Impurity concentration and temperature dependence of the refractive indices of Er3+doped ceramic Y2O3

doi:10.1364/OE.20.004428

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Impurity concentration and temperature dependence of the refractive indices of Er³⁺doped ceramic Y₂O₃

A. Joshi, N. D. Haynes, D. E. Zelmon, O. Stafsudd, and R. Shori »View Author Affiliations

Optics Express, Vol. 20, Issue 4, pp. 4428-4435 (2012)
http://dx.doi.org/10.1364/OE.20.004428

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– Abstract
1. Introduction
2. Experiments
3. Results
4. Discussion
5. Conclusion
– References and links

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Abstract

The refractive indices and thermo-optic coefficients for varying concentrations of Er³⁺ doped polycrystalline yttria were measured at a variety of wavelengths and temperatures. A Lorenz oscillator model was employed to model the room temperature indices and thermo-optic coefficients were calculated based on temperature dependent index measurements from 0.45 to 1.064 microns. Some consequences relating to thermal lensing are discussed.

1. Introduction

Polycrystalline ceramics are a new class of laser gain media that show the promise of mitigating many of the current problems associated with solid state single crystal gain media. Ceramic hosts have numerous advantages over their single crystal counterparts including the ability to control precisely levels and profiles of dopants, scalability to large sizes and lower processing temperatures. A number of successes have been reported in the literature, including lasing with sesquioxide hosts such as Y₂O₃ and Sc₂O₃ doped with Yb [1

K. Petermann, L. Fornasiero, E. Mix, and V. Peters, “High melting sesquioxides: crystal growth, spectroscopy, and laser experiments,” Opt. Mater. 19(1), 67–71 (2002). [CrossRef]

–3

J. Lu, J. F. Bisson, K. Takaichi, T. Uematsu, A. Shirakawa, M. Musha, K. Ueda, H. Yagi, T. Yanagitani, and A. A. Kaminskii, “Yb³⁺:Sc₂O₃ ceramic laser,” Appl. Phys. Lett. 83(6), 1101–1103 (2003). [CrossRef]

], and increased lasing efficiency in the Nd³⁺:YAG system [4

J. Lu, M. Prabhu, J. Xu, K. Ueda, H. Yagi, T. Yanagitani, and A. A. Kaminskii, “Highly efficient 2% Nd:yttrium aluminum garnet ceramic laser,” Appl. Phys. Lett. 77(23), 3707–3709 (2000). [CrossRef]

]. High power operation has also been reported with powers thus far reaching over 1.4 kW in Nd³⁺:YAG [5

J. Lu, K. Ueda, H. Yagi, T. Yanagitani, Y. Akiyama, and A. A. Kaminskii, “Neodymium doped yttrium aluminum garnet (Y₃Al₅O₁₂) nanocrystalline ceramics-a new generation of solid state laser and optical materials,” J. Alloy. Comp. 341(1-2), 220–225 (2002). [CrossRef]

Compensation for the thermal effects to which high power lasers are subject requires accurate measurements of the thermal and mechanical properties of the lasing medium. Among these properties are the refractive index and its variation with temperature. We present new measurements of the refractive index at wavelengths from 0.4 to 5.0 microns and thermo-optic coefficient from 0.45 to 1.06 microns for several Er³⁺ impurity levels in ceramic yttria. The Lorentz equation is employed to model the room temperature indices and used along with temperature dependent refractive index measurements as the basis of modeling the thermal behavior of the refractive index.

