A unified materials approach to mitigating optical ...righini/TC20/Ballato_Mitigating Nonlinearities III... · optical fibers whose enhanced performance—in particular, marked reductions

OR I G I N A L AR T I C L E

A unified materials approach to mitigating optical nonlinearitiesin optical fiber. III. Canonical examples and materials road map

Maxime Cavillon1 | Courtney Kucera1 | Thomas Hawkins1 | Jay Dawson2 |

Peter D. Dragic3 | John Ballato1

1The Center for Optical Materials Scienceand Engineering Technologies(COMSET), Department of MaterialsScience and Engineering, ClemsonUniversity, Clemson, SC, USA2Lawrence Livermore NationalLaboratory, Livermore, CA, USA3Department of Electrical and ComputerEngineering, University of Illinois atUrbana—Champaign, Urbana, IL, USA

CorrespondenceJohn BallatoEmail: [email protected]

Funding informationUS Department of Defense JointTechnology Office, Grant/Award Number:N00014-17-1-2546; J. E. SirrineFoundation; U.S. Department of Energyby Lawrence Livermore NationalLaboratory, Grant/Award Number: DE-AC52-07NA27344

AbstractThis paper, Part III in the Trilogy (Ballato, Cavillon, Dragic, 2018; Dragic, Cavillon,

Ballato, et al., 2018a,b), provides a road map for the development of simple core/clad

optical fibers whose enhanced performance—in particular, marked reductions in

optical nonlinearities—is achieved materially and not through the more conventional

present routes of geometrically complex fiber design. More specifically, the material

properties that give rise to Brillouin, Raman and Rayleigh scattering, transverse

mode instabilities (TMI), and n2-mediated nonlinear effects are compiled and results

on a wide range of optical fibers are discussed with a focus on trends in performance

with glass composition. Furthermore, optical power scaling estimations as well as

binary and ternary property diagrams associated with Rayleigh scattering, the Bril-

louin gain coefficient (BGC) and the thermo-optic coefficient (dn/dT) are developed

and employed to graphically represent general trends with composition along with

compositional targets for a single intrinsically low nonlinearity, silica-based optical

fiber that can achieve the power scaling goals of future high energy fiber laser appli-

cations. A foundational finding of this work is that the high-silica content optical

fibers fabricated using conventional chemical vapor deposition methods will not suf-

fice to meet the power scaling demands of future high-power and high-energy fiber

lasers.

KEYWORD S

glass products, lasers, optical fibers, optical glasses, optical properties

1 | INTRODUCTION

This trilogy of papers generally is focused on mitigating theoptical nonlinearities that arise when high optical powersare propagated through modern optical fibers. These nonlin-earities, which include stimulated Brillouin scattering(SBS), stimulated Raman scattering (SRS), transverse modeinstability (TMI), and nonlinear refractive index (n2)-mediated wave-mixing phenomena, are parasitic effects inthat they limit the achievable output powers from fiber

lasers. While the fiber and laser community has largely con-fronted these issues through tailoring of the fiber geometry,this work lays the foundation for a unified materialsapproach. The benefits of which are that each nonlinearityis attacked at its most fundamental origin—the interactionof the light with the material through which it propagates—and, accordingly, simpler fiber designs and ease of manu-facturing result.

Companion Paper I1 provided a fundamental descriptionof the thermodynamical and physical origins of each effect

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided theoriginal work is properly cited.© 2017 The Authors. International Journal of Applied Glass Science published by American Ceramic Society (ACERS) and Wiley Periodicals, Inc.

Received: 6 October 2017 | Accepted: 28 November 2017

DOI: 10.1111/ijag.12336

Int J Appl Glass Sci. 2018;9:447–470. wileyonlinelibrary.com/journal/ijag | 447

http://orcid.org/0000-0002-4413-9130

http://orcid.org/0000-0002-4413-9130

http://orcid.org/0000-0002-4413-9130

http://orcid.org/0000-0001-5910-3504

http://orcid.org/0000-0001-5910-3504

http://orcid.org/0000-0001-5910-3504

http://creativecommons.org/licenses/by/4.0/

http://www.wileyonlinelibrary.com/journal/IJAG

along with the general dependencies of each on materialproperties and parameters. Companion Papers II2,3 dis-cussed simple macroscopic additivity models that haveproved quite useful for estimating the relevant optical,acoustic, thermal, and physical properties of multicompo-nent glasses. The intent of this paper is to build from thefundamentals of Companion Paper I and describe the prop-erties of specific glass families as they relate to the afore-mentioned performance-limiting optical nonlinearities.

By way of a compositional baseline, modern telecommu-nications optical fibers possess a pure silica cladding with agermania (GeO2)-doped single-mode core. The use of ger-mania originates from its processibility using chemical vapordeposition (CVD) methods to yield extremely low lossfibers. High energy laser (HEL) fibers, and to some extenterbium-doped fiber amplifier (EDFA) fibers, replace theGeO2 with combinations of alumina (Al2O3) and phosphoruspentoxide (P2O5), in order to limit photo-darkening, alongwith facilitating the incorporation of the appropriate rare-earth species (typically either Er2O3 or Yb2O3). Other spe-cies, such as SiF4 or boria (B2O3) are added to further tailorthe refractive index, viscosity, or stress state in the glass. Asummary of the role of each of these dopants on the resultingglass can be found in Refs. 4,5. Complementing this discus-sion is the nice comparison of preform fabrication methodsfor silicate fibers that is found in Ref. 5.

Ideally, the compositions discussed herein would be real-ized using conventional CVD methods.6 However, given thehigh processing temperatures associated with preform consol-idation and collapse, which usually exceed 2200°C (and areoften closer to 2400°C), volatile species such as germania(GeO2), boria (B2O3), and fluorine (F) are difficult to maintainin the necessary concentrations required for marked reductionin parasitic nonlinearities. In this sense, the molten coreapproach to fiber fabrication,4,7 employed to make many ofthe fibers described in this work, can be considered a “lowtemperature” method since the highest temperature experi-enced is approximately the melting point of the core precur-sor. This can be several hundreds of degrees lower than thoseexperienced in CVD processing, which permits greater con-centrations of the more volatile species to persist in the finalfiber. However, while convenient and amenable to a widerange of materials, the reaction between core melt and clad-ding glass can make achieving low-silica core compositions achallenge. Additionally, the attenuation from molten core-derived all-glass fibers is predicated on the purity of the start-ing materials, which usually are powder-derived. While sub-20 dB/km loss values have been obtained,8 this is presentlymore the exception than the rule without significant purifica-tion efforts.

Accordingly, the following ground rules have been con-sidered from the perspective of practicality. First, whetherfor telecommunications or HEL applications, fibers must be

robust, spliceable to existing (silica) fibers, capable of rea-sonable rare-earth doping levels, and low loss (20-30 dB/kmfor HEL laser fibers although less is always better).“Robust,” in these cases, refers to their fieldability, whichrequires high strength, flexibility, and reasonably high tem-perature capacity (HEL fibers can experience temperaturesof several hundred degrees Celsius during operation). Aswaveguides, the modality of the fiber is important from theperspective of dispersion (telecommunications) and beamquality (HEL). In the former, single-mode operation gener-ally is required, whereas in the latter, single-mode operationwould be preferred but multi-mode operation might suffice.When considering all of these attributes together, particularlywith hopes of operation at > kW optical power levels, onlysilica-based optical fibers fulfill these conditions.

In specific regard to the nonlinearities themselves, thiswork assumes the following reductions to be both practicaland viable. Practical here means that achieving these levels ofreduction would be meaningful from a HEL systems perspec-tive: �15 dB in Brillouin gain coefficient (BGC); �5 dB inRaman scattering; a thermo-optic coefficient (dn/dT) of�5 dB; and an n2 value equivalent to that of pure SiO2. Whilethe last goal does not sound like an improvement, achievingthe other reductions will necessitate reasonably high concen-trations of non-SiO2 compounds. Accordingly, this n2 goalessentially means that these non-SiO2 dopants would nothave any additional contribution to the nonlinear refractiveindex beyond that of the SiO2 component.

2 | TRENDS WITH GLASSCOMPONENTS AND FAMILIES

The properties of multicomponent glass optical fibers werestudied in detail in the 1970s and 1980s while efforts to opti-mize optical fibers for long-haul communications were beingundertaken with great enthusiasm. In those days, low opticalloss was the principal driver and so compositions that exhib-ited intrinsically low Rayleigh scattering garnered the mostattention. Seminal material examples of such fibers will nowbe described as a preamble to the discussions that follow.

Among the first studies were those conducted on theclassic soda-lime-silica (SLS) system.9 An analysis similarto that provided in Companion Paper I1 was conducted,although focused primarily on losses associated with Ray-leigh scattering. Due to the reduced fictive temperature, thedensity-related Rayleigh scattering was predicted to belower for the SLS than for fused silica. However, addi-tional scattering due to compositional fluctuations in themulticomponent SLS glass led to a calculated intrinsic lossthat was slightly over three times larger than that for silicaacross the visible and near infrared spectral range (extrinsicimpurities notwithstanding).

448 | CAVILLON ET AL.

Contemporaneously, the binary potassium silicate systemwas studied with both Rayleigh and Brillouin scatteringbeing investigated as a function of K2O concentration.10

With increasing K2O, both p12 and p44 photoelasticity coeffi-cients, shear and longitudinal wave velocities, and fictivetemperature were found to decrease. Conversely, the refrac-tive index and isothermal compressibility were shown toincrease with increasing K2O concentration. These trendswere shown by LaBerge et al, to yield density fluctuations,<Dq2>, that were nearly 50% lower than those for SiO2 at aconcentration of about 20 mol% K2O.

11 However, Schroederet al,10 found that the immiscibility gap that exists in theK2O-SiO2 system, which extends over the range from nomi-nally 0-25 mol% K2O, led to significant compositional fluc-tuation-induced scattering. For K2O concentrations greaterthan 25 mol%, the scattering losses were found to be roughly30% lower than those for fused silica due primarily to thevery small compositional fluctuation term associated withRayleigh scattering. Taken in total, potassium silicates areintrinsically low Brillouin and Rayleigh glasses for K2O con-centrations in excess of 20-25 mol%. Again, it is worth not-ing that extrinsic losses associated with impurities likelywould make this system impractical from the perspective oflow loss telecommunication fibers. However, given the dif-fering focus of this present trilogy, where ultimate low loss isnot as critical, such a simple system with intrinsically lowBrillouin and (classical) Rayleigh scattering could be ofinterest.

