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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 18 — Sep. 9, 2013
  • pp: 21254–21263
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Study of the thermo-optical constants of Yb doped Y2O3, Lu2O3 and Sc2O3 ceramic materials

Ilya L. Snetkov, Dmitry E. Silin, Oleg V. Palashov, Efim A. Khazanov, Hideki Yagi, Takagimi Yanagitani, Hitoki Yoneda, Akira Shirakawa, Ken-ichi Ueda, and Alexander A. Kaminskii  »View Author Affiliations


Optics Express, Vol. 21, Issue 18, pp. 21254-21263 (2013)
http://dx.doi.org/10.1364/OE.21.021254


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Abstract

Thermally induced depolarization and thermal lens of three Konoshima Chemical Co. laser-ceramics samples Yb3+:Lu2O3(CYb≈1.8 at.%), Yb3+:Y2O3(CYb≈1.8 at.%), and Yb3+:Sc2O3 (CYb≈2.5 at.%) were measured in experiment at different pump power. The results allowed us to estimate the thermal conductivity of the investigated ceramic samples and compare their thermo-optical properties. The thermo-optical constants P and Q and its sign measured for these materials at the first time.

© 2013 OSA

1. Introduction

High-average-power laser systems have rigid restrictions on active-gain materials. Heat generation in optical elements leads not only to increased mean bulk temperature, but also to temperature gradients, which, in turn, give rise to elastic stresses, that may destroy the elements and give rise to parasitic thermal effects – the thermal lens and thermally induced birefringence. These effects, in turn, degrade the quality of the generated radiation and are one of the limiting factors of further laser power enhancement [1

1. W. Koechner, Solid-State Laser Engineering (Springer, 1999).

].

In the present work we studied samples of Yb3+-doped Y2O3 (10x10x1 mm), Lu2O3 (10x10x0.5 mm), and Sc2O3 (6.7x5.2x1.2 mm) Konoshima Сhemical Co. ceramics with different concentrations of lasant ions ≈1.8 at.%, ≈1.8 at.%, and ≈2.5 at.%, respectively. Thermo-optical properties responsible for the thermal lens and the thermally induced birefringence considering the influence of the photoelastic effect of these samples were investigated and compared.

2. Estimation of thermo-optical constant Q

One of the key parameters in studying of thermo-optical properties is the heat release power caused by linear absorption of transmitted radiation in the medium, quantum defect, reabsorption of luminescence radiation in active elements, and so on. Knowing which part of the laser power in the studied elements is converted into heat, one can measure thermal effects.

For assessing the power of heat generation the following experiment was conducted. The studied sample was thermally connected to a buffer element that was an Y3Al5O12 single crystal 15 mm in diameter and 6 mm in thickness with a dielectric coating on one side reflecting at wavelengths of 940 nm and 1030 nm. According to our estimates the heat transfer coefficient of connection studied sample - buffer element was two order more than convective heat transfer between studied sample and atmosphere. Therefore, we assumed that all of the absorbed heat is distributed in the system: the buffer element – the studied sample. The volume of the buffer element was several times more that the studied sample. The temperature on the surface of the buffer element was measured with and without pump radiation. The buffer element temperature did not change at switched on heating radiation in the absence of the studied sample, which indicates that absorption in dielectric mirrors is weak and absorption in the studied sample is the only source of heat. Assuming that all the absorbed heat is distributed uniformly over the buffer element – the studied sample volume during the times less than the measurement time, supposing that the heat stored in the studied sample is negligible compared to that stored in the buffer element, and knowing the heat capacity, volume and density of the buffer element material and the dependence of temperature on time at switched on heating radiation and at its passive cooling, one can readily determine the heat release power in the studied sample. The pump-power-into-heat conversion coefficient at wavelength 940 nm for our samples were measured and are presented in Table 1

Table 1. Coefficients of proportionality between the heat release power and the laser radiation power at wavelength 940 nm for our studied samples

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In the case of heat generation in an optical element there arise temperature gradients which, in turn, lead to thermal stresses. Due to the photoelastic effect these stresses result in changes in the index of refraction that depends on the magnitude and direction of the stresses and, for the optical element made of crystal material, on the orientation of its crystallographic axes. Thus, as linearly polarized radiation is passing through a thermally loaded optical element to each point of its cross section, its polarization state changes, which results in appearance at the output of the optical element of a portion of orthogonally polarized radiation with the intensity distributed over the cross section [14

14. J. D. Foster and L. M. Osterink, “Thermal effects in a Nd:YAG laser,” J. Appl. Phys. 41(9), 3656–3663 (1970). [CrossRef]

, 15

15. W. Koechner and D. K. Rice, “Effect of birefringence on the performance of linearly polarized YAG:Nd lasers,” IEEE J. Quantum Electron. 6(9), 557–566 (1970). [CrossRef]

].

A ceramics consist of a large number of monocrystalline granules with average size 1-100 μm (depending on process of fabrication) separated by thin (~1 nm) boundaries. A significant distinction between such ceramics and a single crystal is that the crystallographic axes in each granule are oriented randomly. The orientation of crystallographic axes in a given ceramic grain is determined by three Euler angles α, β, and γ, which are random variables within their respective intervals. In the absence of thermal load, the ceramics from cubic crystal is almost free from depolarization.

