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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 7 — Mar. 26, 2012
  • pp: 6944–6951
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Thermal and laser properties of Nd:Lu3Sc1.5Ga3.5O12 for high power dual-wavelength laser

K. Wu, L. Z. Hao, H. H. Yu, Z. P. Wang, J. Y. Wang, and H. J. Zhang  »View Author Affiliations


Optics Express, Vol. 20, Issue 7, pp. 6944-6951 (2012)
http://dx.doi.org/10.1364/OE.20.006944


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Abstract

We measured the thermal properties of Nd:Lu3Sc1.5Ga3.5O12 (Nd:LuSGG) crystal, including the thermal expansion coefficient, specific heat, and thermal diffusion coefficient. The calculated thermal conductivity is 4.4 W/mK at room temperature. A high-power continuous-wave and passively Q-switched Nd:LuSGG laser was also demonstrated. Continuous-wave output power of 6.96 W is obtained which is the highest power with this material. For the first time to our knowledge, the passively Q-switched Nd:LuSGG laser is reported with the shortest pulse width, largest pulse energy, and highest peak power are achieved to be 5.1 ns, 62.5 μJ, and 12 kW, respectively. By spectral analysis, it has been found that the Nd:LuSGG laser was located at 1059 nm under low pump power, and became dual-wavelength at 1061.5 and 1059 nm when the incident pump power is over 2.27 W. The generating mechanism of dual-wavelength laser is also discussed.

© 2012 OSA

1. Introduction

2. Experimental

The good quality Nd:LuSGG crystal with Nd doping concentrations of 1 at.% was successfully achieved in oxygen atmosphere by the optical floating-zone method since the change in the valence of Ga and the volatilization of Ga2O3 can be greatly decreased in an oxygen atmosphere.

2.1 Specific heat

Specific heat measurement was performed on a (Mettler Toledo DSC822e) differential scanning calorimeter (DSC) using the following procedure: first, two empty aluminum pans, with one for reference, were heated together from 20 to 300 °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 sample used for thermal expansion measurements was cut into a specimen with dimensions of 4 × 4 × 2 mm3. The measurement was performed on a thermal-mechanical analyzer (TMA) made by Perkin-Elmer over the temperature range from 30 to 500 °C. During the thermal expansion measurement, the sample was heated slowly to 500 °C at a constant rate of 5 °C /min.

2.3 Thermal diffusion coefficient

The thermal diffusion coefficient is also a second rank tensor and has only one independent principle component λ1 for Nd:LuSGG crystal. Using the laser flash method, measurement of thermal diffusion coefficient of Nd:LuSGG crystal was carried out on NETZSCH LFA 457/2/G over a temperature range of 30-300 °C. The sample used was <111> direction oriented with dimensions of 4 × 4 × 1 mm3 and both the 4 × 4 mm2 faces were coated with graphite. During the experiment, a short light pulse is used to heat the front surface of the wafer, and the temperature rise versus time on the opposite surface is measured using an IR detector. The thermal diffusivity can be calculated by using the analytical software provided (Netzsch Co.).

2.4 Laser performance

Based on a simple plano–concave resonator, the pump source employed in the experiment was a fiber-coupled LD with a central wavelength around 808 nm. Through the focusing optics (NA = 0.22), the output of the source was focused into the laser crystal with a spot radius of 0.1 mm. The input mirror M1 is a concave one with a curvature radius of 200 mm, AR coated at 808 nm on the flat face, high-reflection coated at 1.06 μm, and high-transmission coated at 808 nm on the concave face. The output coupler (OC) M2 is two flat mirrors with different transmissions at 1.06 μm of 5% and 10%, respectively. A Cr4+:YAG crystal with initial transmission (T0) of 77% was selected as the saturable absorber and OC, simultaneously. The face of Cr4+:YAG crystal toward the cavity is AR coated at 1.06 μm, and the other face is coated with the transmission of 25% at 1.06 μm. The sample was cut with the dimensions of 3 mm × 3 mm × 5 mm along the <111> direction. To efficiently remove the generated heat, the crystal was wrapped with indium foil and mounted in a water-cooled copper holder, and Cr4+:YAG was attached on a copper block without cooling water. The temperature of the circulating water was set at 15 °C during the experiment. The laser output power was measured by a power meter (EPM 2000-Molectron, Inc.), and temporal behaviors of the Q-switched laser were recorded by a TGS 3052 digital oscilloscope (500 MHZ bandwidth and 2.5 Gs/s sampling rate, Tektronix, Inc.). The laser spectra were achieved with an optical spectrum analyzer (Ocean Optics Inc. HR4000CG-UV-NIR).

