge gap t o accomm o-

date the glass sensing element, some sensitivity to the conductor position

an d to exter na l fields will rema in.

A more funda ment al appr oach is to use a basic propert y of the m agnetic

field encircling th e conductor,

O∫ L

H.dl = ∫ ∫ S

i .ds = I

where i is the current density through the surface S, with the contour L,

and I is the total cur rent th rough S.

This means that if the sensing light path completely encircles the con-

ductor, fig 9, th e sensor becomes in sensitive to extern al fields an d indepen -

dent of the conductor position in the sensing element. This can be approxi-

ma ted with a bu lk sensing element with a centr al h ole for th e condu ctor or

sensing element assembled from several pieces of glass. The reflections at

th e corn ers m ust be suitably arra nged not to influence th e polarization st at e

of the light .54



Hans Sohlström

16

Conductor

Polarizer

In

Polarizer

Ou t

Faradayrotatorelement

Fig. 9. A glass sensing element that encircles the conductor, after55

The early experiments were made with glass sensing element s ha ving

relat ively small Verdet const an ts, t ypically about 10–5 rad/A, requiring long

sensin g element s for good sen sitivity. Alth ough YIG (Y3Fe5O12 ) and other

ma ter ials with mu ch lar ger polar izat ion r ota tion were stu died56 , no tr ans-

ducers using such materials were presented. Multiple reflections were,

however, tried to reduce the physical size of the sensing element without

sacrificing optical p at h length57 ,58.

Devices to mea sur e both th e cur ren t a nd t he voltage simult an eously werealso presented.59,60

With optical fibres m an y of the pr oblems associat ed with th e open optical

pat h could be elimina ted 61. The possibilities with opt ical fibres, h owever, go

further than that. The sensing element can be made from an optical fibre.

Although the Verdet constant of the fibre material is not high, about

4.10 -6rad/A, a m easur able rotat ion can be achieved with a long fibre, and

with the fibre wound round the conductor, a good approximation of the

closed line in tegr al of the field is achieved.

There was a considerable interest in this type of device at the end of the

70’s a nd th e result s were pr omising62 . The bendin g of the fibre in th e coil,however, causes a temperature dependent l inear birefringence that

quenches the circular birefringence caused by the Faraday effect. Several

met hods ha ve been t ried t o overcome t his pr oblem.

If the fibre is twisted, a circular birefringence ”bias” is introduced, which

is magnetic field independent and large enough to quench the linear bire-

fringence. This bias birefringence is, however, temperature dependent63.

With the sensing fibre divided into sections with opposite twists, the bias

rotat ion a nd t he tem perat ur e dependence can be cancelled an d with t he use

of polar ization ma int ain ing fibre for t he downlead, the vibrat ion sen sitivity

is r educed 64. A similar a pproach is to use a fibre with a str ong birefringence

which is a lmost c ircular 6 5 . This c ircular birefringence is s trongly




17

temper at ur e dependent. Techn iques to compensa te for th is have, however,

been studied66.

The fibre can be woun d int o a coil in su ch a way th at th e beat length (th e

fibre length th at cau ses a ph ase differen ce of 2π between th e two ort hogona l

linear polarization modes) is equal to the circumference of the fibre coil.

When an external field is then applied to the fibre coil, the periodic mag-netic field t ha t is in th is way applied t o the fibre will cau se a n et polar iza-

tion rotation.67 ,68 ,69 . A principally similar scheme is to use a polarization

maintaining fibre with a very short beat length and arrange a periodic

ma gnetic field with t he sa me period70.

A more funda men ta l appr oach is to ann eal th e coiled fibre t o rem ove the

tempera tu re dependent linear birefringence71.

Also, the Faraday effect is temperature dependent. The use of a tempera-

tu re dependent linear ly birefringent optical element has been su ggested as

a way to introduce a temperature dependent part ia l quenching of the

Fa ra day effect, th ereby reducing the effective temper at ur e dependence72.In addit ion to th e simple polar ization detection syst em described above, a

number of interferometric systems to detect the polarization rotation has

been presented73 . Closed-loop systems7 4 and heterodyne detection

systems75 have been studied. A system for simultaneous measurement of

two currents has also been presented76 . To eliminate the influence of

reciprocal effects in the fibre, some of these systems utilize Sagnac in te r-

ferometers77 ,78 . The non-reciprocity of the Faraday effect also makes it

possible to use a Fabry-Perot resonat or to increase t he effective polar ization

rotation79.

Experiments with techniques to make the sensor output independent of

variations in the Verdet constant80 , or to convert the polarization rotation

to a spectr al modulat ion81, have been m ade.

Th e measurement bandwidth of Fa ra day sensors with bulk glass or fibre

coil sensing elements is limited by the transit time of the light in the

sensing element82,

B3dB=0.44τ =0.44.

cn

.1

2πr.

1N

where c/n is the speed of light in the fibre, N the number of turns in the

fibre coil and r is the radius of the fibre coil. With N=100, r=0.1 and n=1.5 a

bandwidth of 1.4MHz is achieved. Obviously, there is a trade-off between

sensitivity and bandwidth. With high pulsed currents the sensing element

can be mad e short, giving very lar ge bandwidth s. A nu mber of system s with

bulk glass83 or fibre sensing elements84 ,85 for measur ement of tran sient

curren ts in the 106A range have been presented. Other specialized

applications such as aerospace86 current measuring and space plasma

current measurements87 have been studied. There is also a potential for

distr ibuted m agnet ic field sensing88.

Alth ough t he u se of an optical fibre coil for cur ren t m easu rem ent s ma y in

principle seem straightforward, the practical application of the technology



Hans Sohlström

18

is, however, complicated by the linear birefringence of the fibre and many

optical cur ren t m eterin g devices th at ar e insta lled in th e high volta ge power

lines ar e of the bu lk optical t ype89,90.

Other materials

Optical fibres with high Verdet constants may increase the applicability of cur ren t sen sing using fibre sensin g elemen ts. Terbium doped silica fibre91 ,

with a Verdet constant of 1.2.10–5 ra d/A, an d doped plast ic fibre92 , with a

Verdet const an t of 2.10–5 ra d/A, ha ve been developed.

The alt ern at ive solution is to use a compa ct sen sing element ma de from a

material with a Faraday rotation larger than that of the glasses. A small

sensor head is an advantage in many applications , including current

measur ement u sing an iron core.

BGO (Bi12GeO20)93 , BSO(Bi12SiO20)94,95 and ZnSe96 offer Verdet

constants of about 7.10–5 rad/A, which is about an order of magnitude

higher than that of the silica fibre material. Certain glasses also haveVerdet const an ts t ha t a re a lmost as h igh. A considera bly higher Verdet con -

stan t, about 2 .10–3 ra d/A, is achieved with Cd1–xMnxTe97 ,98 ,99 ,100,101 ,102.

YIG and substituted YIG offer polarization rotations which, for many

applications, is larger than that of Cd 1–xM nxTe by about an order of

magnitude. As YIG is a ferrimagnetic material, it can, however, not be

d irec t ly compared to the paramagne t ic and d iamagne t ic mate r ia ls

men tioned. Since YIG is th e ma ter ial chosen in t his work , it will be fur th er

described below.

YIG

YIG, Yttriu m iron garnet is a ferrimagnetic garn et crystal with t he composi-

tion Y3Fe5O12. It is transparent for light with a wavelength longer than

about 1.1µm. At 1.3µm and 1.5µm, wavelengths at which reliable light

sour ces an d det ectors ar e r eadily available, the optical loss is very low. YIG

has a substantia l Faraday rota t ion in large parts of the optical and

microwave spectrum. Crystals of optical quality can be grown from flux

melts or grown epitaxially on substrates. Epitaxially grown films can be

used as high quality optical waveguides exhibiting the Faraday effect10 3.YIG crystal material, often in the form of polished spheres, are used in

microwave components.

The crystal lattice of YIG is rhombohedral, almost cubic, with the iron

at oms occupying two different kinds of sites in t he lat tice, figur e10. For t his

reason th e form ula is sometimes writt en Y3+3 Fe

3+2 Fe

3+3 O

2–12 .

