A bulk mixed Nd3+:(LaxGd1-x)3Ga5O12 (Nd:LaGGG) laser crystal with dimensions of Ф 26 × 30 mm3 was successfully grown by the Czochralski (Cz) method. The structure and the effective segregation coefficients of Nd3+ and La3+ ions in the as-grown Nd:LaGGG crystal were measured. The thermal properties were also investigated as a function of temperature. In addition, the spectral properties were measured and the Judd-Ofelt (J-O) theory was applied to calculate the spectral parameters. In the 1062 nm CW laser operation, the maximum output power of 8.75 W was achieved. All the properties show that the Nd:LaGGG crystal is a promising laser materials.
©2012 Optical Society of America
Nowadays solid-state lasers are of current interest and great importance owing to their extensive applications in industrial, medical and scientific fields . Considerable efforts have been devoted to the research for excellent laser materials, which are the research keystones for developing new solid-state lasers. The Nd3+-doped glass, which has broad fluorescence lines that are favorable for mode-locking, was studied in detail. However, the poor thermal properties of Nd3+-doped glass limit its applications at high pump power level . The Yb3+-doped media also attract much attention duo to their outstanding properties, such as simple electronic structure, long fluorescence lifetime and broad absorption and emission bandwidth . However, the main disadvantage of Yb3+-doped materials is associated with the quite high threshold pump power required by the quasi-three-level system. The Nd3+-doped mixed laser crystal can be an excellent candidate to achieve both high power and ultrashort pulse laser, not only for its excellent spectral and laser properties , but also for its disordered nature resulting in inhomogeneous broadening of fluorescence lines, which are suitable for the mode-locking operation [4,5].
The Nd3+:Gd3Ga5O12 (Nd:GGG) crystal has been proved to be a good medium for the laser-diode (LD)-pumped solid-state laser at high power application and was chosen as the laser amplifier disk to build the 100-kW system by the Lawrence Livermore National laboratory . Compared with Nd3+:Y3Al5O12 (Nd:YAG), the Nd:GGG crystal has several advantages, including: easy to get larger size (no core growth), with higher Nd-ions concentration (greater than 4 at.%), and wider phase homogeneity with high pulling rate (up to 5 mm/h) . Actually the congruent melting composition of the GGG crystal is not stoichiometric, which should be expressed as Gd3[Gd0.02Ga1.98]Ga3O12 . Therefore, the Gd3+ ions occupy the big dodecahedral site and middle-size octahedral site at the same time. Additionally, the spectroscopic analysis of the Nd:GGG crystal confirms that there are two different kinds of sites occupied by the Nd3+ ions . It was found that a mixed crystal Nd3+:(LuxGd1-x)3Ga5O12 (Nd:LGGG) was produced by substituting a fraction of Gd3+ ions with Lu3+ ions in the Nd:GGG crystal . Compared with the Nd3+ single doped GGG crystal, in Nd:LGGG crystal both the Nd3+ and Lu3+ ions have the chance to enter the dodecahedral site and octahedral site, which makes the crystal structure more complex and more disordered. As a result the Nd3+ emission brand in the LGGG crystal was broadened dramatically comparing with that in the Nd:GGG crystal, and the spectroscopy and laser performance have been studied, which demonstrates that the Nd:LGGG crystal is suitable for Q-switching and mode-locking operation because of its broader fluorescence line width [11,12]. In consideration of lower price, but with similar property as host laser crystal, of La2O3 powder comparing with Lu2O3, the Nd:LaGGG mixed crystal could be grown with La3+ ions replacing a fraction of Gd3+ ions in the Nd:GGG crystal. Similar to Lu3+ ions in the Nd:LGGG crystal, the La3+ ions can make the structure of Nd:LaGGG more disordered. In addition, the random distribution of the La3+ and Gd3+ ions neighboring the Nd3+ ions can offer a number of nonequivalent crystal field for Nd3+ ions. Due to Nd3+ multi-center distribution and the more complex structure of host material, we believe that the Nd:LaGGG crystal can possess wider inhomogeneous broadened spectra, which would be suitable for mode-locking operation. However, the growth of mixed single crystal Nd:LaGGG has not yet been reported up to now.