3. Results and discussion

3.1 Specific heat

The measured specific heat versus temperature curve of 1at% Nd:LuSGG is shown in Fig. 1
Fig. 1 Specific heat versus temperature.
from which it can be found that specific heat of crystal increases slightly with raising temperature. The specific heat is 0.38 J·g−1·K−1 at 300K, which is smaller than that of Nd:YAG (0.59 J·g−1·K−1 at 300K) [13

13. W. Koechner, Solid-State Laser Engineering (Science Press, Beijing, in Chinese, 42, 2002).

], but comparable to that of Nd:GGG (0.42 J·g−1·K−1) [14

14. 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]

], which can be applied in high power systems. So it can be indicated that Nd:LuSGG crystal should have high damage threshold as in the case of Nd:GGG crystal.

3.2 Thermal expansion coefficient

The thermal expansion coefficient is a second rank tensor and compliant with crystal symmetry. Thus, for the cubic crystal of Nd:LuSGG, it has only one independent principle component. The thermal expansion versus temperature of Nd:LuSGG is shown in Fig. 2
Fig. 2 Thermal expansion versus temperature.
. The average linear thermal expansion coefficient was calculated to be 8.3 × 10−6 K−1, which is slightly larger than that of Nd:YAG (7.9 × 10−6 K−1) [15

15. W. Koechner, “Thermal lensing in a Nd:YAG laser rod,” Appl. Opt. 9(11), 2548–2553 (1970). [CrossRef] [PubMed]

]. As for laser gain medium, duo to appropriate thermal expansion will be helpful in crystal growth and may decrease the thermal lens effect in high laser system, we think that Nd:LuSGG crystal should have the ability to ensure the optical quality of a laser beam and laser efficiency.

3.3 Thermal diffusion coefficient and thermal conductivity

The thermal diffusion coefficient versus temperature of Nd:LuSGG is shown in Fig. 3
Fig. 3 Thermal diffusion coefficient and thermal conductivity versus temperature.
, the thermal diffusivity decreases from 1.604 to 0.875 mm2s−1 as the temperature increases from 298K to 673K. Thermal conductivity of Nd:LuSGG was calculated using the following equation:
κ=ρCpλ
(1)
where ρ, cp, and λ denote the density, specific heat, and the thermal diffusion coefficient, respectively.

With measured data on ρ, cp, and λ, the thermal conductivity of Nd:LuSGG was calculated. The thermal conductivity versus temperature curve over the whole measuring temperature range is also shown in Fig. 3, and the curve indicates that thermal conductivity shows a decreasing tendency with increasing temperature. The thermal conductivity of Nd:LuSGG is calculated to be 4.4 W·m−1·K−1 at room temperature, which is larger than Nd:CNGG (3.43 W·m−1·K−1) [16

16. Y. G. Yu, J. Y. Wang, H. J. Zhang, Z. P. Wang, H. H. Yu, S. Q. Sun, H. R. Xia, and M. H. Jiang, “Thermal characterization of lowly Nd3+ doped disordered Nd:CNGG crystal,” Opt. Express 17(11), 9270–9275 (2009). [CrossRef] [PubMed]

] and nearly one third of that of Nd:YAG (13 W·m−1·K−1) [15

15. W. Koechner, “Thermal lensing in a Nd:YAG laser rod,” Appl. Opt. 9(11), 2548–2553 (1970). [CrossRef] [PubMed]

].

