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A series of high quality Yb3+-doped gadolinium scandium gallium garnet (Yb:GSGG) single crystals with different Yb3+ ion concentration (7.5, 10, 15 and 30 at.%) has been grown by means of optical floating zone (OFZ). Crystal structure was analyzed with X-ray powder diffraction (XRPD), showing that the Yb:GSGG crystal possesses a cubic structure with space group Ia3d, and the lattice constants decrease linearly as the Yb3+ concentration increases. Effective elemental segregation coefficients and chemical composition were investigated by X-ray fluorescence (XRF), suggesting that some Yb3+ ions occupy the octahedral site when the Yb3+ ion concentration is higher than 10 at.%. The thermal properties of Yb:GSGG crystals were systematically studied by measuring the specific heat, thermal expansion and thermal diffusion coefficients. Thermal conductivity was then calculated, and it exhibits a tendency to decrease with increasing Yb3+ ion concentration. Spectroscopic characterization of Yb:GSGG crystals was performed at room temperature (RT), and the stimulated emission cross section was calculated using the reciprocity method (RM) and the Füchtbauer−Ladenburg (F−L) formula, respectively. In comparison with the radiative lifetime of the 2F5/2→2F7/2 transition, the effect of radiation trapping on the fluorescence lifetime is discussed. These research results indicate that Yb:GSGG can be regarded as a promising candidate for use in an ultrashort pulsed and tunable laser.
© 2014 Optical Society of America
1. Introduction
Over the last few decades, Yb3+-doped laser materials have received considerable attention owing to the development of high-power InGaAs laser diodes (LD) that emit around the 0.87−1.0 μm range. The main interest depends on the simpler electronic structure scheme ([Xe]4f13 [1],) when compared with Nd3+-doped materials, which results in no excited-state absorption or upconversion loss, long fluorescence lifetime of the upper laser level (milliseconds) and few quantum defects (≤ 8.6%). In addition, the emission bandwidth is approximately 3 or 4 times wider than that of the Nd3+ ion, which makes it possible to generate ultra-short pulses and kW-range average power. Currently, various Yb3+-doped gain materials have been successfully prepared to generate femtosecond laser operation, such as the borates Yb:YAB and Yb:YCOB [2], the tungstates Yb:KGW and Yb:KYW [3, 4], the oxyorthosilicates Yb:GSO and Yb: GYSO [5, 6], the sesquioxides Yb:Y2O3, Yb:Lu2O3 and Yb:Sc2O3 [7, 8], the vanadates [9], and the garnets Yb:YAG and Yb:CALGO [10–12], etc. Among the various laser crystals, Yb3+-doped gain media with the garnet structure have attracted a great deal of attention in the fields of CW, mode-locked and Q-switched operations because of their excellent optical and thermo-mechanical properties. Specifically, the Yb-doped YAG is considered to be one of the dominant gain media utilized for commercial applications. In 2003, Chénais et al. [13] demonstrated that the Yb:GGG crystal is potentially a better host for high average power solid state laser than Yb:YAG for several reasons [14]: first, its thermal conductivity is larger than that of Yb:YAG when the Yb doping level is greater than 4 at.%; second, it has a smaller Stokes shift between absorption and emission, which can reduce thermal loading; third, it can be grown core-free up to a larger size and with a better optical quality than YAG. In addition, it has been reported that the Yb:GGG crystal has an excellent passive Q-switching properties with a Cr4+:YAG crystal used as saturable absorber, producing an average output power of 5.31 W at a pulse repetition rate of 62.5 kHz, 140 μJ in energy and 5.8 ns in duration [15].
