Fabrication of fibers with high rare-earthconcentrations for Faraday isolator applications

John Ballato and Elias Snitzer

The Faraday effect provides a mechanism for achieving unidirectional light propagation in opticalisolators; however, miniaturization requires large Verdet constants. High rare-earth content glassesproduce suitably large Verdet values, but intrinsic fabrication problems remain. The novel powder-in-tube method, or a single-draw rod-in-tube method, obviates these difficulties. The powder-in-tubemethod was used to make silica-clad optical fibers with a high terbium oxide content aluminosilicatecore. Core diameters of 2.4 µm were achieved in 125-µm-diameter fibers, with a numerical aperture of0.35 and a Verdet constant of 220.0 rad@1T m2 at 1.06 µm. This value is greater than 50% for crystalsfound in current isolator systems. This development could lead to all-fiber isolators of dramaticallylower cost and ease of fabrication compared with their crystalline competitors. r 1995 Optical Society ofAmerica

1. Introduction

Modern photonic devices for optical computing, tele-communications, etc., require classes of elements thatexhibit nonreciprocal behavior. One such class isbased on the Faraday effect,1 in which the rotation ofplane-polarized light is dependent on only the appliedmagnetic field and is not dependent on the direction oflight propagation. This provides unidirectional prop-agation of light in an optical fiber. In this paper webriefly describe this effect to illustrate the factors thatinfluence the Verdet constant,2 characterizing themagnitude of the effect, and our choice of the highrare-earth content glass composition for its attain-ment. This is followed by a short discussion of anovel method of fabricating optical fibers with theseconstituents and the experimental realization of fi-bers with large Verdet constants.

2. Faraday Effect

The Faraday effect in glass is a well-understoodphenomenon and has been intensively studied anddocumented.3–10 It is present in all materials and isclosely related to the magnetic behavior of the compo-nent ions. The rotation varies with temperature in

The authors are with the Fiber Optic Materials Research Pro-gram, Rutgers, The State University of New Jersey, Piscataway,New Jersey 08855-0909.Received 21 November 1994; revised manuscript received 31

March 1995.0003-6935@95@306848-07$06.00@0.

r 1995 Optical Society of America.

6848 APPLIED OPTICS @ Vol. 34, No. 30 @ 20 October 1995

paramagnetic and ferromagnetic materials, but istemperature independent in diamagnetic materials.Its magnitude also tends to decrease with increasingwavelength. The Faraday effect is a magnetic-field-induced circular birefringence, providing a means ofcontrolling the polarization state of light. The effectis distinct from intrinsic circular birefringence 1opti-cal chiralty or activity2 in that its rotation directiondepends on only the direction of the magnetic fieldalong the path of light propagation and not on thedirection of light propagation. The optical rotationarises from the inequality of the refractive indices forright- and left-circularly polarized light; these, inturn, stem from the ground- and excited-state split-ting in the mediumwhen an external magnetic field isapplied.At a more fundamental level, Faraday rotation can

be implicitly inferred from the time-reversal asymme-try of Maxwell’s equations. These are

= 3 E 5 2≠B

≠t,

= 3 H 5≠D

≠t1 J,

= · D 5 r,

= · B 5 0.

When 1t2 is replaced with 12t2 for E and D, this isequivalent to replacing x, y, and z by 12x2, 12y2, and12z2, respectively 3similarly, r by 12r24. The physical

implication is that time reversal causes a similarreversal in the directions of E andD 1i.e., they retracetheir values in amplitude and polarization2. How-ever, for the magnetic field to be retraced, the orienta-tion of B must be reversed. Therefore in Faradayisolator systems in whichB is not replaced by 12B2, weachieve the unique behavior that separates the Fara-day effect from the natural optical rotation found inchiral crystals and other enantiomorphous materials.The existence of Faraday rotation in all materialsstems directly from this proof 1i.e., light’s electromag-netic interaction with any media is determined byMaxwell’s equations coupled with the proper materialconstitutive equations2.The rotation in the plane of polarization, U, may be

represented as

U 5 V e B · dl,

where V is defined by this equation as a materialparameter known as the Verdet constant, B is theapplied axial magnetic flux density,11 and dl is thedifferential length along the propagation path ex-posed to the magnetic field.The Faraday effect per unit length can be alterna-

tively defined as

U 5v

2c1n2 2 n12,

where n2 and n1 are the refractive indices for left- andright-circularly polarized light of angular frequencyv. The expressions for n2 and n1 can be obtainedfromMaxwell’s equations, combinedwith the constitu-tive equations for conductivity and dielectric constant.From this it follows11 that

