Optical Materials 36 (2014) 608–610

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Optical Materials

journal homepage: www.elsevier .com/locate /optmat

Stress-induced birefringence for the Er3+: Y2O3 ceramic system

0925-3467/$ - see front matter � 2013 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.optmat.2013.10.037

⁄ Corresponding author.E-mail address: abhijeet@ucla.edu (A. Joshi).

Abhijeet Joshi ⁄, Oscar M. StafsuddDepartment of Electrical Engineering, University of California, Los Angeles, CA 90095, United States

a r t i c l e i n f o a b s t r a c t

Article history:Received 23 June 2012Received in revised form 14 October 2013Accepted 29 October 2013Available online 2 December 2013

Keywords:BirefringenceStress-opticLaser materialsCeramics

The stress-induced birefringence for erbium doped yttria ceramics were measured at room temperature.An ellipsometer was used to measure the retardation effect of static loading on a set of ceramic equilat-eral prisms and the stress-optic co-efficients were obtained. The samples measured were equilateralprisms of pure Y2O3, (Er0.1Y0.9)2O3 and (Er0.2Y0.8)2O3. The stress-optic co-efficients were found to be inthe range 1.6 M 2.5 � 10�5 [nm/cm]/Pa showing no dependence on erbium concentration.

� 2013 Elsevier B.V. All rights reserved.

1. Introduction fect is to squeeze the rod radially. This causes birefringence in the

Ceramic yttria (Y2O3) has become a material of interest to makegain media for high-power solid-state lasers. The physical charac-terization of such a material is crucial for engineering laser devices.Data for the refractive index and temperature-dependent change inthe refractive index for erbium doped ceramic yttria was providedpreviously [1]. Here we provide the stress-optic coefficients for thesame material system.

Thermal optical distortion in laser materials stems from energydissipated as heat in the material as the laser is pumped optically.The dissipating heat causes two physical effects on the index ofrefraction n of the solid-state laser material.

n ¼ n0 þ Dnthermal þ Dnstress

The first effect, Dnthermal, is the change in refractive index of the mate-rial with the temperature of the material. This effect is characterizedby calculating the thermo-optic coefficients of the material by directmeasurement of the change in refractive index as a function of thetemperature of the material (dn

dT ½ 1�C�). The second effect, Dnstress, is thechange in polarizability of the medium with the application of con-strictive stress, which is in turn due to the change of the material vol-ume due to temperature. Applied stress causes a change in refractiveindex of the material in differing directions which gives rise to bire-fringence affecting the polarization of the transmitted light. Thestress-optic coefficient Retardation

AppliedPressure ½nm=cm

Pa � characterizes this effect.

Considering the rod design routinely employed while buildingwater-cooled solid-state lasers, the thermal flux from flash-lampsor diode pumps causes expansion of the clamped laser-rod. The ef-

radial and tangential direction throughout the length of the rod. Asa consequence, a linearly polarized beam propagating through thegain medium will experience phase retardation as a function of thelength of the rod (see Fig. 1).

During operation, lasers are subjected to various mechanicalforces including stresses within the laser-rod mount, thermally in-duced stresses generated from thermal gradients, pressure gradi-ents, vibrations, etc. For design verification and inspection duringoperation, it is desirable to have a full aperture description of theeffect of the stress field on light passing through the laser rod.These birefringence measurements fulfill these conditions.

Ceramic laser gain media are now gaining prominence due tothe various advantages ceramics have over single crystal hosts. Asimple stress-optic law is most notably one of them. We have mea-sured the stress-optic behavior of erbium-doped yttria at varyingconcentrations of the dopant using He–Ne laser illumination.

Ceramic materials, such as Y2O3 or ceramic YAG, are made up ofcrystallites with particles with sizes ranging from �100 nm to�10 lm [2]. And although individually the crystallites might beanisotropic in character, when in the random arrangement that de-fines this class of material, we may safely assume isotropy in bulk.Therefore, fine grained ceramics are expected to behave as amor-phous or isotropic media with a stress-optic matrix described by,

p11 p12 p12 0 0 0p12 p11 p12 0 0 0p12 p12 p11 0 0 00 0 0 � 0 00 0 0 0 � 00 0 0 0 0 �

0BBBBBBBB@

1CCCCCCCCA

Fig. 1. The compressed ends of the laser rod impose stress on the laser rod causingbirefringence. This is also related to thermal lensing.

A. Joshi, O.M. Stafsudd / Optical Materials 36 (2014) 608–610 609

where the � components are proportional to the difference be-tween the non-zero p11 and p12 components. A stress in the X direc-tion results in a uniaxial optical medium with the index for lightproperties in the Y–Z plane, i.e. perpendicular to the stress, havingindices of refraction of,

nY ¼ nZ ¼ n0 � 12ðn0Þ3p12r

In the direction of the stress, the index of refraction is,

nX ¼ n0 � 12ðn0Þ3p11r

In the isotropic case we have, nY = nZ since the p components areequal. r is the stress load applied [3].

The experiment performed directly gives us the birefringence inpolarization when light passes through the media. The birefrin-gence B can then be written as,

Bnmcm

h i¼ Dn� k½nm�

length½cm� ¼D/

180�� k½nm�

length½cm�

2. Experimental

Retardation caused by static-loading was studied in a polaro-scopic arrangement in which the angular phase change was

Fig. 2. Schematic of the experimental set-up. The measurements were carried outat the angle of minimum angle of deviation.