In this paper, a new bulk mixed Nd:LaGGG laser crystal with dimensions of Ф 26 × 30 mm3 was successfully grown by the Cz method. The structure and the effective segregation coefficients of Nd3+ and La3+ ions in the as-grown Nd:LaGGG crystal were investigated. A study of the thermal properties, including average linear thermal expansion coefficient, specific heat, thermal diffusion coefficient and thermal conductivity, was also carried out. Additionally, the spectral properties of the crystal at room temperature were also measured. Based on the room-temperature absorption spectrum, the spectral parameters of the Nd:LaGGG crystal were calculated using the Judd-Ofelt theory. In the 1062 nm CW laser operation, the maximum output power of 8.75 W was achieved with the optical-to-optical and slope efficiency of 39.7% and 40.4%, respectively.
2.1 Crystal growth
The Nd:LaGGG single crystal was grown by the Cz method in an iridium crucible with dimensions of Ф 60 × 60 mm3, under an argon atmosphere to prevent the oxidization of the crucible. The starting materials Nd2O3, La2O3, Gd2O3 and Ga2O3 with purity of 99.99% were accurately weighed and adequately mixed, and then pressed into tablets. Afterwards the polycrystalline materials were synthesized by conventional solid-state reaction according to the following chemical formula:
The Nd:LaGGG crystal was grown using the automatic diameter control (ADC) Czochralski furnace with an RF induction heating. The synthesized polycrystalline materials were loaded into the iridium crucible and melted at right temperature. A <111> direction Nd:GGG crystal with a rectangular piece of dimensions 5 × 5 × 40 mm3 was used as a seed. The pulling rate and rotation rate were set to be 1-1.5 mm/h and 20-25 rpm, respectively. After the growth was completed, the crystal was cooled down to the room temperature at a rate of 50-55 °C/h. Because the crystal growth was carried out in an oxygen deficient atmosphere, the Nd:LaGGG crystal with dimensions of Ф 26 × 30 mm3, shown in Fig. 1 , was annealed at 1400 °C for 15 h in air in order to eliminate the oxygen vacancies. Additionally, the annealing procedure can also release the thermal stress formed during the growing process.
2.2 X-ray powder diffraction
The structure and lattice parameters of the as-grown Nd:LaGGG crystal were determined by X-ray powder diffraction (XRPD). The crystal was ground into powder form for examination with a Bruker-AXS D8 ADVANCE X-ray diffractometer, which was equipped with a diffracted-beam monochromator set for Cu-Kα radiation (λ = 1.54056 Å) in the 2θ range of 15-85° with a step size of 0.02° and a step time of 16 s at room temperature.
2.3 Effective segregation coefficients measurement
The concentrations of Nd3+, La3+, Gd3+ and Ga3+ ions in the obtained crystal were measured by the X-ray fluorescence (XRF) analysis method (Rigaku, ZSX primus II). The effective segregation coefficients of Nd3+, La3+, Gd3+ and Ga3+ ions were calculated according to the measured results of specimen (shoulder part of the as-grown crystal) and polycrystalline materials.
2.4 Density measurement
The density of Nd:LaGGG crystal was measured by the Archimedian buoyancy method and calculated using the following equation :
2.5 Measurements of thermal properties
The thermal expansion coefficient ([αij]) is an important parameter for laser crystal. During the laser operation, the mechanical stresses can be generated in the crystal owing to the thermal effect, which can make the crystal fracture if the thermal stresses are sufficiently high. The fracture temperature is inversely proportional to the thermal expansion coefficient . As a symmetric second-rank tensor, the quadratic representation equation for [αij] referred to the principal axes is α11x12 + α22x22 + α33x32 = 1 . For the Nd:LaGGG crystal with Ia3d symmetry, only one independent principal component exists (α11 = α22 = α33) based on the Neumann’s principle . The thermal expansion of the Nd:LaGGG crystal was measured using a Mettler-Toledo thermal-mechanical analyzer (TMA/SDTA840) in the temperature range of 29-500 °C at a heating rate of 5 °C/min. The measured sample with dimensions of 8 × 8 × 2 mm3 was along <111> direction.
The specific heat was measured with the temperature up to 303 °C at a heating rate of 5 °C/min using a differential scanning calorimeter (Perkin-Elmer Diamond model DSC-ZC). The accurancy of calorimetry and temperature for the instrument are less than 0.1% and ± 0.01 °C, respectively. A sample weighing 103.8 mg was used for the measurement.