Thanks to the partial substitution of Ga3+ ions with Sc3+ in the GGG crystal octahedrons, a new class of GSGG crystal is formed. It has been shown that a Cr, Nd co-doped GSGG crystal exhibits much better laser performance than Nd:YAG, owing to its excellent optical properties [16–19]. Recently, Er3+-doped and Yb,Er co-doped GSGG crystals have exhibited good laser performance operating at about 2.7−3.0 μm [20, 21]. Thus, a great deal of effort has been made to search for other prospective Yb-doped materials in the garnet family. Moreover, it has been confirmed that the GSGG shows better radiation resistance than YAG when exposed to ionizing radiation [22]. This observation means that the GSGG is a potentially new radiation-resistant laser material, which can be operated in a hostile environment. Constrained by the high melting temperature (1850 °C), all GSGG crystals at present are grown by the Czochraski (Cz) method using an iridium crucible [23]. Composition control is problematic because of the easy volatilization of Ga2O3 at such a high temperature. What is more, the O2 partial pressure must be carefully controlled to avoid oxidation of the crucible during the process of crystal growth. Fortunately, the OFZ (optical floating zone) method is suitable for growing such a high temperature crystal because of its advantages (higher growth rate, no need for a crucible and growth in a high oxygen atmosphere). The effectiveness of the OFZ method has been demonstrated, for example, in the growth of LuGG, YGG, LuSGG and YSGG, and so on [24–27]. It is supposed that this technique offers a unique opportunity to obtain a high quality GSGG crystal to overcome the shortcomings of Cz method, because the variability of the Ga valence can be better controlled in an oxygen atmosphere. Up to now, however, there is little information on Yb-doped GSGG crystals [10], and doping the Yb3+ ion into the GSGG crystal has only been investigated as a sensitizing mechanism [21]. It is currently accepted that thermal loading will degrade laser performance and may lead to crystal fracture, even in the Yb3+-doped materials. So, it is very significant to investigate the effect of the Yb3+-doping concentration on its structural, thermal and spectroscopic properties.
In this paper, a series of Yb:GSGG crystals with different Yb3+ concentrations (7.5, 10, 15 and 30 at.%) was grown by the OFZ technique. Particular attention was paid to the investigation of the dependence of the structural and thermal properties (including specific heat, thermal expansion coefficient, thermal diffusion coefficient and thermal conductivity) on increasing Yb3+ concentration. Spectroscopic investigation of Yb:GSGG crystals was carried out at RT, based on the measured absorption and fluorescence spectra as well as on the fluorescence decay curves. The radiative lifetime of Yb:GSGG crystals was calculated, and the effect of radiation trapping on the fluorescence lifetime was discussed. All the results show that Yb:GSGG is a promising candidate for use in high power and ultrashort laser systems.
2. Experimental section
2.1 Synthesis of polycrystalline materials and crystal growth
A series of Yb:GSGG single crystals was grown by the OFZ method using the starting oxides of Yb2O3, Gd2O3, Sc2O3 and Ga2O3 with a purity of 99.99%. An excess of 2wt.% Ga2O3 was added to the initial mixture in order to compensate for its evaporation loss. For the preparation of polycrystalline Yb:GSGG, a certain amount of Yb2O3 with Yb concentration equal to 7.5, 10, 15 and 30 at.% replacing Gd was introduced, thoroughly mixed with Gd2O3, Sc2O3, and Ga2O3 in proper proportion, and pre-sintered at 1100 °C for 10 h according to the following the solid-state reaction:
The as-synthesized materials were ground and loaded into a rubber membrane to prepare a feed rod of 6−8 mm in diameter and 50−70 mm in length. Next, they were treated under vacuum, hydrostatically pressed to about 60 MPa, and calcined in air at 1300 °C for 5 h. Finally, the growth was carried out in an optical floating-zone furnace (Crystal Systems Inc., FZ-T-12000-X-I-S-SU) equipped with four 3 kW Xenon lamps along the 〈111〉 direction using a seed crystal cut from un-doped GGG. During the process of crystallization, oxygen gas with 99.9% purity was passed into the growth chamber, and the flow rate was regulated at 30 mL·min−1. The growth rate of single crystal was kept in the range of 5−8 mm·h−1, and typical rotation rates of the feed rod and the seed rod were both maintained at 15−20 rpm in opposite directions. To prevent the crystal from cracking, the crystals were cooled slowly after growth to RT within 3 h. Finally, these crystals were annealed slowly to 1100 °C for 40 h to eliminate thermal stress formed during the growth process, and then cooled to RT at a rate of 30 °C·h−1.
2.2 Crystal structure, elemental composition and thermal properties
The phase purity and crystal structure of the as-grown crystals were characterized by XRPD with an X-ray powder diffractometer (Bruker AXS, D8 Advance) at RT. The measured data were collected with a step size of 0.02 °·s−1 over range from 10° to 90°. The elemental composition of Yb, Gd, Sc and Ga in the as-grown crystals was determined using a Rigaku ZSX Primus II XRF spectrometer.
The specific heat at constant pressure (Cp) was measured on a (Mettler Toledo DSC822e) differential scanning calorimeter (DSC) over the range from RT to 300 °C at a rate of 10 °C·min−1. The thermal expansion coefficient of the as-grown crystals (dimensions: 3 × 3 × 5 mm3) was measured using a thermal mechanical analyzer (TMA) over the temperature range from 25 to 400 °C at a constant rate of 5 °C·min−1. The thermal diffusion coefficient was measured by the laser flash method using a laser flash apparatus (NETZSCH model LFA457/2/G) on square wafers (4 × 4 × 1 mm3) over the temperature range from 30 to 300 °C. The 4 × 4 cm2 faces of the square wafer were coated with graphite. During this experiment, a short light pulse heated the front surface of the square wafer, and the temperature rise on the rear surface was measured as a function of time by an IR detector.