The thermal conductivity of Nd:LuSGG can be explained by the following formula:
κ=13ρCpυL
(2)
where ρ is the density of different temperature, ν is the sound velocity, which is considered as a constant, Cp is the specific heat of the crystal at different temperature, and L is the phonon mean free path. We know that the thermal conductivity is mainly influenced by the variation in the mean free path of phonons. For Nd-doped LuSGG crystal, due to the very large mass difference between Sc3+ ions and Ga3+ ions, Sc-doped garnet crystal exhibits a certain degree of disorder, which leads to a high phonon scattering and induces a reduction of the mean free path of phonons.

3.4 Laser performance

The cw laser operation was obtained by optimizing the cavity length to be as short as 3 cm. Figure 4
Fig. 4 Average output powers versus absorbed pump power.
shows the output power of the Nd:LuSGG crystal under different output couplers (OC = 5% and 10% at 1.06 μm). The thresholds are 0.17, 0.25 W for OC = 5, and 10%. The output power is observed to increase linearly with the absorbed pump power. The slope efficiencies were measured to be 26.6, and 33% for OC = 5, and 10%. Maximum output power of 6.96 W was measured with OC = 10% at absorbed pump power of 21.9 W, corresponding to optical-to-optical efficiency of 31.8%. In addition, the round-trip loss inside the cavity mainly induced by the laser crystal was calculated to be about 4.7% using the Findlay-clay method [17

17. D. Findlay and R. A. Clay, “The measurement of internal losses in 4-level lasers,” Phys. Lett. 20(3), 277–278 (1966). [CrossRef]

], which indicated that the laser performance could be better if the quality of the laser crystal improved. Nevertheless, this is the highest output power and slope efficiency with this crystal as a gain material, which also indentified that this crystal is an excellent laser crystal applied in the moderate and even high laser systems.

Shortening the length of the cavity to be 1.5 cm and replacing the OC for Cr4+:YAG, the passive Q-switching performance was obtained. After appropriate alignment, passive Q-switching of the laser started at a threshold absorbed pump power of 3.2 W. The passive Q-switching output power characteristic is also shown in Fig. 5
Fig. 5 Repetition rate and pulse width with the increase of absorbed pump power.
. Under the absorbed pump power of 13.1 W, a maximum average output power of 1.16 W was achieved with optical conversion efficiency of 8.8% and the slope efficiency of 11.5%. As for high threshold of Q-switching, we believed that it was induced by the relative low quality of the crystal, small emission cross section at 1.06 μm (about 1.84 × 10−19 cm2) [12

12. K. Wu, L. Z. Hao, H. J. Zhang, H. H. Yu, H. J. Cong, and J. Y. Wang, “Growth and characterization of Nd:Lu3ScxGa5−xO12 series laser crystals,” Opt. Commun. 284(21), 5192–5198 (2011). [CrossRef]

] and lower thermal conductivity that measured in this experiment (4.4 W/mK) which brought large thermal induced loss when the pump power was high. Avoiding damage on the optical devices, the pump power was limited to be 13.1W. In order to achieve much higher output power, the saturable absorber should be coated with higher transmission for reducing the interactivity intensity.

With a digital oscilloscope, the variations of the Q-switching pulse repetition rate and pulse width with the absorbed pump powers were measured and are presented in Fig. 5. It can be found that the repetition rate increases linearly from 2.5 kHz to 18.6 kHz with the increase of pump powers. The narrowest Q-switched pulse width obtained was about 5.1 ns under the pump power of 13.1W. With the repetition rate and average output power, the pulse energy can be calculated. The maximum pulse energy was 62.5 μJ under pump power of 13.1 W. After combining the pulse width, the peak power can be achieved. The highest peak was 12 kW under pump power of 13.1 W.