The thermal diffusivity of Nd:LaGGG was measured using a Netzsch Nanoflash model LFA 457 apparatus by laser pulse method over the temperature range of 24.5-500 °C. The sample with dimensions of 4 × 4 × 1 mm3, which was coated with graphite on both of 4 × 4 mm2 faces, was heated using a short light pulse on the front surface, then the temperature versus time on the rear surface was measured with an IR detector.
2.6 Spectra measurements
Samples with dimensions of 8 × 8 × 2 mm3, where both of the 8 × 8 mm2 faces were perpendicular to the <111> direction and polished, were used to measure the absorption spectrum, the fluorescence spectrum and the excited state fluorescence lifetime. The absorption spectrum was measured using a Hitachi U-3500 spectrophotometer with the resolution of 0.1 nm and the wavelength accuracy of 0.2 nm in ultraviolet-visible region and 1 nm in infrared region. The two detectors, which were used to collect the experimental data for ultraviolet-visible region and infrared region, were switched at 850 nm. The sampling interval and slit width were set to be 0.5 nm and 3 nm, respectively, with a scan speed of 60 nm/min from 300 to 850 nm and 150 nm/min from 850 to 1000 nm. The photoluminescence spectrum and excited state fluorescence lifetime, which were both excited by 808 nm laser diode (LD), were measured using an Edinburgh Instruments FLS920 spectrophotometer with the resolution of 0.1 nm and 1 µs, respectively. The step size and step time were given to be 0.3 nm and 0.2 s during the photoluminescence spectrum measurement. All the spectra measurements were performed at room temperature.
2.7 Laser measurements
The continuous-wave (CW) operation was carried out in a compact concave-plano resonator, schematically shown in Fig. 2 . The sample used in laser experiment was cut along the <111> direction with dimensions of 4 × 4 × 5 mm3, and was uncoated. It was wrapped with indium foil and held in water cooling aluminum block to maintain a temperature of 20 °C. The input concave mirror M1 with the curvature radius of 200 mm was anti-reflection (AR) coated at 808nm (R<0.5%) on the flat face and high-reflection coated at 1.06 µm (R>99.8%) and high-transmission coated at 808nm on the concave face. M2 was a flat mirror with the transmission of 5% at 1062 nm. The pump source was a fiber coupled diode laser emitting at 805 nm. The fiber bundle was with a diameter of 600 µm and a numerical aperture of 0.22. Its radiation was coupled into the laser crystal by a focusing optical system with a focal length of 15 mm. The beam-waist radius in the Nd:LaGGG crystal was estimated to be 170 µm. The laser pulse signal was recorded by a Tektronix DPL7104 digital oscilloscope (1G bandwidth, 5 Gs/s sampling rate) and a photo detector (New focus, model 1623, rise time ≤1ns). The average output power was measured by a laser power meter (Fieldmax II, Coherent).
3. Results and discussion
3.1 Structural properties
The XRPD pattern of the Nd:LaGGG crystal is shown in Fig. 3 , which indicates that the as-grown crystal is iso-structural to GGG. According to the peak 2θ values in the XRPD pattern, the lattice parameters were calculated to be a = b = c = 12.387 Å using the Le Bail method and TOPAS program. These values are lager than those of GGG (a = b = c = 12.376 Å) , which is ascribed to the larger radius of doping Nd3+ and La3+ ions than that of Gd3+ ions in the dodecahedral site.
3.2 Effective segregation coefficients
The doping concentration of a sample can be calculated by the equation :Eq. (2) under the condition of g = 0. According to the measured results, the effective segregation coefficients of Nd3+, La3+, Gd3+ and Ga3+ ions in the Nd:LaGGG crystal were calculated to be 0.52, 0.16, 1.10 and 0.97, respectively. Here the keff of Nd3+ ions in Nd:LaGGG is larger than in Nd:GGG (0.40) [16,17], which can be ascribed to the larger radius of doping La3+ ions than that of Gd3+ ions in the dodecahedral site.