V 5Ne3

2nm2

1

ce0

v2

1v2 2 v0222

for a material of electronic resonant frequency v0 andnominal refractive index n, withN charge carriers perunit volume of charge e and mass m, operating at awavelength l 5 12pc@v2 1the case for an undampedharmonic oscillator that gives rise to a resonantdenominator2. Depending on the magnetic nature ofthe isolator material, simplifications to the aboveequation may be made. These simplifications areaddressed below for two broad classes of opticalmaterials.Faraday rotation has a number of significant practi-

cal applications. It lends itself to the construction ofoptical switches, modulators, circulators, field sen-sors, and optical isolators. The optical isolator greatlybenefits from high Verdet constant materials. Isola-tors are analogous to electronic diodes, permittinglight propagation in one direction only. In thesedevices, the incident-plane polarized light is passedthrough a Faraday rotating material in a magneticfield so as to produce a 45° rotation of the polarization

plane. It is then transmitted through a polarizationanalyzer oriented at 45° with respect to the firstpolarizer. A schematic of this configuration is de-picted in Fig. 1. Backreflected light traversing in theopposite direction experiences an added 45° rotation,leading to a polarization in the direction blocked bythe first polarizer. This is important in sensitivelaser systems in which backreflected radiation isdetrimental to the laser source, as well as in fiberlaser schemes in which reflected pulses experiencegain with each amplifier pass causing ghosted signals.There are several factors that affect the extent ofattenuation. Among themost important are inhomo-geneities in the magnetic field, in the refractive index,and in the magnetic ion distribution. To achievespecified rotations with a minimum of material andwith magnetic fields as low as possible, the Verdetconstant should be as large as possible.The classical Verdet relation for diamagnetic mate-

rials was derived by Becquerel.12 It showed therotation to be linearly dependent on the optical disper-sion. The form often given, in cgs units normalizedto the magnetic intensity H, rather than the prefer-able definition11 in terms of the flux density givenabove, is

V 5el

2mc2dn

dl,

where e and m are the charge and the mass, respec-tively, of the electron, c is the speed of light, and dn@dl

is the refractive-index dispersion with wavelength.This equation holds closely for most diamagneticmaterials. A factor g called the magneto-opticanomaly, is often used as a multiplier to account forthe nature of the chemical bond in these diamagneticmaterials. The anomaly factor ranges from roughly1@4 for highly covalent bonds 1e.g., diamond2 to approxi-mately unity for ionic bonding 1e.g., ZnS2.In dealing with paramagnetic materials or materi-

als with both diamagnetic and paramagnetic species1as is the case with rare-earth aluminosilicate glasses2,other terms must be included to account for themagnetic susceptibilities of the paramagnetic ions.In those materials, the Verdet constant is propor-

Fig. 1. Schematic of a bulk Faraday rotation isolator configura-tion with electromagnetic polarization states.

20 October 1995 @ Vol. 34, No. 30 @ APPLIED OPTICS 6849

tional to13,14

n23oi

Ai

1vi2 2 v222

1 oi

oj

Bij

1vi2 2 v221vj

2 2 v2245 n21D 1 P2,

where n is the frequency of the light, D is thediamagnetic component that can be simply calculatedfrom the Becquerel equation, and P is the paramag-netic component that can be calculated from quantum-mechanical considerations of the ground- and excited-state splitting.6