The magnetic properties of the crystal are mainly determined by the iron

atoms. The iron atoms in the two kinds of sites interact antiferromagneti-

cally with each other, giving a net magnetic moment equal to that of one

atom. The Yttrium is magnetically polarized by the field from the iron

at oms, but it h as litt le influence on t he str ength of th e magnet ic int era ction.




19

Y3+, etc.

O2–

Fe3+, etc.

Tetra hedral site

Octah edral siteDodecah edra l site

Fig.10. The different kin ds of atom ic sites in Y IG, after 106 .

Fig.11. Qualitative behaviour of the different contributions to the net m agnetization of rare earth garnets havin g a com pensation point . From 107 .

This is evident from t he fact t hat all rare-earth iron garnets (RIG, R3Fe5O12

where R is a rare earth) have a Curie temperature of about 550K 104. The

Curie temperature is the temperature a t which the thermal agita t ion

breaks down t he ma gnetic ordering of the at oms a nd t he ma terial ceases to

be ferromagnetic . The Curie temperature can therefore be used as a

measur e of the str ength of th e magnetic int eraction. The Curie temperat ur e

for pure YIG is 559K105. The net magnetic moment for the rare earth

garnets is, however, influenced by the rare earth, in several cases giving

compensation points, where th e temperat ure dependent magnetic moments

of the different kinds of atoms cancel each other at a specific temperature,

figur e11. YIG, however , does not h ave any compens at ion point .

It is possible to substitute part of the yttrium with other rare earths,

giving mixed rar e eart h garnet s. Also, oth er su bstitut ions can be made, but

th is norm ally has little effect on t he ma gnetic inter action. Bismut h su bsti-

tution is an exception as it increases the strength of the magnetic inter-

action, th ereby increasing th e Curie tem perat ur e.

If the iron is subst itut ed, the m agnetic int eraction is weaken ed, giving a

lower Curie temperat ur e.



Hans Sohlström

20

Fig.12. Two-dim ensional d om ain pattern in thin sam ple with an out of plane anisotropy.

Th e lattice const an t of pure YIG is such that it can be epitaxially grown

on substrates of GGG, Gadolinium gallium garnet (Gd3 Ga 5O 12). Such

substrates of high quality are readily available. For substituted films, the

substitutions of the film and substrate must be combined to give the proper

lattice constants.

Th e magnetic anisotropy in pure YIG is mainly cubic and not so strong.Strain, however, strongly affects the magnetic anisotropy108. Epita xially

grown YIG films can, t her efore, ha ve easy directions of ma gnetization in th e

plane of the film, or perpendicularly to it, depending on the film strain

caused by the lattice mismatch. In addition to the strain anisotropy, there

can also be a growth-induced anisotropy, arising from a certain ordering of

th e ma gnetic ions in t he growth pr ocess.

Becau se of the ferrim agnet ic propert ies of the m at erial, volum es of equa l

direction of magnetization, so called magnet ic domains will form. The

domains are separated by thin Bloch walls where the magnetization

direction is changed. The domain size is determined by a magnetostaticenergy balance that depends on the material properties and the sample

geometry.

With thin bulk samples and epitaxia l ly grown fi lms with suitable

anisotropy, the domains can form two-dimensional patterns extending

th rough t he ent ire th ickn ess of th e film, figure12. Un der certa in condit ions

th is patt ern degenerat es to sma ll circular doma ins, bubbles . These bu bbles

can be moved ar oun d in th e film, creat ed and a nn ihilat ed by sma ll pertu r -

bations in the field. This is the phenomenon that was used in the bubble

memories, in which more than 1Mbit of information could be stored in the

form of a bubble pat ter n in 1cm 2 of iron ga rnet film 109.

For a large sample with m an y domains, t he a ctu al form of the individual

doma ins an d th eir movement when a n extern al field is applied seems t o be

stocha stic. For th e entir e sample or a large par t of th e sample th e beha viour

of the domains, however, averages out and the net magnetization reflects

th e varia tions in t he a pplied magnet ic field. There is h owever a t endency for

the domain walls to stick to imperfections in the material, such as lattice

dislocat ions, causing discont inuit ies in t he m agnet izat ion cha nge.

The dir ection of ma gnetizat ion of the individua l doma ins will also cha nge




21

under the influence of an applied field. The magnetic anisotropy will,

however, keep t he m agnetizat ion appr oxima tely along t he ea sy directions.

When the net magnetization of the sample cannot be adjus ted to the

external field through redistribution of the domains between the easy

directions only, a rotat ion of th e ma gnetizat ion dir ection within t he domains

will occur. For a very strong applied field, the magnetization will becompletely aligned with the field.

The rapidity with which the magnetization of the materia l can be

changed is limited by the dynamic properties of the domain wall move-

ments. This gives an upper frequency limit somewhere in the 10MHz to

GHz ran ge11 0. Very little work has however been done in measuring the

frequen cy res ponse of YIG ma teria l based devices111.

The cont ribut ion t o th e magnet o-optical rota tion per un it length from th e

different at oms can be described by a form ula from 112,

θ = (Am+Ae)MoFe+(Bm+Be)MtFe+(Cm+Ce)MR

The indices ”m” and ”e” indicate contributions from different kinds of

resonances and the superscripts ”o” and ”t” indicate octahedric and

tetrahedric positions for the iron atoms. Apparently, the contributions from

the iron atoms in the two kinds of sites are different. In the reference,

Ae /Be=1.72 is given.

The ma gneto-optical rotat ion in crea ses with decreasin g wavelength from

3µm to 0.5µm 11 3. At 1.15µm, the saturation rotation is about 200° /cm

(3.5.102rad/m) for pu re YIG. Bismu th substitu tion can in crease t his value

by a factor of more than 10 depending on the composition; 7400 ° /cm(13.103 rad/m) has been reported at 1.15µm 114 . The magneto-optical

rotation is temperat ur e dependent, but it has been shown th at su bstitut ions

can r educe th is dependen ce substa nt ially115,116.

It is important to remember that the magneto-optical rotation of ferri-

ma gnetic mat erials, just as th e ma gnetization, m icroscopically always has

th e satu ra tion value. When m easurement s show other values, it is either

because the magnetization is not parallel to the measuring light beam or

because the l ight path goes through several domains with different

ma gnetizat ion directions.

The ra re ear th garn ets also possess a ma gnetic linear birefringence in t heorder of 100° /cm (1.7.10 2rad/m)117,118 . For bismuth substi tuted YIG,

literature data also indicate a magnitude which is about half that of the

ma gneto-optical r ota tion119.

The in dex of refraction for pu re YIG is 2.15. As t he in dex for GGG is 1.95,

a YIG film on a GGG substr at e can form a h igh qu ality optical waveguide.

Using ion beam etching, or wet etching and multilayer growth, it is

possible to mak e strip or channel waveguides in YIG film120. The technolo-

gies used to define the channel are, however, not so well developed. Fur-

th erm ore, all cha nges ma de in t he m agnet o-optical film will cha nge not only

the optical propert ies , but a lso the magnetic propert ies such as theanisotropy, etc.



Hans Sohlström

22

3. Star t ing point s for the sen sor development work

A conclusion from t he a bove descript ion of YIG an d other ra re ea rt h gar net s

is that they, compared to other magneto-optical materials , have many

favourable features such as a large magneto-optic rotation, well-defined

magnetic properties and good optical quality in the near IR. Furthermore,

particularly with the epitaxially grown films, many of these properties can

be a l tered a t wil l through a number of substi tut ions . Unfortunately

however, some of the propert ies are interl inked, mainly through the

mechanical strain, in such a way that they cannot easily be independently

optimized. We have, therefore, not considered it fruitful to design any

devices based on a ”perfect” ma gneto-optical ma ter ial th at ha s not yet beendeveloped. Inst ead, our appr oach ha s been to find device str uctur es tha t a re

useful for a demonstration with existing mat erials or with r elatively simple

modifications of known compositions. For similar reasons, no experiments

have specifically been made to measure the bandwidths of the experimental

sensors. No evidence of bandwidt h limita tions h as, h owever, been foun d in

mea sur ement s of ma gnetic fields at frequen cies up to about 1MHz.