Ternary silicate glasses also received considerable atten-tion, particularly those in the sodium borosilicate (Na2O-B2O3-SiO2) and sodium aluminosilicate (Na2O-Al2O3-SiO2)systems. As noted by Tynes et al.12 a glass system that exhi-bits both refractive index and density values that are roughlyindependent of composition must then exhibit a @e/@C valueof zero (or nearly so), which implies low Rayleigh scatter-ing. Akin to the concept employed here of component addi-tivity to achieve multiple property tailoring, Tynes et al,further postulated that a ternary borosilicate with low totalRayleigh scattering could be achieved by mixing a binaryborosilicate (B2O3-SiO2) having reduced @e/@q with a bin-ary alkali silicate exhibiting a reduced <Dq2> value (seeCompanion Paper I for more detail on these factors1). Theseconditions occur over a fairly broad compositional range inthe sodium borosilicate system, where, for a composition ofabout 50 SiO2-20 B2O3-30 Na2O (mol%) a minimum in Ray-leigh scattering occurs due to the aforementioned combinedeffects of reduced density fluctuations and reduced changein permittivity (hence refractive index) with density.

A similar approach was followed in the sodium alumi-nosilicate system, where Rayleigh scattering was reducedthrough reductions in fictive temperature to minimize den-sity fluctuations coupled with components well-matched indielectric properties to minimize compositional

fluctuations.13 A composition of 78 SiO2-6 Al2O3-16 Na2O(mol%) was found to exhibit scattering losses 60% lowerthan fused silica.

Quaternary systems also have been studied with themixed alkali, alkaline earth silicate system being espe-cially interesting. Specifically, Tsujikawa and Ohashi eval-uated glasses in the K2O-Na2O-MgO-SiO2 system.14 Theyfound a marked reduction in Rayleigh scattering for acomposition of 22 K2O-8 Na2O-10 MgO-60 SiO2 (mol%)where the scattering losses are only about 38% those forfused silica. For this composition, the combined effects atplay are a reduced glass transition temperature (surrogatefor fictive temperature), hence reduced density-relatedscattering, as well as the reduced concentration fluctua-tions postulated to arise from a maximum at this compo-sition in the difference between the glass transition andspinodal temperatures. This later consideration beingthought to occur based on the mixed alkali effect,whereby the mobility of the faster diffusing alkali speciesexhibits a minimum at a ratio of K2O/(K2O + Na2O) ofabout 0.73.14

A more general and systematic consideration of alkaliion effects in silica-based optical fiber glasses was madeby Lines.15 Shown there were changes in fictive tempera-ture, Tf, refractive index, n, photoelastic constant p12, anddifference between glass transition and spinodal tempera-tures, (Tg-Ts), with small (<4 mol%) alkali addition into sil-ica. Of the alkali ions, sodium and potassium silicates werefound to have the lowest overall scattering loss, relative tothe other alkali, due primarily to their having the greatestreduction in Tf, larger Tg-Ts difference (particularly forK2O-SiO2), and smallest increase in refractive index. Aminimum in scattering was found at a concentration ofabout 2 mol% alkali with the sodium and potassium sili-cates exhibiting a calculated Rayleigh scattering that was15-20% lower than for fused silica. These dependencies,however, in some part derive from the formation of non-bridging oxygen (NBO) ions upon alkali addition into sil-ica. Such defects will not be helpful at higher intensities inactive optical fibers because they are believed to facilitatephoto-darkening. However, this is set aside for the timebeing in the present discussion.

For completeness, it is noted that in all of these aforemen-tioned cases, only the cationic species are changed. Theinfluence of fluorine addition was studied by Lines inthe alkali silicate system.16 Fluorine is known to reduce therefractive index and, when added into glass with small alkaliconcentrations, it was found also to decrease @e/@C. For flu-orine concentrations up to 2 wt% (N.B., weight percent; notmole percent as previously employed), the total attenuationof low alkali content (fluoro)silicate was shown to bereduced by 15-20% relative to fused silica. This is instructivesince, below, examples will be provided on multicomponent

CAVILLON ET AL. | 449

oxyfluoride glass that are used to further tailor Raman scat-tering and the nonlinear refractive index, n2.

The point of this section has not been to provide anexhaustive literature survey of multicomponent glasses forlow loss optical fibers. Instead it has been to offer a fewexamples of how simple, well known and studied glasssystems, offer opportunities for reducing what are todaythe performance-limiting parasitic effects in some of themost advanced optical fiber laser and communicationsystems.

Table 1 provides the general trends in selected proper-ties of interest to this work with the addition of saiddopants into SiO2. As can be seen, in each case, com-pounds can be found that either increase or decrease agiven property, and so the consideration here is to identifythose compounds that suitably reduce each or, preferably,several nonlinearities, while forming a homogeneous coreglass that meets the aforementioned practicality conditions;this is no simple task. Where no trend (arrow) is given, thedirection of the change with said compound into silica hasnot yet been determined.

3 | COMPOSITIONAL EFFECT ONINDIVIDUAL OPTICALNONLINEARITIES

As noted above, it is infeasible to thoroughly review theimpact of each possible compound on all of the materialproperties that influence the parasitic nonlinearities dis-cussed in this trilogy. Accordingly, this section discussescompositional effects of a few compounds and compoundfamilies that have been shown to influence each nonlinear-ity in the manner desired. Section 5 then takes these indi-vidual considerations and brings them together into acommon set of exemplar fibers.

3.1 | Brillouin scattering

As detailed in Companion Paper I,1 spontaneous Brillouinscattering materially depends on the refractive index, trans-verse photoelastic coefficient, and adiabatic compressibility.In its stimulated form (SBS), the Brillouin gain coefficient,BGC, is materially dependent upon the Brillouin linewidth,

TABLE 1 General property trends on addition of noted compound into silicaa

Compound

Physicalb BrillouinbSTRSb Ramanb Wave-Mixingb

n q CTE Va DmB p12 dn/dT Vm n2

SiO2c 1.444 2200 0.55 9 10�6 5970 17 0.226 10.4 9 10�6 27.31 2.5 9 10�20

GeO2 ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑

F ↓ ↓ ↑ ↓ ↓ ↓

P2O5 ↑ ↑ ↑ ↓ ↑ ↑ ↓ ↑

B2O3 ↓ ↓ ↑ ↓ ↑ ↑ ↓ ↑

Al2O3 ↑ ↑ ↑ ↑ ↑ ↓ � ↑ ↑

Yb2O3 ↑ ↑ ↓ ↓ ↑

La2O3 ↑ ↑ ↓ ↓ ↑

Lu2O3 ↑ ↑ ↓ ↓ ↑

MgO ↑ ↑ ↑ ↑ ↓

CaO ↑ ↑ ↑

SrO ↑ ↑ ↑ ↓ ↑ ↓ ↓ ↓

BaO ↑ ↑ ↑ ↓ ↑ ↓ ↑ ↑

Li2O ↑ ↑ ↑ ↑ ↓ ↓ ↓

Na2O ↑ ↑ ↑ ↓ ↓

K2O ↑ ↑ ↑ ↓ ↓

Y3Al5O12 ↑ ↑ ↑ ↑ ↓ ↑

aTrend strictly valid over homogeneous glass-forming range and for the binary composition with silica. Ternary and n-ary glasses may show equivalent trends butwill depend on the relative concentrations of each component. Additionally, trends presume that no new phase or structure is formed such as with the mixed alkalieffect61,62 or in the Al2O3-P2O5 system where both Al2O3 and P2O5 increase the refractive index, for example, when individually added to silica but decrease it whenboth Al2O3 and P2O5 are added in equal proportions to silica due to the formation of AlPO4.

63

bProperty abbreviations and units: n is the linear refractive index [dimensionless], q is the density [kg/m3], CTE is the coefficient of thermal expansion [K�1], VA isthe acoustic velocity [m/s], DmB is the Brillouin linewidth [MHz], p12 is the transverse photoelastic coefficient [dimensionless], dn/dT is the thermo-optic coefficient[K�1], Vm is the molar volume (cm3/mol), and n2 is the nonlinear refractive index (m2/W).cValues for silica: refractive index, n, measured at a wavelength of 1550 nm. Brillouin linewidth, DmB, measured in MHz at a Brillouin frequency of 11 GHz.


DmB, (which is inversely proportional to the phonon life-time) in addition to the factors noted above. Accordingly,to determine the magnitude of Brillouin scattering or, forthe more specific purposes of these works, the BGC, oneneeds either to directly measure or accurately deduce thefollowing material properties: refractive index, p12 photoe-lasticity, density, acoustic wave velocities, and Brillouinspectral width.

Considerable literature exists detailing compositionaleffects on refractive index and density. To a lesser extent,photoelasticity and acoustic wave velocities (hence, elasticconstants and, therefore, adiabatic compressibility values)are known as are, to an even lesser extent, Brillouin spec-tral widths. Furthermore, care should be taken when citingphotoelastic coefficients from the literature since many con-ventional methods for their determination measure magni-tude but not sign, the latter being quite critical here.

Figure 1 provides an overlay of the Brillouin gain coef-ficient, relative to a conventional telecommunications opti-cal fiber, as a function of non-SiO2 content of the coreglass composition. More specifically, it depictsBGClog ¼ 10Log10ðBGCcore=BGCSMF�28Þ where the BGCsin the operand are in units of m/W. Consequently, wherethe BGC goes to zero, the graph takes on a singularity thatextends to �∞ on the vertical scale. This composition is

referred to as Zero Brillouin Activity, or ZeBrA.17 Figure 1is equivalent to Figure 6 in Companion Paper IIB,3 whichemploys data from Table 1 in Companion Paper IIB,3

except that experimental values are overlaid here as theopen color-coded circles to show the fit between measure-ments and modeling. For completeness, the compositionaldependencies in Figure 1 (and Figure 6 in CompanionPaper IIB3) on the p12 photoelasticity values are those fromFigure 5 in Companion Paper IIA,2 remembering that theBrillouin gain coefficient is proportional to p12

2.From the perspective of specific glass systems to be

employed for the reduction of Brillouin scattering, severalfeatures of interest are observed in Figure 1. The first, andperhaps most obvious features are the minima that areshown for selected binary and ternary silicates; particularlyfor alkaline earth silicates (eg, barium and strontium sili-cates) and sesquioxide silicates (eg, aluminosilicates andlanthanum aluminosilicates). As noted in Companion PaperI,1 the p12 photoelasticity has the potential to take on avalue of zero and, under such conditions, Brillouin scatter-ing then goes to zero. It is further worth noting that,despite the possibility to completely eradicate an otherwisefundamental physical phenomenon, a reduction in BGC of>15 dB is sufficient for the present and foreseeable futurefiber-based systems. If one focuses instead on the �15 dBpoints for each curve, and not these singular ZeBrA points,then considerable compositional ranges exhibiting thisreduction exist.