3. Rare-Earth Glasses

Suitably largeVerdet constants are possible in diamag-netic glasses 1e.g., As2S32; however, paramagneticglasses that contain certain rare-earth ions in highconcentrations are preferred because of the glasses’greater durability and lower absorption in the spec-tral regions of interest. In these rare-earth-dopedglasses, the rotation involves the 4f–5d virtual elec-tronic electric-dipole transition, which is a function ofatomic number. At high concentrations, the Verdetconstant is approximately linear with concentration.High rare-earth content glasses should, therefore,yield large magneto-optic rotations. However, theconcentration of paramagnetic ions that can be addedto a glass is limited by its glass-forming properties.Advantages of doped aluminosilicate glasses includetheir high solubilities for rare-earth species, theircompatibility with pure silica claddings, and theircapacity for splicing into existing fiber networks.Most glasses that contain trivalent rare-earth ions,

although transparent in some regions, typically havenumerous absorption lines extending from the nearinfrared to the near ultraviolet. In contrast to this,Ce31, Gd31, Yb31, and Tb31 are transparent in thevisible and near infrared. The energy-level dia-grams for Tb31 as well as for Ce31, Gd31, and Yb31 aredepicted in Fig. 2. The Tb31 ion is transparent fromthe green down to 1.6 µm and has the largest Faradayrotation per ion.6 It is for these reasons that terbiumaluminosilicates are indicated as materials of specialimportance.

4. Powder-in-Tube Method

Traditional preform fabrication techniques 1e.g., modi-fied chemical vapor deposition2 limit rare-earth concen-trations to approximately 15 wt% because of theresultant thermal expansion mismatch from the nec-essary addition of aluminum to promote solubilityand dispersion of the rare-earth species. Fibers withhigh rare-earth content cores have also been made bythe selective volatization method.15 Fabrication ofhigh rare-earth content glasses typically uses a batch-ing technique.16 This calls for the weighing andmixing of component powders that ultimately aremelted in a crucible. This melt then is poured into arod-shaped mold. After cooling to an amorphoussolid, the rod subsequently is inserted in a tube anddrawn into a fiber. Great care is required for reduc-

6850 APPLIED OPTICS @ Vol. 34, No. 30 @ 20 October 1995

Fig. 2. Electronic energy-level diagram for Ce31, Gd31, Tb31, andYb31. Note transparency in the visible region.

ing crucible contamination for low-loss optical fibersystems. An alternative approach is the powder-in-tube method outlined below.To overcome the crucible contamination problems

associated with core-glass fabrication before fiberdrawing, it was considered that melting the powdercomposition in a silica capillary tube during the drawprocess could circumvent this problem. This tech-nique has been termed the powder-in-tube process.The powder-in-tube process calls for chemical reduc-tion of the rare-earth powder to the trivalent stateand intimate mixing of the powders to enhance themelt characteristics. The formulation is similar tothat of the batch process, but the composition is theninserted into the hollow core of a silica capillary tube.Certain applications necessitate specific core–claddiameter ratios. This requirementmay be accommo-dated in several ways. Onemay resleeve the powder-filled capillary into a second glass tube or cane; thisstill requires but a single draw. When large clad-to-core ratios are desired, one may alternatively startwith a small capillary inside a large one. A sche-matic representation of the latter arrangement isshown in Fig. 3. On drawing this powder-filledcapillary into an optical fiber, the high rare-earthcontent center melts to a fluent liquid that thensolidifies to a glassy core when the fiber cools. Thecapillary actually acts as a silica crucible for melting,but ultimately draws into the fiber cladding as thefabrication progresses. Because the capillary is puresilica and the core glass is an aluminosilicate, thediffusion of silica between the core and the clad is notviewed as a contamination detrimental to the opticalproperties of the fiber. If the diffusion were exces-sive it would lower the numerical aperture and theVerdet constant. Although some diffusion does oc-cur, we did not think it was a troublesome amount.