The expression for thermally induced polarization distortions introduced by a ceramic element to linearly polarized radiation consists of two components, one of which does not depend on the number of grains in the beam path (it is polarization distortions averaged over cross-section and all possible directions of the crystallographic axes in each grain), and the other is inversely proportional to it [16

16. M. A. Kagan and E. A. Khazanov, “Compensation for thermally induced birefringence in polycrystalline ceramic active elements,” Quantum Electron. 33(10), 876–882 (2003). [CrossRef]

, 17

17. A. G. Vyatkin and E. A. Khazanov, “Thermally induced scattering of radiation in laser ceramics with arbitrary grain size,” J. Opt. Soc. Am. B 29(12), 3307–3316 (2012). [CrossRef]

]. In the approximation of a large number of grains in the beam path, the second term can be neglected and the thermally induced depolarization is defined by
γ=A(Qeffλκ)2Ph2,
(1)
where λ is the wavelength of probe radiation; κ is the thermal conductivity; Ph is the power of heat generation; A is the constant, depended on profiles of pump and signal beams and equal 0.017 when both beam have Gaussian intensity distribution and equal radius,
Qeff=QS1=aTn033E1ν(π11π12)S1,
(2)
where αT is the thermal expansion coefficient; n0 is the index of refraction at the wavelength λ; E is Young’s modulus; ν is Poisson’s ratio; πij are the elements of the piezo-optic tensor in the two-index Nye notation [18

18. J. F. Nye, Physical Properties of Crystals (Oxford University, 1964).

]; and S1 is a factor which for ceramics element depends on assumptions about the statistical properties of directions of crystallographic axes in each grain: S1 = (75 + 53ξ)/128 for the Euler angles α, β, and γ uniformly distributed, respectively, in the ranges [-π,π], [0, π], and [-π, π] [16

16. M. A. Kagan and E. A. Khazanov, “Compensation for thermally induced birefringence in polycrystalline ceramic active elements,” Quantum Electron. 33(10), 876–882 (2003). [CrossRef]

]; and S1 = (2 + 3ξ)/5 for the Euler angles α and γ distributed uniformly and β with the probability density sin(β)/2 [17

17. A. G. Vyatkin and E. A. Khazanov, “Thermally induced scattering of radiation in laser ceramics with arbitrary grain size,” J. Opt. Soc. Am. B 29(12), 3307–3316 (2012). [CrossRef]

], where ξ = π44/(π11-π12) is the stress-optic anisotropy ratio. For all glasses S1 = 1, for single crystals with [111] orientation S1 = (1 + 2ξ)/3. The typical ceramics crystallite size that are made by this technology of the order of 1 micron, so the approximation that we have done, performed for all our ceramics samples. The values of the most of material constants in the Eq. (2) for the sesquioxides are unknown. So we have made estimates of the thermo-optical parameter Qeff based on experimental measurements of thermally induced depolarization by using Eq. (1).

The Eq. (1) and (2) holds true for the case of a side-cooling optical element, when the heat flow to the end surface is negligible compared to the heat flow to the side of the sample (rod geometry). In our experiments we have met this requirement by providing efficient heat transfer from the side surface of the samples. Equation (1) was obtained in [16

16. M. A. Kagan and E. A. Khazanov, “Compensation for thermally induced birefringence in polycrystalline ceramic active elements,” Quantum Electron. 33(10), 876–882 (2003). [CrossRef]

, 17

17. A. G. Vyatkin and E. A. Khazanov, “Thermally induced scattering of radiation in laser ceramics with arbitrary grain size,” J. Opt. Soc. Am. B 29(12), 3307–3316 (2012). [CrossRef]

] for materials with symmetry m3m, 432, 4¯3m(garnets, fluorides and others). The crystal lattice of the studied sesquioxides has m3-symmetry point group. For single crystals of this symmetry, the expressions for the thermally induced depolarization are different, but Eq. (1) for γ in the case of ceramic optical elements remains valid without any changes (theoretically, it will be shown in our nearest publications).

The radiation wavelength and the heat release power Ph are known. Then, by measuring the dependence of integral depolarization on the power of heat generation in a ceramic sample and using the Eq. (1) we can readily find the value of Qeff. The stress-optic anisotropy ratio ξ may be found by measuring thermally induced polarization distortions [19

19. I. L. Snetkov, A. G. Vyatkin, O. V. Palashov, and E. A. Khazanov, “Drastic reduction of thermally induced depolarization in CaF₂ crystals with [111] orientation,” Opt. Express 20(12), 13357–13367 (2012). [CrossRef] [PubMed]

] or by measuring values of the elements of piezo-optical tensor. Both these measurements can be done on a single crystal sample that is hard to obtain.

In ceramics, Qeff is a quantitative characteristic of the material in terms of thermally induced polarization distortions. The less the Qeff value, the less (at a fixed power of heat generation) the level of polarization distortions induced by the thermally loaded optical element, and therefore is less losses in the fundamental mode and higher quality of the transmitted radiation.

The thermally induced depolarization was measured using the scheme presented in Fig. 1
Fig. 1 а) Schematic of the experiment on measuring thermally induced depolarization; b) cross-sections of intensity distribution of probe – blue curve and heating – red curve radiation in the region of the studied sample.
(а).