A second feature is that the (modeled) curve associatedwith the YAG-derived yttrium aluminosilicate (Y2O3-Al2O3-SiO2) fiber does not show such a BGClog ? �∞minima18 while the (modeled) curve for lanthanum alumi-nosilicate (SiO2-Al2O3-La2O3; SAL) does.

19 In the yttriumaluminosilicate fiber, single crystalline YAG (Y3Al5O12)was employed as the core precursor during the moltencore fabrication. In the lanthanum aluminosilicate fiber, ahomogenous SAL glass rod was first made and thenemployed as the core phase in a rod-in-tube fiber drawarrangement. In conducting the modeling, per those meth-ods outlined in Companion Paper IIB,3 the measured datafit both systems best when the properties of crystallineYAG were employed in the former case and the propertiesof a mixture of La2O3 and Al2O3 were used in the latter.Since homogeneous crystalline YAG possesses a small butpositive p12 value,18 when mixed with the p12 > 0 SiO2

(p12 = 0.226 at a wavelength of 1550 nm for fused silica),there is no composition where the resultant “YAG-derived” silicate glass would show a BGClog ? �∞feature.

For the SAL fiber, the measured Brillouin gain data fitbest when the individual La2O3 and Al2O3 components,along with SiO2, were used. Based on the known proper-ties of fused silica, along with previously additivity-

FIGURE 1 Relative Brillouin gain coefficient, BGC (in decibels,dB), relative to conventional, telecommunications single-mode fiber(SMF-28TM) as a function of non-silica concentration (in molepercent) for a variety of molten core-derived optical fibers. Thecurves are modeled results based on the additivity approachesdescribed in Companion Papers II 2,3 and the open circles, color-coded to match the glass systems associated with the model curves,are experimental results. Data on each fiber and specific compositionsof the ternaries are provided in the associated References noted[Color figure can be viewed at wileyonlinelibrary.com]


deduced properties of the Al2O3 component from measure-ments on aluminosilicate glasses, contributions from theLa2O3 components also can be deduced and are shown inTable 1 in Companion Paper IIB.3 Based on the p12 < 0values deduced for Al2O3 and La2O3, the resultant (mod-eled) curve exhibits the p12 = 0 minima. This clearly is apoint for continued study: other than being the source ofthe individual components, what other roles might the form(crystal vs glass, homogeneous vs heterogeneous powder)of the precursor play in the properties of the final glassfiber? For completeness, the compositions achieved are notespecially near the ZeBrA compositions for either of theseglasses and so perhaps the argument is moot and one sim-ply cannot extrapolate property trends over the entire rangeof compositions. Over what range of compositions thencan property values be extrapolated is another question forcontinued study.

As a brief aside, it is of direct benefit to the amplifierand laser fibers that these sesquioxides lower the Brillouingain coefficient when added into silica. Sesquioxide Al2O3

is added to silica in order to reduce the thermodynamic ten-dency for rare-earth dopant clustering. Such clusteringdiminishes the quantum efficiency of the light emission.20–22 Accordingly, the typical dopants employed for makingactive silica-based optical fibers are intrinsically low Bril-louin materials, although, in most applications, their con-centrations are fairly low (~few weight percent) and so theeffect is less obvious.

In conclusion, with respect to this section, while theconventional dopants into SiO2 that are employed in com-munication optical fibers do lower the Brillouin gain coeffi-cient (Figure 6 in Companion Paper IIB3), markedly lowerBGC values are possible when compounds possessing neg-ative p12 values are incorporated into silica, whose p12 ispositive. This “mean value theorem” additivity yieldsp12 = 0 compositions that could, if realized in practice,negate Brillouin scattering. As will be discussed in moredetail below, dopants of choice for reduced Brillouin scat-tering are the alkaline earth oxides, (AE)O, specificallySrO and BaO. They possess the most negative p12 valuesdeduced to date and have miscibility limits in SiO2 of 42and 40 mol%, respectively,23 although subsolidus meta-stable immiscibility is known.24 The inclusion of 5-10 mol% Al2O3 has proven an effective approach to miti-gating phase separation at high (AE)O concentrationsshould glass formation be problematic25; see the (Classical)Rayleigh Scattering section.

3.2 | Raman scattering

In both its spontaneous and stimulated forms, Raman scatter-ing is reduced for glasses comprised of compounds possess-ing low molar volume, Vm, and small bond compressibility

parameters, Λ; specifically, PRamanS / Vm � K2.* As two

points of reference: (a) in the well-studied alkali halidesystem, Λ decreases with both increasing cationic(ΛLi > ΛNa > ΛK > ΛRb for a given halide) and anionic(ΛF > ΛCl > ΛBr > ΛI for a given cation) mass 26–28 and (b)of greater relevance here, Λ for SiO2 is quite small (0.1) andtends to increase with increasing modifier content.15,29 Giventhe few tangible material parameters that directly influenceRaman scattering and, for those factors, the scarcity of avail-able data on their magnitude as a function of composition,Figure 2 provides a meager compilation of results from morecommon glass systems. The data employed in Figure 2 iseither directly provided or computed from Refs. 27,30–32and the fractional cationic concentrations were calculated perLines.29

While the bond compressibility parameter is not asdirectly measureable as is, for example, the photoelasticcoefficient(s), as noted in Companion Paper I, Λ does takeon positive and negative values depending on the molecu-lar structure and polarizability of the compound at hand.Thus, at least in theory, Λ = 0 (Λ2 = 0) glasses could be

FIGURE 2 The product Vm 9 Λ2 (molar volume and squaredbond compressibility parameter), which is proportional to the totalRaman scattering intensity,1,29 as a function of non-silica cationicfraction for a series of binary and ternary oxide glasses.30 Linesconnecting data within each glass family are guides-to-the-eye. SiO2

is included as a point of reference [Color figure can be viewed atwileyonlinelibrary.com]

*Two points of caution for the reader planning to use the data fromRef. 30. First, note the typographical error in Table 1 of Ref. 30, wherethe refractive index value for the 15Al2O3-33Na2O-52SiO2 glass should be1.51229. Second, as noted by Lines,29 if the reader is interested in com-puting the hydrostatic photoelasticity, p = ð1=3Þ½p11 þ 2p12� � p12�ð2=3Þjp44j, then the ½(p11-p12) values provided in Table 1 of Ref. 30should be preceded by a negative sign.


possible. However, as with all nonlinearities, diminution isof greater practical consequence than eradication.

Figure 3 provides a compilation of measured relativepeak Raman scattering values for a variety of fibers studiedfor their intrinsically low optical nonlinearities. The Ramanscattering data shown in Figure 3 were obtained as dis-cussed in Companion Paper II using a normalization proce-dure similar to that in Ref. 33.

Care should be taken in comparing the results of Fig-ures 2 and 3. As noted, Figure 2 is comparing the bondcompressibility and molar volume, which are proportionalto the total Raman scattering intensity. Figure 3 is compar-ing the Raman gain coefficient, which is proportional tothe peak Raman intensity suitably normalized. If 2 mole-cules scatter with equivalent (spontaneous) Raman strength,but 1 molecule has twice the spectral bandwidth (or twiceas many spectral components), then it will exhibit half thepeak Raman gain coefficient.

Additionally, the Raman response is dependent both onthe polarizability of the species, the overlap of each species’Raman spectral components, and the degree of disorder inthe glass structure. For example, as discussed in Ref. 34,relative to yttrium aluminosilicate glasses, the molten core-derived core possessed broader SiO2-related Raman spectralfeatures than the pure SiO2 cladding, implying a morerandom molecular structure. Additionally, there is littleoverlap between the Raman peaks of the individual compo-nents in these multicomponent glasses. As a result, both the

peak SiO2 scattering intensity is reduced by virtue of alower silica content in the resultant glass, and the broaderdistribution of Raman spectral features yields a reducedintensity at any given wave-number. These “structural” fac-tors are not accounted for in the theories that yielded Fig-ure 2 and suggest that the glass structure (and fiber drawprocessing) may be more deterministic in measured Ramanscattering intensity for a given family of glasses.

Interestingly, Λ also factors into laser damage thresh-olds; a separate but still important factor in the practicalityof the HEL fibers considered in this trilogy. More specifi-cally, Λ, which formally is defined asK ¼ �ðoa=aÞ=ðoq=qÞ,35 can be evaluated through the rela-tionship: qðdn=dqÞ ¼ ð1� KÞqðon=oqÞ. As noted by Wax-ler, a material with zero qðon=oqÞ value (or Λ = 1) wouldexhibit no electrostrictive effects, including laser damage or(electrostrictive) self-focusing.36,37 Perhaps the more impor-tant lesson here is that, fundamentally, there are only ahandful of material parameters/coefficients that relate tomost (optical) phenomena; for example, Table 2 in Com-panion Paper I.1 It is in this simplicity that the sophistica-tion of a unified materials approach to reducingnonlinearities originates.

Lastly, and for completeness, although not shown inFigure 3, conventional telecommunication dopants, namelyGeO2, B2O3, and P2O5, all possess larger Raman scatteringcross sections than SiO2.

38 More specifically, the relativeRaman cross sections are about 5, 6, and 9 times larger forB2O3, P2O5, and GeO2 than for SiO2, respectively.

38 Fur-thermore, GeO2 is well known to increase the nonlinearrefractive index, n2, of silicate glasses;39 see Figure 4 inCompanion Paper IIB.3 Accordingly, for the purposes ofthis Trilogy, these dopants will not be considered otherthan to provide baseline comparisons for the intrinsicallylow nonlinearity glasses discussed later against conven-tional optical fiber core compositions.

3.3 | (Classical) Rayleigh scattering

As relates to HEL fibers, losses are not as critical as in long-haul communication fibers since path lengths are markedlyshorter than for telecomm fibers. For example, an oceanicfiber cable can extend several thousand kilometers, whereasan amplifier or laser fiber typically is 10-20 m in length. Thisis not to say that loss is irrelevant, lower losses are alwayspreferred. However, the attenuation of telecommunicationfibers is specified as being <0.2 dB/km, whereas for laserfiber’s, the attenuation is typically <10-20 dB/km.