With an optical spectrum analyzer, the spectra of the cw laser were recorded and are shown in Fig. 6
Fig. 6 Measured laser spectrum of Nd:Lu3Sc1.5Ga3.5O12 crystal.
. From Fig. 6(a), it can be seen that only the mode at 1059 nm oscillated at the threshold. The mode at 1061.5 nm appeared when the incident pump power was 2.27 W and is shown in Fig. 6(b). However, we have also found that the laser oscillation at 1061.5nm still much lower than at 1059 nm until the incident pump power is up to 14 W. According to the analysis on the spectroscopic characteristics of Nd:LuSGG, two most intense lines for Nd:LuSGG appear at 1059 nm and 1061.5 nm, corresponding to the R1→Y1 and R2→Y3 transitions, respectively, which can be seen from the illustration in Fig. 6 [12

12. K. Wu, L. Z. Hao, H. J. Zhang, H. H. Yu, H. J. Cong, and J. Y. Wang, “Growth and characterization of Nd:Lu3ScxGa5−xO12 series laser crystals,” Opt. Commun. 284(21), 5192–5198 (2011). [CrossRef]

]. We have calculated the branching ratios and emission cross-sections of the two different wavelengths. The branching ratios are 0.068 and 0.057, and the emission cross-sections are 8.5 × 10−20 cm2 and 7.1 × 10−20 cm2 at 1059 nm and 1061.5 nm, respectively. From the model of four-level systems, the gain was determined by the population density on the upper state and their emission cross sections. The ratio of population density on the top (nt) and bottom (nb) components can follow the Boltzmann statistics,
ntnb=exp(ΔEKT)
(3)
where ΔE = 44 cm−1 is the energy gap between Stark levels of metastable 4F3/2 state at room temperature, k is the Boltzmann constant, and T = 300 K is the temperature. The calculated result shows that nt = 0.81 nb and the gain ratios of the two lines were achieved to be 1:0.68. According to the incident pump power, the population-inversion densities on the top (nt) and bottom (nb) are calculated to be 4.15 × 1018 and 5.08 × 1018 cm−3, respectively. By the population density on the top (nt) and emission cross section at 1061.5nm, the value of gain factor (G) of R2→Y3 is calculated to be 0.294. In theory, we know that the generation of laser needs the gain greater than the loss. According to the laser oscillation condition,
Glδ
(4)
where l is the crystal length, δ is the single pass loss, G is the gain factor. The value of gain is calculated to be 0.147, which is equal to the loss of the cavity. The general knowledge told us that the temperature of laser crystal should increase with the increasing pump power for any Nd laser with quantum efficiency lower than one [18

18. U. O. Farrukh, A. M. Buoncristiani, and C. E. Byvik, “An analysis of the temperature distribution in finite solid-state laser rods,” IEEE J. Quantum Electron. 24(11), 2253–2263 (1988). [CrossRef]

]. The increasing temperature will also affect the gain ratio of two lines and increase the gain of R2→Y3. So when the pump power is increased to be 2.27 W, the gain of R2→Y3 is more than loss and causes the oscillation at the wavelength of 1061.5 nm. Furthermore, the laser oscillation at 1061.5 nm is still much lower than that of 1059 nm with the increasing pump power is up to 14 W, which may be induced by the smaller gain of 1061.5 nm than that of 1059 nm. Therefore, the intensity of 1061.5 nm is in the increase with the increasing pump power but still much smaller compared to that of 1059 nm. We think that it has the potential to achieve the efficient dual-wavelength Nd:LuSGG laser with comparable intensity if the cavity is optimized. Furthermore, it can be believed that this simultaneous dual-wavelength pulsed Nd:LuSGG laser at 1061.5 and 1059 nm may be used as a source for the generation of THz radiation with fixed wavelength, pump–probe experiments, optical beating, remote sensing.