The sample was heated by continuous radiation of a diode laser at 940 nm wavelength. The maximum power of the heating radiation was 75 W. A continuous ytterbium fiber laser at 1076 nm was used as a source of linearly polarized probe radiation. The intensity distributions of heating and probe radiation over beam cross section in the area of the studied sample had a profile close to a Gaussian one [see Fig. 1(b)]. A calcite wedge ensured linearity of the polarization and good contrast of the scheme (less than 2∙10−6 for the entire power range of the heating radiation). Fused quartz wedges attenuated radiation. Glan prism was adjusted to a minimum of the transmitted signal whose intensity distribution was measured by a CCD camera. By turning the Glan prism by 90° we could record using the CCD camera intensity distribution of the main component of the field. The value of integral depolarization was calculated as a ratio of the radiation power incident on the CCD camera at crossed calcite wedge and the Glan prism to the total power of probe radiation incident on the Glan prism.

The dependence of integral depolarization on heat release power measured in experiment for three sesquioxide ceramic samples are shown by the squares in Fig. 2
Fig. 2 Integral depolarization plotted versus heat release power. Red –Yb3 + :Y2O3, blue – Yb3 + :Sc2O3, green – Yb3 + :Lu2O3.
. The straight lines are for the theoretical curves plotted according to Eq. (1), and the values of Qeff at which the experimental and theoretical data agree best are presented in Table 2

Table 2. Thermo-optical constants of the studied sesquioxide ceramics and comparison with available data from the literature

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. The integral depolarization at small heat generation power arising due to the inhomogeneity and imperfection of these polycrystalline ceramics small (<10−5) and close to the value of “cold” depolarization in good optical quality single crystal. Local distribution of depolarization at small heat generation power was uniformly distributed across the whole aperture of the each samples.

The sign of Qeff may be determined by the behavior of the local depolarization distribution as a function of the character of ellipticity of incident radiation polarization. When small ellipticity is induced in the incident radiation the four-leaf symmetry of spatial distribution of the depolarization will change in different ways, depending on the sign of Qeff. Knowing the sign of this coefficient for an Y3Al5O12 single crystal and comparing the behavior of local depolarization distribution in Y3Al5O12 and in sesquioxide samples we found that they have the same sign of thermo-optical constant Q. Now we know Qeff /κ and its sign for all three sesquioxide materials at room temperature and at wavelength 1076 nm.

3. Estimation of thermo-optical constant P

P=dndTαTn033E1ν(π11+π12).
(4)

The parameter P is proportional to the wave aberration averaged for two orthogonal polarizations and includes changes of the refractive index as a function of temperature stresses. Not all material constants for the studied sesquioxides materials in the Eq. (4) are known. So we have made estimates of the thermo-optical parameter P based on experimental measurements of thermal lens.

For the parabolic temperature distribution in the sample P is proportional to the strength of the thermal lens. The Eq. (4) was derived [20

20. I. L. Snetkov, I. B. Mukhin, O. V. Palashov, and E. A. Khazanov, “Properties of a thermal lens in laser ceramics,” Quantum Electron. 37(7), 633–638 (2007). [CrossRef]

] for axisymmetric heating radiation with flat-top intensity distribution over the cross section and holds true for polar radii smaller than the radius of heating radiation r<rh. The phase incursion constant over the cross-section is neglected in this expression, as it does not contribute to the thermal lens strength. For the majority of optical materials the magnitude of thermo-optical constant P is an order of magnitude larger than the magnitude of thermo-optical constant Q, hence the second term in the square brackets in (3) may be omitted and the expression will be written in the form

Ψn=kP4πrh2κPhr2,
(5)

For thick samples the optical force of the thermal lens is determined by the thermo-optical constant P and the contribution of thermal expansion can be neglected. For thin samples, when the contributions of sample expansion and of refractive index changes to the optical force of thermal lens 1/F are comparable, necessary to measure its contributions separately. We measured phase distortions using the method of phase-shift interferometry described, for example, in [21

21. A. A. Soloviev, I. L. Snetkov, V. V. Zelenogorsky, I. E. Kozhevatov, O. V. Palashov, and E. A. Khazanov, “Experimental study of thermal lens features in laser ceramics,” Opt. Express 16(25), 21012–21021 (2008). [CrossRef] [PubMed]

, 23

23. V. V. Zelenogorsky, A. A. Solovyov, I. E. Kozhevatov, E. E. Kamenetsky, E. A. Rudenchik, O. V. Palashov, D. E. Silin, and E. A. Khazanov, “High-precision methods and devices for in situ measurements of thermally induced aberrations in optical elements,” Appl. Opt. 45(17), 4092–4101 (2006). [CrossRef] [PubMed]

]. The schematic of the experiment is shown in Fig. 3
Fig. 3 Interference scheme of the experiment (а) and scheme of measuring phase distortions (b).
(а). The studied sample was heated by continuous radiation of a diode laser at the wavelength of 940 nm. The beam radius of the heating radiation was 1.08 mm and had flat-top profile. A diode laser with central wavelength of 1060 nm was used as a probe signal source. Michelson interferometer was assembled for measurements. The measured sample was placed in one of its arms, and in the second arm the radiation was reflected from a reference mirror whose position was varied within half wavelength by applying voltage to piezo-electric stacks. A series of interferograms were recorded that were then processed to find phase distortion distributions [24

24. D. E. Silin and I. E. Kozhevatov, “A single mode fiber based point diffraction interferometer,” Opt. Spectrosc. 113(2), 216–221 (2012). [CrossRef]

]. Interference patterns were measured with and without pump radiation, at beam interference from the reference mirror and from three surfaces: the front surface of the studied sample, its rear surface and the mirror behind the sample by turn [Fig. 3(b)].

