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Thermal properties of a lowly Nd3+-doped disordered Nd:CNGG crystal have been symmetrically investigated. At room temperature, the specific heat, thermal diffusion coefficient and density were determined to be 0.595 J/g.K, 1.223 mm2/s and 4.718 g/cm3, corresponding the thermal conductivity of 3.43 W/m.K. By measuring the thermal lens at different pump power, the thermal-optical coefficient was calculated to be 9.2×10-6K-1 for the first time to our knowledge. All the thermal properties recovered that this material can be used in the moderate and even high pump power.
©2009 Optical Society of America
1. Introduction
Recent years, rare-earth ions doped disordered crystals have been attracted more and more attentions, due to their unique thermal and spectral properties [1–6]. Compared with rare-earth ions doped glasses, these crystals have more excellent thermal properties [1]. Because of the inhomogeneous broadening in the spectra, disordered laser crystals have much broad absorption and emission spectra than the same ions-doped ordered crystals [2–4], including Nd:YAG, Yb:YAG, and Nd:YVO4. Among them, Nd3+-doped CNGG is the one, which has been most extensively studied. In the past, limited by its small fracture limited power, the maximum cw output power was just 1.65 W at 1.06 μm [7]. Based on the research by our group [8] and Chen [9], the fracture limited power can be improved by lowly doping concentrations of Nd3+ in the host crystals. Recently, Yu et al. have achieved the cw output power to be as high as over than 4 W with a 0.5 at.% Nd3+-doped CNGG crystal and shown that this lowly Nd3+-doped crystal are more favorable in the moderate and even high pump power [10]. As a laser material, its fracture limited power was influenced by its thermal properties which are also critical for its laser properties. The pump-induced thermal lens, greatly depending on the thermal conductivity and thermal-optical coefficient (dn/dT), is also important for the laser output and cavity design especially in the high pump power. Unfortunately, up to now, the thermal properties, including specific heat, thermal diffusion coefficient, thermal conductivity and even the thermal–optical coefficient of lowly doped Nd:CNGG have not been reported yet. In this paper, the thermal properties of lowly Nd3+-doped Nd:CNGG crystal with concentration of 0.5 at.% was symmetrically studied. The change of thermal expansion, specific heat, thermal diffusion, and thermal conductivity with temperature were investigated detailedly. By measuring the thermal lens, the thermal-optical coefficient of Nd:CNGG was calculated. All the results show that this crystal can be used in the moderate and even high pump power.
2. Experiments
The Nd:CNGG was grown by the Czochralski method with Nd2O3, Nb2O5, Ga2O3 and CaCO3 as raw materials. By the X-ray fluorescence method, the Nd-doped concentration in the crystal was measured to be 0.5at.%. A rectangular YAG single crystal bar cut along <111> direction with dimensions of 3 mm×3 mm×20 mm was used as the seed. As-grown Nd:CNGG crystal was found with no inclusions, no low-angle boundaries and other macroscopic defects. Observed under a 10 mW He-Ne laser, there are no light-scattering pellets in the crystal, which means the as-grown Nd:CNGG crystal has good optical qualities. Before measurement, the as-grown Nd:CNGG crystal boule was annealed to release any thermal stresses.
2.1. Specific heat
The specific heat is one of the important factors that greatly determine the optical damage threshold of a laser crystal. Crystals with larger specific heat usually have higher optical damage threshold and can maintain the least temperature change when absorbing the same amount of pump power.
Specific heat measurement of 0.5 at% Nd:CNGG was performed on a differential scanning calorimeter (NETZSCH DSC 204 F1) using the following procedure: First, two empty aluminum pans, with one for reference, were heated together from 20–400 °C at a rate of 10 °C /min to carry out the baseline measurement. Then, a sapphire calibration sample was placed in the sample pan and heated together with the reference pan over the same temperature range. Next, the same operation was performed with one of the crystal samples weighing around 60 mg in the sample pan. Finally, the specific heat was calculated using the associated software.
2.2. Thermal expansion coefficient
The thermal expansion coefficient is a second rank tensor and compliant with crystal symmetry. Thus, for the cubic crystal of Nd:CNGG, it has only one independent principle component α1 which can be obtained by measuring the thermal expansion of crystal sample processed along any direction. Here, a rectangular shape of 0.5at% Nd:CNGG crystal sample oriented along <001> direction with dimensions of 6.010 mm×6.300 mm×7.524 mm was used for the thermal expansion experiment. The measurement was performed on a thermal-mechanical analyzer (TMA) made by Perkin-Elmer over a temperature range of 30–500 °C.
2.3. Density
Using Eq. (1), density of 0.5at% Nd:CNGG crystal was measured by the buoyancy method at room temperature(29.5 °C):
where m is the mass of the crystal sample in air, m’ is the mass when it is immersed in water, and ρwater is the density of water at the measurement temperature (ρwater = 0.9958 g/cm3, 29.5 °C).
2.4. Thermal diffusion coefficient
The thermal diffusion coefficient is also a second rank tensor and has only one independent principle component λ1 for Nd:CNGG crystal. Using the laser flash method, measurement of thermal diffusion coefficient of 0.5 at% Nd:CNGG was carried out on Nanoflash model LFA447 over a temperature range of 30–300 °C. The sample used was <001> direction oriented with dimensions of 6×6×2.5 mm3 and coated with graphite on both sides.