From Companion Paper I,1 it is known that 2 contribu-tions to Rayleigh scattering exist in optical fibers; thoserelating to fluctuations in concentration (composition) andin density. Materially, the intensity associated with concen-tration-related scattering is linearly proportional to the

FIGURE 3 Relative peak Raman gain coefficient, relative to thatof pure SiO2 versus cationic fraction for a series of binary and ternaryoxide and oxyfluoride core optical fibers reported in the Referencesnoted. Dashed lines connecting data within a specific glass family areguides-to-the-eye. SiO2 is included as a point of reference. The corecompositions represent those of the initial precursor compounds usedto fabricate the fibers [Color figure can be viewed atwileyonlinelibrary.com]


fictive temperature, quadratically proportional to the changein dielectric constant with composition (@e/@q), and inver-sely proportional to the change in chemical potential withcomposition. The chemical potential approximately scalesinversely with the difference between the fictive and spin-odal temperatures.1,31 Accordingly, for large (Tf-Ts), oneprefers then a system with no immiscibility or, for thosethat do, lower TS values are better.

From the perspective of specific systems, as noted in Com-panion Paper I,1 a glass system that possesses both refractiveindex and density values that are roughly independent of com-position should exhibit intrinsically low Rayleigh scattering.As an example, binary borosilicates (B2O3-SiO2) possessreduced @e/@q values, whereas binary alkali silicates exhibitreduced <Dq2> values.12 Accordingly, the sodium borosili-cate system is particularly interesting because it exhibitsreduced Rayleigh scattering due to these combined effects.

With respect to increasing (Tf-Ts), one approach wouldbe the addition of alumina, which is known to aid in glassformation by shifting the upper consulate point to lowertemperatures.21 In other words, relative to a compositionwithout Al2O3, an alumina-containing glass will exhibitphase separation at a larger degree of undercooling, wherekinetics are slower and such instability is therefore lesslikely. Accordingly, in a system containing Al2O3, (Tf-Ts)would be larger, which suggests that Rayleigh scatteringshould be reduced; all other properties being equal.Another approach to increasing (Tf-Ts) is to use an isostruc-tural additive that reduces the upper consulate point relativeto that compound it is replacing.10

Contributions to Raleigh scattering associated with den-sity fluctuations are materially dependent on the refractiveindex, n, the fictive temperature, Tf, the photoelasticitycoefficient, p [p = p12 + (2/3)p44], and the adiabatic com-pressibility, KS, through the elastic stiffnesses.1 Of thesedependencies, the trend with refractive index is most pro-nounced, scaling as n8, followed by that with photoelastic-ity, scaling as p2, and then linearly with Tf and KS.

From the perspective of specific glass systems, the samecompounds discussed above with respect to reduced Bril-louin scattering are useful here for reducing the p12 contri-bution to photoelastic influences on Rayleigh scattering. Inthe limiting case of a p12 = 0 zero Brillouin Activity“ZeBrA” composition, only the p44 contribution wouldremain as a photoelastic contributor for Rayleigh scattering.Taken from the other perspective, p44 = 0 glasses have notonly been identified but have been realized.40,41 Represen-tative glasses include those in the SnO-B2O3, SnO-P2O5,SnO-SiO2, PbO-B2O3, PbO-P2O5, and PbO-SiO2 fami-lies.41,42 Unfortunately, these glasses all exhibit high refrac-tive indices and low melting points making them unlikelycandidates for the silica-clad fibers preferred in this Tril-ogy. That said, they do represent excellent systems through

which to study the underlying correlations between glasschemistry and structure and optical physics.

Figure 4 provides the photoelastic properties of theseglasses, along with those for silica and selected commercialglasses and crystals.10,26,27,31,41,43–45 As a general trend, theoxide glasses tend to exhibit larger p12 values than dohalide crystals. Furthermore, PbO-based glasses, includingthe SF6 dense flint glass, possess near-zero p44 values. Ofparticular interest is YAG, which has both p12 and p44 val-ues quite near to the p = 0 line. Accordingly, YAG-derivedyttrium aluminosilicate glasses might be of interest forintrinsically low Rayleigh scattering optical fibers.

As noted in Table 1 of Companion Paper I,1 the den-sity-related component of Rayleigh scattering would go tozero for a glass possessing a zero hydrostatic photoelastic-ity value, p = 0. This is analogous to the p12 = 0“ZeBrA” condition for Brillouin scattering previouslymentioned. Accordingly, Figure 4 also displays thep = p12 + (2/3)p44 = 0 line. Assuming equivalent additiv-ity of p to that of p12 discussed in Companion PaperIIA,2 Section 4 that follows will discuss potential p = 0compositions that would negate this contribution to Ray-leigh scattering. As noted in Companion Paper I,1 whileRayleigh is not a limitation in high-power laser systems,any scattering may contribute to other stimulated pro-cesses or, more generally, loss. Thus, any diminution inscattering is generally of benefit.

3.4 | Transverse mode instability (TMI)

As noted in Companion Paper I,1 transverse mode instabil-ity is widely believed to be associated with stimulated ther-mal Rayleigh scattering (STRS). From a materialsperspective, per Dong,46 TMI-related mode coupling viaSTRS is proportional to the thermo-optic coefficient (short-ened to TOC or dn/dT in the text) and inversely propor-tional to the product of density with heat capacity.

From this, two important considerations arise as relatesto this Trilogy. First is that, over the range of glass compo-sitions from which practical HEL fibers are made, neitherthe density nor heat capacity (or thermal conductivity47)change very much.48 The second, and perhaps more impor-tant consideration, is that the thermo-optic coefficient hasthe potential to take on a value of zero; see, for example,Figure 2 of Companion Paper IIB.3 In an analogous mannerto which p12 = 0 negates Brillouin scattering, dn/dT = 0would negate STRS, although, again, negating such physi-cal properties are not always needed in practice as long assufficient reductions are achieved. Accordingly, for the pur-poses of this work, dopants into silica that yield reductionsin the thermo-optic coefficient, such as B2O3 and P2O5, (or,at least, do not dramatically raise dn/dT values, such as thealkaline earth oxides) will be considered further.


Exemplifying this is Figure 5, which represents thedependence of TOC/q (heat capacity not considered sinceit changes very little with composition) for three canonicalglass families treated in this Trilogy. Values deduced usingthe additivity models presented in Companion Paper IIA2

and, in the particular case of the TOC, values do not takeinto account thermal expansion mismatches with the clad-ding. Of note here, as expected based on the dn/dT = 0potential in the B2O3-SiO2 and P2O5-SiO2 systems, suchzero STRS glasses are identified and will be further dis-cussed in Section 4.

4 | PROPERTY VALUECOMPOSITIONAL DIAGRAMS

The underlying goals of this Trilogy are to explicate thefundamental physical origins of performance-limiting non-linear phenomena in optical fibers, determine or deducetheir material dependencies, and identify glass families andcompositions that collectively reduce all of the parasiticeffects. In other words, to create a path to the “perfectfiber;” that is, an optical fiber that exhibits intrinsically lownonlinearities based on the materials from which it is madeand not through geometric/waveguide microstructuring.

Prior activities investigating the effect of variousdopants have largely focused on binary systems for reasonsof simplicity in trying to understand the underlying factorsat play. Examples of how the nonlinearities scale withcomposition of single additives into SiO2 can be found in

Figure 2 above, for the Brillouin gain coefficient (BGC),and in Figure 2 in Companion Paper IIB,3 for the thermo-optic coefficient that drives TMI. Since no single additiveis likely to reduce all of the parasitic nonlinearities to thelevels desired, more complex multicomponent systems needto be studied and their influences understood.

Accordingly, this section provides ternary propertyvalue diagrams of representative intrinsically low nonlinear-ity glass systems for continued consideration and develop-ment. Such representations are useful for gauging globaltrends and property dependencies within a given composi-tional family. These examples are chosen principallybecause they exhibit the properties that most effectivelylead to significant reductions in optical nonlinearities, suchas p12 = 0, p = 0, or dn/dT = 0 compositions which would,respectively, negate Brillouin scattering, density-dependentRayleigh scattering, and stimulated thermal Rayleigh scat-tering (STRS). They represent, in the authors’ opinion, theglasses having the best potential to achieve the singleintrinsically low nonlinearities optical fibers that are thegoal of this Trilogy.

In accordance with Table 1, the following compoundsare, therefore, more specifically considered:

• SiO2: Glass formation, thermal and mechanical stability,high laser damage threshold, compatibility with existingfibers and global manufacturing processes. SiO2 alsoexhibits a very low Raman cross section and nonlinearrefractive index.Needs Attention: Additives to reduce p12 and dn/dT (seebelow).

• Al2O3: Facilitates glass formation, hence lowers Ts,which reduces Rayleigh scattering; and has (slightly)negative p12 value. Its large longitudinal acoustic veloc-ity can be used to make a fiber acoustically antiguidingand decrease the phonon lifetime (broaden DmB). It isalso known to reduce photo-darkening, and can allowgreater introduction of active rare-earth ions relative tosilica.Needs Attention: Additive for reduction in dn/dT.

• BaO or SrO: Strongly negative p12 value to reduce Bril-louin and density-related Rayleigh scattering; althoughwould likely contribute to stronger Raman scattering andwave-mixing given the higher molar volume, (likely)bond compressibility, and polarizability of these heavymetal oxides. However, when added to silica in fairlylow proportion (up to 10-15 mol%), it reduces the mag-nitude of the Raman gain.Needs Attention: Additive(s) to offset increased n and n2values as well as dn/dT of BaO (SrO is found todecrease it relative to silica).

• P2O5: Negative dn/dT values, which, when incorporatedinto silica (dn/dT > 0), offer potential to negate STRS,

FIGURE 4 Compilation of p12 and p44 photoelastic coefficientsfor a variety of glasses, glass families, and crystals (measured at awavelength of 632 nm). Rayleigh scattering scales quadratically withthe Pockels coefficient, p = p12 + (2/3)p44. Also shown are linesrepresenting a zero Pockels coefficient material, where Rayleighscattering would be zero. Data taken from the References noted[Color figure can be viewed at wileyonlinelibrary.com]


hence greatly reduce TMI. P2O5 facilitates reducedphoto-darkening.

• B2O3: Glasses containing B2O3 typically exhibit lowerdensity, linear and nonlinear refractive indices, negativedn/dT value; and significantly increases Brillouin line-width.Needs Attention: Both B2O3 and P2O5 greatly increaseRaman gain relative to silica, but only a small additionmay be beneficial such as for alkaline earth oxides. Fur-thermore, effect of B2O3 on photo-darkening has not yetbeen determined.