2. Experiments

Four yttria prisms were fabricated with Er³⁺ concentrations of 0%, 5%, 10%, and 20% and were approximately 2 cm high and 1.5 cm in length. The apex angles of the prisms were measured using an auto collimator attached to a Moller-Wedel divided circle spectrometer and are listed in Table 1 . The tolerance on each of the angular measurements is the standard deviation of 10 separate measurements performed on each prism. The Moller-Wedel divided-circle spectrometer was used to obtain measurements of the angles of minimum deviation [6

M. Born and E. Wolf, Principles of Optics,7^th ed. (Cambridge University Press, 1999).

]. The output from a mercury xenon lamp or an Oriel IR6363 infrared source was coupled into an Oriel Cornerstone ¼ m monochromator to provide the discrete wavelengths used in the experiment. Appropriate detectors were used to measure the position of the refracted beams. The system was standardized by measuring the index of a calcium fluoride prism from 0.4 to 5.0 μ. These measurements gave values that were within 1.0X10⁻⁴ of the published literature [7

I. Malitson, “A redetermination of some optical properties of calcium fluoride,” Appl. Opt. 2(11), 1103–1107 (1963). [CrossRef]

]. Five measurements of the minimum deviation angle were made at each wavelength. The standard deviation of the five minimum deviation angle measurements taken at each wavelength was less than 15 arc sec. Using the equation for the refractive index at minimum deviation, and assuming the error in the measurement is due to errors in measurement of the minimum deviation and apex angles, we can calculate the error in the measured index.

Table 1 Prism Apex angles and Lorentz parameters for Er³⁺ doped ceramic Yttria

Prism	Apex Angle	A	B	C	D	E	F
Undoped	60.667° ± 0.002°	2.5393	0.017724	0.006142	0.40862	0.82096	0.0094725
5%	59.856° ± 0.001°	2.5464	0.017844	0.0072499	0.33624	0.78135	0.0094384
Er³⁺
10%	59.995° ± 0.001°	2.5553	0.017803	0.0062244	0.41091	0.90343	0.0093965
Er³⁺
20%	60.666° ± 0.001°	2.5766	0.017518	0.0021551	0.52397	0.06287	0.0093815
Er³⁺

Δ n = \frac{\partial n}{\partial ε} Δ ε + \frac{\partial n}{\partial α} Δ α = \frac{1}{2} (\frac{\cos (\frac{ε + α}{2})}{\sin (\frac{α}{2})} Δ ε - \frac{\sin (\frac{ε}{2})}{\sin^{2} (\frac{α}{2})} Δ α)

(1)

Using the standard deviations in the measurements for the minimum deviation and apex angles for

Δ ε

and

Δ α

respectively, and adding the terms in quadrature, we estimate the error of the refractive index calculated from the standard equation to be less than 2.0X10⁻⁴ at any individual wavelength. Room temperature measurements were carried out at 23 ± 1 C^o

The temperature dependent measurements of the refractive index were also carried out using the method of minimum deviation. Each sample was placed between two copper blocks which were heated by two cartridge heaters mounted in each block. The temperature of the prism was controlled by a Eurotherm model 2416 temperature controller and monitored by a type K thermocouple mounted in a cavity drilled into the back of the prism. The temperature was brought to the set point and allowed to stabilize for 45 minutes before taking refractive index data. Temperature stability of the system was ± 1 C^o. Standardization of the system was carried out by comparing data obtained from calcium fluoride in our laboratory to that obtained on the same material at NIST [8

A. Feldman, D. Horowitz, R. M. Waxler, and M. J. Dodge, “Optical Material Characterization,” NBS Technical Note 993 (U. S. GPO, 1978).

]. The error in the measurement of dn/dT is estimated to be ± 10%.

3. Results

The room temperature refractive index measurements are shown in Fig. 1 in which the refractive index for each of the samples is plotted vs. wavelength.

Fig. 1 Refractive Indices of Er:Yttria

Erbium doped yttria is known to have absorption peaks in the visible and near IR spectral range [9

R. Dekker and K. Worhoff, J. W. Stouwdam, and F. J. C. M, van Veggel and A. Driessen, “Absorption spectroscopy of complex rare earth ion doped hybrid materials over a broad wavelength range,” 7th International Conference on Photonics in Europe, 12-17 June 2005, Munich, Germany.