2.5. Thermal-optical coefficient
Based on the analysis by Zhang et al. [11], the thermal-optical coefficient can be estimated by the thermal lens (f) of a laser crystal as Eq. (2):
Where k is the thermal conductivity, ωp is the radius of the pump-beam, Pth is the fraction of pump power that results in heat, Pth=(1-808/1060) Pabs=0.238Pabs, Pabs is the absorption power of Nd:CNGG, f is the thermal focal length of this crystal. By using the simple method presented by Song et al. [12], the thermal focal length of Nd:CNGG under different pump power can be obtained with a flat-flat resonator. The pump source was a fiber coupled LD with the emission wavelength centered at 808 nm. The beam of the source was collimated by a focusing optical system (N. A. = 0.22), and the focused spot in the laser crystal was about 0.256 mm in radius. The cavity was consisted of a flat-flat resonator. M1 was anti-reflection (AR) coated at 808 nm on the pump face, high-reflectance (HR) coated at 1.06 μm and high-transmittance (HT) coated at 808 nm on the other face. The output coupler M2 was HR coated at 808 nm and an output transmission of 1.6% at 1.06mm. The Nd:CNGG crystal sample with dimensions of 3×3×6 mm3 was AR coated at 1.06 μm on 3×3 mm2 faces. During the experiment, crystal sample was wrapped with indium foil and mounted on a copper block cooled by water. The cooling water was maintained at a temperature of 10 °C.
3. Results and discussion
3.1. Specific heat
The measured specific heat versus temperature curve of 0.5 at% Nd:CNGG is shown in Fig. 1 from which it can be noted that specific heat of crystal increases slightly with rinsing temperature. The behavior of this disordered crystal is similar with that of ordered crystals [15]. Nd:CNGG has a relatively large specific heat value of 0.595 J/g.K at 303K, comparable with that of Nd:YAG (0.59 J/g.K at 300K) [13] which has been used in the high pump power level.
3.2. Thermal expansion coefficient
Figure 2 shows the dependence of thermal expansion of 0.5 at% Nd:CNGG on temperature. The curve indicates that thermal expansion along <001> direction is almost linear over the measuring temperature range of 20–400 °C, and the crystal exhibits only expansion. The average linear thermal expansion coefficient, according to the measured thermal expansion curve, is calculated to be 7.88 × 10-6/K.
3.3. Density
The experimental density of Nd:CNGG, measured by buoyancy method, is found to be 4.718 g/cm3 at the measuring temperature of 29.5 °C.
The density can also be calculated theoretically with Eq. (3):
where m is the atomic weight of Nd:CNGG crystal, Z is the number of molecules in a unit cell, which is 8 for the disordered crystal, NA is Avogadro’s constant, V is the cell volume obtained from the cell parameter of Nd:CNGG which is 12.505Å. Theoretical density of 0.5 at%Nd:CNGG was calculated to be 4.756 g/cm3.
Due to thermal expansion, the density of a crystal will decrease when temperature increases. This dependence can be calculated using the equations as employed in Ref [14] when crystal sample is processed into a rectangular shape. With the measured density by buoyancy method and the thermal expansion, density of 0.5at% Nd:CNGG crystal as a function of temperature was obtained and shown in Fig. 3, which shows that density of the crystal almost linearly decreases with increasing temperature.
3.4. Thermal diffusion coefficient and thermal conductivity
Dependence of measured thermal diffusion coefficient of 0.5at% Nd:CNGG on temperature is shown in Fig. 4, which shows that the thermal diffusion coefficient decreases with increasing temperature and has a value of 1.223 mm2/s at 303K.
Thermal conductivity of Nd:CNGG also has only one independent principle component k1 which can be calculated using Eq. (4):
where ρ, cp, and λ denote the density, specific heat, and the thermal diffusion coefficient of Nd:CNGG crystal, respectively.
With measured data on ρ, cp, and λ, the thermal conductivity of 0.5at% Nd:CNGG was calculated. Results show that the thermal conductivity is 3.43 W/m.K at room temperature, which is nearly one third of that of Nd:YAG (14 W/m.K), but much higher than that of Nd:glass [13]. Figure 5 presents the thermal conductivity versus temperature curve over the whole measuring temperature range, the curve indicates that thermal conductivity shows a decreasing tendency with increasing temperature which is also similar with the ordered crystals [15].
According the analysis of thermal conductivity [16], the thermal conductivity of Nd:CNGG is mainly influenced by the variation in the mean free path of phonons. When the crystal is heated, interactions between phonons increase which in turns can lead to the reduction of the mean free path of the phonons, correspondingly, the decreasing of thermal conductivity with increasing of temperature. Compared with the higher thermal conductivity of Nd:YAG and Nd:GGG, we believed that the relative small value of Nd:CNGG may be attributed to the existence of large quantity of cationic vacancies and randomly substituting of Nb5+ and Ga3+ in a certain range [1, 17] in the disordered crystals, which in turns can lead to the reduction of the mean free path of phonons.
3.5. Thermal-optical coefficient
According to the stability theory of laser resonators, when the thermal focal length is equal to the length of cavity, this resonator becomes unstable and the output power decreases. So the thermal lens length can be measured experimentally. The thermal focal length at different absorbed pump power was shown in Fig. 6. By functional fitting with Eq. (2), the thermal-optical coefficient can be achieved to be 9.2×10-6 K-1, which is three times than that of Nd:GdVO4 crystal (2.7×10-6 K-1)[11].
4. Conclusions
A disordered Nd:CNGG crystal with lowly Nd3+-doping concentration has been successfully grown by the Czochralski method. Its thermal properties, including the thermal expansion, specific heat, thermal diffusion, thermal conductivity and thermal-optical coefficient have been investigated systematically. We believed that this thermal characterization of Nd:CNGG is necessary for the application of this material especially in the design of laser resonator.
Acknowledgment
This work is supported by the National Natural Science Foundation of China (No.50672050, 50721002 and 50911120083) and the Grant for State Key Program of China (2004CB619002).
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