The most st rikin g feat ur e of th is type of ma ter ial for sen sors, is th e large

Fa ra day r ota tion. To achieve a polarizat ion r ota tion of 90° (or a complete TE

to TM conversion in th e waveguide case) at 1.3µm, from less tha n 1 mm to

about 6 mm of optical pat h length is needed, depending on t he m at erial inquest ion. The volume of th e sensing elemen t can, t hu s, be ma de very small,

in the order of 1mm 3. With a sensing volume of this size, the spatial

variations of the magnetic field can be resolved. This is in contrast to the

sensors using glass sensing elements. They often require a large sensing

element and/or a closed measur ement path .

In t he design of a measur ement system t hat ut ilizes a YIG or su bstitut ed

YIG sensing element either in the form of a bulk crystal or a waveguide,

there are a number of system design options. To be able to choose between

these, we had to acquire a thorough knowledge of the properties of the

ma ter ial. As the available litera tu re dat a, relevan t for t his applicat ion, wereinsufficient, th is knowledge had t o be gained t hr ough m easur ement s.

For the single mode sensors we have, in order to avoid alignment

problems, decided to work with waveguiding sensing elements only. The

relatively large index difference between GGG and YIG, however, poses

some pr oblems. Guides tha t a re single mode in th e near infra red r egion a re

very th in, less tha n 1µm. A slab guide of this kin d will have a la rge linear

birefrin gence th at prevent s th e TM–TE conversion.

A num ber of techniques h ave been u sed to solve this pr oblem. Multilayer

structures with a layer between the GGG and the iron garnet film have

been investigated121. A ma gnetic field th at shifts its dir ection with a periodth at is equal to the beat length between t he TE an d TM modes can a lso be




23

used. In th is way, a net conversion can be obtain ed even with a relat ively

large ∆β122.

At a n ea rly st age of our project a per iodic cover st ru ctu re in GGG on t op

of the YIG waveguide was suggested a s a mea ns t o achieve a n et conversion

with a sin gle mode YIG waveguide123 .

We have, however, used another approach. Because of the high opticalqua lity of the YIG waveguides, th e coupling between th e differen t modes in

a mu ltimode guide is n egligible for th e pr opagat ion distan ces in qu estion.

As it is also possible to achieve a fibre to waveguide coupling that only

excites t he funda men ta l mode of the wa veguide, a r elatively th ick guide can

effectively be used for single mode use124. For t he fundam enta l mode, th is

kind of guide has a relatively small ∆β th at can be can celled by a modera te

strain-induced ∆β introduced during the film growth125 . The magnetic

propert ies of th e film ar e also influen ced by th e str ain n ecessar y to achieve

a small net ∆β but it is possible to achieve a usable device with this

approach.Some of th e cr itical design decisions t hen were:

• To use or not to use a ma gnetic bias field.

• One fibre for sending light t o the sensing element and for r eceiving the

signa l, or separ at e fibres for th e t wo fun ctions.

• The selection of a suita ble optical configurat ion th at a llows a measur able

polarization modulation and an acceptable optical loss. A channel

waveguide structure or a slab guide combined with some other means of

cont rolling th e light propagat ion ar e two of the options for th is pur pose.

The available selection of film types for waveguiding sensors was quitesma ll. The YIG films wer e origina lly developed for bubble mem ory u se a nd

have later been modified for use in display units , printers126,12 7, wave-

guiding optical isolat or s128 an d sensors.

For t he m ultimode sensors, which ar e of a m ore imm ediat e interest from

th e app licat ion p oint of view, a design which is suit able for production mu st

be selected.

In the mult imode case a larger se lection of useful materia ls was

available. The bulk YIG ma ter ial th at we initially used for th e mu ltimode

sensors was originally produced for microwave applications and had to be

cut and polished to optical quality. Later when the thick (≈100µm) epitaxi-ally grown films with lar ge ma gneto-optical rota tion were developed, ma inly

for optical isolat or use, we could u se t his t ype of mat erial for th e mu ltimode

sensors.

As th e mat erial char acterizat ion m easur ements went on, we were gra du-

ally able to tr an sform th e original sensor ideas envisioned at th e sta rt of th e

project, into practical sensor designs. In reality, of course, the influence also

went the other way: The sensor design ideas m ade fur ther measur ements

necessary. Below, however, the material characterization measurements

and th e sensor prototype experiments a re pr esent ed in separa te sections.



Hans Sohlström

24

4. Material cha ra cter izat ion measu rements

Bulk materials

Mea surem ent opt ions

The magnetic and ma gneto-optical measu rement s th at can be made on bulk

YIG crystals can be divided into two categories, those made on homoge-

neously m agnetically satu rated samples and those made on non-saturated

samples. Microscopically, the saturated state is the only one that exists and

macroscopically, it is the only well-defined state. Examples of phenomena

that are studied are the influence of material composition, temperature,

wavelength, etc. on the saturation rotation. Such measurements are of

interest not only from an application point of view, but also for material

science, as t hey provide inform at ion a bout th e nat ur e of th e magn etic int er -

actions. Results from these types of measurements are, however, relatively

well covered in litera tu re, an d will not be fur th er described here.

For sensor applications, the properties of YIG also at low applied fields

are of interest. These include the domain structure and how it is influenced

by the crys ta l orienta t ion, sample geometry, sample treatment and

temperature.

Some measurements such as the measurement of the net magnetization

of the sample and its dependence on external factors, can be made using

ma gnetic methods129. Most of these r esults can , however, also be indir ectly

obtained from m agneto-optical measu rement s an d as our main interest is in

the magneto-optical properties, this is the approach we have taken. The

optical meth ods a lso facilitat e cha nges of th e mea sur ement volum e, which is

a key measurement par ameter.

If the sample is thin and the domains are large enough, a focused light

beam , figure13a, a llows t he beh aviour of a sin gle domain or doma in wa ll tobe studied. Ideally, with a beam passing through only one domain, one

should obtain the same results as those obtained for a homogeneously

saturated material. One can then study changes in the domain magneti-

zation direction and the effect on the magnetization and magneto-optical

rota tion cau sed by, for example, temper a tu re.

With a large diameter beam , figure13 b, the contributions from the

different domains will be averaged. The exact nature of the averaging

process is rather complicated as the pattern of the domains will act as a

phase grat ing. For a t hin sam ple with a t wo-dimensional doma in pat tern as

in figur e13, the r esulting polar izat ion rotat ion can often be appr oxima tedusing th e area r at io between th e two kinds of doma ins.




25

E

B

θ

Measurement object

I1=I 0cos2 θ

I2=I 0sin 2 θ

I0

Fig.14. Measurement system principle.

Fig.13 a. S m all m easurem ent v olum e.

Fig.13 b. Large m easurem ent volum e.

Mea sur emen t set-up

To stu dy the m agneto-optical pr operties of bulk m at erials, a mea sur ement

system according to the principle shown in figure14 has been used.

Linearly polarized light is sent th rough th e measu rement object. The beam

tr an smitt ed by th e measur ement object h as its plane of polarisat ion r ota ted

by an an gle θ. In a polarizat ion splitt ing Wollaston pr ism, th e beam is split

into two orthogonal polarization components with the intensities I 1 and I2.

Fr om t hese two values, an d the input intensity I0, the polarization rotation

an d t he optical loss of th e ma ter ial can be calculat ed.

Other polarization detection principles such as the use of polarization

modulation or rotating analysers are also possible130 . The simple two-

detector system was chosen mainly because it was also adaptable for

evaluat ion of sensor p rototypes.

The holder for the measurement object was temperature controlled and

surrounded by coils allowing a magnetic field of arbitrary direction to be



Hans Sohlström

26

Polar izer Polar izerYIG

sampleIR vidiconor arr ay

Lens

Fig.15. Dom ain visualizin g set-up.

Fig.16. Magneto-optical rotation versus the applied magnetic field for a

2× 2× 2mm YIG cube as m easured w ith a 200µ m diam eter light beam withλ =1.15µ m .

generated. To allow automatic calibration and measurement routines, thesystem wa s designed with compu ter ized cont rol and da ta acquisition.