], so traditional Sellmeier formula failed to model the index data adequately. Therefore, the Lorentz equation [10

J. M. Ziman, Principles of the Theory of Solids, (Cambridge University Press, 1964.)

] was used to model the data which adds a damping term to the traditional Sellmeier oscillators that eliminates the singularities of the Sellmeier formula while permitting the accurate reproduction of the index data near the absorption peak. We stress that the wavelength calculated by the fitting routine does not represent the actual absorption wavelength but is only a fitting parameter which reproduces the index data. Accordingly, the room temperature index data were fitted to a 6 parameter, Lorentz model of the form

n^{2} - 1 = \frac{A λ^{2}}{λ^{2} - B} + \frac{C λ^{2} (λ^{2} - D)}{{(λ^{2} - D)}^{2} + E λ^{2}} - F λ^{2}

(2)

using the Levenburg-Marquardt algorithm. The first term represents the oscillators at wavelengths shorter than those at which measurements were taken in our experiment. The second term is the Lorentz term which accounts for the indices in the spectral range where the absorption peaks occur. The final term models any absorptions at wavelengths much longer than those used in our experiment. This model gave values for the refractive index which were within experimental error, which we noted above was less than 2.0X10⁻⁴ at any individual wavelength. The values for A-F are given in Table 1 for each of the samples measured. It should be noted that the fitted values for the spectral positions of the oscillators and the values for the damping factor do not reflect real values for these parameters. To obtain those would require modeling each individual oscillator and require transmission data to model accurately the spectral dependence of the absorption.

The dependence of the refractive index on Er³⁺ concentration is shown in Fig. 2 . The data showed a linear dependence of the refractive index on erbium concentration at all wavelengths. The change in index with respect to concentration was 4.78X10⁻⁴ ± 0.17/% Er concentration and showed a statistically insignificant dependence on wavelength.

Fig. 2a Refractive Index vs. Er concentration, 0.56 μ −0.7 μ

Fig. 2b Refractive Index vs. Er concentration, 0.75 μ −1.15 μ

Fig. 2c Refractive Index vs. Er concentration, 1.2 μ −3.2 μ

Fig. 2d Refractive Index vs. Er concentration, 3.4 μ −5.2 μ

Values for the refractive index vs. temperature are shown in Fig. 3 .

Fig. 3a Refractive Index vs. Temperature 0.45-1.064 μ Undoped Yttria

Fig. 3b Refractive Index vs. Temperature 5% Er:Yttria

Fig. 3c Refractive Index vs. Temperature 10% Er:Yttria

Fig. 3d Refractive Index vs. Temperature 20% Er:Yttria

We observed a linear increase of the refractive index with temperature indicating a temperature independent value for dn/dT at all wavelengths. The measured values for dn/dT at each wavelength are shown in Table 2 as

{(\frac{\partial n}{\partial T})}_{σ}

, the change in index with respect to temperature at constant strain. The meaning of this number and its relationship to the accompanying value of

{(\frac{\partial n}{\partial T})}_{ε}

, the change in index with respect to temperature at constant stress are discussed later. Given the tolerances cited above for these measurements, we did not discern any statistically significant trend in the value of dn/dT as a function of erbium concentration but there is a strong dependence on wavelength.