By subtracting the phase distributions obtained without pump radiation from the distortion with pump radiation we obtained difference phase distributions Δ. Taking into consideration that Δ1, Δ2 and Δ3 were obtained at the interference from the front and rear surfaces of the studied sample and from the mirror behind the sample, respectively, we can obtain the following expressions

{Δ1=ΔS1Δ2=ΔS1+Δn(S2S1)+n0(ΔS2ΔS1)Δ3=ΔS1+Δn(S2S1)+n0(ΔS2ΔS1)ΔS2.
(8)

Taking into account that
S1S2=LΔS1ΔS2=ΔL,
(9)
for the change of sample’s length and refractive index we obtain

{ΔL=Δ2Δ3Δ1Δn=[Δ3(n01)(Δ2Δ3Δ1)]/L.
(10)

Thus, on finding phase distortions in the three above measurements we can separate the heat induced contributions associated with the change of sample’s geometrical dimensions and with the volume changes of the index of refraction. For further estimates we used the area of phase distortion distribution that did not exceed the transverse size of heating radiation. The experimental data were approximated by the paraboloid of revolution in the sense of minimizing root mean square deviation. The characteristic distributions of phase distortions and of the approximating paraboloid are depicted in Fig. 4
Fig. 4 Characteristic distribution of phase distortions and the approximating paraboloid of revolution.
.

The strength of the thermal lens was calculated from parameters of the approximating paraboloid. The approximation was done for phase distortion distributions ΔL and Δn separately for all values of power in each studied sample. The dependence of thermal lens strength on heat release power is plotted in Fig. 5
Fig. 5 The strength of thermal lens arising due to thermal expansion of the sample (blue squares) and due to changes of the index of refraction in the sample bulk (red circles) as a function of heat release power for three samples of sesquioxide ceramics.
for all the studied samples.

Using Eq. (5)-(7) and values of thermal lens strength for the studied samples of sesquioxide ceramics we determined values of the P/κ and αT/κ that are listed in Table 2. The values of κ, αT and dn/dT found in the literature for all studied materials are also given in the Table 2.

The Eq. (5) was derived neglecting the term containing Q. Comparison of the data from Table 2 shows that the thermo-optical constant P is about an order of magnitude larger than Q (exact values of the stress-optic anisotropy ratio ξ for sesquioxides are unknown, as was mentioned above, but generally they were of order 1).

It is well known that impurity concentration and the method of manufacturing material greatly influence thermal conductivity [5

5. R. Peters, C. Krankel, S. T. Fredrich-Thornton, K. Beil, K. Petermann, G. Huber, O. H. Heckl, C. R. E. Baer, C. J. Saraceno, T. Südmeyer, and U. Keller, “Thermal analysis and efficient high power continuous-wave and mode-locked thin disk laser operation of Yb-doped sesquioxides,” Appl. Phys. B 102(3), 509–514 (2011). [CrossRef]

]. The data obtained from the experiment measurements depend on the value of thermal conductivity, unknown for our samples. As was shown in [25

25. V. Cardinali, E. Marmois, B. Le Garrec, and G. Bourdet, “Determination of the thermo-optic coefficient dn/dT of ytterbium doped ceramics (Sc2O3,Y2O3,Lu2O3, YAG), crystals (YAG, CaF2) and neodymium doped phosphate glass at cryogenic temperature,” Opt. Mater. 34(6), 990–994 (2012). [CrossRef]

, 26

26. R. Yasuhara, H. Furuse, A. Iwamoto, J. Kawanaka, and T. Yanagitani, “Evaluation of thermo-optic characteristics of cryogenically cooled Yb:YAG ceramics,” Opt. Express 20(28), 29531–29539 (2012). [CrossRef] [PubMed]

], the coefficients of linear expansion of the single-crystal and ceramic samples are the same and are practically independent of the concentration of the Yb3+ (at reasonable of its values 0-10 at.%). Using the values of the coefficients of linear expansion from [6

6. J. Sanghera, W. Kim, G. Villalobos, B. Shaw, C. Baker, J. Frantz, B. Sadowski, and I. Aggarwal, “Ceramic laser materials,” Proc. SPIE 7912, 79121K (2011). [CrossRef]

, 25

25. V. Cardinali, E. Marmois, B. Le Garrec, and G. Bourdet, “Determination of the thermo-optic coefficient dn/dT of ytterbium doped ceramics (Sc2O3,Y2O3,Lu2O3, YAG), crystals (YAG, CaF2) and neodymium doped phosphate glass at cryogenic temperature,” Opt. Mater. 34(6), 990–994 (2012). [CrossRef]

] we can estimate the thermal conductivity of our ceramic samples (see line 4 in Table 2).