For a qualitative display of domain patterns, a set-up according to

figure15 was u sed.

Mea surem ent resul ts

Large measurem ent volum e

Our first measu remen ts of th e ma gneto-optical rotat ion versus th e applied

field were made with a 200µm diameter l ight beam through a cube

2×2×2mm of YIG, figure16. This rather discouraging result was, however

soon supplemented with other results indicating t hat a larger light beamdiameter and sample annealing improved the results , cf. the prototype

sensor r esults below.




27

We also found that a thinner sample with a two-dimensional domain

structure gave a more reproducible result, though at the cost of a lower

rota tion, about 5° for a single pass t hr ough a 0.3mm YIG slice.

Later, however, epitaxially grown Bi-substituted thick YIG films giving

22.5° rota tion in a 0.13mm film becam e available. The domains in t his type

of film a re also sma ller, giving a more efficient avera ging effect. Th e well-controlled growth conditions for these films should also give a smaller

nu mber of defects wh ich sh ould allow th e doma in wa lls to move more freely.

S m all measurem ent volum e

When a 0.13mm thick (YbTbBi)IG film on a GGG substrate is observed in

the IR through suitably arranged polarizers in a se t-up according to

figure15, a two-dimensional domain pattern is observed. The average

domain width is in the order of 12µm. The application of an external

magnetic field changes the area ratio between the two kinds of domains,

figure17a,b. At high field levels, close to saturation, the majority of thesmall domains disappear, leaving a pattern with a lower spatial periodicity,

figure 17c. For this specific material, the remaining domains shrink to

bubble-like form just before sat ur at ion, figur e 17d.

When measu remen ts on mat erials of th is kind a re to be interpr eted, one

should remember that the periodic domain structure will work as a phase

grating for th e light component with a polarization stat e th at is perpendicu-

lar to that of the input beam. Fig 17e,f,g show examples of diffraction

patterns obtained with the (YbTbBi)IG film for similar conditions as those

used for 17a,c,d. The diffraction patterns have been recorded with a set-up

similar to the one in figure15, though with the camera focused on infinity,i.e. the light source. The second polarizer is set to block the central beam

when no field is applied. The central beam is, however, not completely

extinguished in 17e. With field applied, the central beam will have its

polarisat ion r ota ted, and it will thus pa ss th e second polar izer an d sat ur at e

th e CCD arr ay. The polar ization of the diffra cted light is a lways perpendic-

ular t o th at of th e input beam.

Fig. 17a. Dom ains in 0.13m m

(YbT bBi)IG film with no external

field applied. Picture height

corresponds to 0.54m m .

Fig. 17e. Diffraction from a d omain

pattern lik e the one in 17a. T he

diffraction angle is approxim ately

2.6 ° , corresponding to a domainwid th of 12µ m .



Hans Sohlström

28

Fig. 17b. Dom ains in 0.13m m

(Y bTbB i)IG film with 50m T applied

perpendicularly to the film . Th e do-

m ain pattern is nearly unchan ged.

Only the wid th ratio has changed.

Fig. 17c. Dom ains in 0.13m m

(Y bTbB i)IG film with slightly less

than 100m T ap plied perpend icu -

larly to the film . S ome of the do-

m ains from a an d b are still visible.

Fig. 17f. Diffraction from dom ain

pattern sim ilar to the one in 17c.

First order diffraction at 1.6 ° ,

ind icating a domain width of 20µ m .

S econd order d iffraction just visible.

Fig. 17d. Domains in 0.13mm

(Y bTbB i)IG film with about 100mT

applied perpend icularly to the film .

Fig. 17g. No diffraction is observed

wh en all d om ains ha ve disappeared.




29

Fig.19. Polarization rotation as m easured w ith a 30µ m diam eter beam

scann ed across a 0.3m m th ick Y IG sam ple. App lied field perpendicular toslice plane 33m T . Measured at 20° C and 100° C.

a) b)

Fig.18. Dom ain p atterns in 0.3m m slice of pure Y IG.

a)with no external field applied.

b) with a m agnetic field applied perpend icularly to the plane of the sam ple.

Similar resu lts obtained with a 0.3mm YIG slice ar e shown in figure18.

The avera ge doma in width is, in t his case, in t he order of 0.1mm.To get m ore qua nt itat ive results we used t he above ment ioned measu re-

ment system with t he beam focused down to a diameter sm aller t han th e

doma in width. Results a s th e one in figure19 were t hen obtain ed.

In this figure, the domain structure at two different temperatures is

shown. It can be seen that both the rotation within the domains and the

doma in pa tt ern differ. The polarization rotat ion in each domain is sm aller

a t the higher temperature . Our measurements of polarization rota t ion

versus magnetic field over a larger volume, however, show an increase in

th e sensitivity (dφ /dB) with t empera tu re. This can be explained by a sat u -

ration field H s th at decreases with increasing tempera tur e. These results ,th at ar e both in agreement with work published by oth ers, indicat e a way to

reduce the temperature dependence of sensors made from YIG and

substitut ed YIG mat erial131 .



Hans Sohlström

30

Monitor orcomputer

CCD arrayPolarizer

Laser1152 n m

SamplePolarizer

Fig.20. Experim ental set-up for the grating based m easurem ent s

Sensor des ign cons idera t ions

From the measurement results , we were able to draw some conclusions

concern ing how to design sen sors bas ed on bu lk YIG crysta ls:

• A th in crystal with a one-layered domain pat tern , simplified the ana lysis

an d gave good resu lts, th ough a t t he cost of a r educed rota tion.• A probing light beam m uch wider tha n th e domain size, and preferably

covering a large part of the crystal surface, reduced the effect of single

doma in behaviour .

• Annealing the crystal after sawing and polishing improved the r esults .

Waveguides

Mea surem ent opt ionsMost of the magneto-optical measurements on waveguiding samples are,

principally, s imilar to those made on bulk samples. The situation is ,

however, complicated by the role of the linear birefringence. Furthermore,

th e cases differ in th e mean s by which t he light is coupled into an d out of

the material. For the waveguide characterization measurements, methods

based on holographic grating, prism and end-fire light coupling, have been

used.

The grating based method was used to determine accurately the linear

birefringence and the saturation value of the magneto-optical rotation. In

th ese measur ement s a grat ing, which is form ed in photoresist on top of thewaveguide, works as a distribut ed light coupler. A sketch of the m easur e-

men t set -up is sh own in figur e20.

The sample is turned to the coupling angle corresponding to the mode to

be studied. As the coupling angle is, within the divergence of the laser

beam, th e same for t he TE a nd TM modes of th e same order, a polar izer an d

a retarder can be used to excite an arbitrary state of polarization at the

input point. As the light propagates along the guide, a small fraction will

cont inu ously be coupled out , allowing th e evolut ion of the int ensity a nd th e

polarizat ion st at e to be studied.

To determ ine th e linear birefringence and t he m agneto-optical r ota tion,




31

TM

TM

TE

Rutileprisms

Fig.21. Prism coupling m ethod.

the spatial distributions of the outcoupled light under different magnetic

field a nd input polar izat ion condit ions is r ecorded132

.Even th ough t he grat ing method can be used to measure t he polar izat ion

rotation under different magnetic field conditions, it is more convenient to

use t he pr ism coupling meth od to study t he varia tions in th e rotat ion once

th e satur at ion value is determined.

A prism with an index of refraction equal to or higher than that of the

guide is brought into contact with the guide by mechanical pressure,

figure21. Light impinging on the prism–guide interface with a suitable

an gle can th en couple t o a waveguide mode. Similar ly, light can be coupled

out through a second prism. For YIG waveguides, rutile is a suitable prism

ma ter ial. As ru tile is birefringent, t he TE a nd TM modes will have differen tcoupling angles. With only one of the polarization modes excited at the

input , th e fraction of light convert ed can ea sily be monitored u nder different

magnetic field conditions. Just as in the bulk measurement case, we have

used a computer controlled measurement se t-up to provide re levant

ma gnetic field var iat ions.