Table 2 Temperature dependence of the refractive index, X10⁻⁵ (C^o)⁻¹

λ (μ)	Undoped	Undoped	5%	5%	10%	10%	20%	20%
	Y₂O₃	Y₂O₃	Er:Y₂O₃	Er:Y₂O₃	Er:Y₂O₃	Er:Y₂O₃	Er:Y₂O₃	Er:Y₂O₃
	${(\frac{\partial n}{\partial T})}_{σ}$	${(\frac{\partial n}{\partial T})}_{ε}$	${(\frac{\partial n}{\partial T})}_{σ}$	${(\frac{\partial n}{\partial T})}_{ε}$	${(\frac{\partial n}{\partial T})}_{σ}$	${(\frac{\partial n}{\partial T})}_{ε}$	${(\frac{\partial n}{\partial T})}_{σ}$	${(\frac{\partial n}{\partial T})}_{ε}$
0.45	1.3964	4.107	1.3439	4.065	1.450	4.181	1.3726	4.124
0.50	1.2326	3.889	1.2168	3.883	1.3007	3.977	1.1874	3.884
0.55	1.1630	3.781	1.1126	3.740	1.2042	3.841	1.1287	3.785
0.60	1.0699	3.659	1.0675	3.666	1.1281	3.736	1.0382	3.665
1.064	0.8568	3.344	0.8557	3.352	0.8979	3.403	0.8091	3.337

4. Discussion

One of the serious problems in the design of high power lasers is the calculation of the thermal lensing arising from a number of different sources. In their recent review [11

S. Chénais, F. Druon, S. Forget, F. Balembois, and P. Georges, “On thermal effects in solid state lasers: The case of Ytterbium doped materials,” Prog. Quantum Electron. 30(4), 89–153 (2006). [CrossRef]

], Chenais et al point out the significant errors associated with inappropriate use of the value of dn/dT for the calculation of thermal lens effects. They correctly point out that the measured value for dn/dT also includes a term describing photo-elastic effects inside the lasing material. They also emphasize the fact that the true thermo-optic coefficient contains other terms describing the strain induced birefringence and deformation of the material at its endpoints. Further, the assumption that dn/dT is the dominant term in the thermo-optic coefficient is invalid for many materials. Using the notation of [11

], we find

{\frac{d n}{d T}}_{m e a s} = \frac{d n}{d T_{σ}} = \frac{(n^{2} + 2) (n^{2} - 1)}{6 n} [\frac{1}{α_{e}} \frac{\partial α_{e}}{\partial T} - 3 α_{T} (1 + \frac{ρ}{α_{e}} \frac{\partial α_{e}}{\partial ρ})]

(3)

where

\frac{d n}{d T} = \frac{d n}{d T_{σ}}

is the measured change in the refractive index (equal to the change in index with temperature at constant strain), n is the refractive index,

α_{e}

is the electric polarizability and ρ is the density of the material. The first of the three terms,

\frac{(n^{2} + 2) (n^{2} - 1)}{6 n} [\frac{1}{α_{e}} \frac{\partial α_{e}}{\partial T}]

is the portion of the measured

\frac{d n}{d T}

which is independent of thermal expansion. Physically, it represents the value of

\frac{d n}{d T}

at constant strain,

{(\frac{\partial n}{\partial T})}_{ε}

. As we shall see later, this term is required to calculate the complete thermo-optic coefficient. The second term is due solely to thermal expansion, and the last term is due to the effect of thermal expansion on the polarizability.

Rearranging (3)

{(\frac{\partial n}{\partial T})}_{ε} = {(\frac{\partial n}{\partial T})}_{m e a s} + α_{T} \frac{(n^{2} + 2) (n^{2} - 1))}{2 n} (1 + \frac{ρ}{α_{e}} \frac{\partial α_{e}}{\partial ρ})

(4)

Assuming that the term

\frac{ρ}{α_{e}} \frac{\partial α_{e}}{\partial ρ}

is small, the correction to the measured

{(\frac{\partial n}{\partial T})}_{σ}

is shown in Table 2. The complete expression for the thermo-optic coefficient is [11

]

χ = {(\frac{\partial n}{\partial T})}_{ε} + n_{o}^{3} α_{T} (C_{r}^{'} + C_{θ}^{'}) + (n_{o} - 1) (1 + ν) α_{T} \pm n_{o}^{3} α_{T} (C_{r}^{'} - C_{θ}^{'})

(5)

where

C_{r}^{'}

and

C_{θ}^{'}

are the photo-elastic coefficients for polarization in the radial and tangential directions. The second term in the equation represents the photo-elastic contribution to the thermo-optic coefficient, the third term describes the amount of curvature at the ends of the lasing material and the final term accounts for stress birefringence. This is the relevant parameter when making calculations for thermal lensing.

