Thermal and spectroscopic characteristics of disordered melilite Nd:BaLaGa₃O₇ crystal

Abstract

A disordered Nd:BaLaGa₃O₇ laser crystal was successfully grown by the Czochralski method. The effective segregation coefficient of Nd³⁺ in BaLaGa₃O₇ crystals was measured to be 1.12. A series of thermal properties, including specific heat, average linear thermal expansion coefficient, thermal diffusivity and thermal conductivity, were systematically determined as a function of temperature. The thermal conductivity increased with increasing temperature. The polarized absorption and emission spectra were measured at room temperature. Nd:BaLaGa₃O₇ possessed a large absorption bandwidth of 18 nm at 808 nm and an emission bandwidth of 32 nm at 1060 nm. According to the Judd–Ofelt theory, the spontaneous transition probabilities, the fluorescence branching ratios, and the radiation lifetime were calculated. The stimulated emission cross section for the⁴F_3/2 → ⁴I_11/2 transition was calculated to be 4.24 × 10⁻²⁰ cm². Thermal and optical properties have shown that Nd:BaLaGa₃O₇ crystals are potential alternative gain media for ultrafast lasers.

---

1. Introduction

Neodymium (Nd)-doped laser crystals are very common as a type of bulk laser gain media around 1 μm. Such an active ion behaves as a four level energy system and can be conveniently diode pumped at ∼800 nm.^1–4 It is well known that Nd:glass has significant line broadening, with fluorescence spectra of ∼20–30 nm FWHM, allowing generation of ultrashort pulses in laser oscillators.^5–9 However, the poor thermo-mechanical properties of the glassy matrix hinder the development of multiwatt femtosecond Nd:glass oscillators, thus far, efforts have been devoted to developing new gain media for high-energy ultrafast pulse lasers.¹⁰

Nd disordered laser crystals are attracting much interest due to their favorable thermo-mechanical features and relatively broad spectra linewidths. Disordered crystals have broad absorption and emission spectra arising from inhomogeneous spectra broadening, and have been proved to be a type of potential ultrafast laser media.^11,12 With disordered Nd,Y:CaF₂ crystals, Xie et al. demonstrated mode-locked pulse generation with pulse duration of 103 fs.¹³ In addition, 900 fs and 534 fs subpicosecond pulses were also generated from Ca₃(NbGa)_2−xGa₃O₁₂ and Nd:Ca₃Li_xNb_1.5+xGa_3.5−xO₁₂, respectively.^14,15

Single crystals of Nd:BaLaGa₃O₇ (Nd:BLGM) belong to a large disordered ABC₃O₇ group, where A = Ca, Sr, Ba; B = La, Gd; and C = Ga, Al.^16–18 The BaLaGa₃O₇ crystal has a disordered structure due to the random distribution of Ba²⁺ and La³⁺ ions. Nd³⁺ ions can substitute for the Ba²⁺ and La³⁺ ion lattice sites, causing a different crystal lattice field. The disordered crystal lattice field around Nd³⁺ ions in the host can cause spectra inhomogeneous broadening of laser media.

As a potential alternative for ultrafast laser, the spectroscopic characteristics, laser performance of Nd:BLGM and its family have been reported.¹⁹ The Nd:BLGM crystal has a long upper-level lifetime and considerable emission cross section which are beneficial to energy storing.²⁰ Continuous wave output powers of 0.35 W at 1.06 μm wavelength have been generated.²¹ A Nd:BLGM laser oscillator, which was passively mode locked and pumped by a Ti:sapphire laser, generated pulses of 316 fs duration at 1060 nm.²² To our best knowledge, this is a short pulse generated from Nd-doped crystal lasers so far. The excellent laser properties of Nd:BLGM make attractive to study it extensively. In addition, the thermal conductivity of Nd:BLGM crystal was reported to be 11 W m⁻¹ K⁻¹,²⁰ higher than that of Nd:glass. But this value may be overestimated because Nd:BLGM with a disordered structure should not have such a high thermal conductivity. In the disordered materials, the local disorder structure causes greater phonon density, which increases the number of possibilities for a given phonon to interact with other phonons. As a result, the average free path for the disordered crystal is lower than that of crystal. So we think the disordered crystal has lower thermal conductivity.²³ It is well known that thermal properties are important parameters for laser media. The optical pumping process in a laser material is associated with the generation of heat. The temperature gradients setup in the gain material as a result of heating can lead to thermal lensing, depolarization losses, and eventually, stress fracture, thus provide an upper limit on the average power obtainable from a laser material. Thermal loading also adversely affects the output beam quality. Heat generation inside a laser medium is due to the quantum defect between the pump energy and the emitted radiation, and also to non-ideal radiative quantum efficiency.^24,25 Thus the thermal properties of Nd:BLGM have served as a strong field of research interest. In addition, in order to fairly evaluate the potential of Nd:BLGM as lasers, the determination of the precise spectroscopic parameters is considered to be very important.