• Alkali oxides: Lowers Tf and facilitates glass formation,which reduces Rayleigh scattering.Unfortunately, beyond Li2O,

49 insufficient data existfrom which to deduce all of the properties of interesthere, so these glasses, including alkali boro- and alumi-nosilicates, will not be discussed, but clearly representareas for further study. That said, there is considerablereason to further investigate their role in reducing para-sitic optical nonlinearities given their known potentialfor reducing Rayleigh scattering at small concentra-tions.15,16

The property value ternary diagrams treated next do notinclude fluorine or fluorides. This is because, to date, theexact bonding of the fluorine in the multicomponent sili-cate systems investigated has not been determined. Since,therefore, the exact compound composition cannot bedetermined, then neither can properties be deduced basedon the additivity procedures of Companion Paper II. Thatsaid, the following compounds, and related oxyfluorideglasses, are worthy of further consideration.

• F: Reduces linear (n) and nonlinear (n2) refractiveindices; reduces Raman scattering and increases ten-dency for binary systems to phase separate/devitrify.50

• Alkaline earth fluorides: Reduces n, n2, dn/dT, and,likely, Raman scattering.

• Rare-earth fluorides: Rare-earth ions make the glass lightemissive while the fluorine contributes to off-setting theindex-raising qualities of the rare-earth.

4.1 | Caveats

The section that follows begins by providing propertyvalue representations for selected ternary and quaternaryglass systems based on the compounds noted above.Specifically, compositional trends in the transverse photoe-lastic coefficient, p12, the hydrostatic photoelastic coeffi-cient, p, and the thermo-optic coefficient [(dn/dT), TOC].These coefficients are chosen because they materially influ-ence Brillouin scattering, density-related Rayleigh scatter-ing, and stimulated thermal Rayleigh scattering, whichmediates TMI. Furthermore, among the material parametersthat factor into each parasitic nonlinearity, these are theones that change most with composition and, most impor-tantly, they have the potential to take on values of zero.

Compositional representations for Raman scattering andnonlinear wave-mixing will not be provided since, at pre-sent, there are insufficient data available on the governingmaterial properties (specifically Λ and n2) to deduce com-positional trends. However, as shown in Paper IIB,3 whenthose properties are known (eg, GeO2

39), the additivityapproaches seem to offer sufficient accuracy for the pur-poses of this work in identifying glass families and compo-sitional ranges for intrinsically low nonlinearity opticalfibers.

SiO2 is employed as a base constituent in all cases con-sidered in this Section for reasons of practicality; specifi-cally that silicate core compositions would be mostcompatible with an SiO2 cladding that would yield highstrength, potentially low loss, and integration with conven-tional fibers to which these fibers would be spliced; forexample, pump couplers. That said, as long as attenuationlevels were suitably low and strength were to be sufficient,there is no practical reason why a core/clad preform withdesired NA and dimensions could not be fashioned anddrawn using these multicomponent glasses directly.

Lastly, the diagrams that follow cover the entire ternarycompositional regions and are not limited to specific glass-forming regions. The reasoning for this is 3-fold: (i) theirpurpose is to show global compositional trends; (ii) theglass-forming “limits” are not well known for all of thesesystems; and (iii) glass-forming is kinetically enabled anddependent on the glass (or fiber) forming method. It is

FIGURE 5 Effect of composition on the quotient of thermo-optic coefficient (TOC, dn/dT) and density, which is proportional tothe stimulated thermal Rayleigh scattering (STRS) couplingcoefficient.46 STRS is widely held to originate transverse modeinstabilities (TMI) in high-power fiber lasers [Color figure can beviewed at wileyonlinelibrary.com]


known that, for example, the molten core approach enablesfiber compositions that are not possible using conventionalmelting/casting or optical fiber chemical vapor depositionsmethods.4,51 Hence, future efforts and approaches may con-tinue to open up the compositional space over which glassoptical fibers can be achieved.

Prior to delving into each nonlinearity individually (andthen collectively), Figure 6 provides a representative exam-ple for the Brillouin gain coefficient, BGC in theSrO-Al2O3-SiO2 system. The associated Al2O3-SiO2 andSrO-SiO2 BGC binaries are overlaid to illustrate the com-plementary nature of this graphical approach. As expected,although Zero Brillouin Activity (ZeBrA) occurs at a singlecomposition in a binary system, it occurs over a range ofcompositions in a ternary system. In addition to providinga simple graphical representation of compositional depen-dence on the parasitic nonlinearities, this approach alsoprovides a simple way to visualize wide ranges of compo-sitions that meet selected criteria, such as a �30 dB sup-pression in Brillouin gain coefficient relative to aconventional fiber, which is shown as the dashed lines con-necting the binaries to the associated edges of the ternaryin Figure 6.

4.2 | Intrinsically low (classical) Rayleighscattering glasses

As a brief reminder, Rayleigh scattering arises from fluctu-ations in both composition and density.1 Admittedly, com-positional contributions are more difficult to estimate givenunknown additivity/deduction of fictive temperatures andchemical potential. As such, just the contributions associ-ated with density will be considered in this Section. Thatsaid, while both the refractive index and isothermal com-pressibility (through the elastic constants) can be estimated,only the photoelasticity (p) will be discussed as it, of thematerial factors influencing Rayleigh scattering, has themost reasonable potential to take on a value of zero or, atleast, be significantly reduced.

Based on deduction of the photoelasticity as describedin Companion Paper IIA,2 Figure 7 provides property valuediagrams for hydrostatic photoelasticity coefficient,p = p12 + (2/3)p44, for selected compositional families forthe compounds noted above. In the glass systems com-monly employed in telecommunication fibers (GeO2, P2O5,and B2O3), there are no markedly interesting effects toemploy. The inclusion of Al2O3, however, begins to drivereductions in aggregate p values due to its low photoelas-ticity. This is further exemplified with alkaline earth oxidedopants, notably SrO and BaO, whereby p = 0 composi-tions can be identified. At these compositions, density con-tributions to Rayleigh scattering should be zero andmarked reductions in the overall Rayleigh scattering should

be significant. Again, as noted in Companion Paper I,1

while Rayleigh scattering is not, per se, a parasitic nonlin-earity as relates to high energy fiber lasers, it can seedother stimulated processes. Furthermore, it contributes tothe fiber’s base attenuation. Accordingly, any reduction ofRayleigh scattering is beneficial.

4.3 | Intrinsically low transverse modeinstability glasses

Mode instabilities in “effectively single mode” large modearea optical fibers are driven by thermo-optic effects asso-ciated with stimulated thermal Rayleigh scattering (STRS).As noted in Companion Paper I, STRS is distinct from the“classical” Rayleigh scattering just treated.1 Based on theadditivity approaches of Companion Paper IIA,2 thededuced thermo-optic coefficients for the glass familiestreated herein are provided in Figure 8.

With respect to conventional telecommunicationdopants, P2O5 and B2O3 possess negative dn/dT values,whereas GeO2 and SiO2 possess positive ones. Accord-ingly, compositions exhibiting intrinsically low thermo-optic effects can be realized using conventional fibermaterials and processes, although compatibility with indexprofiles and modality may be challenging. Of the additionaldopants identified in this Trilogy, the alkaline earth oxidesagain show intriguing opportunities for low and possiblyzero dn/dT values at high SiO2 concentrations. For com-pleteness, it is worth noting that one would normallyexpect SrO and BaO to behave somewhat similarly. Thedifferences in compositional thermo-optic trends shown inFigure 8 between the SrO-P2O5-SiO2/BaO-P2O5-SiO2 andSrO-Al2O3-SiO2/BaO-Al2O3-SiO2 ternaries result from theTOC for BaO being positive, whereas the TOC for SrO isnegative.3

4.4 | Intrinsically low Brillouin scatteringglasses

In a similar manner, the deduced transverse p12 photoelas-ticity values are shown in Figure 9 for the same glass fami-lies. The counterplay between positive and negative p12compounds that was discussed in Companion Papers I andII,1–3 can most clearly be seen in the ternaries comprisingAl2O3, SrO, and BaO. As expected, given the weak andonly slightly negative p12 value for Al2O3, the zero p12compositions necessarily occur at Al2O3 concentrations toohigh to likely be feasibly made into glass and drawn intofibers.

However, both SrO and BaO possess sufficiently largeand negative p12 values that it is reasonable to expect thatbulk glasses could be formed at p12 = 0 ternary composi-tions where Brillouin scattering should be negated.


Although mapping out individual material parameters,for example, p, TOC, and p12, that most influence a givennonlinearity is useful, it is more impactful to understand,where able, all of the underlying factors taken together.Such a complete property value ternary representation isshown in Figure 10 for the Brillouin gain coefficient,BGC, associated with the same systems as described above.Each of the factors used to compute the BGC, as describedin Companion Paper I,1 were deduced using the approachesdescribed in Companion Papers II.2,3

Given the dependence of the BGC on multiple proper-ties (n, p12, q, Va, DmB), each one possessing its own com-positional trends, the curvature of the contour lines aremore complicated than in the single property ternary dia-grams; for example, Figures 7-9. In the ternary diagrams,this manifests interesting and occasionally unexpected com-positional trends.

The individual BGC binaries that comprise the GeO2-,P2O5-, B2O3-related ternaries with SiO2 were shown in Fig-ure 6 of Companion Paper IIB 3 and, not surprisingly, thosetrends are equally evident in Figure 10. In short, whilesome reductions (3-8 dB) in BGC result from doping SiO2

with these conventional telecommunication dopants, theydo not offer marked mitigations. Important (>10 dB)

reductions are possible with p12 < 0 dopants, such asAl2O3, SrO, and BaO. As noted with respect to Figure 9, itis the large and negative p12 values of the alkaline earth oxi-des that lead to significant (>15 dB) reductions in BGCeven at reasonably high SiO2 concentrations of about80 mol%.

The representations of Figure 10 can be overlaid withsimilarly important reductions in other parameters, such asin the TOC that drives transverse mode instability (TMI).As a case in point, Figure 11 provides a comparison ofcompositions that provide significant reductions in bothSBS (>15 dB) and TMI (>5 dB), relative to conventionalsingle-mode fiber, based on the BGC and TOC propertyvalue diagrams of Figures 10 and 8.