The presence of ceramic grains and the boundaries between them in ceramics by the theory could leads only to a reduction of the thermal conductivity value. But the small fraction of volume boundaries in the ceramic material and the comparable number of inclusions and inhomogeneity of structure may result in the ceramics to the same value of thermal conductivity, as in the single crystal. Therefore, at all other equal conditions the value of thermal conductivity allow to judge the quality of the ceramic material. As can be seen from Table 2, the estimates of the thermal conductivity obtained for Y2O3 and Lu2O3 ceramic samples are very close to presented in [5

5. R. Peters, C. Krankel, S. T. Fredrich-Thornton, K. Beil, K. Petermann, G. Huber, O. H. Heckl, C. R. E. Baer, C. J. Saraceno, T. Südmeyer, and U. Keller, “Thermal analysis and efficient high power continuous-wave and mode-locked thin disk laser operation of Yb-doped sesquioxides,” Appl. Phys. B 102(3), 509–514 (2011). [CrossRef]

] for single crystals with the same concentration of Yb3+. This indicates comparable quality of investigated ceramic samples. The Sc2O3 ceramic sample demonstrated quite smaller value of thermal conductivity coefficient than single-crystal.

Using the obtained values of the thermal conductivity from experimental data can be estimated value of thermo-optical constants of P and Qeff (see line 5 and 6 in Table 2).

4. Discussion

Parasitic thermal effects (thermal depolarization and thermal lens) of three samples of Konoshima Chemical Co. laser ceramics Yb3+:Lu2O3 (CYb≈1.8 at.%), Yb3+:Y2O3 (CYb≈1.8 at.%), and Yb3+:Sc2O3 (CYb≈2.5 at.%), were measured in experiments as a function of laser radiation power. The results of measurements were used to calculate thermo-optical constants κ, P and Qeff.

We’d like to note, that all three samples of sesquioxide ceramic samples had very good optical quality (did not distort profile of the transmitted radiation, had a weak “cold” scattering). Analyzing the data from Table 2, we’d like to mention, that our estimations of the thermal conductivity for studied sesquioxide ceramic samples are close to thermal conductivity of a single crystal with same concentration of Yb ion. It may be an additional proof of the high (comparable to the single crystals) quality of the investigated ceramic samples.

It could be seen, that the Lu2O3 and Sc2O3 for the same heat release power have very similar to each other Qeff value and for Y2O3 sample Qeff value is 30% less. Since the thermally induced depolarization is proportional to the squared Qeff, this difference leads to more than twofold decrease of the integral depolarization value with the same heat dissipation.

Comparing the Qeff values, and taking into account the dependence of the thermal conductivity of these materials on the concentration of Yb3+ [5

5. R. Peters, C. Krankel, S. T. Fredrich-Thornton, K. Beil, K. Petermann, G. Huber, O. H. Heckl, C. R. E. Baer, C. J. Saraceno, T. Südmeyer, and U. Keller, “Thermal analysis and efficient high power continuous-wave and mode-locked thin disk laser operation of Yb-doped sesquioxides,” Appl. Phys. B 102(3), 509–514 (2011). [CrossRef]

], we can say that the active elements with a high concentration of Yb3+ in terms of thermally induced polarization distortions preferable Lu2O3, since at concentrations greater than 4 at.% thermally induced depolarization in this material will be less than in Y2O3 and in Sc2O3. On the contrary, in the active elements with a low concentration value Yb3+ is preferable to use a material Sc2O3, since its Qeff less on 15% and the thermal conductivity with decreasing concentration of Yb3+ grows significantly faster than in Y2O3. At concentrations of less than 1 at.% of Yb3+ thermally induced depolarization arising in Sc2O3 is less than in the material of Y2O3 or Lu2O3. In comparison for Y3Al5O12 Qeff = −12,8∙10−7 1/K at room temperature and wavelength of 1030 nm [27

27. I. B. Mukhin, O. V. Palashov, E. A. Khazanov, A. G. Vyatkin, and E. A. Perevezentsev, “Laser and thermal characteristics of Yb:YAG crystals in the 80 – 300 K temperature range,” Quantum Electron. 41(11), 1045–1050 (2011). [CrossRef]

]. It should be noted that the above arguments are valid only on the assumption that the thermal conductivity in the sesqui-oxide ceramic samples has the same dependence on the concentration of Yb3+, as in the single crystals, which in itself requires experimental confirmation. I’d only note that good quality Y3Al5O12 ceramics shows the same amount of thermal conductivity as a single crystal with the same dopant concentration [28

28. A. Ikesue, I. Furusato, and K. Kamata, “Fabrication of polycrystalline, transparent YAG ceramics by a solid-state reaction method,” J. Am. Ceram. Soc. 78(1), 225–228 (1995). [CrossRef]

].