The values for

C_{r}^{'}

and

C_{θ}^{'}

may be calculated using the photo-elastic coefficients [12

J. F. Nye, Physical Properties of Crystals (Clarendon Press, Oxford, 1957).

]. Alternatively, one may calculate the photo-elastic tensor components from the piezo-optic tensor and the compliance tensor [12

J. F. Nye, Physical Properties of Crystals (Clarendon Press, Oxford, 1957).

]. Regrettably, there does not appear to exist any measurements of enough of these quantities to calculate

C_{r}^{'}

and

C_{θ}^{'}

for yttria as of this writing. The Handbook of Optics [13

W. Tropf, M. Thomas, and T. Harris, “Properties of Crystals and Glasses”, in Handbook of Optics, v. II 2^nd ed., M. Bass, Ed. In Chief, E. Van Stryland, D. Williams, and W. Wolfe, Assoc. Eds. (McGraw-Hill, 1995)

] gives values for both the stiffness and compliance tensors but admits that for Y₂O₃, these parameters were calculated based on published elastic moduli [14

I. C. Albayrak, S. Basu, A. Sakulich, O. Yeheskel, and M. W. Barsoum, “Elastic and Mechanical Properties of polycrystalline transparent yttria determined by indentation techniques,” J. Am. Ceram. Soc. 93, 2028–2034 (2010).

, 15

O. Yeheskel and O. Tevet, “Elastic Moduli of transparent yttria,” J. Am. Ceram. Soc. 82(1), 136–144 (1999). [CrossRef]

] and there is no reference to the piezo-optic tensor. For that reason, it is not possible to give a prediction of the dioptric power of a thermal lens formed by lasing in Er³⁺:Yttria which includes all of the photo-elastic properties of the material. While the thermal expansion coefficient and Poisson’s ratio are both known for undoped yttria [16

W. J. Tropf and D. C. Harris, “Mechancal, thermal, and optical properties of yttria and lanthana doped yttria,” Proceedings of the SPIE, v1112, pp. 9-19 (1989).

] no measurements have been made of these parameters for doped yttria. Using the values of the refractive index and dn/dT from this work, we have calculated the value of

{(\frac{\partial n}{\partial T})}_{ε}

for the four levels of Er⁺³ concentration studied in this work and shown them in Table 2. This is as far as the calculations can be taken unless the contributions from the end faces and elasto-optic effects can be considered small. Data does not exist to support this assumption at this time.

5. Conclusion

We have conducted measurements of the refractive index as a function of wavelength and its dependence on temperature at constant strain of Er:Yttria with varying concentrations of erbium over a wide spectral range and at temperatures from 23 to 225 C^o. The values for

{(\frac{\partial n}{\partial T})}_{σ}

do not vary significantly with erbium concentration and are somewhat smaller than those found for materials such as Nd doped vanadates.

The refractive index change with concentration was 4.78 ± 0.17 X 10⁻⁴/% doping and appeared to be independent of the wavelength. Given that it is conceivable to use concentrations of Er³⁺ up to 20%, it is possible that the refractive index could vary as much as 0.01 from its undoped value, a fact which would need to be accounted for when designing optics for the compensation of thermal effect.