In this paper, we extensively measure thermal expansion, specific heat and thermal diffusion properties, to determine the temperature dependence of thermal conductivity. Considering the polarization dependence, J–O theory was used to demonstrate the spectroscopic characterization of the Nd:BLGM, including the absorption cross section σ_ab, the stimulated emission section σ_em, fluorescence quantum efficiency η and σ_emτ_f product. We believe that this crystal will be a potential alternative as gain medium for ultrafast lasers.

2. Experimental section

A Nd:BLGM single crystal was grown by the Czochralski method under a nitrogen atmosphere containing 2% oxygen (v/v) in an iridium crucible.¹⁹ Raw materials were 99.99% pure Nd₂O₃, BaCO₃, La₂O₃ and Ga₂O₃ powders. Taking the evaporation of Ga₂O₃ during the growth process into account, an excess of Ga₂O₃ (1.0% of the total mass) was added to the starting components. The pulling rate was maintained at 1–3 mm h⁻¹ and the crystal rotation speed at 20 rpm. The crystal was cooled to room temperature at a rate of 15–25 K h⁻¹ after completion of the growth.

Fig. 1 shows the as-grown Nd:BLGM crystal grown along the c-direction. Its dimensions are about Φ 30 × 40 mm². Several samples of different sizes were produced from the crystal boule for experimentations. High-resolution X-ray diffraction (HRXRD) were performed on a Bruker-AXS D5005HR diffractometer equipped with a four-crystal Ge (220) monochromator set (Cu Kα, step 0.0005°, time 0.2 s, voltage 30 kV and current 30 mA). The area of X-ray is about 10 × 0.6 mm². A thermal mechanical analyzer (Perkin-Elmer model: Diamond TMA) was used to measure the average linear thermal expansion tensor components. The sample used for thermal expansion measurements was processed into a rectangular piece of dimensions 4.00 × 5.00 × 6.00 mm³ (a × b × c). The specific heat was measured by the differential scanning calorimetry method using a simultaneous thermal analyzer (Perkin-Elmer Diamond: DSC). The thermal diffusivity coefficient was measured by the laser flash method using a laser flash apparatus (Netzsch LFA457), from which the thermal conductivity was calculated. Two square wafers were used for the measurements with dimensions of [6 × 6 × 2 mm³ (a × b × c) and 6 × 6 × 2 mm³ (a × c × b)]. They were coated with graphite on opposite sides.

Fig. 1 1 at% Nd:BLGM crystal grown along c-direction.

The room temperature polarized absorption spectra were measured using a UV/visible/IR spectrophotometer (JASCO model V-570) over the range of 300–1100 nm. The wafer was cut along the a-axis, with dimensions of 6 × 6 × 2 mm³ (b × c × a) and the two 6 × 6 mm² faces polished. We used a continuous wave laser diode at a wavelength of 808 nm as the pump source to measure the fluorescence spectrum and an optical spectrum analyzer to record the fluorescence spectra.