Comparing the value of thermo-optical constant P, we note material Sc2O3, where its value is much smaller than in the materials Y2O3, and Lu2O3. As with the polarization distortion, power of the thermal lens is inversely proportional to thermal conductivity, which is a function of the concentration of Yb3+. For Sc2O3 value for P/κ less than in Y2O3 and in Lu2O3, for the whole range of Yb3+ concentrations, represented in [5

5. R. Peters, C. Krankel, S. T. Fredrich-Thornton, K. Beil, K. Petermann, G. Huber, O. H. Heckl, C. R. E. Baer, C. J. Saraceno, T. Südmeyer, and U. Keller, “Thermal analysis and efficient high power continuous-wave and mode-locked thin disk laser operation of Yb-doped sesquioxides,” Appl. Phys. B 102(3), 509–514 (2011). [CrossRef]

]. The lower the value thermo-optical constant P, the smaller the power of induced thermal lens in the volume of optical element. For comparison we give value the of P for Y3Al5O12, which is 9,4∙10−6 [1/K] at room temperature for radiation at 1030 nm wavelength [27

27. I. B. Mukhin, O. V. Palashov, E. A. Khazanov, A. G. Vyatkin, and E. A. Perevezentsev, “Laser and thermal characteristics of Yb:YAG crystals in the 80 – 300 K temperature range,” Quantum Electron. 41(11), 1045–1050 (2011). [CrossRef]

].

5. Conclusion

Acknowledgments

Authors acknowledge Program of Presidium of Russian Academy of Science “Extreme light and its application” and Mega Grant of Government of the Russian Federation “Diagnosis of new optical media for the advanced lasers” Nº 14.B25.31.0024.

References and links

1.

W. Koechner, Solid-State Laser Engineering (Springer, 1999).

2.

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3.

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4.

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5.

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6.

J. Sanghera, W. Kim, G. Villalobos, B. Shaw, C. Baker, J. Frantz, B. Sadowski, and I. Aggarwal, “Ceramic laser materials,” Proc. SPIE 7912, 79121K (2011). [CrossRef]

7.

C. R. E. Baer, C. Kränkel, C. J. Saraceno, O. H. Heckl, M. Golling, R. Peters, K. Petermann, T. Südmeyer, G. Huber, and U. Keller, “Femtosecond thin-disk laser with 141 W of average power,” Opt. Lett. 35(13), 2302–2304 (2010). [CrossRef] [PubMed]

8.

R. Peters, C. Krankel, K. Petermann, and G. Huber, “Crystal growth by the heat exchanger method, spectroscopic characterization and laser operation of high-purity Yb:Lu2O3,” J. Cryst. Growth 310(7-9), 1934–1938 (2008). [CrossRef]

9.

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]

10.

J. Lu, J. Song, M. Prabhu, J. Xu, K. Ueda, H. Yagi, T. Yanagitani, and A. Kudryashov, “High-power Nd:Y3Al5O12 ceramic laser,” Jpn. J. Appl. Phys. 39(Part 2, No. 10B), L1048–L1050 (2000). [CrossRef]

11.

J. R. Lu, J. H. Lu, T. Murai, K. Takaichi, T. Uematsu, K. Ueda, H. Yagi, T. Yanagitani, and A. A. Kaminskii, “Nd3+:Y2O3 ceramic laser,” Jpn. J. Appl. Phys. 40(Part 2, No. 12A), L1277–L1279 (2001). [CrossRef]

12.

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

13.

J. Lu, K. Takaichi, T. Uematsu, A. Shirakawa, M. Musha, K. Ueda, H. Yagi, T. Yanagitani, and A. Kaminskii, “Promising ceramic laser material: highly transparent Nd3+:Lu2O3 ceramic,” Appl. Phys. Lett. 81(23), 4324–4326 (2002). [CrossRef]

14.

J. D. Foster and L. M. Osterink, “Thermal effects in a Nd:YAG laser,” J. Appl. Phys. 41(9), 3656–3663 (1970). [CrossRef]

15.

W. Koechner and D. K. Rice, “Effect of birefringence on the performance of linearly polarized YAG:Nd lasers,” IEEE J. Quantum Electron. 6(9), 557–566 (1970). [CrossRef]

16.

M. A. Kagan and E. A. Khazanov, “Compensation for thermally induced birefringence in polycrystalline ceramic active elements,” Quantum Electron. 33(10), 876–882 (2003). [CrossRef]

17.

A. G. Vyatkin and E. A. Khazanov, “Thermally induced scattering of radiation in laser ceramics with arbitrary grain size,” J. Opt. Soc. Am. B 29(12), 3307–3316 (2012). [CrossRef]

18.

J. F. Nye, Physical Properties of Crystals (Oxford University, 1964).

19.

I. L. Snetkov, A. G. Vyatkin, O. V. Palashov, and E. A. Khazanov, “Drastic reduction of thermally induced depolarization in CaF₂ crystals with [111] orientation,” Opt. Express 20(12), 13357–13367 (2012). [CrossRef] [PubMed]

20.

I. L. Snetkov, I. B. Mukhin, O. V. Palashov, and E. A. Khazanov, “Properties of a thermal lens in laser ceramics,” Quantum Electron. 37(7), 633–638 (2007). [CrossRef]

21.

A. A. Soloviev, I. L. Snetkov, V. V. Zelenogorsky, I. E. Kozhevatov, O. V. Palashov, and E. A. Khazanov, “Experimental study of thermal lens features in laser ceramics,” Opt. Express 16(25), 21012–21021 (2008). [CrossRef] [PubMed]

22.

A. V. Mezenov, L. N. Soms, and A. I. Stepanov, Thermooptics of Solid-State Lasers (Mashinebuilding, 1986).

23.