References and links

1.	K. Petermann, L. Fornasiero, E. Mix, and V. Peters, “High melting sesquioxides: crystal growth, spectroscopy, and laser experiments,” Opt. Mater. 19(1), 67–71 (2002). [CrossRef]
2.	A. Shirakawa, K. Takaichi, H. Yagi, J. Bisson, J. Lu, M. Musha, K. Ueda, T. Yanagitani, T. Petrov, and A. A. Kaminskii, “Diode-pumped mode-locked Yb³⁺:Y₂O₃ ceramic laser,” Opt. Express 11(22), 2911–2916 (2003). [CrossRef] [PubMed]
3.	J. Lu, J. F. Bisson, K. Takaichi, T. Uematsu, A. Shirakawa, M. Musha, K. Ueda, H. Yagi, T. Yanagitani, and A. A. Kaminskii, “Yb³⁺:Sc₂O₃ ceramic laser,” Appl. Phys. Lett. 83(6), 1101–1103 (2003). [CrossRef]
4.	J. Lu, M. Prabhu, J. Xu, K. Ueda, H. Yagi, T. Yanagitani, and A. A. Kaminskii, “Highly efficient 2% Nd:yttrium aluminum garnet ceramic laser,” Appl. Phys. Lett. 77(23), 3707–3709 (2000). [CrossRef]
5.	J. Lu, K. Ueda, H. Yagi, T. Yanagitani, Y. Akiyama, and A. A. Kaminskii, “Neodymium doped yttrium aluminum garnet (Y₃Al₅O₁₂) nanocrystalline ceramics-a new generation of solid state laser and optical materials,” J. Alloy. Comp. 341(1-2), 220–225 (2002). [CrossRef]
6.	M. Born and E. Wolf, Principles of Optics,7^th ed. (Cambridge University Press, 1999).
7.	I. Malitson, “A redetermination of some optical properties of calcium fluoride,” Appl. Opt. 2(11), 1103–1107 (1963). [CrossRef]
8.	A. Feldman, D. Horowitz, R. M. Waxler, and M. J. Dodge, “Optical Material Characterization,” NBS Technical Note 993 (U. S. GPO, 1978).
9.	R. Dekker and K. Worhoff, J. W. Stouwdam, and F. J. C. M, van Veggel and A. Driessen, “Absorption spectroscopy of complex rare earth ion doped hybrid materials over a broad wavelength range,” 7th International Conference on Photonics in Europe, 12-17 June 2005, Munich, Germany.
10.	J. M. Ziman, Principles of the Theory of Solids, (Cambridge University Press, 1964.)
11.	S. Chénais, F. Druon, S. Forget, F. Balembois, and P. Georges, “On thermal effects in solid state lasers: The case of Ytterbium doped materials,” Prog. Quantum Electron. 30(4), 89–153 (2006). [CrossRef]
12.	J. F. Nye, Physical Properties of Crystals (Clarendon Press, Oxford, 1957).
13.	W. Tropf, M. Thomas, and T. Harris, “Properties of Crystals and Glasses”, in Handbook of Optics, v. II 2^nd ed., M. Bass, Ed. In Chief, E. Van Stryland, D. Williams, and W. Wolfe, Assoc. Eds. (McGraw-Hill, 1995)
14.	I. C. Albayrak, S. Basu, A. Sakulich, O. Yeheskel, and M. W. Barsoum, “Elastic and Mechanical Properties of polycrystalline transparent yttria determined by indentation techniques,” J. Am. Ceram. Soc. 93, 2028–2034 (2010).
15.	O. Yeheskel and O. Tevet, “Elastic Moduli of transparent yttria,” J. Am. Ceram. Soc. 82(1), 136–144 (1999). [CrossRef]
16.	W. J. Tropf and D. C. Harris, “Mechancal, thermal, and optical properties of yttria and lanthana doped yttria,” Proceedings of the SPIE, v1112, pp. 9-19 (1989).