3. Results and discussions

3.1. XRPD characterization and effective segregation coefficients

The structure of the Nd:BLGM crystal was studied by X-ray powder diffraction (XRD), and results are shown in Fig. 2. It shows that all peaks can be indexed in accordance with the standard XRD pattern of BLGM, and the as-grown crystal consists of an BLGM single phase belonging to the p4̄2₁m space group. According to the peak 2θ values in the XRD pattern, the tetragonal unit cell parameters were calculated to be a = b = 8.158 Å, c = 5.387 Å, which is in good agreement with the data for BLGM (a = b = 8.145 Å, c = 5.382 Å).

Fig. 2 XRD patterns of Nd:BLGM.

To check the quality of the as-grown single crystal, the high-resolution X-ray diffraction (HRXRD) method was used. Fig. 3 shows the rocking curve from the (200) diffraction plane. The diffraction peak with good symmetry appears at ω = 9.80°. The peak has an FWHM value of 19.6′′, implying high optical quality of the crystal.

Fig. 3 HR XRD curve of Nd:BLGM.

The concentrations of elemental Nd, Ba, La and Ga in the crystal were measured using X-ray fluorescence analysis. The polycrystalline material used for growing the crystal was referenced as the comparison standard. The effective segregation coefficients k for Nd³⁺, Ba²⁺, La²⁺, and Ga³⁺ in the Nd:BLGM crystal were calculated by K_eff = c1/c2, where c1 and c2 are the respective concentrations of the ions in the crystal and raw materials. From Table 1, it can be seen that the effective segregation coefficient of Nd³⁺ was larger than 1, which indicates that Nd³⁺ ions are easily doped into this crystal. The Nd³⁺ concentration is 1.12 at% in the as-grown crystal. Because of the volatilization of Ga₂O₃, the Ga³⁺ content deviated from the stoichiometric ratio.

Table 1 Effective segregation coefficients of some ions in Nd:BLGM

	Standard (wt%)	Sample (wt%)	Keff
Nd	0.2414	0.2704	1.12
Ba	22.9855	21.8362	0.95
La	23.0172	24.1681	1.05
Ga	35.0103	32.2095	0.92

---

3.2. Thermal properties

Fig. 4 shows the thermal expansion curves of Nd:BLGM versus temperature. From the plot, it can be seen that the thermal expansion along the a and c-axis is almost linear over the entire temperature range from 303–773 K. The average linear thermal expansion coefficients along the a- and c-axis were calculated to be 4.49 × 10⁻⁶ K⁻¹ and 6.34 × 10⁻⁶ K⁻¹, respectively. Both are near the value for Nd:Ca₃(Nb,Ga)₅O₁₂ (7.88 × 10⁻⁶ K⁻¹). The latter material has been identified as a representative disordered crystal.²⁶ A small difference between the thermal expansion coefficient components along the a- and c-axes is favorable for ease of crystal growth and for laser applications.

Fig. 4 Thermal expansion ratio coefficients of Nd:BLGM.

Fig. 5 shows the variation of the specific heat of Nd:BLGM with temperature. It can be seen that the specific heat (C_p) varies approximately linearly with temperature, increasing smoothly from 0.354 to 0.525 J g⁻¹ K⁻¹, as the temperature is increased from 293 K to 573 K. At 303 K, the C_p of Nd:BLGM is 0.365 J g⁻¹ K⁻¹, a value that is comparable to that of Nd:YVO₄ (0.36 J g⁻¹ K⁻¹).²⁷ Because Nd:YVO₄ possesses a quite high damage threshold, we project that Nd:BLGM should also have a high damage threshold and thus can be applied in high power lasers.

Fig. 5 Specific heat variation of Nd:BLGM with temperature.

Fig. 6 shows the thermal diffusivity coefficients of the Nd:BLGM crystal. It can be seen that the thermal diffusivities along the a- and c-axis decrease slowly with increasing temperature. At 303 K, the thermal diffusivity along the a-axis is 0.97 mm s⁻¹, and along the c-axis, 0.85 mm s⁻¹, respectively.

Fig. 6 Thermal diffusivity variation of Nd:BLGM with temperature.