5 | MODELING OF THE HIGH-POWER/-ENERGY PERFORMANCE

The power scaling potential of the intrinsically low nonlin-earity fibers fabricated to date were modeled using the pro-cedures described in Ref. 52. These results, compared tovalues for conventional Yb3+-doped silica fiber lasers, arepresented in Figure 12 with the underlying known and

FIGURE 6 Representative ternaryproperty diagram of Brillouin gaincoefficient, BGC, in units of dB relative toa conventional single-modetelecommunications optical fiber (SMF-28TM), as a function of composition in theSrO-Al2O3-SiO2 system. The associatedbinary BGC diagrams for the SrO-SiO2 andAl2O3-SiO2 systems also are shown as aguide-to-the-eye regarding trends in theternary. Values are deduced using theapproaches described in Companion PaperIIA2 [Color figure can be viewed atwileyonlinelibrary.com]


estimated material parameters provided in Table 2. As inRef. 52, the simplest fiber geometry is assumed (noadvanced waveguide schemes) and for the SBS-limitedcase, single frequency amplification is assumed. Controlledline broadening is well known to increase the SBS-limitedoutput power, however, when this technique is employed,53

one must understand the acceptable line-broadeningallowed by the application as well as the SBS linewidth ofthe proposed material. The SBS linewidth is not includedin Table 2 and is not relevant to Figure 12 due to theassumption of single frequency amplification for the SBS-limited case.

It is important to note that the research by Dawsonet al,52 pre-dates the discovery of transverse modal instabil-ity, TMI.46,54 Given that a simple predictive model fortransverse modal instability is still not fully formed and

agreed upon, included here is the better understood effectof thermal lensing as an (imperfect) proxy for transversemodal instability. A study of Table 2 will reveal that anumber of important material properties are not known forthe candidate all-glass fibers treated: YAG-derived yttriumaluminosilicates,18 sapphire-derived aluminosilicates,51 andlow-silica content strontium aluminosilicates.25 Of these,damage threshold and thermal conductivity are the greatestsources of uncertainty in the calculation that produced Fig-ure 12.

The graphs in Figure 12 are generated by the methodol-ogy of Dawson et al.52 In this methodology, the physicaleffects that limit the power scaling of a single-fiber laserare expressed as functions of fiber core diameter and fiberlength. All parameters except core diameter and fiberlength are either state-of-the-art parameters (such as diode

TABLE 2 Material parameters employed for the calculation of power scaling plots based on Ref. 52

Property (unit)aConventionalvalue for SiO2

YAG-derivedyttriumaluminosilicates

Sapphire-derivedaluminosilicates

Low-silica strontiumaluminosilicates

Non-SiO2 Content (mole %) – Al2O3: 19.9Y2O3: 12.6

Al2O3: 54.0 SrO: 23.7Al2O3: 15.0

Rupture ModulusRm (W/m)b

4300 4300 4300 4300

Thermal Conductivityj (W/m/K)b

1.38 1.38 1.38 1.38

Convective film coefficienth (W/m2/K)b

10000 10000 10000 10000

Melt temperatureTm (K)b

1983 1983 1983 1983

dn/dT (K�1) 11.8 9 10�6 10.1 9 10�6 11.9 9 10�6 5.3 9 10�6

gR (m/W) 1 9 10�13 0.52 9 10�13 0.54 9 10�13 0.5 9 10�13 (est.)

BGC (m/W) 5 9 10�11 0.5 9 10�11 3.1 9 10�13 2.2 9 10�13

Ac 20 20 20 20

Gc 10 10 10 10

Гc 0.8 0.8 0.8 0.8

Damage thresholdIdamage (W/lm2)

35 35 35 35

Tc (K)c 300 300 300 300

Ipump (W/lm2/sr)c 0.1 0.1 0.1 0.1

acore (dB/m)d 250 1500 1500 1500

glaserc 0.85 0.85 0.85 0.85

gheatc 0.1 0.1 0.1 0.1

NAc 0.45 0.45 0.45 0.45

k (nm)c 1088 1088 1088 1088

aWhere not specified, see Ref. 52 for details on a given property.bValues are unknown for the 3 aluminosilicate systems but, given their relatively high SiO2 contents, the values for silica are employed as a limit.cValues reasonably carried over to the 3 aluminosilicate systems.dTailorable via precursor Yb concentration.


FIGURE 7 Contribution of density fluctuations to Rayleigh scattering: ternary diagrams of hydrostatic photoelasticity coefficient,p = p12 + (2/3)p44, for selected compositional families. Values are deduced using the approaches described in Companion Papers II2,3 [Colorfigure can be viewed at wileyonlinelibrary.com]


FIGURE 8 Stimulated thermal Rayleigh scattering (STRS): ternary diagrams of thermo-optic coefficient, TOC (dn/dT), for selectedcompositional families. Values are deduced using the approaches described in Companion Papers II2,3 [Color figure can be viewed atwileyonlinelibrary.com]


FIGURE 9 Brillouin scattering: ternary diagrams of transverse photoelasticity coefficient, p12, for selected compositional families. Valuesare deduced using the approaches described in Companion Papers II2,3 [Color figure can be viewed at wileyonlinelibrary.com]


FIGURE 10 Stimulated Brillouin scattering (SBS): ternary diagrams of the Brillouin gain coefficient, BGC, for selected compositionalfamilies. Values are deduced using the approaches described in Companion Papers II2,3 [Color figure can be viewed at wileyonlinelibrary.com]


laser brightness, which is generally improving with time)or physical constants of the material system, which are var-ied to greater extent in this trilogy. The main physicaleffects that are considered are thermal (melting, rupture,lensing), optical nonlinearities (SRS and SBS, note theseare typically considered on separate plots depending uponwhich one dominates based on laser spectral line-width),optical damage and limitations on pump power. Pumppower limitations come about from the necessity for ahigh-power laser to be efficient in order to be practical.This requirement means that most of the pump light mustbe absorbed in the length of the fiber. Thus, Dawsonet al52 show that if the fiber length is known, then thecore diameter, doping concentration, and state-of-the-artdiode brightness determine the allowed fiber claddingdiameter, which in turn limits the total coupled pumppower. As the fiber laser efficiency is typically ~85%, this,

in turn, creates a power-limit based on the amount ofpump power that can be efficiently coupled into the fiberlaser.

The contour plots in Figure 12 are formed by calculat-ing all the physical limits for each pair of coordinates(core diameter and fiber length) and plotting the lowestlimit. What emerges are regions where different limitsdominate. At the smallest core diameters and shortestlengths (lower left hand corner of the graphs), the pump-coupling limit typically dominates. For large core diame-ters and short fiber lengths (lower right side of the plots),the heat load per unit length is high and thermal effectstypically are dominant. For small core diameters and longlengths (upper left side of the plots), the light is intenseover a long length of fiber and either damage or nonlinearoptical effects limit the fiber output power. A key findingof Dawson et al52 is that the interaction of thermal and

FIGURE 11 Representative ternary compositional diagrams overlaying both Brillouin gain coefficient, BGC, and thermo-optic coefficient,TOC, relative to those for conventional telecommunications single mode fiber, for the reduced magnitudes for these nonlinearities that are thegoal of this Trilogy [Color figure can be viewed at wileyonlinelibrary.com]


FIGURE 12 Power scaling diagrams representing the threshold optical power levels where power scaling is limited by either pumpbrightness, laser damage, thermal lensing, and (A) stimulated Raman scattering (SRS) and (B) stimulated Brillouin scattering (SBS) regimes. Inboth sets of Figures, the optical fibers modeled are: (i) conventional SiO2,

52 (ii) YAG derived yttrium aluminosilicate glass,18 (iii) sapphirederived aluminosilicate glass,51 (iv) strontium aluminosilicate glass.25 Property values that yielded these modeled results are provided in Table 2.The maximum achievable power is noted in the box [Color figure can be viewed at wileyonlinelibrary.com]


nonlinear effects typically set a hard upper limit on outputpower from a single optical fiber laser for a given materialsystem that is largely independent of core diameter andfiber length, although there is a specific length associatedwith each core diameter at which this limit is attained.Below, the variations of material parameters considered inthis paper are discussed in terms of how they affect therelative size of the regions and ultimate scaling limit of agiven material system.

Four main parameters are assumed to be improved inthe three materials: rare-earth doping concentration, TOC(dn/dT), Raman, and Brillouin gain coefficients. The pri-mary impact of increased doping concentration is to reducethe parameter space over which limited pump-couplingdominates the fiber laser output power. More specifically:

• YAG-derived yttrium aluminosilicates: A slight increasein the SRS-limited power due to reduced Raman gaincoefficient is observed as is an expected reduction inpump-limited parameter space. However, this reductionis offset by the formation of a damage threshold-limitedregion (again, accurate knowledge of the damage thresh-old is needed). The SBS-limited case shows a > three-fold increase in output power due to a significantreduction in the BGC. Importantly, this is attained at a40 lm core diameter due to the reduction in the pump-limited parameter space.

• Sapphire-derived aluminosilicates: As with the YAG-derived glass, slight improvements are observed in theSRS-limited case other than the reduction in the pump-limited zone and appearance of the damage-limited zone.However, there is now a dramatic increase in the SBS-limited power to >10 times the conventional silica case.This is a direct result of the 100 times decrease in BGC.Core size remains in the 40 lm region, a relatively prac-tical zone from the standpoint of both fabrication andbending.

• Low-silica strontium aluminosilicates: In this case a 2time increase in power in the SRS-limited power isobserved due to the reduced Raman gain and reducedTOC. Here, the calculation’s exclusion of an analysis ofTMI is cause for some skepticism of this result. TheSBS-limited case shows a further increase in the SBS-limited power due to the additional reduction in the SBSgain coefficient as well as the reduction in TOC.

Overall, these results show promise for improved mate-rials for high-energy lasers, particularly narrow bandwidthlasers limited by SBS. The improvements are predomi-nantly due to the increase in doping concentration (reduc-tion in SiO2 content), which allows the maximum power tobe attained at smaller core diameters which reduces thermaleffects in general, and is known to be desirable for

decreased TMI as the purely single-mode waveguideregime is more effectively maintained. Furthermore, dra-matically reduced Brillouin gain greatly raises the powerthreshold for the onset of SBS. Note the maximum powerin the SBS case increases as the square root of the recipro-cal of the BGC per Equation 27 in Ref. 52. This suggestsfurther development of these classes of materials are apromising approach for scaling power in SBS-limited fiberlaser systems with the caveat that a number of the assumedmaterial parameters in Table 2 need to be determined andFigure 12 needs to be updated to validate that the true val-ues of these parameters do not affect the conclusions madehere.