2.3 Optical and spectroscopic characterization
The RT absorption spectra of the as-grown Yb:GSGG crystals were recorded using a spectrophotometer (JASCO model V-570) on double-sided polished samples (3 × 3 × 0.5 mm3) with a spectral resolution of 0.2 nm. The RT fluorescence lifetime was acquired by the time-correlated single-photon counting (TCSPC) method with an Edinburgh Instruments FLS920 fluorescence spectrometer equipped with an ANDO Shamrock SR-303i high-resolution optical spectrum analyzer and a tunable Opolette 355 II (5 ns, 20 Hz) pump source. The excitation and detection wavelengths were 945 and 1025 nm, respectively. In order to weaken the effect of radiation trapping, all polished samples were prepared with a thickness of 0.5 mm, and a focusing prism was placed in edge of the sample.
3. Results and discussion
3.1 Crystal growth
The series of as-grown Yb:GSGG crystals with dimensions of 5 mm in diameter and 20~30 mm in length are shown in Fig. 1. It can be seen that these crystals have no inclusions or other macroscopic defects. However, the color of the 7.5 at.% Yb:GSGG as-grown crystal was light yellow, which can be attributed to the presence of a small amount of Yb2+ ions [28], and the color could be bleached out by annealing. The conversion of Yb2+→Yb3+ in YAG can be completed by annealing the crystal in an oxidizing atmosphere over the temperature range from 861 to 1065 °C [29]. Therefore, it is believed that the OFZ method is a good way not only for reducing the concentration of Yb2+ ions, but also for restraining the evaporation of Ga2O3 and avoiding pollution of the crucible, which is considered to be a common problem in the Cz method. Four crystal samples were cut from the post-annealed crystal perpendicular to the growth direction, each having dimensions of 3 × 3 mm2 with different thickness (5 mm for 7.5 at.%, 5 mm for 10 at.%, 3 mm for 15 at.% and 1 mm for 30 at.%) and polished on both sides (as shown the inset in Fig. 1(a)). No light scattering was observed under a 10 mW He−Ne laser, indicating that these as-grown crystals exhibit excellent optical quality, and can readily be used for laser experiments.
Fig. 1 Photographs of Yb:GSGG crystals grown by OFZ technique with different Yb3+ doping concentration: (A) 7.5 at.%, (B) 10.0 at.%, (C) 15.0 at.% and (D) 30.0 at.%.
3.2 Crystal structure and composition
The phase purity of as-grown Yb-doped GSGG crystals was studied by using XRPD, and the results are displayed in Fig. 2(a). The entire set of diffraction peaks for the Yb:GSGG crystals is consistent with the JCPDS file on Gd3.0Sc1.84Ga2.93O11.64 (No.82−1950), indicating that these materials crystallized in the cubic garnet phase with a space group Ia3d. From the partial view of Fig. 2(a) (i.e. Figure 2(b)), it can be clearly seen that the diffraction peaks shift toward a larger angle with increasing Yb3+ concentration. This result can be explained by considering that the ionic radius of Yb3+ is smaller than that of Gd3+ when Yb3+ replaces Gd3+ in the dodecahedron. By using the XRPD results, the unit-cell parameters of the Yb:GSGG crystals were calculated to be a = 12.5608 Å for 7.5 at.%, a = 12.5464 Å for 10 at.%, a = 12.5423 Å for 15 at.% and a = 12.5396 Å for 30 at.% (as shown in Table 1), respectively, implying that the Yb:GSGG unit-cell parameters decrease with increasing Yb3+ concentration. Compared with pure GSGG (a0 = 12.5588 Å [30],), it is found that all the Yb:GSGG unit-cell parameters are smaller than those of GSGG, except for the 7.5 at.% Yb:GSGG. This result can be explained with the following arguments: because the Gd3+ and Yb3+ ions have the same electric charge and the similar ionic radius, Yb3+ can easily replace Gd3+ at the 24(c) sites. However, the effective ionic radius of Yb3+ (0.985 Å for CN = 8) is slightly smaller than that of Gd3+ (1.053 Å for CN = 8), resulting in a small shrinkage when compared to the pure GSGG lattice [31].