The density of the Nd:BLGM crystal was measured by the Archimedian buoyancy method. The density was calculated using the following equation:

where m is the sample weight in air, m′ is the sample weight in distilled water, and ρ_water is the density of the distilled water at the measurement temperature (301 K). The density was determined to be 5.531 g cm⁻³ by averaging the values obtained with four samples.

Fig. 7 shows the temperature dependence of the thermal conductivity of Nd:BLGM along the a and c-axis, determined by using the formula κ = λρC_P, where λ is the thermal diffusivity coefficient, ρ is the measured density, and C_p is the specific heat. The thermal conductivity along the a-axis increases from 1.96 to 2.39 W m⁻¹ K⁻¹ over the temperature range from 303.1 to 559.5 K. Along the c-axis, it increases from 1.72 to 2.17 W m⁻¹ K⁻¹ over the temperature range from 302.8 to 559.2 K. Considering the errors caused by the Diamond model DSC-ZC differential scanning calorimeter, Nanoflash LFA447 equipment and buoyancy method, we believe that the accuracy for the thermal conductivity measurements is over 95%. Thermal conductivity of Nd:BLGM increases with increasing temperature, which indicates glasslike behavior, because of the possible effects of the disordered structure.

Fig. 7 Thermal conductivity variation of Nd:BLGM with temperature.

3.3. Spectroscopic characteristics

The calculated absorption cross section of Nd:BLGM from 300 to 1100 nm at room temperature are shown in Fig. 8. The oscillator strengths are greater for σ polarization relative to π polarization. There exist six strong Nd³⁺ absorption bands located at 360 nm, 528 nm, 588 nm, 754 nm, 808 nm and 868 nm, which correspond to the transitions of Nd³⁺ from ground state ⁴I_9/2 to its excited states, ⁴D_1/2, ⁴G_9/2 + ⁴G_7/2, ⁴G_5/2, ⁴S_3/2 + ⁴F_7/2, ²H_9/2 + ⁴F_5/2, ⁴F_3/2, respectively. The strong absorption band at 808 nm is suitable for diode pumping. The 808 nm absorption band on σ polarization has a FWHM of 18 nm, which provides great flexibility for diode pumping. As a result of the broad absorption bandwidth of 808 nm band, the absorption of the disordered crystal will not decrease sharply, as the wavelength of the diode emission shifts. Measured σ polarized absorption coefficient of Nd:BLGM at 808 nm was 1.95 cm⁻¹, which corresponded to the σ_ab of 3.49 × 10⁻²⁰ cm². The value is an order of magnitude larger than that of Nd:YVO₄,²⁸ and this trend is reasonable regarding the difference of σ_ab. In ref. 20, at 778–835 nm absorption band, the max absorption coefficient was measured to be 1.39 cm⁻¹. In our experiments, Nd³⁺ ions were better doped into the crystals.

Fig. 8 Polarized absorption spectra of the Nd³⁺ ion doped into Nd:BLGM.

Fig. 9 shows the RT normal and polarized fluorescence spectra. We can see that, in two polarization directions, the fluorescence intensities near 1060 nm are all the strongest. From the figure, it can be seen that the ⁴F_3/2 → ⁴I_11/2 luminescence bandwidth is about 32 nm, all greater than in Nd³⁺:YVO₄ (1.1 nm)²⁷ or Nd³⁺ doped vanadate crystals (1–2 nm).^29,30 The inhomogenous broadening of the Nd³⁺ lines is caused by the variation in the local crystal field surrounding the Nd³⁺ ions. The broad emission linewidth of Nd:BLGM disordered crystal facilitates femtosecond pulse generation by passive mode locking.

Fig. 9 Fluorescence spectrum of the Nd³⁺ ion doped into Nd:BLGM.