The concentrations of Nd3+ and La3+ ions in the polycrystalline materials are 1.9 and 10.0 at.%, respectively. According to Eq. (2), the doping levels of Nd3+ and La3+ ions in the crystal were calculated to be 1.0-1.1 at.% and 1.6-1.8 at.% along the crytal growth direction, respectively, with the value of g ranging from 0 to 0.13 in the whole crystal growth. Here we neglect the interaction of Nd3+ and La3+ on each keff since their doping level in the crystal are low (less than 2 at.%). Therefore, the concentrations of Nd3+ and La3+ ions in measured samples in this paper are determined to be 1.0 at.% (1.26 × 1020 cm−3) and 1.6 at.% (2.02 × 1020 cm−3), respectively, since all the samples are cut from the very first part of the as-grown crystal.
The average experimental density of Nd:LaGGG was measured to be 7.107 g cm−3. For comparison, the density was also calculated using the structural parameters according to the following equation :
3.4 Thermal properties
The thermal expansion of Nd:LaGGG versus temperature curve is shown in Fig. 4(a) , in which the thermal expansion is almost linear in the temperature range of 29-500 °C. The average thermal expansion coefficient is given by :Eq. (4), which is comparable to that of Nd:YAG (7.9 × 10−6 K−1) .
According to the experimental density at 21 °C and average thermal expansion coefficient, the density of Nd:LaGGG at 29 °C was calculated to be 7.106 g cm−3. Therefore, based on the thermal expansion of Nd:LaGGG versus temperature curve, the density over the temperature range of 29-500 °C was calculated, which is shown in the up left inset in Fig. 4(a). The density of the Nd:LaGGG crystal decreases linearly as the temperature increased.
The dependence of specific heat on temperature is illustrated in Fig. 4(b), in which the specific heat of Nd:LaGGG increases almost linearly from 0.375 to 0.478 J (g K)−1 as the temperature increased from 20 to 303 °C. The molar mass of Nd:LaGGG is 1011.07 g mol−1 in this study, thus the molar specific heat (Cp) is calculated to be 483.29 J (K mol)−1 at 303 °C. Based on the Neumann-Kopp law, the specific heat of Nd:LaGGG can be calculated as Cv = (3 + 5 + 12) × 24.94 = 498.8 J (K mol)−1 , which is comparable to the measured value of Cp.
Similar to the thermal expansion coefficient, the thermal diffusivity [λij] is also a symmetric second-rank tensor, which has only one independent principal component in the principal coordinate system for the Nd:LaGGG crystal. Figure 4(c) shows the thermal diffusivity of the Nd:LaGGG crystal versus temperature. It can be seen that the thermal diffusivity decreases from 3.07 mm2 s−1 (at 24.5 °C) to 1.07 mm2 s−1 (at 500 °C).
The thermal conductivity is one of the most important properties used for evaluating the effectiveness of laser crystal. If a crystal possesses a high thermal conductivity, the deposited heat can be easily transferred to the environment, thus decreasing the thermal loading effect. The thermal conductivity κ can be calculated using the following equation :Fig. 4(d), in which the thermal conductivity decreases from 8.28 to 4.76 W (m K)−1 over the temperature range of 24.5 to 290 °C. As can be seen, the room-temperature thermal conductivity of Nd:LaGGG is comparable to that of Nd:GGG (9 W m−1 K−1) .
3.5 Spectral properties
The absorption cross section of Nd:LaGGG from 300 to 1000 nm at room temperature is shown in Fig. 5 , in which six strong-absorption bands centered at the wavelengths of 354, 530, 588, 747, 805 and 873 nm have been revealed in the crystal. They are assigned to different spin- and electric- dipole-allowed transitions from the ground state (4I9/2) to 4D3/2, 4G7/2 + 4G9/2, 4G5/2 + 2G7/2, 4F7/2 + 4S3/2, 4F5/2 + 2H9/2 and 4F3/2 energy levels, respectively [10,13]. The strongest absorption peak is centered at 805 nm with a full width at half maximum (FWHM) of 8.6 nm, which is much larger than that of Nd:YAG (2 nm) . Therefore, the Nd:LaGGG crystal can be suitable for LD pumping because of the large absorption bandwidth.