Fig. 3. Stress-Optic behavior fo

measured for samples with varying concentrations of the rare-earth dopant.

A polarized beam from a He–Ne laser served as a probe. Afterstatic loading and the subsequent polarization phase shift, theprobe light suffered depolarization and was partially transmittedby the analyzer.

The polaroscopic experiment was constructed around a high-accuracy ellipsometer (Rudolph Scientific, angular measurementaccuracy of 0.001�), with the sample stage modified to hold incre-mental static loads of up to 1 � 106 Pa (rmax ¼ 1� 106 Pa) (seeFig. 2 for the schematic of the setup).

The control sample was a fused silica prism, roughly of the samedimension as the ceramic prisms. The known stress-optic coeffi-cient for fused quartz is �3.52 � 10�5 ½nm=cm

Pa � [4]. It compares well

with our value of 3.54 � 10�5 ½nm=cmPa � (see Fig. 3).

The samples were transparent ceramic equilateral prisms ofpure Y2O3, (Er0.1Y0.9)2O3 and (Er0.2Y0.8)2O3. They were producedby hot-isostatic pressing (HIP) using nanocrystalline precursors[5]. The samples were subsequently cut into prisms (approxi-mately 2 cm high and 1.5 cm in length) and mirror polished.

All the measurements were at the minimum angle of deviationdmin, ensuring minimum variation in the signal beam as it propa-gated through the prism due to minor disturbances of the setupduring loading and unloading.

3. Results and discussion

The stress-optic coefficients (Fig. 4, Table 1) characterize the ef-fect of mechanical stress applied to ceramic yttria doped to varyingpercentages of active rare-earth dopants.

There have not been, to the authors’ knowledge, publicly avail-able numbers for the thermal expansion coefficient for ceramic yt-tria or any sort of correlation to the presented stress-opticnumbers. The closest system studied is yttria-stabilized zirconia(with an a � 10�5 range around 600–700 K [6]), which is

r the UV-quartz standard.

Table 1Stress-optic coefficients.

Sample SO co-eff. [nm/cm]/Pa

Undoped Y2O3 1.781 � 10�5

5% Y2O3 1.928 � 10�5

10% Y2O3 2.481 � 10�5

20% Y2O3 1.627 � 10�5

Fig. 4. Stress-Optic behavior for the erbium doped yttria (0%, 5%, 10% and 20% at. wt.).

610 A. Joshi, O.M. Stafsudd / Optical Materials 36 (2014) 608–610

significantly different from bulk ceramic yttria made up of crystal-lite particles. There has been a recent publication of refractive in-dex data on the ceramic material, along with the change in therefractive index due to temperature [1].

We expect the results presented here will provide quantitativeoptical characterization of the erbium doped yttria system.

The results show retardation on the order of 1 M 3 � 10�5 nano-meters per centimeter for every pascal of load the sample is placedunder. The plots are also linear, indicating an application of loadswell within the elastic region of deformation.

The results show no dependence on the increasing amount ofthe erbium ion. Other properties such as the refractive indices [1]and the unit cell size on the other hand do differ, even if veryslightly. The unit cell sizes of the sesquioxide forms of Y2O3 andEr2O3 are noted to be a = 10.605 ± 0.001 Å (for yttria) anda = 10.550 ± 0.001 Å (for the erbium sesquioxide) [7].

4. Conclusion

The operation of liquid-cooled, high-powered lasers (PkWrange) demand sharp constraints on the limits of physical defor-mation due to high heat loads. Ensuring a material can withstandthe heat loads and, furthermore, that has a predictable change isa major concern. The above report adds to the amount of informa-tion regarding ceramic media that are now gaining interest as fu-ture high-powered gain media.

The rich infra-red lasing behavior shown by erbium in insulat-ing hosts drove the decision to study this particular system.

We expect this information along with the thermal-effect onthe refractive index of the similar ceramic samples previously re-ported [1] to be of value for the ceramic yttria laser materialsystem.

References

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[2] A. Joshi, O.M. Stafsudd, K. Serivalsatit, J. Ballato, Multiphonon-based comparisonof erbium-doped yttria in large, fine grain polycrystalline ceramics andprecursor forms, Optical Materials 34 (1) (2011) 95–98.

[3] J.F. Nye, Physical Properties of Crystals, Oxford Science Publications, 1985.[4] N.K. Sinha, Normalised dispersion of birefringence of quartz and stress optical

coefficient of fused silica and plate glass, Physics and Chemistry of Glasses 19(4) (1978).

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[6] Hideko Hayashi, Tetsuya Saitou, Naotaka Maruyama, Hideaki Inaba, KatsuyukiKawamura, Masashi Mori, Thermal expansion coefficient of yttriastabilized zirconia for various yttria contents, Solid State Ionics 176 (5–6)(2005) 613–619.

[7] E. Staritzky, Crystallographic data. 144–147. Rare earth oxides. Yttriumsesquioxide, Y2O3; dysprosium sesquioxide, Dy2O3; erbium sesquioxide,Er2O3; ytterbium sesquioxide, Yb2O3, E. Staritzky, Analytical Chemistry 28.12(1956) 2023–2024.