A Judd–Ofelt analysis of the absorption bands was used to calculate the integrated absorption coefficient ∫K(λ)dλ, the transition-line intensity S_exp, the oscillator strength for the absorption P_exp and the absorption cross section σ_a(λ).^31,32 The detailed calculation procedures are written below

where l, e, n, N₀, N_g and D(λ) are the sample thickness, the electron charge, the refractive index, the average Nd³⁺ density in the lattice structure, the number of Nd³⁺ ions in the ground state per unit volume and the optical density, respectively. The polarization averaged line strengths were evaluated by combining the σ and π absorption spectra with 2/3 and 1/3 weighting, respectively.³³ The three intensity parameters Ω_t (t = 2, 4, 6) are fitted as 1.52 × 10⁻²⁰, 4.15 × 10⁻²⁰ and 1.85 × 10⁻²⁰ cm². The root means square deviation (rms error) is 4.15 × 10⁻²⁰ cm². When the J–O theory is applied to Nd:BLGM, the measured absorption spectrum exhibits a good fit. The results calculated for the absorption spectra are shown in Table 2.

Table 2 Line intensities and optical parameters of the absorption spectrum in Nd:BLGM

Transition final state 4f^nψ′J′	Central wavelength [small lambda, Greek, macron] (nm)	Absorption coefficient KC (cm^−1)	Sexp (J → J′) (×10^−20 cm^2)	Pexp (J → J′) (×10^−6)	σa(λ) (×10^−20 cm^2)
^4D1/2 + ^4D3/2	360	1.49	1.42	7.86	2.66
^2P1/2	432	0.98	0.14	0.61	1.75
^4G11/2 + ^2P3/2 + ^2D3/2 + ^2G9/2	472	0.95	0.34	1.31	1.71
^4G9/2 + ^4G7/2	528	1.14	1.1	3.83	2.04
^4G5/2	588	1.97	3.18	9.91	3.53
^4F9/2	684	0.87	0.11	0.31	1.55
^4S3/2 + ^4F7/2	754	1.31	1.49	3.66	2.36
^2H9/2 + ^4F5/2	808	1.68	1.98	4.50	3.00
^4F3/2	868	1.06	0.94	1.96	1.89

---

According to the calculated J–O intensity parameters, the polarized spontaneous emission probabilities A(J′′ → J′), the radiative lifetime of τ_rad and the fluorescence emission β_J′′J′ were calculated using the following formulas:

Some of the calculation results are listed in Table 3. The fluorescence branch ratio at about 1060 nm is 0.509, which favors laser operation at about 1060 nm. The radiative lifetime τ_r was calculated from decay rate obtained by J–O analysis and was 338 μs, which was comparable to the value in previous reports.³⁴ The fluorescence decay curve of Nd:BLGM crystal is shown in Fig. 10. By double exponential fitting, the fluorescence lifetime is found to be 294 μs. The value of the relation coefficient R̂2 is 0.99881. The results ignore the rapid reduction of fluorescence intensity immediately after optical pumping. Thus, a fluorescence quantum efficiency can be calculated by η = τ_f/τ_r, and determined to be 87%. This indicates that the nonradiative energy dissipation of Nd:BLGM is weak, and in a nonlasing condition, there will be less hear generating.

Table 3 Luminescence parameters of Nd:BLGM for the radiative ⁴F_3/2 → ⁴I_J′transition

Final state	Radiation λ (nm)	Scal (J′′ → J′) (×10^−20 cm^2)	A (J′′ → J′) (s^−1)	τrad (μs)	βJ′′→J′ (%)
^4I9/2	906	1.06	1587	338	52
^4I11/2	1060	1.34	1260		41
^4I13/2	1333	0.39	184		6
^4I15/2	1880	0.05	8		0.3

---

Fig. 10 Fluorescence density decay curve in Nd:BLGM at room temperature.

The stimulated emission cross section σ_e can be calculated from

where λ_p is the wavelength of the fluorescence peak, n is the refractive index at the fluorescence wavelength, Δν is the frequency full-width at half-maximum, and A is the ⁴F_3/2 → ⁴I_11/2 radiative transition rate. The stimulated emission cross section at about 1060 nm for the ⁴F_3/2 → ⁴I_11/2 transition is 4.24 × 10⁻²⁰ cm², which is smaller than that of 1.1 at% Nd:YAG (3.2 × 10⁻¹⁹ cm²).²⁴ In ref. 20, W. Ryba–Romanski team calculated the polarized emission cross section to be 8.72 × 10⁻²⁰ cm². The σ_emτ_f product at 1.06 μm, which has direct reciprocal influence on the pump threshold, is 11% for Nd:BLGM. The smaller emission cross-section and longer fluorescence lifetime indicate that Nd:BLGM should have a higher energy storage capacity and excellent Q-switched laser properties.