5. Experimental Results

The fabrication of optical fibers that contained a highrare-earth concentration required several stages.As mentioned, the trivalent rare-earth ions have thelargest paramagnetic Faraday rotation.17 One of thehighest rotation per ion is realized in Tb31, and it istransparent over wide sections of the visible andnear-infrared regions. For this reason Tb2O3 waschosen as the rare-earth oxide powder component to

Fig. 3. Schematic of powder-in-tube method for the fabrication ofhigh rare-earth content optical fibers.

be investigated. Commercially available is the higheroxide Tb4O7; this is presumably Tb2O3 · 2TbO2, withan unacceptable mixed valency of Tb31 and Tb41 ions.The literature shows18 that Tb4O7 will reduce toTb2O3 at approximately 800 °C in a nitrogen or hydro-gen atmosphere. Samples were reduced in a carboncrucible at 800 °C for 5 h under an ultrahigh-puritynitrogen atmosphere. Powder x-ray diffraction analy-sis of this sample showed excellent correlation withthe existing diffraction pattern for pure Tb2O3.Fibers that contained 54 wt.% Tb2O3, 27 wt.% SiO2,

18 wt.% Al2O3, and 1 wt.% Sb2O3 1as a fining agent2were successfully produced by the powder-in-tubeprocedure. A complete fusion between the silicacane and capillary was observed in a test section of250 m of fiber. This optical assessment agreed wellwith electron microscopy results, which indicatedcore–clad fusion without interfacial crystallization.A major concern was that unfined bubbles would befound in the core. These could lead to voids in thedrawn fiber. This concern did not turn out to be aproblem, as no scattering centers could be visuallyobserved. The test section contained a continuoushigh rare-earth concentration core, which had cooledfrom a melt at the preform neckdown region.The numerical aperture, which is a measure of the

angle for light acceptance and emission in and out ofthe fiber core, was determined for the powder-in-tubesample to be 0.35. From the definition of the numeri-cal aperture, the core glass refractive index was 1.501at 632.8 nm2. An index of 1.62 was determined byellipsometry on a bulk sample. These index differ-ences are attributed to diffusion of silica between thecore and the cladding.We observed optical waveguide modal patterns on

viewing sample fiber lengths under a light microscopein transmission. The low-order modes 1TE02, TM02,or HE222 were clear and easily distinguishable in thered end of the visible spectrum, from which weconclude that there was only limited scattering of thepropagation modes. Aluminum in the core composi-tion lowers the melt viscosity, thereby producing anincreased constituent diffusion and a radial refractive-index grading 1Figs. 4 and 52. The existence of agraded index across the fiber diameter causes a lower

Fig. 4. Refractive-index profile of powder-in-tube fiber 1125-µmdiameter2.

20 October 1995 @ Vol. 34, No. 30 @ APPLIED OPTICS 6851

effective numerical aperture and larger modal pat-tern diameters. From the fact that the modal pat-terns were easily viewed and resolved, we concludethat the core glass had homogeneously mixed andfined as it progressed from the powder stage, throughthe melt, to the glassy core. Poorly mixed glasswould produce scattering among all the propagationmodes, and simple mode patterns would not be ob-served. The powder-to-glass transition is shown inFig. 6.Optical absorption measurements were attempted

on a several-meters length of fiber. Spectral losseswere too high over this length, whereas shorter fiberlengths were not long enough to yield accurate lossresults. Fiber samples of 10 cm were viewed, asmentioned above, under a transmission light micro-scope, and waveguide modal patterns, consistent witha symmetric-step geometry,19 were easily viewed.The existence of high loss is attributed to the purity ofthe starting powders and not to axially irregularcore–clad interdiffusion. Powders utilized for bothbulk preparation and fiber fabrication were of 99%purity. Bulk samples 3 mm thick exhibited a broadabsorption centered at approximately 1 µm; this isattributed primarily to Fe21 and, secondarily, to Cu21

Fig. 5. Refractive-index profile of powder-in-tube fiber core region.Note distribution indicative of diffusional processes 1profile asym-metry from instrumental optical aberrations2.

Fig. 6. Opticalmicrograph of powder-to-glass transition in powder-in-tube core region.