V. V. Zelenogorsky, A. A. Solovyov, I. E. Kozhevatov, E. E. Kamenetsky, E. A. Rudenchik, O. V. Palashov, D. E. Silin, and E. A. Khazanov, “High-precision methods and devices for in situ measurements of thermally induced aberrations in optical elements,” Appl. Opt. 45(17), 4092–4101 (2006). [CrossRef] [PubMed]

24.

D. E. Silin and I. E. Kozhevatov, “A single mode fiber based point diffraction interferometer,” Opt. Spectrosc. 113(2), 216–221 (2012). [CrossRef]

25.

V. Cardinali, E. Marmois, B. Le Garrec, and G. Bourdet, “Determination of the thermo-optic coefficient dn/dT of ytterbium doped ceramics (Sc2O3,Y2O3,Lu2O3, YAG), crystals (YAG, CaF2) and neodymium doped phosphate glass at cryogenic temperature,” Opt. Mater. 34(6), 990–994 (2012). [CrossRef]

26.

R. Yasuhara, H. Furuse, A. Iwamoto, J. Kawanaka, and T. Yanagitani, “Evaluation of thermo-optic characteristics of cryogenically cooled Yb:YAG ceramics,” Opt. Express 20(28), 29531–29539 (2012). [CrossRef] [PubMed]

27.

I. B. Mukhin, O. V. Palashov, E. A. Khazanov, A. G. Vyatkin, and E. A. Perevezentsev, “Laser and thermal characteristics of Yb:YAG crystals in the 80 – 300 K temperature range,” Quantum Electron. 41(11), 1045–1050 (2011). [CrossRef]

28.

A. Ikesue, I. Furusato, and K. Kamata, “Fabrication of polycrystalline, transparent YAG ceramics by a solid-state reaction method,” J. Am. Ceram. Soc. 78(1), 225–228 (1995). [CrossRef]

OCIS Codes
(120.4530) Instrumentation, measurement, and metrology : Optical constants
(120.6810) Instrumentation, measurement, and metrology : Thermal effects
(140.3380) Lasers and laser optics : Laser materials
(140.6810) Lasers and laser optics : Thermal effects
(160.3380) Materials : Laser materials
(160.4760) Materials : Optical properties

ToC Category:
Materials

History
Original Manuscript: July 1, 2013
Revised Manuscript: August 23, 2013
Manuscript Accepted: August 23, 2013
Published: September 4, 2013

Citation
Ilya L. Snetkov, Dmitry E. Silin, Oleg V. Palashov, Efim A. Khazanov, Hideki Yagi, Takagimi Yanagitani, Hitoki Yoneda, Akira Shirakawa, Ken-ichi Ueda, and Alexander A. Kaminskii, "Study of the thermo-optical constants of Yb doped Y2O3, Lu2O3 and Sc2O3 ceramic materials," Opt. Express 21, 21254-21263 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-18-21254