A number of experiments were also made with the fibre end coupled

directly to the waveguide edge (butt-coupled). This method, in contrast to

the prism method, does not involve any mechanical perturbation of the

sample during the measurement . On t he other han d, the samples must be

specially prepar ed with polished edges.

Resul t s o f the w aveguide measur ements

The gra tin g based meth od was u sed in an ear ly sta ge of th e project t o select

sam ples with su fficiently sma ll linea r birefrin gence to allow a la rge TE–TM

mode conversion in the fundamental mode. Most of the samples we have

used allowed a conversion of 90% or more. The results shown in this

summary, except where is otherwise indicated, are obtained with 6.4µm

thick samples of Gd,Ga substituted YIG film on GGG substrate with a

saturation polarization rotation of 150° /cm (2.6.102rad/m) at λ=1.15µm.

This m at erial wa s kn own t o be ”easy in pla ne”, i.e. th e ma gnetizat ion of the



Hans Sohlström

32

Fig.22. TM to TE m ode conversion versus a m agnetic field applied in the

plane of the film and parallel to the light p ropagation d irection. Th einteraction length was 4m m .

Fig.23. TM to TE conversion, m easured th rough a bu tt-coup le fibre, versus

the m agnetic field applied in th e plane of the film and parallel to the light

propagation d irection. T he param eter is the pressure applied t o the coup ling prism.

film could move relatively easily in the plane of the film but could not easily

be tur ned from t he plan e of th e film133,134.

Our f irs t results with prism coupling seemed, jus t as in the bulk

measurement case, somewhat discouraging, figure22. With a 50µT field

applied parallel or anti-parallel to the light propagation direction, the

conversion is ra th er h igh an d between t hose two extrem es, the conversion

goes down. There is, however, a large hysteresis, and the magnetization

appar ently chan ges in steps.We foun d th at th e mecha nical waveguide str ain indu ced by th e pressure

applied to the prisms was responsible for part of the hysteresis. This is




33

1. 2. 3. 4. 5. 6.Field angle

0.2

0.4

0.6

0.8

1.Signal

1. 2. 3. 4. 5. 6.Field angle

0.2

0.4

0.6

0.8

1.Signal

1. 2. 3. 4. 5. 6.Field angle

0.2

0.4

0.6

0.8

1.Signal

Fig.24. The conversion versus th e di rection [rad ] of an app lied field for a

two-way light pass in a 7.6m m long sam ple. a) 100µ T field m agnitud e, b)

1mT field magnitude c) 5mT field magnitude (thick line) and theoreticalcalculation (thin line)

demonstrated by the results shown in figure23. Here, the conversion is

measured through a fibre, butt-coupled to the edge of the waveguide

sample. A coupling prism was also applied to the sample using different

am oun ts of pressu re. Evidently the pressu re applied to th e prism influen ced

the magnetic behaviour.

With t he m at erial used a ”bias” field, in t he plan e of th e film an d perpen -dicular to the field to be measured, was found to be necessary to obtain an

un am biguous a nd sm ooth result even with th e prism removed. To select an

appropriate magnitude for this bias field, we applied a field of constant

am plitude but with var iable angle in th e plane of th e guide. The conversion

was then plotted versus the angle of the applied field. One could then

observe the variat ion in conversion an d, th us, also how the m agnetization

followed the direction of the applied field. Starting with a very weak field,

figure24a, we noticed that even though the magnetization followed the

applied field there was a strong anisotropy. With higher field magnitude,



Hans Sohlström

34

figure24b, we could observe how the magnetization direction more and

more closely followed the direction of the field. In figure24c, with a 5mT

field, the magnetization almost completely follows the direction of the

applied field. Although t her e ar e some deviat ions from t he t heoretical curve,

th e measu red curve is smooth an d free from hyster esis. This indicat es th at

the 5mT field was strong enough to create a single domain with ama gnetization which could t hen be rotat ed by th e field to be measu red.

In order to study the magnetic behaviour of a channel structure in the

film, experiments were made with strip waveguides delimited by parallel

slits sawn through the waveguiding film. The hysteresis problems were,

however, found to increase. A probable explanation is that the ”channel

str uctur e”, and t he r ough sa wn edges, affected t he domain st ru ctu re. Some

experim ent s with etching of YIG were a lso ma de135.

Sensor des ign cons idera t ions

Fr om m easu rem ent s such as t hose described above, we drew th e conclusionth at with th is type of mater ial, which wa s known to have a r elatively small

an isotr opy, a bias field of about 5mT was needed t o achieve a r eproducible

sensor behaviour .

The use of a bias field, however, limits the applicability of the sensor in

several ways. The bias field may disturb the measurement situation in an

un accepta ble way. If th e bias field is to be supplied by a per ma nen t m agnet ,

the effects of strong overload fields on this magnet must be considered. It

may also prove difficult to find a magnet material that maintains the bias

field constant over the temperature range required. On the other hand,

th ere is in principle also a possibility to use a t empera tu re dependent bias

field to partly compensate the temperature dependence of the sensor

material.

An alternative approach is, as will be shown below, to use a material

with a st rong anisotr opy.

Partly because of the results that were obtained in the channel wave-

guide experim ent s, and par tly becau se of the exten t of process developmen t

work necessar y to mak e cha nn el waveguide stru ctu res, we also decided to

us e slab guides only.

Pa per reference

The design an d perform ance of the m easurem ent system for bulk sam ples are

discussed in paperA. In t his paper, som e exam ples of result s are also given.

The results are more fully described in paper C, and the sensor design rules

are given in paper B.

The different w aveguide characterization m ethods and the role played by the

pressure applied to the prisms are covered in paper E.

The use of a variable in-plane field to select a suitable bias field, is

described in paper G.




35

GGG

Y IG

Fig.25. Basic sensing principle

5. Sensors.

Single-mode systems

The sensing element of a m easur ement system with polarization m aint ain-

ing single-mode fibres could, in principle, be either waveguiding or bulk

optical. To avoid alignment problems, we have decided to work only with

waveguiding sensing element s in our sin gle mode system s. With a t hickn ess

of 5–10µm, the sensing elements have been capable of carrying several

modes, but we have shown that it is possible to use them effectively assingle mode guides, but t-coup led to fibres.

The other two coupling methods that we have used in the characteriza-

tion work can also be used in sensor configurations. The prism coupling

method, however, lacks the ruggedness and potentially low cost that the

butt-coupling and grating methods have. While we have preferred the

simple butt-coupling in our sensors, grating coupling is a good alternative,

particularly for thinner guides which cannot be effectively butt-coupled to

fibres.

The basic principle of a waveguiding sensing element in combination

with p olar ization preser ving fibres is demonstr at ed in figur e25. One of th epolarization modes of the fibre is used to carry linearly polarized light

(white ar row) to the sensing element, where it is launched into th e fun da-

mental TE mode of the planar waveguide. In the waveguide, part of the

optical power is converted to the TM mode (graded arrows). The light is

th en coupled int o th e retu rn fibre, which is orient ed in such a way th at each

of the modes of the planar guide matches one of the fibre polarization

modes. At t he out put end of th e fibre, th e light from t he t wo fibre m odes is

separa ted a nd det ected. The detector output s ar e th en combined to give an

int ensity independent signa l tha t is a measu re of th e magnet ic field.

With this configuration it is not possible to detect the sign of the



Hans Sohlström

36

0.4 mm

10 mm

Fig. 26. Two-fibre sensor with 3.7µ m Bi-substituted wa veguide.

ma gnetic field. Fields tha t a re pa ra llel to, or a nt i-par allel to th e light pr opa -

gation direction, cause TE to TM coupling factors that are equal in magni-

tu de an d, consequen tly, they cau se equal a mount s of light to be coupled int o

th e TM mode. However, if th e ret ur n fibre is mount ed with its birefringence

axes at ±45 ° to those of the waveguide, the amplitude in each of the fibre

modes will be a linear combination of the amplitudes of the TE and TMwaveguide mode fields leaving the waveguide, giving a suitable anti-

symmetric sensor behaviour. This is in analogy with a conventional bulk

optic polarization rotation measurement set-up with the analyzer rotated

45° or –45° from th e inpu t polar izer orienta tion.