6852 APPLIED OPTICS @ Vol. 34, No. 30 @ 20 October 1995

330 parts in 106 1ppm2 in Tb4O74. Problems concern-ing excessive loss over long fiber lengths are notconsidered severe, as the large Verdet constants forthe terbium aluminosilicate treated here set theusable isolator length at roughly double 1or approxi-mately 20 cm2 that of the crystalline alternative.Differential thermal analysis 1DTA2 of the bulk

sample indicated a refractory glass with a meltingpoint of approximately 1340 °C. This is importantbecause the powder-in-tube method requires that thecore glass melt at a temperature lower than that atwhich the clad glass softens, and this indeed was thecase. The thermal expansion coefficient of the ter-bium aluminosilicate core glass measured by thermo-mechanical analysis 1TMA2 was found to be approxi-mately 4.4 3 1026@K over the range of 45 to 600 °C.Table 1 summarizes the physical properties of theglass composition treated in this paper.A commercial vendor, Isowave Inc.,20 performed

Verdet constant measurements on a bulk terbiumaluminosilicate glass sample. Their experimentallydetermined room-temperature Verdet constant wasfound to be V 5 220.0 rad@1T m2 at 1.06 µm. This ismore than one half of the Verdet constant of commer-cially available crystals used in optical isolators.Figure 7 graphs the traditional variation in Verdetconstant with wavelength for the terbium aluminosili-cate and a commercial rare-earth garnet crystal 3ter-bium gallium garnet 1TGG24 used in isolator applica-tions. Table 2 lists the Verdet values for these twomaterials as a function of wavelength. Using theclassical approximation10,21 for the wavelength depen-dence of V,

V 5A

l2 2 l02,

we find from a least-squares fit 1r2 5 0.9942 to thedata of Fig. 7 that A < 219.7 3 106 31nm22 3 rad@1Tm24and l0 < 385 nm. This represents a departurefrom the published values for the Tb31 ion of 250 nm21

and 215 nm.10 Berger et al.10 indicate that l0 doesnot necessarily represent only one transition respon-sible for Faraday rotation, but is a weighted average

Table 1. Physical Properties of Terbium Aluminosilicate Glass

CompositionTb2O3 54 wt.%SiO2 27 wt.%Al2O3 18 wt.%Sb2O3 1 wt.%

Glass transition temperature 880 °CCrystallization temperature 1090 °CMelting temperature 1340 °CCoefficient of thermal expansion 4.4 3 1026@KDensity 3.3 3 103 kg@m3

Bulk refractive index at 632.8 nm 1.62Verdet constant at 1.06 µm 220.0 rad@1T m2a

Fiber numerical aperture 0.35

aIn cgs emu, the Verdet constant at 1.06 µm 5 20.069min@1Oe cm2. The cgs 1emu2 to mks conversion is V3rad@1T m24 5

125@272p 3 100 V3min@1Oe cm24.

of the real transition wavelengths. The averagingreflects the relative transition strengths and devia-tions from the observation frequency. The effectivetransition wavelength, l0, is exact only when there isbut one transition. The variation in l0 values arisesfrom the differing terbium concentrations and theglass hosts. The A parameter above is not simply aformula constant, but rather is a function of tempera-ture, concentration, and effective dipole matrix ele-ments. The previously published values for A corre-spond to Tb31 concentrations of 3.8 3 1021 ions@cm3

and 5.4 3 1021 ions@cm3, which are, respectively,

Fig. 7. Verdet constant 3rad@1T m24 versus wavelength 1nanom-eters2 for a bulk terbium aluminosilicate sample and a commer-cially available TGG isolator crystal.

Table 2. Verdet Constant versus Wavelength for Terbium AluminosilicateGlass and Commercial TGG Isolator Crystal

Wavelength1nm2

Verdet Constanta

for TerbiumAluminosilicate

3rad@1T m24

Verdet Constantfor TGG Crystal

3rad@1T m24

Ratio of Glass@Crystal VerdetConstants

633 273.723 2136.306 0.541670 263.191 2120.686 0.524753 247.393 293.634 0.506780 244.234 286.566 0.511800 241.074 281.737 0.502830 237.915 275.076 0.505849 236.861 271.178 0.518876 233.702 266.030 0.510980 224.223 249.450 0.4901064 220.010 238.891 0.515

aNegative values for the Verdet constants correspond to aparamagnetic-ion-dominated rotation. Diamagnetic ions resultin positive rotations. The sense of the rotation is determined bythe change in polarization direction with respect to the direction ofcurrent producing the magnetic field. Positive Verdet valuesmean that the change in the plane of polarization is in the samesense as the electric current producing the B field. Negativevalues imply an opposite correlation.