6 | TOWARD THE “PERFECT”OPTICAL FIBER

With respect to the best results to date, “best,” is some-what arbitrary as the ideal case is one where all of thenonlinearities are reduced by levels that make the fibermore practical. For example, while ~20 dB suppressionhas been achieved in a sapphire-derived, high-alumina-content aluminosilicate glass fibers,51 these fibers werehighly multimoded and exhibited a 2.5 dB suppression inRaman gain. In terms of collective reductions in nonlin-earities, as is the focus of this Trilogy, an oxyfluoridefiber might represent a “better” opportunity in that initialefforts already have shown nearly single mode operationwith worthy reductions in gR (�0.9 dB), dn/dT(�2.2 dB), and BGC (�6.3 dB), relative to conventionaloptical fiber.55

This section stakes a flag in the ground for the “perfect”fiber. As noted in Table 1 of Companion Paper I,1 anddescribed in terms of specific compositions in this paper,each of the parasitic nonlinearities possess the potential tobe wholly negated. In some cases, such as with Ramanscattering and n2-related wave-mixing, the necessary condi-tions of Λ = 0 and n2 = 0, respectively, although theoreti-cally possible, seem at present not materially practical.However, the two main phenomena that presently limitpower scaling in high-power fiber laser systems, namelySBS and TMI, should be quite reasonably mitigated. Inthese cases, the p12 = 0 and dn/dT = 0 conditions, respec-tively, are well-defined over large, yet practical, composi-tional ranges. Of particular interest are compositionalspaces where these zero points approximately coincide.Examples of these are those shown in Figure 13, which,along with the aforementioned p12 = 0 and dn/dT = 0 com-positions, includes p = 0 compositions where the density-related contribution to Rayleigh scattering also would bezero.


Admittedly (and purposefully) provocative, the compo-sitions identified herein that exhibit markedly reduced col-lective nonlinearities are beyond the capabilities of industrystandard CVD processes used to fabricate conventional(telecom) optical fibers. High-silica-content CVD-derivedfibers will remain the industry standard for long-haul com-munications with evolutionary progress in attenuation beingmade through process-related thermal history (fictive tem-perature1,56) and minor dopant engineering.15,16 However,to be clear, in order to achieve the power scaling goals ofhigh-power/-energy, high beam quality fiber-based lasers,conventional CVD processes will not be sufficient due tothe limited compositional ranges such processes mandate asnoted in the Section 1. Structural/geometric approaches,such as those associated with microstructured and photoniccrystal fibers, employing conventional CVD-derived highsilica content glasses, certainly will continue to make incre-mental improvements. But, revolutionary advances such as>20-30 dB reductions, or even the wholesale negation ofBrillouin-related SBS and thermo-optic-related STRS-induced TMI, can only be achieved through a unified mate-rials approach, whereby parasitic nonlinearities areaddressed at their fundamental origins. This will necessitatethe fiber laser community to adopt a new mindset as relatesto the centrality of glass science and engineering.

To date, the molten core method appears to be the bestapproach to achieve optical fibers possessing the intrinsi-cally low nonlinearity compositions identified in this Tril-ogy. This is due in large part to the fact that many of the

compositions are inherently prone to phase separation. Assuch, bulk glass melting followed by rod/tube fabricationand conventional drawing may not yield high quality, lowloss fiber.

While the molten core approach has proven its composi-tional flexibility, future efforts need to focus on reducingattenuation. Although there is nothing intrinsic about theprocess that should lead to enhanced optical losses, threefactors seem to contribute most significantly to the mea-sured attenuation values. First, the purity of the precursorphase is paramount. The lowest loss molten core-derivedfibers to date have been those fabricated using commercialsingle crystals; specifically the yttrium aluminosilicate glassoptical fibers derived from single crystalline yttrium alu-minum garnet (YAG), which exhibited losses on the orderof 100 dB/km.57 Second, the presence of OH species inthe glass also can lead to parasitic losses. In the moltencore-derived fibers, the OH content also depends on thenature of the core precursors employed. When commer-cially grown bulk crystals are employed, the OH contentscan be quite low. The (single crystal) sapphire-derived alu-minosilicate fibers described originally in Ref. 51, exhib-ited virtually no measured additional OH-related losses.Fibers derived from commercial powders, such as the BaO-derived bariosilicate of Ref. 58 exhibited higher OH-relatedlosses; ~ 8dB/m at a characteristic wavelength of 1390 nm.Third, extrinsic losses may also arise from scattering due tonanoscale phase separation associated with some of thecompositions detailed herein traversing liquid-liquid

FIGURE 13 Ternary compositional diagrams in the SrO-Al2O3-SiO2, and BaO-P2O5-SiO2 systems showing the ranges over which thehydrostatic photoelasticity, p, the transverse photoelasticity, p12, and the thermo-optic coefficient, dn/dT (TOC), are each zero. At compositionswhere they intersect, the glass should exhibit no Brillouin scattering (p12 = 0), density-related Rayleigh scattering (p = 0), and stimulated thermalRayleigh scattering (TOC = 0); the latter driving transverse mode instabilities in high-power fiber lasers [Color figure can be viewed atwileyonlinelibrary.com]


immiscibility regions on cooling from above the upper con-solute point to their glassy state as the (molten core) fiberdraws. Such immiscibilities can be lessened by the additionof alumina,59 for example, which would also further reducethe BGC and gR of the resultant glass.

Interestingly, and importantly, the ~100 dB/km valueachieved to date is only a factor of only 2-5 times higherthan the 20-50 dB/km level considered practical for laserand amplifier fibers since use-lengths are on the order 10-15 meters. Indeed, as noted above, sub-20-30 dB/km lossvalues have been obtained from powder-derived fibers8,60

so achieving optical fibers with practical losses from suchhighly modified silicate compositions is not unreasonable.

7 | CONCLUSIONS

This paper provides a road map to glass compositions thatwould markedly reduce the optical nonlinearities that pla-gue the scaling to higher output powers in presenttelecommunication and high-power fiber lasers. Morespecifically, based on the theoretical foundations of Com-panion Paper I,1 coupled with the property additivity rela-tions of Companion Papers II,2,3 described here arecompositional trends to tailor Brillouin-, Raman-, Ray-leigh-, thermo-optic-, and v(3)-related material properties.Examples from existing fibers and bulk glasses aregenerated where data are available. Furthermore, ternaryproperty value diagrams are generated to more easilyrepresent and identify compositional regions where thegreatest opportunities for mitigating nonlinearities arepossible. In the specific case of yttrium and strontiumaluminosilicate fibers, variations in the material could leadto power increases of 2-39 or more over current fiberlasers based on classical fused silica compositions. Notethis is before other effects such as deliberate line widthbroadening or advanced waveguide design are employedto further scale the output power. Furthermore, the impactof higher concentration by itself should not be underesti-mated as it simplifies the overall requirements on thediode laser portion of the integrated system. Oxyfluoridealuminosilicate glasses containing alkaline earth com-pounds, potentially with B2O3 and P2O5 additions, areespecially worthy of further consideration based on theirpotential to significantly reduce Brillouin, Raman, Ray-leigh, and stimulated thermal Rayleigh scattering whilepossessing a nonlinear refractive index comparable to con-ventional silica and could potentially lead to much greaterpower scaling if, for example, the BGC could be reducedbeyond that assumed in Table 2.

Secondary intentions of this work are to reassert thepower of glass science in the performance of modern opticalfibers and to evoke a reconsideration of the processing

methods employed for the fabrication of specialty opticalfibers (eg, molten core). As shown in this Trilogy, the abilityof glasses that are based on common compounds to exhibitsuch remarkable performance, such as the potential to negateoptical nonlinearities, which is impossible even in the mostcomplex and sophisticated microstructured and photoniccrystal fiber designs, certainly supports the goal of theseintentions.

Lastly, and with purposeful provocation, is the hopethat this Trilogy serves as a clarion call for the develop-ment and acceptance of new material and fabricationapproaches to be considered and evaluated. This is actuallyborn out of the realization that conventional CVD pro-cesses are incompatible with the compositions identifiedherein as enabling truly revolutionary material-drivenadvances in optical power scaling in fiber laser systems.The primary focus on high-energy fiber lasers makes sucha prospect not unreasonable given that relatively short fiberlengths (tens of meters) are employed and higher losses(~20 dB/km) than required for long-haul communicationsare acceptable. With apologies to Oren Harari, the readersof this Trilogy, along with members of the broader glass,fiber, and laser communities are reminded that the laserdid not arise from continuous improvements to the lightbulb.

ACKNOWLEDGMENTS

The authors thank Drs. Siva Mani, Matt Leigh, and SarwatChappell of the US Department of Defense High EnergyLaser Joint Technology Office (HEL JTO) for posing theoriginal question that led to this Trilogy. Thoughtful dis-cussions with Profs. Liang Dong (Clemson University),Roger Stolen (Clemson University), and Anna Peacock(University of Southampton) also are gratefully acknowl-edged as is the financial support from the US Departmentof Defense High Energy Laser Joint Technology Office(HEL JTO) through sustained support over many yearsincluding contracts: W911NF-05-1-0517, FA9550-07-1-0566, W911NF-12-1-0602, FA9451-15-D-0009/0001 and0002, and N00014-17-1-2546. The J. E. Sirrine Foundationalso is gratefully acknowledged for supporting the effortsof Authors (JB, MC, CK, and TH). A portion of this workwas performed under the auspices of the U.S. Departmentof Energy by Lawrence Livermore National Laboratoryunder Contract DE-AC52-07NA27344 (JD).

ORCID

Peter D. Dragic http://orcid.org/0000-0002-4413-9130John Ballato http://orcid.org/0000-0001-5910-3504


http://orcid.org/0000-0002-4413-9130

http://orcid.org/0000-0002-4413-9130

http://orcid.org/0000-0002-4413-9130

http://orcid.org/0000-0001-5910-3504

http://orcid.org/0000-0001-5910-3504

http://orcid.org/0000-0001-5910-3504

REFERENCES

1. Ballato J, Cavillon M, Dragic PD. A unified materials approachto mitigating optical nonlinearities in optical fiber. I. Thermody-namics of optical scattering. Int J Appl Glass Sci. 2018 in press.

2. Dragic PD, Cavillon M, Ballato A, et al. “A unified materialsapproach to mitigating optical nonlinearities in optical fiber. II.A. Material additivity models and basic glass properties. Int JAppl Glass Sci. 2018a in press.

3. Dragic P, Cavillon M, Ballato A, et al. A unified materialsapproach to mitigating optical nonlinearities in optical fiber. II. B.The optical fiber, material additivity and the nonlinear coeffi-cients. Int J Appl Glass Sci. 2018b, submitted.

4. Ballato J, Dragic PD. Rethinking optical fiber: new demands, oldglasses. J Am Ceram Soc. 2013;96:2675-2692.

5. Schuster K, Unger S, Aichele C, et al. Material and technologytrends in fiber optics. Adv Opt Technol. 2014;3:447-468.