The absence of a lateral light confinement leads to a severe light loss

when a configuration as the one in figure25 is used. The loss can be of

accepta ble size only if th e sensor is very short. Consequently, th ere is t hen a

tr ade-off between polarization rotat ion an d loss, but with ma teria ls having

a very large Faraday rotation, it is possible to find a useful compromise.

This is demonstra ted by the r esults obtained with a sensor using a sh ortbismuth-substituted YIG waveguide having a saturation magneto-optic

rotation of about 1000° /cm (1.7.103 rad/m) at 1.15µm, figure 26. This

waveguide had a str ong out-of-plane an isotr opy.

The idea was that this anisotropy should replace the bias field necessary

with the other waveguiding sensors. The sensor output versus the applied

field is shown in figur e 27. A hyst eresis effect appea rs for field magn itu des

less than 1mT. For such field levels, the magnetization direction is almost

perpend icular to th e film plan e. For larger field levels, th e perform an ce is as

expected , i.e. a smooth field vers us conver sion r elat ions hip. It is also evident

from th e non-symmetr y of the cur ve tha t t he r etur n fibre was n ot corr ectly

mounted, but was r ota ted slight ly off the int ended an gular position with its

birefrin gence axes at 45° from th ose of th e inpu t fibre. The im perfections of

th is experiment al pr ototype should, however, not conceal t he fact th at th e

design principle is working. With another material having a stronger

an isotr opy it ma y be a viable concept.




37

a)

Polarizationmaintaining fibres

YIG waveguide Mirrorededge

b)

Polarizationmaintaining fibre

YIG waveguide Mirrorededge

Fig.28. Configurations for waveguiding sensors with focusing reflectors.a) With tw o fibres. b) With one fibre.

Fig. 27. Sensor output versus th e applied field for a sensor accordin g to

figure 26.

An a ppr oach th at in ad dition to solving th e loss pr oblems also allows th einput and output fibres to be mounted side by side instead of in line on

opposite edges of the waveguide, is to make a focusing reflector on the

waveguide, figure28a. In th e experimen ta l sensors, th is reflector was m ade

by polishing th e rea r edge int o a semicircular form . A th in gold coat ing was

then applied. Etched waveguide mirrors or grating reflectors are alter-

na tives tha t could be ta ken int o considera tion. An experiment al pr ototype is

shown in figure 29.

As the Faraday effect is nonreciprocal in nature, the mode conversion of

the forward and backward trip will add, making the effective interaction

length t wice the sensing element length.

This is the single-mode sensor design for which we have recorded the

largest am ount of test dat a. Results obtained with a sensor prototype with a

7.6mm long Gd,Ga substituted YIG waveguide of the kind previously

men tioned, ar e shown in figur e 29. A bias field of 5mT was used accordin g

to th e sensor design considera tions in t he pr evious section of th e sum ma ry.



Hans Sohlström

38

Fig.29. Experimental sensor according to fig 28a.

Fig. 30. Sensor outp ut versus the applied field for th e folded two-fibredesign. Bias field 5 m T perpend icular t o the axis of the sensin g elem ent .

The results show the expected sensor function with a central smooth

sensing ran ge and a slope reversa l at appr oxima tely ±2mT, figure30. This

indicates that the optical power couples back into the mode which it was

originally launched into, equivalent to a polarization rotation of more than

45°. A sensor with a shorter interaction length would give a monotonous

relationship.

Tests made with a spectrum analyzer, confirm the good signal quality

an d indicat e a det ector a nd a mplifier noise level equivalent to about 8nT in

a 1Hz ban dwidth with a 5mT bias field. The detection limit of th e sensing




39

Fig.31. Experim ental one-fibre sensor according to figure28b.

element is, thus, lower than this value. By increasing the bias field, the

mea sur ement ra nge can , of cour se, also be scaled t o higher values.

We have also made a sensor where th e same polar izat ion maint aining

fibre is used to guide the light both t o an d from t he sensin g element , figures

28b and 31. In s uch a configur at ion, th e 45° displacement of th e retu rn fibre

needed to a chieve directional discrim ina tion, is obviously n ot possible. Forsystems covering large distances, it is an advantage with only one fibre.

Typically, however, such systems will include discontinuities in the fibre,

e.g. removable connectors without index matching. Reflections from such

discont inuit ies will be a problem in a one-fibre system . The r eflected power

will interfere with the light returning from the sensing element. As the

pha se angle between th e unwa nt ed reflection a nd t he signal is deter mined

by the length of the optical path to the sensing element, which will vary

with t he environm ent, r apid am plitu de variat ions will ta ke place. Although

only one of the channels is affected, the performance of the balanced sensing

system can be severely degra ded.The optoelectronic unit needed in a one-fibre system is also much more

complex than the one in a two-fibre system. In addition to the polarization

splitter, an extra beamsplitter, to couple the laser light into the fibre, is

needed, figure 32. As th e light h as t o pass t his extra beamsp litter twice, th e

loss intr oduced is large. Fur th ermore, the r isk of stra y light from th e laser

falling on t he detectors is subst an tia l.



Hans Sohlström

40

Fig. 33. Output signal from one-fibre sensor according to figure 28 b with an

optoelectronic un it according to figure 32. A bias field of 3mT in the plane of the waveguid e is used.

Laser diode1.3 µm

Polarizer

Beam-splitter

Wollastonprism

Detectors

Polarizationmaintaining fibre

Fig. 32. Optoelectronic un it for one-fibre sensing system .

Using a 1.3µm laser with short coherence length we have, however,

obta ined good r esults with a one fibre syst em wit h n o removable conn ectors

and with the fibre ends obliquely cut to avoid reflections, figure 33. The

sensing element is similar t o th e one u sed in th e two-fibre sensor. The non-

symmetry of the curve is, at least partly, due to the non-symmetry of the

sensing element cau sed by the oblique m oun ting of th e fibre.The systems described here are balanced, i.e., the sum of the optical

power from the two channels is independent of the measurand and only

dependent on th e system loss, while th e distr ibution of power between t he

two channels is ideally only dependent on the measurand. This is

complete ly true for the l ight path to the sensing e lement but only

approximately so for the path from the sensing element to the detectors.

Loss mechanisms that unequally affect the two fibre polarization modes in

th e retu rn fibre, will influence th e out put signal.




41

polarizer s YIG m u l t i m o de f i b res

mirror

Fig.35. Folded m ultim ode sensor design

Mult imode syste ms

Ir on gar net ma ter ials can also be ut ilized in mu ltimode fibre optic magnet ic

field sensors. Such sen sors provide a technologically simpler a ppr oach t ha t

may be more appropriate for many applications. Figure34 shows the basic

principle. Light is launched into and returns from the sensing elementth rough m ult imode optical fibres. Polar izers a re pla ced on both sides of the

crysta l. The int ensity of the light tr an smitt ed th rough th e second polar izer

depends on t he polar izat ion r ota tion in the crystal.

pola rizer pola rizerYIG m u l t i m

o de f i b re m u l t i m o d e f i b r e

Fig. 34. Basic principle for th e intensity based m ultim ode sensors.

Differen t r elat ive orien ta tions of th e tr an smission axes of th e two sensor

polarizers will produce very different sensor characteristics. To achieve a

sensitivity to the direction of th e applied magnet ic field, a m aximu m u na m -

biguous range and a maximum sensitivity to small fields, an angle of 45°between the polarizer axes can be chosen. In this case, the polarization

rotation in the sensing element should not exceed 45°. For certa in a pplica -

tions, oth er polarizer orient at ions a re m ore favour able.

In most a pplicat ions, it is u npr actical t o have th e fibres on opposite sides

of the sensing element. Thanks to the non-reciprocity of the Faraday effect

it is, just as in the single-mode case, possible to use a folded design,figure35. In this illustration, I have also indicated the use of a thick YIG

film r at her t han a bulk crystal.

The DC field characteristics of such a sensor is shown in figure36. The

sensor was realized with an epitaxially grown 0.13 mm thick (YbTbBi)IG

layer on a GGG substrate. The thickness of the layer was chosen to give a

single pass ma ximum rota tion of 22.5° at 1.3µm.