Table 1. Cell parameters of Yb:GSGG for different Yb3+ concentrations
The cell volumes of the Yb:GSGG crystals were calculated from the cell parameters, and the results are also listed in Table 1. The relationship between the lattice constants and Yb3+ ion concentration was plotted. From Fig. 3, it is clear that there is a linearly decreasing variation of the lattice constant as the Yb3+ concentration increases. This tendency agrees well with the Bragg diffraction equation and Vegard’s law [32]. A similar phenomenon is observed in Yb-doped GGG and YSGG crystals [33, 34].
The elemental concentration (e.g. Yb, Gd, Sc and Ga) in the as-grown Yb:GSGG crystals was analyzed by the XRF method. The effective segregation coefficients k of the Yb3+, Gd3+, Sc3+ and Ga3+ ions in Yb:GSGG were calculated by
where Cs and C0 are the concentration of doping ions in the crystal and in the polycrystalline feed rod, respectively. The k values of Yb3+, Gd3+, Sc3+ and Ga3+ was calculated, and the results are listed in Table 2. From this table, it can be seen that the segregation coefficients of Yb3+ in the as-grown crystals is close to 1, indicating that the Yb3+ has been successfully doped into the GSGG lattice crystals as an active ion. The actual concentration of the Yb3+ ion in the as-grown crystal was 6.70, 9.31, 14.96 and 29.46 at.% for the 7.5, 10, 15 and 30 at.%, respectively. For elements Gd and Sc in the Yb:GSGG crystal, the segregation coefficients are also close to 1, meaning that the composition ratios are favorable for obtaining a high quality crystal. However, the segregation coefficient of Ga is slightly greater than 1 with respect to the stoichmetric formula (Gd3.0Sc1.84Ga2.93O11.64), which can be attributed to an excess of Ga2O3 in the starting materials. And, the excess of Ga2O3 is estimated to be 0.28, 0.27, 0.24 and 0.21 at.% for the 7.5, 10, 15 and 30 at.% Yb-doped GSGG crystals, respectively. In the light of the work by Shimamura et al. [35], the Yb3+ ions were able to selectively occupy the Gd3+ and Ga3+ sites depending on the Yb3+ concentrations. When the Yb3+ concentration is low, they substitute for the Gd3+ ions. But, in the case of higher Yb3+ concentration, the Yb3+ ions begin to replace the Ga3+. Therefore, we calculated the chemical composition and the CYb + Gd to CSc + Ga ratio for the Yb:GSGG crystals, and the results are listed in Table 2. From this Table, it can be seen that the ratio increases as the Yb3+ concentration increased. When the Yb3+ concentration is higher than 10 at.%, the ratio of CYb + Gd/CSc + Ga is greater than that of 3:5, indicating that some Yb3+ ions had occupied the octahedral sites that were generally considered to be occupied by Sc3+ or Ga3+ ions. This phenomenon will make the crystal structure of Yb:GSGG more disordered, thus resulting in broader absorption and emission spectra.Table 2. XRF analysis of Yb:GSGG crystals with different Yb3+ concentrations
3.3 Thermal properties
At atmospheric pressure, the specific heat (Cp) is defined as the ratio of heat energy change to the change of temperature. Generally, the bigger Cp is for a crystal, the greater will be the laser damage threshold obtained during laser operation. The measured Cp versus temperature curves for the Yb:GSGG crystals are shown in Fig. 4(a), from which it can be seen that the Cp curves display a nearly linear increase with temperature. The Cp values of these crystals decrease from 0.417 to 0.375 J·g−1·K−1 with increasing Yb3+ concentration over the range from 7.5 to 30 at.% at RT. Compared with similar Yb3+ doping levels, the Cp value of 10 at.% Yb:GSGG (0.405 J·g−1·K−1) is smaller than that of Yb:YAG (0.63 J·g−1·K−1 [36],) or Yb:YGG (0.43 J·g−1·K−1 [25],), but larger than that of 7.5 at.% Yb:LuGG (0.35 J·g−1·K−1 [37],). So, we speculate that the 10 at.% Yb:GSGG crystal should display a moderate laser damage threshold, which is higher than Yb:LuGG, but lower than Yb:YAG or Yb:YGG.
Fig. 4 Thermal survey of Yb:GSGG crystals versus temperature (A) specific heat, (B) thermal expansion coefficient, (C) thermal diffusion coefficient and (D) thermal conductivity. (Inset of B) Density of Yb:GSGG crystals as a function of temperature.