4. Conclusion

In this paper, we have reported the thermal properties of Nd:LuSGG crystal, including the thermal expansion coefficient, specific heat, thermal diffusion coefficient and thermal conductivity and demonstrated its high power cw and passively Q-switched laser performance for the first time, to our knowledge. The thermal conductivity is 4.4 W/mK at room temperature. Continuous-wave output power of 6.96 W is obtained which is the highest power with this material. By loss analysis, we believed that the laser performance could become better if the laser crystal quality was improved. In the passively Q-switched operation, the shortest pulse width and maximum pulse energy were measured to be 5.1 ns and 62.5 μJ, respectively. The spectral analysis is shown that the Nd:LuSGG laser wavelengths are centered at 1061.5 and 1059 nm when the incident pump power is over 2.27W. We conclude that the laser wavelengths of this crystal can be selected by varying the pump power and this crystal has the potential to achieve the dual-wavelengths output. In addition, this dual-wavelength laser may be used as a laser source for the generation of THz radiation, pump–probe experiments, optical beating, and remote sensing.

Acknowledgments

This work is supported by the National Natural Science Foundation of China (No. 51025210, 51032004 and 51021062), Grant for State Key Program of China (2010CB630702) and the Program of Introducing Talents of Discipline to Universities in China (111 program).

References and links

1.

J. E. Geusic, H. M. Marcos, and L. G. Van-Uitert, “Laser oscillations in Nd-doped yttrium aluminum, yttrium gallium, and gadolinium garnets,” Appl. Phys. Lett. 4(10), 182–184 (1964). [CrossRef]

2.

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]

3.

H. H. Yu, K. Wu, B. Yao, H. J. Zhang, Z. P. Wang, J. Y. Wang, X. Y. Zhang, and M. H. Jiang, “Efficient triwavelength laser with a Nd:YGG garnet crystal,” Opt. Lett. 35(11), 1801–1803 (2010). [CrossRef] [PubMed]

4.

J. K. Weber, S. Krishnan, S. Ansell, A. D. Hixson, and P. C. Nordine, “Structure of liquid Y3Al5O12 (YAG),” Phys. Rev. Lett. 84(16), 3622–3625 (2000). [CrossRef] [PubMed]

5.

K. Wu, B. Yao, H. J. Zhang, H. H. Yu, Z. P. Wang, J. Y. Wang, and M. H. Jiang, “Growth and properties of Nd:Lu3Ga5O12 laser crystal by floating-zone method,” J. Cryst. Growth 312(24), 3631–3636 (2010). [CrossRef]

6.

L. J. Qin, X. L. Meng, L. Zhu, J. H. Liu, B. C. Xu, H. Z. Xu, F. Y. Jiang, C. L. Du, X. Q. Wang, and Z. S. Shao, “Influence of the different Gd/Y ratio on the properties of Nd:YxGd1−xVO4 mixed crystals,” Chem. Phys. Lett. 380(3-4), 273–278 (2003). [CrossRef]

7.

J. Liu, X. Meng, Z. Shao, M. Jiang, B. Ozygus, A. Ding, and H. Weber, “Pulse energy enhancement in passive Q-switching operation with a class of Nd:GdxY1−xVO4 crystals,” Appl. Phys. Lett. 83(7), 1289–1291 (2003). [CrossRef]

8.

Y. F. Chen, M. L. Ku, L. Y. Tsai, and Y. C. Chen, “Diode-pumped passively Q-switched picosecond Nd:GDxY1-xVO4 self-stimulated Raman laser,” Opt. Lett. 29(19), 2279–2281 (2004). [CrossRef] [PubMed]

9.

H. H. Yu, H. J. Zhang, Z. P. Wang, J. Y. Wang, Y. G. Yu, Z. Shao, and M. H. Jiang, “Enhancement of passive Q-switching performance with mixed Nd:LuxGd1-xVO4 laser crystals,” Opt. Lett. 32(15), 2152–2154 (2007). [CrossRef] [PubMed]

10.

J. L. He, Y. X. Fan, J. Du, Y. G. Wang, S. Liu, H. T. Wang, L. H. Zhang, and Y. Hang, “4-ps passively mode-locked Nd:Gd0.5Y0.5VO4 laser with a semiconductor saturable-absorber mirror,” Opt. Lett. 29(23), 2803–2805 (2004). [CrossRef] [PubMed]

11.