4. Conclusions

A Nd-doped BaLaGa₃O₇ single crystal was grown by the Czochralski method. Several thermal, optical and laser properties were measured. The effective segregation coefficient of Nd³⁺ was found to be 1.12. Thermal conductivity at room temperature was investigated to be 1.96 W m⁻¹ K⁻¹, and the thermal conductivity increased with increasing temperature, which was an advantage using in high power system. The absorption and emission spectra of Nd³⁺ were inhomogeneously broadened, which was associated with the disordered melilite structure. The width of the absorption band around 808 nm for matching to laser-diode pumping was about 18 nm. At room temperature, the ⁴F_3/2 → ⁴I_11/2 luminescence bandwidth was nearly 32 nm, which facilitated ultra-short pulses generation. The J–O theory was used to calculate the values of optical parameter. The peaks of σ_ab and σ_em of Nd:BLGM were determined to be 3.49 × 10⁻²⁰ and 4.24 × 10⁻²⁰ cm², respectively. The fluorescence lifetime of 1 at% Nd:BLGM was evaluated to be 294 μs, with the radiative quantum efficiency as high as 87%. All of the results show that Nd:BLGM is a promising disordered media for ultrafast sources in multiwatt power applications.

Acknowledgements

This work is supported financially by the National Science Foundation of China (Grant no. 51202135 and 51302158), Natural Science Foundation of Shandong Province (Grant no. ZR2014EMQ004), Open Foundation of Key Laboratory of Functional Crystal Materials and Device (Shandong University, Ministry of Education, Grant no. JG1402), and Youth Foundation of Shandong Academy of Sciences (Grant no. 2013QN011, 2014QN027 and 2014QN028).