The saturation points fall at approximately ±100mT. Using a spectru m

analyzer the output signal was measured for different levels of applied

1kHz field from 27mT (1% distor tion) down to 270nT.

The measur ement r esults ar e summ ar ized in figure 37, where th e signalam plitu de is plott ed versu s th e applied 1kHz field am plitu de. Appar ently

the sensor is, within the experimental accuracy, linear over a range of at

least 100dB. The experiment al dat a sh ow a 1Hz noise equivalent m agnet ic

field of 1µT. By decrea sing t he optical loss of th e sensor a nd by improving



Hans Sohlström

42

th e am plifier, a r eduction of th is value to 100nT sh ould be within rea ch.

The a ccur acy of this type of sensor is, in most cases, limit ed by th e loss

variat ions in t he system a nd by the t empera tu re dependence of th e sensor

ma ter ial. In some applicat ions, e.g. AC mea sur ement , th e avera ge value of

the mesurand is known. One can then compensate for the slow loss

variation. By optimizing the sensor material composition and thickness thetem perat ur e dependence of the m at erial can be r educed considera bly, less

th an 1% between –20°C and 80°C has been r eport ed136.

A recent prototype version of the multimode sensor is shown in fig38.

Oth er versions ar e shown in fig 39.

Fig. 36. The m agnetic field characteristics of a m ultim ode sensor wit h an

epitaxially grown 0.13 mm th ick (YbT bBi)IG layer on a GGG su bstrate.

APPLIED FIELD [dB RE 1 T]

S I G N A L [ d B R E S I G .

A T 2 7 m T ]

-120

-100

-80

-60

-40

-20

0

-140 -120 -100 -80 -60 -40 -20

1 Hz noise level

Fig. 37. Th e signal am plitud e versus the applied field.




43

Fig38. Prototype sensor developed for a field t rial in co-operation w ith AB B

Power S ystem s, with p rotective cover removed , lying on a p iece of paper with

m m rulin gs. a:YIG/ GGG sensin g elem ent w ith gold coating, b:grad ient

index lens, c:polarizers, d:fibre holder m ade from a p iece of glass t ube.

Fig39. Th ree versions of multim ode sensors with folded d esign

Pa per reference

The waveguiding sensors are first introduced in paper D. Results from an

experiment with a two-fibre unfolded system are shown, but the paper is

mainly about the one-fibre folded design according to figure27b in this

summary. Different techniques to avoid interference effects are also

described.

In paper F, a similar folded sensor is used but with an 1.3µ m sem icon -

ductor laser diode light source to reduce the interference problems. A sensor utilizing a very short piece of highly magnetically anisotropic Bi-YIG wave-



Hans Sohlström

44

guide is also described. In the same paper there is also a description of a

nu m ber of m ultim ode sensors.

The two-fibre folded design sensor and its performance is treated in

paperG.

The perform ance of the folded m ultim ode sensor is treated in paper H.




45

6. Conclusions

Fibre optic magnetic field sensors based on iron garnet material have a

nu mber of favoura ble feat ur es. They can be ma de very compa ct, h ave lar ge

measu remen t r anges an d resolut ions in t he nT r egion. The small size is an

advantage not only for the point sensing of magnetic fields, but also for

cur rent measur ement t ogeth er with an iron core.

Both single-mode and multimode systems are demonstrated in this

th esis. The two types of system s differ both in th eir mea sur emen t possibili-

ties an d in more practical ha ndling aspects.

Using polar izat ion ma inta ining single-mode fibre an d sensing element s

made from few-mode YIG waveguide, several versions of balanced mea-sur ement system ha ve been built. The out put signa l from such a system is

appr oximat ely independent of the system loss. Sensors h ave been ma de both

with separ at e fibres to guide the light to and from th e sensing element a nd

with a single fibre for both functions. The two fibre version is, however, less

complicat ed and h as a bett er perform an ce.

While the waveguiding s ingle-mode sensors have some attractive

features and perhaps potentially the best performance, the multimode

sensors are less complicated to manufacture. As they can be produced at a

low cost, they could replace Hall elements, not only in magnetic field

sensors, but also for rotation speed sensing, etc. Also for electric currentmeasur ement th ey are a viable altern at ive. While an a ccur acy equal to tha t

of precision current transformers has not yet been demonstrated, sensor

prototypes suitable for other current monitoring applications in the electric

power grid have been developed.

The temperat ure dependence of the Fa ra day rotation which at present

limits the accuracy of the sensors can be substantially reduced with new

sensor m at erial compositions.

The renewed interest in magneto-optical ma terials ma y make suitable

sensor m at erials more r eadily available in t he near fut ure.



Hans Sohlström

46

7. Acknowledgements

There a re a n um ber of persons who ha ve helped me dur ing the work .

Firs t I would l ike to express my grati tude to professor Kjell G.

Svantesson, who has been my supervisor and friend during the major and

last part of the work, for his constant support and encouragement. Also I

would like to thank professor Gunnar Brodin and professor Torgny

Brogårdh who have, for differen t per iods of tim e, been m y super visors.

I would also like to thank my co-worker Ulf Holm , not only for his

collaboration in the work and good advice, but also for the many almost

endless, but indeed fruitful, discussions about work and life in general.

Bengt Molin is not mentioned as a co-worker in the papers, but his helpwith the mechanical design and fabrication of the sensors and laboratory

equipment h as been very import an t, an d I would like to tha nk h im for t his.

In fact, I would like to thank the entire staff of the Instrumentation

Laborat ory an d a nu mber of oth er pers ons a t KTH, who ha ve all, in various

ways, helped me. Carolyn Kyrnin g, who ha s helped me to rem ove a nu mber

of language mistakes in the summary, should also be mentioned. New

err ors h ave, however, undoubtedly been a dded afterwa rds.

Finally, I would like to thank my wife and children for their support and

for making the thesis work possible by taking over a lot of responsibilities

during t he last months of intense work.The th esis is based on work support ed by th e Nat iona l Swedish Board for

Techn ical Development (STU).




47

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51

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Hans Sohlström

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53

110 S. N. Bar ybin, A. N. Grigoren ko, V. I. Konov an d P. I. Nik itin , ”Magn etic field fibre -

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125 K. G. Svan tesson, to be published.

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130 P.S. Hague, ”Techn iques of measurem ent of th e polarization-alter ing properties of

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Tokyo 198, Ja pan .




55

Comm ent s on t he aut horsh ip of th e papers

The papers u pon which th is thesis is based, ar e writt en by myself and one

or more co-authors from the fibre optic sensor group at the Instrumentation

Laboratory. Torgny Brogårdh and Kjell Svantesson have been my super-

visors, and their contributions have primarily been to provide good ideas

and guidance. Also, their help in the actual writing of the text has been

importa nt . It is, however, difficult to qua nt ify th ese cont ribut ions.

Most of th e actual r esearch work ha s been car ried out by Ulf Holm a nd

myself. Below I will indicat e our differen t cont ribut ions to th e paper s. In t he

cases where Kjell Svantesson has made more active contributions to the

work, th is will also be ind icat ed.Paper A

Ulf Holm a nd I h ave taken equal part s in th e development of th e measur e-

ment system. The ma th emat ical an alysis of the perform an ce was h owever

ma de by Ulf Holm a lone.

Papers B and C

Ulf Holm and I h ave mad e equa l cont ribut ions t o th is work .

Paper D

I have done a major part of this work. The use of a few-mode waveguide

with selective excitation was, however, originally suggested by Kjell

Svantesson and the basic concepts behind the sensor design were jointly

devised by th e pr oject group. Ulf Holm’s m ain cont ribut ion is in t he

application of phase modulation to reduce the influence of the reflected

light.

Paper E

This pa per gives an overview of differen t met hods applied in our cha ra cter i-

zation measurements. The grating method was devised by Kjell Svantesson

and th e results shown in th e paper were obta ined by him a nd Ulf Holm. The

work on prism coup ling an d edge coup ling was main ly done by myself.

Paper F

This paper gives a sum ma ry of our sensor work up t o th at tim e. Most of th e

work on multimode sensors was done by Ulf Holm and the work on single-

mode system s was done by myself.