Figure 6 shows the fluorescence spectrum of Nd:LaGGG in the wavelength range of 850-1450 nm. Three main bands centered at 937.5, 1062.6 and 1331.1 nm have been found, which are associated with the transitions of 4F3/2→4I9/2, 4F3/2→4I11/2 and 4F3/2→4I13/2, respectively . The most important transition of Nd3+ ions for laser application is the 4F3/2→4I11/2 transition, which includes two intense emission regions at around 1.06 and 1.15 µm in the Nd:LaGGG crystal. As can be seen, three strong peaks centered at 1059.6, 1061.1 and 1062.6 nm have been found with the FWHM of 1.5, 1.2 and 1.3 nm (Gauss fitting), respectively. The 4F3/2→4I9/2 transition consists of two wavelength regions at around 0.88 and 0.94 µm. The first band (0.88 µm) is not interesting for the laser application due to the large ground state re-absorption . More attention can be paid to the band of 0.94 µm because of its promising application in water vapor DIAL in future . Additionally, the band centered at around 1.33 µm is also promising for laser operation in the 1.3 µm region. The fluorescence decay curve of Nd:LaGGG versus time at 1062 nm is shown in Fig. 7 , in which the excited state fluorescence lifetime was determined to be 243 µs by a single-exponential fitting. This value is larger than that of Nd:GGG (180 µs) , which indicates that the Nd:LaGGG crystal could have a better capacity of power storage than that of Nd:GGG.
The spectral parameters calculated by the Judd-Ofelt theory [21,22], which was performed on the absorption spectrum at room temperature, are important for the crystal to evaluate the potential of laser emission. During the calculation of the Nd:LaGGG crystal, the refractive index of the Nd:GGG crystal (n = 1.94) was used, and the reduced matrix elements of the absorption transitions were cited from the Carnall’s data . The results of J-O analysis, including the central wavelength , the experimental transition-line intensity Sexp(J→J’), the calculated transition-line intensity Scal(J→J’) and the oscillator strength Pexp(J→J’), are listed in Table 1 . The (J→J’) represents the transition from the ground state J to the final state J’. Then the intensity parameters Ωt (t = 2, 4 and 6) can be fitted to be 1.099, 3.492 and 4.373 × 10−20 cm2, respectively, with the root mean-square deviation (RMS error) of 0.316 × 10−20 cm2.
Given Ωt (t = 2, 4 and 6), the spontaneous emission probabilities A(J”→J’), the branching ratio βcal and the radiative lifetime τr were also calculated, which are listed in Table 2 . In view of the intrinsic error of Judd-Ofelt theory ( ± 30%), it is reasonable that the radiative lifetime is smaller than the excited state fluorescence lifetime . Additionally, the effect of radiation trapping, which always increases the value of measured lifetime, cannot be completely neglected.
The spectroscopic quality parameter of Nd3+ ions is defined as X = Ω4/Ω6 . In our study, X was calculated to be 0.80, which is smaller than the criteria (0.984) for the Nd3+-doped laser crystals. Therefore, the 1.06 µm fluorescence can be stronger than that of 0.94 µm , which is in good agreement with the calculated branching ratio of 4F3/2→4I11/2 transition (0.534) and the fluorescence spectrum.
The stimulated emission cross section (σem) of 4F3/2→4IJ (J = 9/2, 11/2 and 13/2) transitions at room temperature, which were calculated according to the Fuchtbauer-Landenburg theory (the integral β-τ method) , are reported in Fig. 8 . The calculated σem of Nd:LaGGG at 1062.6 nm is 1.24 × 10−19 cm2, which is in the same level with some other Nd3+-doped garnet crystals . In additon, the emission cross section of Nd:LaGGG is slight smaller than that of Nd:GGG at 1062.1 nm (2.9 × 10−19 cm2) , which can be attributed to the inhomogeneous broadening of fluorescence line . The small emission cross section indicates that the Nd:LaGGG crystal can have excellent Q-switched laser performance.
3.6 Laser performance
The CW laser operation of Nd:LaGGG was performed by optimizing the cavity length to be 15 mm. Figure 9 shows the CW output power versus the absorbed pump power at 1062 nm with the output coupler of 5%. As can be seen, the highest output power of 8.75 W was obtained with the maximum slope efficiency of 40.4% and the optical conversion efficiency of 39.7%, which indicates that the Nd:LaGGG crystal can be a promising material for laser applications.