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References

  1. W. Koechner, Solid-State Laser Engineering (Springer, 1999).
  2. P. Klein and W. Croft, “Thermal conductivity, diffusivity, and expansion of Y2O3, Y3Al5O12, and LaF3 in the range 77-300 K,” J. Appl. Phys.38(4), 1603–1607 (1967). [CrossRef]
  3. T. Y. Fan, D. J. Ripin, R. L. Aggarwal, J. R. Ochoa, B. Chann, M. Tilleman, and J. Spitzberg, “Cryogenic Yb3+-doped solid-state lasers,” IEEE J. Sel. Top. Quantum Electron.13(3), 448–459 (2007). [CrossRef]
  4. T. Südmeyer, C. Kränkel, C. R. E. Baer, O. H. Heckl, C. J. Saraceno, M. Golling, R. Peters, K. Petermann, G. Huber, and U. Keller, “High-power ultrafast thin disk laser oscillators and their potential for sub-100-femtosecond pulse generation,” Appl. Phys. B97(2), 281–295 (2009). [CrossRef]
  5. R. Peters, C. Krankel, S. T. Fredrich-Thornton, K. Beil, K. Petermann, G. Huber, O. H. Heckl, C. R. E. Baer, C. J. Saraceno, T. Südmeyer, and U. Keller, “Thermal analysis and efficient high power continuous-wave and mode-locked thin disk laser operation of Yb-doped sesquioxides,” Appl. Phys. B102(3), 509–514 (2011). [CrossRef]
  6. J. Sanghera, W. Kim, G. Villalobos, B. Shaw, C. Baker, J. Frantz, B. Sadowski, and I. Aggarwal, “Ceramic laser materials,” Proc. SPIE7912, 79121K (2011). [CrossRef]
  7. C. R. E. Baer, C. Kränkel, C. J. Saraceno, O. H. Heckl, M. Golling, R. Peters, K. Petermann, T. Südmeyer, G. Huber, and U. Keller, “Femtosecond thin-disk laser with 141 W of average power,” Opt. Lett.35(13), 2302–2304 (2010). [CrossRef] [PubMed]
  8. R. Peters, C. Krankel, K. Petermann, and G. Huber, “Crystal growth by the heat exchanger method, spectroscopic characterization and laser operation of high-purity Yb:Lu2O3,” J. Cryst. Growth310(7-9), 1934–1938 (2008). [CrossRef]
  9. 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]
  10. J. Lu, J. Song, M. Prabhu, J. Xu, K. Ueda, H. Yagi, T. Yanagitani, and A. Kudryashov, “High-power Nd:Y3Al5O12 ceramic laser,” Jpn. J. Appl. Phys.39(Part 2, No. 10B), L1048–L1050 (2000). [CrossRef]
  11. J. R. Lu, J. H. Lu, T. Murai, K. Takaichi, T. Uematsu, K. Ueda, H. Yagi, T. Yanagitani, and A. A. Kaminskii, “Nd3+:Y2O3 ceramic laser,” Jpn. J. Appl. Phys.40(Part 2, No. 12A), L1277–L1279 (2001). [CrossRef]
  12. J. Lu, J.-F. Bisson, K. Takaichi, T. Uematsu, A. Shirakawa, M. Musha, K. Ueda, H. Yagi, T. Yanagitani, and A. Kaminskii, “Yb3+:Sc2O3 ceramic laser,” Appl. Phys. Lett.83(6), 1101–1103 (2003). [CrossRef]
  13. J. Lu, K. Takaichi, T. Uematsu, A. Shirakawa, M. Musha, K. Ueda, H. Yagi, T. Yanagitani, and A. Kaminskii, “Promising ceramic laser material: highly transparent Nd3+:Lu2O3 ceramic,” Appl. Phys. Lett.81(23), 4324–4326 (2002). [CrossRef]
  14. J. D. Foster and L. M. Osterink, “Thermal effects in a Nd:YAG laser,” J. Appl. Phys.41(9), 3656–3663 (1970). [CrossRef]
  15. W. Koechner and D. K. Rice, “Effect of birefringence on the performance of linearly polarized YAG:Nd lasers,” IEEE J. Quantum Electron.6(9), 557–566 (1970). [CrossRef]
  16. M. A. Kagan and E. A. Khazanov, “Compensation for thermally induced birefringence in polycrystalline ceramic active elements,” Quantum Electron.33(10), 876–882 (2003). [CrossRef]
  17. A. G. Vyatkin and E. A. Khazanov, “Thermally induced scattering of radiation in laser ceramics with arbitrary grain size,” J. Opt. Soc. Am. B29(12), 3307–3316 (2012). [CrossRef]
  18. J. F. Nye, Physical Properties of Crystals (Oxford University, 1964).
  19. I. L. Snetkov, A. G. Vyatkin, O. V. Palashov, and E. A. Khazanov, “Drastic reduction of thermally induced depolarization in CaF₂ crystals with [111] orientation,” Opt. Express20(12), 13357–13367 (2012). [CrossRef] [PubMed]
  20. I. L. Snetkov, I. B. Mukhin, O. V. Palashov, and E. A. Khazanov, “Properties of a thermal lens in laser ceramics,” Quantum Electron.37(7), 633–638 (2007). [CrossRef]
  21. A. A. Soloviev, I. L. Snetkov, V. V. Zelenogorsky, I. E. Kozhevatov, O. V. Palashov, and E. A. Khazanov, “Experimental study of thermal lens features in laser ceramics,” Opt. Express16(25), 21012–21021 (2008). [CrossRef] [PubMed]
  22. A. V. Mezenov, L. N. Soms, and A. I. Stepanov, Thermooptics of Solid-State Lasers (Mashinebuilding, 1986).
  23. V. V. Zelenogorsky, A. A. Solovyov, I. E. Kozhevatov, E. E. Kamenetsky, E. A. Rudenchik, O. V. Palashov, D. E. Silin, and E. A. Khazanov, “High-precision methods and devices for in situ measurements of thermally induced aberrations in optical elements,” Appl. Opt.45(17), 4092–4101 (2006). [CrossRef] [PubMed]
  24. D. E. Silin and I. E. Kozhevatov, “A single mode fiber based point diffraction interferometer,” Opt. Spectrosc.113(2), 216–221 (2012). [CrossRef]
  25. V. Cardinali, E. Marmois, B. Le Garrec, and G. Bourdet, “Determination of the thermo-optic coefficient dn/dT of ytterbium doped ceramics (Sc2O3,Y2O3,Lu2O3, YAG), crystals (YAG, CaF2) and neodymium doped phosphate glass at cryogenic temperature,” Opt. Mater.34(6), 990–994 (2012). [CrossRef]
  26. R. Yasuhara, H. Furuse, A. Iwamoto, J. Kawanaka, and T. Yanagitani, “Evaluation of thermo-optic characteristics of cryogenically cooled Yb:YAG ceramics,” Opt. Express20(28), 29531–29539 (2012). [CrossRef] [PubMed]
  27. I. B. Mukhin, O. V. Palashov, E. A. Khazanov, A. G. Vyatkin, and E. A. Perevezentsev, “Laser and thermal characteristics of Yb:YAG crystals in the 80 – 300 K temperature range,” Quantum Electron.41(11), 1045–1050 (2011). [CrossRef]
  28. A. Ikesue, I. Furusato, and K. Kamata, “Fabrication of polycrystalline, transparent YAG ceramics by a solid-state reaction method,” J. Am. Ceram. Soc.78(1), 225–228 (1995). [CrossRef]

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