Notes and references

1. A. A. Kaminskii, H. J. Eichler, K. Ueda, N. V. Klassen, B. S. Redkin, L. E. Li, J. Findeisen, D. J. Garcia-Sole and J. Fernandez, Appl. Opt., 1999, 38, 4533.
2. C. Y. Cho, H. P. Cheng, Y. C. Chang, C. Y. Tang and Y. F. Chen, Opt. Express, 2015, 23, 8162.
3. B. L. Wang, L. Tian, H. H. Yu, H. J. Zhang and J. Y. Wang, Opt. Lett., 2015, 40, 3213.
4. H. H. Yu, S. X. Wang, S. Han, K. Wu, L. B. Su, H. J. Zhang, Z. P. Wang, J. Xu and J. Y. Wang, Opt. Lett., 2014, 39, 1341.
5. J. A. Au, D. Kopf, F. Morier-Genoud, M. Moser and U. Keller, Opt. Lett., 1997, 22, 307.
6. A. Agnesi, A. Greborio, F. Pirzio, E. Ugolotti, G. Reali, S. Y. Choi, F. Rotermund, U. Griebner and V. Petrov, IEEE J. Sel. Top. Quantum Electron., 2012, 18, 74.
7. A. Miguel, J. Azkargorta, R. Morea, I. Iparraguirre, J. Gonzalo, J. Fernandez and R. Balda, Opt. Express, 2013, 21, 9298.
8. W. W. Li, D. B. He, S. G. Li, W. Chen and L. L. Hu, Ceram. Int., 2014, 40, 13389.
9. S. Han, W. Lu, B. Y. Sheh, L. Yan, M. Wraback, H. Shen, J. Pamulapati and P. G. Newman, Appl. Phys. B, 2002, 74, S177.
10. I. Iparraguirre, J. Azkargorta, R. Balda, K. V. Krishnaiah, C. K. Jayasankar, M. Al-Saleh and J. Fernandez, Opt. Express, 2011, 19, 19440.
11. Y. G. Zhao, S. D. Zhuang, X. D. Xu, J. Xu, H. H. Yu, Z. P. Wang and X. G. Xu, Opt. Express, 2014, 22, 2228.
12. J. X. Liu, Z. H. Wang, K. N. He, L. Wei, Z. G. Zhang, Z. Y. Wei, H. H. Yu, H. J. Zhang and J. Y. Wang, Opt. Express, 2014, 22, 26933.
13. Z. P. Qin, G. Q. Xie, J. Ma, W. Y. Ge, P. Yuan, L. J. Qian, L. B. Su, D. P. Jiang, F. K. Ma, Q. Zhang, Y. X. Cao and J. Xu, Opt. Lett., 2014, 39, S1737.
14. G. Q. Xie, D. Y. Tang, W. D. Tan, H. Luo, H. J. Zhang, H. H. Yu and J. Y. Wang, Opt. Lett., 2009, 34, 103.
15. G. Q. Xie, L. J. Qian, P. Yuan, D. Y. Tang, W. D. Tan, H. H. Yu, H. J. Zhang and J. Y. Wang, Laser Phys. Lett., 2010, 7, 483.
16. W. Ryba-Romanowski, S. Golab, G. Dominiak-Dzik and M. Berkowski, Mater. Sci. Eng., B, 1992, B15, 217.
17. V. Kushawaha and Y. Chen, Appl. Phys. B, 1995, 60, 67.
18. A. V. Terentiev, P. V. Prokoshin, K. V. Yumashev, V. P. Mikhailov, W. Ryba-Romanowski, S. Golab and W. Pisarski, Appl. Phys. Lett., 1995, 67, 2442.
19. W. Piekarzyk, M. Berkowski and G. Jasiołek, J. Cryst. Growth, 1985, 71, 395.
20. W. Ryba-Romanowski, B. Jezowska-Trzebiatowska, W. Piekarczyk and M. Berkowski, J. Phys. Chem. Solids, 1988, 49, 199.
21. W. Ryba-Romanowski, Int. J. Electron., 1996, 81, 457.
22. A. Agnesi, F. Pirzio, L. Tartara, E. Ugolotti, H. J. Zhang, J. Y. Wang, H. H. Yu and V. Petrov, Laser Phys. Lett., 2014, 11, 035802.
23. C. Kittel, Phys. Rev., 1949, 75, 972.
24. W. Koechner, Solid-State Laser Engineering, Springer-Verlag, Berlin, Germany, 2006, p. 62.
25. Y. F. Chen, IEEE J. Quantum Electron., 1999, 35, 234.
26. 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, Opt. Express, 2009, 17, 9270.
27. L. J. Qin, X. L. Meng, H. Y. Shen, L. Zhu, B. C. Xu, L. X. Huang, H. R. Xia and G. Zheng, Cryst. Res. Technol., 2003, 38, 793.
28. Y. Sato and T. Taira, IEEE J. Sel. Top. Quantum Electron., 2005, 11, 613.
29. T. Jensen, V. G. Ostroumov, J.-P. Meyn, G. Huber, A. I. Zagumennyi and I. A. Shcherbakov, Appl. Phys. B, 1994, 58, 373.
30. C. Maunier, J. L. Doualan, R. Moncorgé, A. Speghini, M. Bettinelli and E. Cavalli, J. Opt. Soc. Am. B, 2002, 19, 1794.
31. L. Guo, Z. P. Wang, H. H. Yu, D. W. Hu, S. D. Zhuang, L. J. Chen, Y. G. Zhao, X. Sun and X. G. Xu, AIP Adv., 2011, 1, 042143.
32. Y. L. Huang, X. Q. Feng, Z. H. Xu, G. J. Zhao, G. S. Huang and S. G. Li, Solid State Commun., 2003, 127, 1.
33. F. Hanson, D. D. Horacio, R. Verdun and M. Kokta, J. Opt. Soc. Am. B, 1991, 8, 1668.
34. W. Ryba-Romanowski, M. U. Gutowska, W. piekarczyk, M. Berkowski, Z. Mazurak and B. Jezowska-trzebiatowska, J. Lumin., 1987, 36, 369.

---