6. Oh K, Paek U-C. Silica Optical Fiber Technology for Devicesand Components: Design, Fabrication, and International Stan-dards. New York, NY: John Wiley & Sons; 2012.

7. Morris S, Ballato J. Molten core fabrication of novel opticalfibers. Bull Am Ceram Soc. 2013;92:24-29.

8. Shibata S, Mitachi S, Takahashi S. High numerical aperture mul-ticomponent glass fiber. Appl Opt. 1980;19:1484-1488.

9. Pinnow D, Rich T, Ostermayer F, et al. Fundamental optical atten-uation limits in the liquid and glassy state with application to fiberoptical waveguide materials. Appl Phys Lett. 1973;22:527-529.

10. Schroeder J, Mohr R, Macedo P, et al. Rayleigh and Brillouin scat-tering in K2O-SiO2 glasses. J Am Ceram Soc. 1973;56:510-514.

11. Laberge N, Vasilescu V, Montrose C, et al. Equilibrium com-pressibilities and density fluctuations in K2O–SiO2 glasses. J AmCeram Soc. 1973;56:506-509.

12. Tynes A, Pearson AD, Northover WR. Rayleigh scattering lossesin soda borosilicate glasses. J Am Ceram Soc. 1979;62:324-326.

13. Pinnow D, Van Uitert L, Rich T, et al. Investigation of the sodaaluminosilicate glass system for application to fiber opticalwaveguides. Mater Res Bull. 1975;10:133-146.

14. Tsujikawa K, Ohashi M. Mixed-alkali effect on Rayleigh scatter-ing in K2O–Na2O–MgO–SiO2 glasses. J Am Ceram Soc.2000;83:660-662.

15. Lines ME. Can the minimum attenuation of fused silica be signif-icantly reduced by small compositional variations? I. Alkali metaldopants. J Non-crystal Solids. 1994;171:209-218.

16. Lines ME. Can the minimum attenuation of fused silica be signif-icantly reduced by small compositional variations? II. Combinedfluorine and alkali metal dopants J Non-crystal Solids.1994;171:219-227.

17. Dragic PD, Ballato J, Morris S, et al. Pockels’ coefficients of alu-mina in aluminosilicate optical fiber. J Opt Soc Am B.2013;30:244-250.

18. Dragic PD, Law P-C, Ballato J, et al. Brillouin spectroscopy ofYAG-derived optical fibers. Opt Exp. 2010;18:10055-10067.

19. Dragic PD, Kucera C, Ballato J, et al. Brillouin scattering proper-ties of lanthano-aluminosilicate-core optical fiber. Appl Opt.2014;53:5660-5671.

20. Arai K, Namikawa H, Kumata K, et al. Fluorescence and its Nd3+

concentration dependence of Nd-doped SiO2 glasses prepared byplasma torch CVD. Jpn J Appl Phys. 1983;22:L397-L399.

21. Hatta B, Tomozawa M. Effect of Al2O3 on phase separation ofSiO2 – Nd2O3 glasses. J Non-Crystal Solids. 2008;354:3184-3193.

22. Ballato J, Dragic P. On the clustering of rare earth dopants infiber lasers. J Dir Energy. 2017;6:175-181.

23. Shelby JE. Effect of morphology on the properties of alkalineearth silicate glasses. J Appl Phys. 1979;50:8010-8015.

24. Seward T, Uhlmann DR, Turnbull D. Phase separation in the sys-tem BaO-SiO2. J Am Ceram Soc. 1968;51:278-285.

25. Cavillon M, Furtick J, Kucera C, et al. Brillouin properties of anovel strontium aluminosilicate glass optical fiber. J LightwaveTechnol. 2016;34:1435-1441.

26. Coker H. The electronic strain polarizability constants of thealkali halides. J Phys Chem Solids. 1979;40:1079-1088.

27. Kucharczyk W. Photoelastic effect and density derivative of therefractive index in alkali halides. J Phys Chem Solids.1989;50:709-712.

28. Sharma HP, Shanker J, Verma MP. Evaluation of strain polariz-ability parameter in alkali halides. J Phys Chem Solids.1977;38:255-256.

29. Lines ME. A possible non-halide route to ultralow loss glasses. JNon-Crystal Solids. 1988;103:279-288.

30. Schroeder J. Brillouin scattering and Pockels coefficients in sili-cate glasses. J Non-Crystal Solids. 1980;40:549-566.

31. Lines ME. Scattering losses in optical fiber materials: I. A newparameterization. J Appl Phys. 1984;55:4052-4057.

32. Lines ME, MacChesney J, Lyons K, et al. Calcium aluminateglasses as potential ultralow-loss optical materials at 1.5 –

1.9 lm. J Non-Crystal Solids 1989;107:251-260.

33. O’Donnell MD, Richardson KC, Stolen RH, et al. Raman gain ofselected tellurite glasses for IR fibre lasers calculated from spon-taneous scattering spectra. Opt Mater. 2008;30:946-951.

34. Dragic PD, Ballato J. Characterization of the Raman gain spectrain Yb:YAG-derived optical fibers. Electron Lett. 2013;49:895-897.

35. Mueller H. Theory of photoelasticity in amorphous solids. Phys.1935;6:179-184.

36. Waxler R. Laser glass composition and the possibility of elimi-nating electrostrictive effects. IEEE J Quant Electron.1971;7:166-167.

37. Feldman A, Horowitz D, Waxler R. Mechanisms for self-focus-ing in optical glasses. IEEE J Quant Electron. 1973;9:1054-1061.

38. Galeener FL, Mikkelsen JC, Geils RH, et al. The relative Ramancross sections of vitreous SiO2, GeO2, B2O3, and P2O5. ApplPhys Lett. 1978;32:34-36.

39. Nakajima K, Ohashi M. Dopant dependence of effective nonlin-ear refractive index in GeO2-and F-doped core single-modefibers. IEEE Photon Technol Lett. 2002;14:492-494.

40. Guignard M, Albrecht L, Zwanziger JW. Zero-stress optic glasswithout lead. Chem Mater. 2007;19:286-290.

41. Galbraith J. Photoelastic properties of oxide and non-oxide glasses.Doctoral dissertation, Dalhousie University Halifax, Canada; 2014.

42. Galbraith J, Chapman L, Zwanziger JW, et al. Elasto-optic coeffi-cients of borate, phosphate, and silicate glasses: determination byBrillouin spectroscopy. J Phys Chem C. 2016;120:21802-21810.

43. Dixon RW. Photoelastic properties of selected materials and theirrelevance for applications to acoustic light modulators and scan-ners. J Appl Phys. 1967;38:5149-5153.

44. Benassi P, Mazzacurati V, Ruocco G, et al. Elasto-optic constantsin silicate glasses: experiment and theory. Phys Rev B.1993;48:5987.

45. Chang IC. Acoustooptic devices and applications. IEEE TransSonics Ultrason. 1976;23:5987-5996.


46. Dong L. Stimulated thermal Rayleigh scattering in optical fibers.Opt Exp. 2013;21:2642-2656.

47. Freeman JJ, Anderson AC. Thermal conductivity of amorphoussolids. Phys Rev B. 1986;34:5684-5690.

48. Van Uitert L. Relations between melting point, glass transitiontemperature, and thermal expansion for inorganic crystals andglasses. J Appl Phys. 1979;50:8052-8061.

49. Dragic PD, Ryan C, Kucera CJ, et al. Single- and few-modedlithium aluminosilicate optical fiber for athermal Brillouin strainsensing. Opt Lett. 2015;40:5030-5033.

50. Markis JH, Clemens K, Tomozawa M. Effect of fluorine on thephase separation of Na2O-SiO2 glasses. J Am Ceram Soc.1981;64:C20.

51. Dragic PD, Hawkins T, Morris S, et al. Sapphire-derived all-glassoptical fibers. Nat Photon. 2012;6:629-635.

52. Dawson J, Messerly M, Beach R, et al. Analysis of the scalabilityof diffraction-limited fiber lasers and amplifiers to high averagepower. Opt Exp. 2008;16:13240-13266.

53. White JO, Vasilyev A, Cahill JP. Suppression of stimulated Bril-louin scattering in optical fibers using a linearly chirped diodelaser. Opt Exp. 2012;20:15872-15881.

54. Eidam T, Wirth C, Jauregui C. Experimental observations ofthreshold-like onset of mode instabilities in high power fiberamplifiers. Opt Exp. 2011;19:13218-13224.

55. Cavillon M, Kucera C, Hawkins T, et al. Oxyfluoride core silicaoptical fiber with intrinsically low nonlinearities for high energylaser applications. IEEE J Lightwave Technol. 2017 in press;https://doi.org/10.1109/jlt.2017.2731602.

56. Tajima K. Low-loss optical fibers realized by reduction of Ray-leigh scattering loss. In: Optical Fiber Communication Confer-ence and Exhibit Technical Digest. Piscataway, NJ: Institute ofElectrical and Electronics Engineers; 1998:305-306.

57. Ballato J, Hawkins T, Foy P, et al. On the fabrication of all-glassoptical fibers from crystals. J Appl Phys. 2009;105:053110.

58. Dragic PD, Kucera C, Furtick J, et al. Brillouin spectroscopy of anovel baria-doped silica glass optical fiber. Opt Exp.2013;21:10924-10941.

59. Tomozawa M, Obara R. Effects of minor third components onmetastable immiscibility boundaries of binary glasses. J AmCeram Soc. 1973;56:378-381.

60. Minelly J, Ellison A. Applications of antimony-silicate glassesfor fiber optic amplifiers. Opt. Fiber Technol. 2002;8:123-138.

61. Isard J. The mixed alkali effect in glass. J Non-Cryst Solids.1969;1:235-261.

62. Ingram M. The mixed alkali effect revisited-a new look at an oldproblem. Glastech Ber. 1994;67:151-155.

63. DiGiovanni DJ, MacChesney J, Kometani T. Structure and prop-erties of silica containing aluminum and phosphorus near theAlPO4 join. J Non-Cryst Solids. 1989;113:58-64.

How to cite this article: Cavillon M, Kucera C,Hawkins T, Dawson J, Dragic PD, Ballato J. Aunified material approach to mitigating opticalnonlinearities in optical fiber. III. Canonicalexamples and materials road map. Int J Appl GlassSci. 2018;9:447-470. https://doi.org/10.1111/ijag.12336


https://doi.org/10.1109/jlt.2017.2731602

https://doi.org/10.1111/ijag.12336

https://doi.org/10.1111/ijag.12336

A unified materials approach to mitigating optical ...righini/TC20/Ballato_Mitigating Nonlinearities III... · optical fibers whose enhanced performance—in particular, marked reductions

Documents