A high quality mixed Nd:LaGGG laser crystal with dimensions of Ф 26 × 30 mm3 was successfully grown by the Czochralski method. The effective segregation coefficients of Nd3+ and La3+ ions in the crystal were measured to be 0.52 and 0.16, respectively. The average linear thermal expansion coefficient from 29 to500 °C was measured to be 8.25 × 10−6 K−1, which is comparable to that of Nd:YAG (7.9 × 10−6 K−1). The specific heat was measured to be 0.375-0.478 J (g K)−1 over the temperature range of 20-303 °C. The thermal diffusivity decreases from 3.07 mm2 s−1 to 1.07 mm2 s−1 as the temperature increased from 24.5 °C to 500 °C. The thermal conductivity was calculated to be 8.28-4.76 W (m K)−1 over the temperature range of 24.5-290 °C. In addition, the absorption spectrum and the fluorescence spectrum of Nd:LaGGG were measured at room temperature, and the excited state fluorescence lifetime was measured to be 243 µs. The Judd-Ofelt theory has been applied to predict the spectroscopic parameters relevant for laser applications. The calculated stimulated emission cross section at about 1.06 µm is smaller than that of Nd:GGG, which indicates that the Nd:LaGGG crystal can have excellent Q-switching laser properties. In the 1062 nm CW laser operation, the maximum output power of 8.75 W was achieved with the optical-to-optical and slope efficiency of 39.7% and 40.4%, respectively. All these results indicate that the Nd:LaGGG crystal is a promising laser material.
This work was supported by the National Natural Science Foundation of China (Grant Nos. 51021062, 50990061), the 973 Program of the People’s Republic of China (Grant No. 2010CB630702), the China Postdoctoral Science Foundation and the Independent Innovation Foundation of Shandong University, and the Program of Introducing Talents of Disciplines to Universities in China (111 program no. b06017).
References and links
1. G. Boulon, “Fifty years of advances in solid-state laser materials,” Opt. Mater. 34(3), 499–512 (2012). [CrossRef]
2. Z. Shi, H. Zhang, J. Wang, Y. Yu, Z. Wang, H. Yu, S. Sun, H. Xia, and M. Jiang, “Growth and characterization of Nd: CLNGG crystal,” J. Cryst. Growth 311(14), 3792–3796 (2009). [CrossRef]
4. H. Yu, H. Zhang, Z. Wang, J. Wang, Y. Yu, Z. Shao, M. Jiang, and X. Zhang, “Continuous wave and passively Q-switched laser performance of a Nd-doped mixed crystal Nd: Lu0.5Gd0.5VO4,” Appl. Phys. Lett. 90(23), 231110 (2007). [CrossRef]
5. H. Yu, H. Zhang, Z. Wang, J. Wang, Y. Yu, D. Tang, G. Xie, H. Luo, and M. Jiang, “Passive mode-locking performance with a mixed Nd:Lu0.5Gd0.5VO4 crystal,” Opt. Express 17(5), 3264–3269 (2009). [CrossRef] [PubMed]
6. A. Parker, “Bright future for compact tactical laser weapons,” LLNL Sci. Technol. Rev. 4, 11–21 (2002).
7. Y. Zhi, C. Dong, J. Zhang, Z. Jia, B. Zhang, Y. Zhang, S. Wang, J. He, and X. Tao, “Continuous-wave and passively Q-switched laser performance of LD-end-pumped 1062 nm Nd:GAGG laser,” Opt. Express 18(8), 7584–7589 (2010). [CrossRef] [PubMed]
8. C. Brandle and R. Barns, “Crystal stoichiometry of Czochralski grown rare-earth gallium garnets,” J. Cryst. Growth 26(1), 169–170 (1974). [CrossRef]
9. Y. Guyot, L. E. Bausá, E. Camarillo, J. García Solé, I. Vergara, A. Monteil, and R. Moncorgé, “Infrared fluorescence spectra of Nd3+ sites in gadolinium gallium garnet:Nd and gadolinium gallium garnet:Nd,Cr,” J. Appl. Phys. 72(12), 5876–5880 (1992). [CrossRef]