Paper G

This is prima rily my work . Alth ough h e is not m ent ioned a s a co-aut hor, Ulf

Holm ha s a ssisted in developing th e model used in fig 6c, 7 an d 8.

Paper H This is prima rily my work .



Hans Sohlström

56

Pa per abstracts

A: Measu reme nt syste m for magneto -optic se nsor mate rials

U Holm, H Sohlstr öm a nd T Brogår dh

A system for th e measu rem ent of magneto-optic propert ies of IR-tr an s-

par ent ma ter ials is described. The system is designed for th e cha ra cter iza -

tion of fibre optic magnetic field sensor materials. Measurement results on

YIG-crystals are presented. The accuracy of Faraday rotation and light

transmission measurements are ±2mrad and ±2% respectively. Important

features for the sensor characterization are light beam scanning, tempera-ture control and flexible magnetic field generation. A desktop computer is

used for system cont rol and dat a acquisition. The system is expected to be of

great importa nce for fut ur e sensor developmen t.

B: YIG-sen sor de sign for f ibre op tical magn etic f ield m eas urem en t

U. Holm, H. Sohlst röm a nd T. Brogår dh,

Aiming at the design of a magnetic field sensor utilizing the Faraday

effect, we give in this paper a description of measurements of magneto-

optical properties of YIG. We also give sensor design rules based upon thesemeasurements.

C: Measurem en t of YIG crystal charac terist ics for the desig n of

opt ica l magnet ic f ie ld sensors

U. Holm a nd H . Sohlstr öm

Measur ement s of th e ma gneto-optic properties of YIG crystals, aim ing at

the design of fiber optic magnetic field sensors are presented. The Faraday

polar ization in YIG sam ples of differen t sha pes, in app lied fields –60mT t o

+60mT is given. The effects of temperature, perpendicular fields andsample tr eatm ent is studied. With thin, 0.3mm sam ples, the linearity of the

relationship between applied field and polarization rotation is found to be

good with deviat ions from linea rit y of less th an 1%.

D: A Polarization Base d Fibre Optical Sen sor Syste m Us ing a YIG

Optical Wavegu ide for Magne tic Field Sen sing

Ha ns Sohlstr öm, Ulf Holm an d Kjell Svan tesson

A sensor system ut ilizing a polarizat ion m ain ta ining fibre for t he optical

signal transmission and a planar optical waveguide for magnetic fieldmea sur ement s is presen ted. The system is based on polar ization m odula tion




57

originating from the TE to TM mode conversion in a magneto-optical thin

film of Gd,Ga subst itu ted YIG (Ytt rium Ir on Ga rn et).

E: Characterization o f Magne to-optical Thin Films for Senso r Use

Ha ns S ohlst röm, Ulf Holm an d Kjell G. Svant essonAs a part of a fibre optical sensor development project we have made an

evaluation of different optical waveguiding techniques to study the proper-

ties of thin magneto-optical films. Because of the application the methods

are focused on the determination of the Faraday rotation, the linear bire-

frin gence an d t he dyna mics and a nisotropy of the m agnet ic propert ies of the

samples. Measurements using holographic grating, prism and edge (end-

fire) light coupling to different substituted YIG films are presented. The

advant ages of th e different meth ods ar e discussed an d it is shown th at th e

laun ching technique ma y affect t he pr operties to be measur ed. Film st ress

caused by the prism coupling method is found to influence the magneticanisotropy.

F: Magne to-Optical Garnet Materials in Fibre Optic Se nsor Sy stem s

for Magne tic Field Sensin g

Kjell Svan tesson, Han s Sohlström a nd U lf Holm

Magneto-optical garnet materials such as YIG, undoped as well as

substituted, exhibit a large Faraday rotation. This fact makes them poten-

tially suitable as sensing elements in fibre optic magnetic field sensor

systems.

We describe both an intensity based mu ltimode system using bulk ma te-

rials and a singlemode polarization based system using waveguiding films.

A nu mber of differen t m at eria l composit ions, su ch a s un doped YIG, (Gd,Ga)-

an d different Bi- substit ut ed YIG ha ve been used for t he sensor elements.

Measur ement results a re present ed and discussed. A detection limit in t he

µT ran ge an d a m easurement ra nge exceeding 104 ha ve been achieved.

G: A w avegu ide base d f ibre optic magn etic f ield sens or with

direct ional se nsi t iv i ty.

Ha ns S ohlst röm, Kjell Svan tesson

In this paper we report on the design and performance of an extrinsic

guided wave fibre optic magnetic field sensor. The sensor utilizes a substi-tuted YIG (Yttrium Iron Garnet, Y3Fe5O12) thin film as th e waveguiding

sensing element. A polarization maintaining fibre downlead was used to

provide insensit ivity t o both power a nd loss fluctua tions. The design m ak es

it possible to determine both the magnitude and the sign of the magnetic

field.



Hans Sohlström

58

Measurement results indicate a usable measurement range of at least

several mT with a noise equivalent magnetic field level of less than

8nT/ √ Hz.

H: The performance of a f ibre optic m agne tic f ield sen sor

uti l izing a magne to-optical garnet

Ha ns S ohlst röm, Kjell Svan tesson

The design and performance of a multimode fibre optic magnetic field

sensor u tilizing th e Fa ra day effect in a n epit axially grown t hick (YbTbBi)IG

film is reported. The sensor is found to be linear over a range of more than

100dB.



Hans S ohlström: Fibre Optic Magn etic Field S ensors Utilizin g Iron Garnet Mat erials

59

Pa per r eprints




Paper A

U Holm, H Sohlstr öm an d T Brogårdh

”Measur ement system for m agnet o-optic sensor ma ter ials”

J . Phys. E: S ci. Instrum . , vol. 17, p. 885–889, 1984.




Paper B

U. Holm, H. Sohlström a nd T. Brogår dh

”YIG-sensor design for fibre optical m agn etic field meas ur emen t”

OFS 84, R. Th. Ker st en a nd R. Kist, p. 333–336, VDE-Ver lag, Berlin, 1984.




Paper C

U. Holm a nd H . Sohlst röm

Measurem ent of Y IG crystal characteristics

for the design of optical m agnetic field sensors

TR84.01 , Instru ment at ion Labora tory;

Royal In st itu te of Techn ology, Stockh olm, 1984.




Paper D

H. Sohlst röm, U. Holm an d K. Svan tesson

”A Polar izat ion Based F ibre Opt ical Sen sor System

Usin g a YIG Opt ical Waveguide for Ma gnet ic Field Sensing”

S prin ger proceedings in Physics 44: Optical Fiber S ensors, H. J. Ardit ty,

J . P. Dakin , an d R. Th. Kerst en, p. 273–278, Sprin ger-Verlag, Berlin, 1989.




Paper E

H. Sohlstr öm, U. Holm an d K. G. Svan tesson

”Cha ra cter ization of Magnetooptical Thin Films for Sensor U se”S PIE Proc Electro-Optic and Magneto-Optic Materials and Applications ,

J . P. Cast era , vol. 1126, p. 77–84, 1989.




Paper F

K. Svan tesson, H. Sohlst röm a nd U . Holm

”Magneto-optical garn et ma ter ials in fibre optic

sensor system s for ma gnetic field sen sing”

S PIE Proc Electro-Optic and Magneto-Optic Mat erials an d App lications II ,

H. Da mm an n, vol. 1274, p.260–269, 1990.




Paper G

H. Sohlst röm an d K. Svant esson

”A waveguide ba sed fibre opt ic magn etic field sen sor

with directional sensit ivity”

S PIE Proc Fiber Optic S ensors: En gineering an d Applications ,

A. J . Bru insm a a nd B. Cu lsha w, vol. 1511, p. 142–148, 1991.




Paper H

H. Sohlst röm an d K. Svant esson

”The performa nce of a fibre opt ic ma gnet ic field sensor

ut ilizing a m agnet o-optical gar net ”Fiber and In tegrated Optics, vol. 11, p.135–139, 1992.

Also presen ted a t t he OFS 8 conference in Mont erey, Ja n. 92.

Fiber Optic Magnetic Field Sensors

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