A. A. Kaminskii, G. Boulon, M. Buoncristiani, B. Dibartolo, A. Kornienko, and V. Mironov, “Spectroscopy of a new laser garnet Lu3Sc2Ga3O12:Nd3+. Intensity luminescence characteristics, stimulated emission, and full set of squared reduced-matrix elements | 〈 ‖U(t)‖ 〉 |2 for Nd3+ ions,” Phys. Status Solidi, A Appl. Res. 141(2), 471–494 (1994). [CrossRef]

12.

K. Wu, L. Z. Hao, H. J. Zhang, H. H. Yu, H. J. Cong, and J. Y. Wang, “Growth and characterization of Nd:Lu3ScxGa5−xO12 series laser crystals,” Opt. Commun. 284(21), 5192–5198 (2011). [CrossRef]

13.

W. Koechner, Solid-State Laser Engineering (Science Press, Beijing, in Chinese, 42, 2002).

14.

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]

15.

W. Koechner, “Thermal lensing in a Nd:YAG laser rod,” Appl. Opt. 9(11), 2548–2553 (1970). [CrossRef] [PubMed]

16.

Y. G. Yu, J. Y. Wang, H. J. Zhang, Z. P. Wang, H. H. Yu, S. Q. Sun, H. R. Xia, and M. H. Jiang, “Thermal characterization of lowly Nd3+ doped disordered Nd:CNGG crystal,” Opt. Express 17(11), 9270–9275 (2009). [CrossRef] [PubMed]

17.

D. Findlay and R. A. Clay, “The measurement of internal losses in 4-level lasers,” Phys. Lett. 20(3), 277–278 (1966). [CrossRef]

18.

U. O. Farrukh, A. M. Buoncristiani, and C. E. Byvik, “An analysis of the temperature distribution in finite solid-state laser rods,” IEEE J. Quantum Electron. 24(11), 2253–2263 (1988). [CrossRef]

OCIS Codes
(140.3530) Lasers and laser optics : Lasers, neodymium
(160.3380) Materials : Laser materials

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: January 18, 2012
Revised Manuscript: March 4, 2012
Manuscript Accepted: March 5, 2012
Published: March 12, 2012

Citation
K. Wu, L. Z. Hao, H. H. Yu, Z. P. Wang, J. Y. Wang, and H. J. Zhang, "Thermal and laser properties of Nd:Lu3Sc1.5Ga3.5O12 for high power dual-wavelength laser," Opt. Express 20, 6944-6951 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-7-6944