10. Z. Jia, X. Tao, H. Yu, C. Dong, J. Zhang, H. Zhang, Z. Wang, and M. Jiang, “Growth and properties of Nd:(LuxGd1−x)3Ga5O12 laser crystal by Czochralski method,” Opt. Mater. 31(2), 346–349 (2008). [CrossRef]
11. Z. Jia, B. Zhang, Y. Li, X. Fu, A. Arcangeli, J. He, X. Tao, and M. Tonelli, “Continuous-wave and passively Q-switched laser of Nd: LGGG crystal at 0.93 μm,” Laser Phys. Lett. 9(1), 20–25 (2012). [CrossRef]
12. A. Agnesi, F. Pirzio, G. Reali, A. Arcangeli, M. Tonelli, Z. Jia, and X. Tao, “Multi-wavelength diode-pumped Nd: LGGG picosecond laser,” Appl. Phys. B 99(1-2), 135–140 (2010). [CrossRef]
13. Y. Y. Zhang, H. J. Zhang, H. H. Yu, J. Y. Wang, W. L. Gao, M. Xu, S. Q. Sun, M. H. Jiang, and R. I. Boughton, “Synthesis, growth, and characterization of Nd-doped SrGdGa3O7 crystal,” J. Appl. Phys. 108(6), 063534 (2010). [CrossRef]
14. J. Zhang, Z. Zhang, Y. Sun, C. Zhang, and X. Tao, “Bulk crystal growth and characterization of a new polar polymorph of BaTeMo2O9: α-BaTeMo2O9,” CrystEngComm 13(23), 6985–6990 (2011). [CrossRef]
15. Z. Jia, A. Arcangeli, X. Tao, J. Zhang, C. Dong, M. Jiang, L. Bonelli, and M. Tonelli, “Efficient Nd3+→ Yb3+ energy transfer in Nd3+, Yb3+: Gd3Ga5O12 multicenter garnet crystal,” J. Appl. Phys. 105(8), 083113 (2009). [CrossRef]
16. D. Sun, Q. Zhang, Z. Wang, J. Su, C. Gu, A. Wang, and S. Yin, “Concentration distribution of Nd3+ in Nd:Gd3Ga5O12 crystals studied by optical absorption method,” Cryst. Res. Technol. 40(7), 698–702 (2005). [CrossRef]
17. Y. Kuwano, “Effective distribution coefficient of neodynium in Nd:Gd3Ga5O12 crystals grown by the Czochralski method,” J. Cryst. Growth 57(2), 353–361 (1982). [CrossRef]
18. L. Zhang, P. Shi, and L. Li, “Semianalytical thermal analysis of rectangle Nd: GGG in heat capacity laser,” Appl. Phys. B 101(1-2), 137–142 (2010). [CrossRef]
19. Z. Jia, X. Tao, C. Dong, M. Jiang, A. Arcangeli, S. Bigotta, and M. Tonelli, “Spectroscopic analysis of Nd3+ doped (Lux + Gd1−x)3Ga5O12 crystal,” Appl. Phys. B 100(3), 485–491 (2010). [CrossRef]
20. S. Field, D. Hanna, A. Large, D. Shepherd, A. Tropper, P. Chandler, P. Townsend, and L. Zhang, “An efficient, diode-pumped, ion-implanted Nd: GGG planar waveguide laser,” Opt. Commun. 86(2), 161–166 (1991). [CrossRef]
21. G. Ofelt, “Intensities of crystal spectra of rare-earth ions,” J. Chem. Phys. 37(3), 511–520 (1962). [CrossRef]
22. B. R. Judd, “Optical absorption intensities of rare-earth ions,” Phys. Rev. 127(3), 750–761 (1962). [CrossRef]
23. W. T. Carnall, P. Fields, and B. Wybourne, “Spectral intensities of the trivalent lanthanides and actinides in solution. I. Pr, Nd, Er, Tm, and Yb,” J. Chem. Phys. 42(11), 3797–3806 (1965). [CrossRef]
24. T. S. Lomheim and L. G. DeShazer, “New procedure of determining neodymium fluorescence branching ratios as applied to 25 crystal and glass hosts,” Opt. Commun. 24(1), 89–94 (1978). [CrossRef]
25. B. Aull and H. Jenssen, “Vibronic interactions in Nd: YAG resulting in nonreciprocity of absorption and stimulated emission cross sections,” IEEE J. Quantum Electron. 18(5), 925–930 (1982). [CrossRef]
26. M. D. Rotter and B. Dane, “Measuring the stimulated-emission cross-section: a case study in Nd: GGG,” Opt. Commun. 198(1–3), 155–161 (2001). [CrossRef]