OCIS Codes
(140.3380) Lasers and laser optics : Laser materials
(160.3380) Materials : Laser materials

ToC Category:
Materials

History
Original Manuscript: August 18, 2011
Revised Manuscript: November 1, 2011
Manuscript Accepted: November 4, 2011
Published: February 8, 2012

Citation
A. Joshi, N. D. Haynes, D. E. Zelmon, O. Stafsudd, and R. Shori, "Impurity concentration and temperature dependence of the refractive indices of Er³⁺doped ceramic Y₂O₃," Opt. Express 20, 4428-4435 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-4-4428

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References

K. Petermann, L. Fornasiero, E. Mix, and V. Peters, “High melting sesquioxides: crystal growth, spectroscopy, and laser experiments,” Opt. Mater.19(1), 67–71 (2002). [CrossRef]
A. Shirakawa, K. Takaichi, H. Yagi, J. Bisson, J. Lu, M. Musha, K. Ueda, T. Yanagitani, T. Petrov, and A. A. Kaminskii, “Diode-pumped mode-locked Yb3+:Y2O3 ceramic laser,” Opt. Express11(22), 2911–2916 (2003). [CrossRef] [PubMed]
J. Lu, J. F. Bisson, K. Takaichi, T. Uematsu, A. Shirakawa, M. Musha, K. Ueda, H. Yagi, T. Yanagitani, and A. A. Kaminskii, “Yb3+:Sc2O3 ceramic laser,” Appl. Phys. Lett.83(6), 1101–1103 (2003). [CrossRef]
J. Lu, M. Prabhu, J. Xu, K. Ueda, H. Yagi, T. Yanagitani, and A. A. Kaminskii, “Highly efficient 2% Nd:yttrium aluminum garnet ceramic laser,” Appl. Phys. Lett.77(23), 3707–3709 (2000). [CrossRef]
J. Lu, K. Ueda, H. Yagi, T. Yanagitani, Y. Akiyama, and A. A. Kaminskii, “Neodymium doped yttrium aluminum garnet (Y3Al5O12) nanocrystalline ceramics-a new generation of solid state laser and optical materials,” J. Alloy. Comp.341(1-2), 220–225 (2002). [CrossRef]
M. Born and E. Wolf, Principles of Optics,7th ed. (Cambridge University Press, 1999).
I. Malitson, “A redetermination of some optical properties of calcium fluoride,” Appl. Opt.2(11), 1103–1107 (1963). [CrossRef]
A. Feldman, D. Horowitz, R. M. Waxler, and M. J. Dodge, “Optical Material Characterization,” NBS Technical Note 993 (U. S. GPO, 1978).
R. Dekker and K. Worhoff, J. W. Stouwdam, and F. J. C. M, van Veggel and A. Driessen, “Absorption spectroscopy of complex rare earth ion doped hybrid materials over a broad wavelength range,” 7th International Conference on Photonics in Europe, 12-17 June 2005, Munich, Germany.
J. M. Ziman, Principles of the Theory of Solids, (Cambridge University Press, 1964.)
S. Chénais, F. Druon, S. Forget, F. Balembois, and P. Georges, “On thermal effects in solid state lasers: The case of Ytterbium doped materials,” Prog. Quantum Electron.30(4), 89–153 (2006). [CrossRef]
J. F. Nye, Physical Properties of Crystals (Clarendon Press, Oxford, 1957).
W. Tropf, M. Thomas, and T. Harris, “Properties of Crystals and Glasses”, in Handbook of Optics, v. II 2nd ed., M. Bass, Ed. In Chief, E. Van Stryland, D. Williams, and W. Wolfe, Assoc. Eds. (McGraw-Hill, 1995)
I. C. Albayrak, S. Basu, A. Sakulich, O. Yeheskel, and M. W. Barsoum, “Elastic and Mechanical Properties of polycrystalline transparent yttria determined by indentation techniques,” J. Am. Ceram. Soc.93, 2028–2034 (2010).
O. Yeheskel and O. Tevet, “Elastic Moduli of transparent yttria,” J. Am. Ceram. Soc.82(1), 136–144 (1999). [CrossRef]
W. J. Tropf and D. C. Harris, “Mechancal, thermal, and optical properties of yttria and lanthana doped yttria,” Proceedings of the SPIE, v1112, pp. 9-19 (1989).

Appl. Opt.