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References

  1. J. E. Geusic, H. M. Marcos, L. G. Van-Uitert, “Laser oscillations in Nd-doped yttrium aluminum, yttrium gallium, and gadolinium garnets,” Appl. Phys. Lett. 4(10), 182–184 (1964). [CrossRef]
  2. L. Zhang, P. Shi, L. Li, “Semianalytical thermal analysis of rectangle Nd:GGG in heat capacity laser,” Appl. Phys. B 101(1-2), 137–142 (2010). [CrossRef]
  3. H. H. Yu, K. Wu, B. Yao, H. J. Zhang, Z. P. Wang, J. Y. Wang, X. Y. Zhang, M. H. Jiang, “Efficient triwavelength laser with a Nd:YGG garnet crystal,” Opt. Lett. 35(11), 1801–1803 (2010). [CrossRef] [PubMed]
  4. J. K. Weber, S. Krishnan, S. Ansell, A. D. Hixson, P. C. Nordine, “Structure of liquid Y3Al5O12 (YAG),” Phys. Rev. Lett. 84(16), 3622–3625 (2000). [CrossRef] [PubMed]
  5. K. Wu, B. Yao, H. J. Zhang, H. H. Yu, Z. P. Wang, J. Y. Wang, M. H. Jiang, “Growth and properties of Nd:Lu3Ga5O12 laser crystal by floating-zone method,” J. Cryst. Growth 312(24), 3631–3636 (2010). [CrossRef]
  6. L. J. Qin, X. L. Meng, L. Zhu, J. H. Liu, B. C. Xu, H. Z. Xu, F. Y. Jiang, C. L. Du, X. Q. Wang, Z. S. Shao, “Influence of the different Gd/Y ratio on the properties of Nd:YxGd1−xVO4 mixed crystals,” Chem. Phys. Lett. 380(3-4), 273–278 (2003). [CrossRef]
  7. J. Liu, X. Meng, Z. Shao, M. Jiang, B. Ozygus, A. Ding, H. Weber, “Pulse energy enhancement in passive Q-switching operation with a class of Nd:GdxY1−xVO4 crystals,” Appl. Phys. Lett. 83(7), 1289–1291 (2003). [CrossRef]
  8. Y. F. Chen, M. L. Ku, L. Y. Tsai, Y. C. Chen, “Diode-pumped passively Q-switched picosecond Nd:GDxY1-xVO4 self-stimulated Raman laser,” Opt. Lett. 29(19), 2279–2281 (2004). [CrossRef] [PubMed]
  9. H. H. Yu, H. J. Zhang, Z. P. Wang, J. Y. Wang, Y. G. Yu, Z. Shao, M. H. Jiang, “Enhancement of passive Q-switching performance with mixed Nd:LuxGd1-xVO4 laser crystals,” Opt. Lett. 32(15), 2152–2154 (2007). [CrossRef] [PubMed]
  10. J. L. He, Y. X. Fan, J. Du, Y. G. Wang, S. Liu, H. T. Wang, L. H. Zhang, Y. Hang, “4-ps passively mode-locked Nd:Gd0.5Y0.5VO4 laser with a semiconductor saturable-absorber mirror,” Opt. Lett. 29(23), 2803–2805 (2004). [CrossRef] [PubMed]
  11. A. A. Kaminskii, G. Boulon, M. Buoncristiani, B. Dibartolo, A. Kornienko, V. Mironov, “Spectroscopy of a new laser garnet Lu3Sc2Ga3O12:Nd3+. Intensity luminescence characteristics, stimulated emission, and full set of squared reduced-matrix elements | 〈 ‖U(t)‖ 〉 |2 for Nd3+ ions,” Phys. Status Solidi, A Appl. Res. 141(2), 471–494 (1994). [CrossRef]
  12. K. Wu, L. Z. Hao, H. J. Zhang, H. H. Yu, H. J. Cong, J. Y. Wang, “Growth and characterization of Nd:Lu3ScxGa5−xO12 series laser crystals,” Opt. Commun. 284(21), 5192–5198 (2011). [CrossRef]
  13. W. Koechner, Solid-State Laser Engineering (Science Press, Beijing, in Chinese, 42, 2002).
  14. T. Y. Fan, D. J. Ripin, R. L. Aggarwal, J. R. Ochoa, B. Chann, M. Tilleman, J. Spitzberg, “Cryogenic Yb3+-doped solid-state lasers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 448–459 (2007). [CrossRef]
  15. W. Koechner, “Thermal lensing in a Nd:YAG laser rod,” Appl. Opt. 9(11), 2548–2553 (1970). [CrossRef] [PubMed]
  16. Y. G. Yu, J. Y. Wang, H. J. Zhang, Z. P. Wang, H. H. Yu, S. Q. Sun, H. R. Xia, M. H. Jiang, “Thermal characterization of lowly Nd3+ doped disordered Nd:CNGG crystal,” Opt. Express 17(11), 9270–9275 (2009). [CrossRef] [PubMed]
  17. D. Findlay, R. A. Clay, “The measurement of internal losses in 4-level lasers,” Phys. Lett. 20(3), 277–278 (1966). [CrossRef]
  18. U. O. Farrukh, A. M. Buoncristiani, C. E. Byvik, “An analysis of the temperature distribution in finite solid-state laser rods,” IEEE J. Quantum Electron. 24(11), 2253–2263 (1988). [CrossRef]

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