57%21 and 82%10 of the 6.6 3 1021 ions@cm3 used inthis study.Further comparison22 of the terbium aluminosili-

cate treated here with other Faraday rotator materi-als may be made from the seminal paper of Weber.5Table B of Ref. 5 contrasts the Verdet constants ofvarious glasses and crystals at 1.06 µm. The 220.0rad@1T m2 Verdet constant of the 54 wt.% terbiumaluminosilicate glass is comparable with the 220.6rad@1T m2 value for a terbium borosilicate glass. Thealuminosilicate composition then ranks fourth onWeber’s list in terms of amorphous rotator materialsand first in terms of aluminosilicates or non-boron-containing silicate glasses.

6. Conclusion

For nonreciprocal applications, e.g., Faraday isola-tors, terbium aluminosilicate glasses are stronglyindicated as future material systems of choice.Currently, terbium glasses are used in Faraday isola-tors at the Lawrence Livermore Laboratory’s largeneodymium oscillator–amplifier laser. The novel fab-rication technique called the powder-in-tube methodwas successfully applied to the production of silica-clad fibers containing more than 50 wt.% terbiumoxide. These glasses exhibited Verdet constants ofgreater than 50% of that shown by the much moreexpensive commercially available crystalline alterna-tive, which is also a miniature bulk configurationrather than a fiber form.The powder-in-tube method is potentially appli-

cable over a wide compositional range, includinghalides and chalcogenides, as the main requirementis that the core powder components melt to form glassbefore the clad glass softening at the preform-fiberneckdown region. Volatile constituents may, how-ever, be a problem with halide glasses.The powder-in-tube method also obviates a poten-

tial problemwith traditional preform fabricationmeth-ods. The differential thermal expansion betweensilica cladding and doped-silica cores may lead tostress-inducedmechanical failure during preform tubecollapse. The powder form of the preform core allowsa single draw directly to final fiber form with a smallcore diameter. The thermal expansion mismatchbetween core and cladding becomes less critical atsmall core sizes.The powder-in-tube procedure can ultimately pro-

vide a method for fabricating high-purity, low-lossfibers and reduce contaminations consistently foundwith core glass fabrication in a crucible. The weaklinks in the process remain the components thatcomprise the powders. Impurities in the powdersaremanifested as impurities in the core glass, therebyincreasing the optical loss. The possibility exists forultrahigh-purity sol–gel powders to be used, makingthe powder-in-tube method extremely useful gener-ally, but particularly so for the production of highrare-earth-content glasses.

This work would never have come to fruition with-out the assistance and valuable input from ToddAbel,

20 October 1995 @ Vol. 34, No. 30 @ APPLIED OPTICS 6853

Paul Foy, Rajiv Datta, Jeff Bonja, Dave Machewirth,Jim Fajardo, and Matt Dejneka of the Fiber OpticMaterials Research Program, members of the U.S.Army Research Laboratory, Fort Monmouth, N.J., aswell as professors of Rutgers University’s Depart-ment of Ceramics. We also recognize thoughtfuland timely contributions from Norbert J. Kreidl.The authors thank the Fiber Optic Materials Re-search Program, Rutgers University, the PolaroidCorporation, Isowave Incorporated, and the New Jer-sey Commission on Science & Technology for theirsupport.

References1. M. Faraday, ‘‘On the magnetization of light, and the illumina-

tion of magnetic lines of force,’’ Philos. Trans. R. Soc. London 1,104–123 118462.

2. E. Verdet, ‘‘Recherches sur les proprietes optiques developpeesdans les corps transparents par l’action du magnetisme,’’Ann.Chim. Phys. 41, 370–412 118542.

3. J. E. Shelby and J. T. Kolhi, ‘‘Rare-earth aluminosilicateglasses,’’ J. Am. Ceram. Soc. 73, 39–42 119902.

4. A. Makishima, M. Kobayashi, and T. Shimohira, ‘‘Formation ofaluminosilicate glasses containing rare-earth oxides,’’ J. Am.Ceram. Soc. 65, C-210 119822.