I. Malitson, “A redetermination of some optical properties of calcium fluoride,” Appl. Opt.2(11), 1103–1107 (1963). [CrossRef]

Appl. Phys. Lett.

J. Lu, J. F. Bisson, K. Takaichi, T. Uematsu, A. Shirakawa, M. Musha, K. Ueda, H. Yagi, T. Yanagitani, and A. A. Kaminskii, “Yb3+:Sc2O3 ceramic laser,” Appl. Phys. Lett.83(6), 1101–1103 (2003). [CrossRef]
J. Lu, M. Prabhu, J. Xu, K. Ueda, H. Yagi, T. Yanagitani, and A. A. Kaminskii, “Highly efficient 2% Nd:yttrium aluminum garnet ceramic laser,” Appl. Phys. Lett.77(23), 3707–3709 (2000). [CrossRef]

J. Alloy. Comp.

J. Lu, K. Ueda, H. Yagi, T. Yanagitani, Y. Akiyama, and A. A. Kaminskii, “Neodymium doped yttrium aluminum garnet (Y3Al5O12) nanocrystalline ceramics-a new generation of solid state laser and optical materials,” J. Alloy. Comp.341(1-2), 220–225 (2002). [CrossRef]

J. Am. Ceram. Soc.

I. C. Albayrak, S. Basu, A. Sakulich, O. Yeheskel, and M. W. Barsoum, “Elastic and Mechanical Properties of polycrystalline transparent yttria determined by indentation techniques,” J. Am. Ceram. Soc.93, 2028–2034 (2010).
O. Yeheskel and O. Tevet, “Elastic Moduli of transparent yttria,” J. Am. Ceram. Soc.82(1), 136–144 (1999). [CrossRef]

Opt. Express

A. Shirakawa, K. Takaichi, H. Yagi, J. Bisson, J. Lu, M. Musha, K. Ueda, T. Yanagitani, T. Petrov, and A. A. Kaminskii, “Diode-pumped mode-locked Yb3+:Y2O3 ceramic laser,” Opt. Express11(22), 2911–2916 (2003). [CrossRef] [PubMed]

Opt. Mater.

K. Petermann, L. Fornasiero, E. Mix, and V. Peters, “High melting sesquioxides: crystal growth, spectroscopy, and laser experiments,” Opt. Mater.19(1), 67–71 (2002). [CrossRef]

Prog. Quantum Electron.

S. Chénais, F. Druon, S. Forget, F. Balembois, and P. Georges, “On thermal effects in solid state lasers: The case of Ytterbium doped materials,” Prog. Quantum Electron.30(4), 89–153 (2006). [CrossRef]

Other

J. F. Nye, Physical Properties of Crystals (Clarendon Press, Oxford, 1957).
W. Tropf, M. Thomas, and T. Harris, “Properties of Crystals and Glasses”, in Handbook of Optics, v. II 2nd ed., M. Bass, Ed. In Chief, E. Van Stryland, D. Williams, and W. Wolfe, Assoc. Eds. (McGraw-Hill, 1995)
W. J. Tropf and D. C. Harris, “Mechancal, thermal, and optical properties of yttria and lanthana doped yttria,” Proceedings of the SPIE, v1112, pp. 9-19 (1989).
M. Born and E. Wolf, Principles of Optics,7th ed. (Cambridge University Press, 1999).
A. Feldman, D. Horowitz, R. M. Waxler, and M. J. Dodge, “Optical Material Characterization,” NBS Technical Note 993 (U. S. GPO, 1978).
R. Dekker and K. Worhoff, J. W. Stouwdam, and F. J. C. M, van Veggel and A. Driessen, “Absorption spectroscopy of complex rare earth ion doped hybrid materials over a broad wavelength range,” 7th International Conference on Photonics in Europe, 12-17 June 2005, Munich, Germany.
J. M. Ziman, Principles of the Theory of Solids, (Cambridge University Press, 1964.)

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