5. M. J.Weber, ‘‘Faraday rotatormaterials,’’Rep.M-103 1LawrenceLivermoreNational Laboratory, University of California, Liver-more, Calif., 19822; M. J. Weber, ‘‘Faraday rotator materials forlaser systems,’’ in Laser and Nonlinear Optical Materials, L.G. DeShazer, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 681,75–90 119862; G. H. Dieke and H. M. Crosswhite, ‘‘The spectraof the doubly and triply ionized rare earths,’’ Appl. Opt. 2,675–686 119632.

6. N. F. Borelli, ‘‘Faraday rotation in glass,’’ J. Chem. Phys. 41,3289–3293 119642.

7. C. C. Robinson, ‘‘The Faraday rotation of diamagnetic glassesfrom 0.334 µm to 1.9 µm,’’Appl. Opt. 3, 1163–1166 119642.

8. M. Daybell, W. C. Overton, Jr., and H. L. Laquer, ‘‘The Faradayeffect at low temperatures in terbium alumina silicate glasses,’’Appl. Phys. Lett. 11, 79–81 119672.

6854 APPLIED OPTICS @ Vol. 34, No. 30 @ 20 October 1995

9. C. C. Robinson and R. E. Graf, ‘‘Faraday rotation in praseo-dymium, terbium, and dysprosium alumino silicate glasses,’’Appl. Opt. 3, 1190–1191 119642.

10. S. B. Berger, C. B. Rubinstein, C. R. Kurkjian, and A. W.Treptow, ‘‘Faraday rotation in rare-earth 1III2 phosphateglasses,’’ Phys. Res. 133,A723–A727 119642.

11. A. Sommerfeld, Optics, Vol. IV of Lectures on TheoreticalPhysics Series 1Academic, NewYork, 19642, p. 105.

12. H. Becquerel, ‘‘Ser une interpretation applicable au phe-nomene de Faraday et au phenomene de Zeeman,’’ C. R. Acad.Sci. Ser. C 125, 679–685 118972.

13. J. H. Van Vleck, The Theory of Electric and Magnetic Suscepti-bilities 1Oxford U. Press, New York, 19322, pp. 367–371; H.Cole, ‘‘Magneto-optic effects in glass. Part 1,’’ J. Soc. GlassTechnol. 34, 220 119502.

14. P.A. Schulz, ‘‘Wavelength-independent Faraday isolator,’’Appl.Opt. 28, 4458–4464 119892.

15. E. Snitzer and R. Tumminelli, ‘‘SiO2-clad fibers with selec-tively volatized soft-glass cores,’’ Opt. Lett. 14, 757–759119892.

16. S. J. Collocott and K. N. R. Taylor, ‘‘Magneto-optical proper-ties of erbium-doped soda glass,’’ J. Phys. 11, 2885–2893119782.

17. Y. R. Shen, ‘‘Faraday rotation of rare-earth ions. I. Theory,’’Phys. Rev. 133,A511–A515 119642.

18. M. W. Urban and B. C. Cornilsen, ‘‘Bonding anomalies in therare earth sesquioxides,’’ J. Phys. Chem. Solids 48, 475–479119872.

19. E. Snitzer, ‘‘Cylindrical dielectric waveguide modes,’’ J. Opt.Soc. Am. 5, 491–498 119612; E. Snitzer and H. Osterberg,‘‘Observed dielectric waveguide modes in the visible spec-trum,’’ J. Opt. Soc. Am. 5, 499–505 119612.

20. Isowave Incorporated, 64 Harding Road, Dover, N.J. 07801.21. G. T. Petrovskii, I. S. Edelman, T. V. Zarubina, A. V. Mala-

khovskii, V. N. Zabluda, and M. Yu. Ivanov, ‘‘Faraday effectand spectral properties of high-concentrated rare earth oxideglasses in visible and near UV region,’’ J. Non-Cryst. Solids130, 35–40 119912.

22. N. J. Kreidl, Santa Fe, N.M. 87501 1personal communication,19942.