The thermal expansion of a laser crystal is the most important factor in determining its growth and applications. If the crystal has a large thermal expansion coefficient, it easily generates thermal gradients when pumped by a LD, a situation that can lead to fracture. Because the thermal expansion coefficient is a second-rank tensor [38], there is only one independent principal thermal expansion component for an isotropic cubic crystal. The experimental data on the Yb:GSGG crystals that was obtained was the value of the length as a function of increasing temperature starting from RT. By calculation, the linear thermal expansion coefficient (α) versus temperature of the Yb:GSGG crystals is displayed in Fig. 4(b). From this figure, it can be observed that the average linear thermal expansion coefficient of 10 at.% Yb:GSGG (4.80 × 10−6 K−1) was the smallest of any other sample. Furthermore, the value for this composition is smaller than that of Yb:YAG (8.18 × 10−6 K−1 [36],), Yb:YGG (5.3 × 10−6 K−1 [25],), Yb:LuGG (7.5 at.%, 6.25 × 10−6 K−1 [37],) and undoped GGG (8.0 × 10−6 K−1 [13],), suggesting that the 10 at.% Yb:GSGG crystal is not especially sensitive to a change in temperature, which results in a reduction of the thermal lensing effect caused by thermal expansion [39, 40].
The density of the Yb:GSGG crystals can theoretically be calculated using the following equation:
where M is the atomic weight of Yb:GSGG, z is the number of molecules in a unit cell, which is 8 for this crystal, NA is Avogadro’s constant, and a is the cell parameter. As a result of thermal expansion, the density of Yb:GSGG crystals is a function of temperature, as shown in inset of Fig. 4(b). The results reveal that the density of these crystals decreases as the temperature increases, however, increases with increasing of Yb3+ concentration, which can be attributed to the cell parameters variation caused by the introduction of Yb3+ ions.The variation of the thermal diffusion coefficient of Yb:GSGG with temperature is shown in Fig. 4(c). It is seen that the thermal diffusion component of the Yb:GSGG crystals decreases with increasing temperature. The coefficients are 2.257~1.341, 2.206~1.129, 2.154~1.098 and 1.871~1.031 mm2·s−1 from RT to 330 °C, respectively, for single crystals with doping level 7.5, 10, 15, and 30 at.%. Moreover, the thermal diffusion coefficient values of Yb:GSGG decrease with increasing Yb3+ concentration at the same temperature. This decrease is possibly due to the structural distortion caused by the presence of Yb3+ ions.
The thermal conductivity (k) of a laser crystal is considered to be an important factor in laser applications, because its magnitude influences the service life of the crystal. Thus, the thermal conductivity of the Yb:GSGG crystals was calculated from the following equation:
where ρ, Cp, and λ are defined as the density, the specific heat, and the thermal diffusion coefficient, respectively. From Fig. 4(d), it can be seen that the thermal conductivity of Yb:GSGG has a decreasing tendency as the temperature increases. At 50 °C, the k value of Yb:GSGG decreases as much as 22.8% from 6.20 to 4.79 W·m−1·K−1 when the doping concentration of Yb3+ increases from 7.5 to 30 at.%, which is about twice what the increases for Yb:YAG is as the Yb3+ concentration increases from 5 to 25 at.% (k decreases from 5.23 to 4.64 W·m−1·K−1 [36]). This result indicates that at this temperature, the introduction of Yb3+ ions has a larger effect on the k of the GSGG matrix than it does with YAG. Because of the scarcity of mobile conduction band electrons in insulator materials (e.g. oxide crystals), heat transport is mainly determined by phonon propagation. In other words, the k of an oxide crystal is influenced by the variation of the phonon mean free path. Thus, the k can also be written as:where ν is the sound velocity, which is considered a constant, and L is the phonon mean free path. With increasing Yb3+ concentration, some Yb3+ ions will occupy the octahedral sites leading to more disorder than what exists in pure GSGG. The structural disorder can reinforce phonon scattering, resulting in a decrease of the phonon mean free path [41]. As a result, the Yb:GSGG crystals display a decreasing value of k as the Yb3+ concentration is increased. Compared with other Yb3+-doped with garnet crystals, such as Yb:GGG (10 at.%, 6.8 W·m−1·K−1 [33],), Yb:LuGG (7.5 at.%, 4.94 W·m−1·K−1 [37],) and Yb:YGG (9.8 at.%, 3.47 W·m−1·K−1 [25],), it can be concluded that the 10 at.% Yb:GSGG crystal (5.90 W·m−1·K−1, in this work) should exhibit good performance in a laser system due to its favorable thermal conductivity.3.4 Spectroscopic investigation and fluorescence lifetime analysis
According to the results of the lattice constant and segregation coefficient variation with Yb3+ concentration, the ion density of Yb3+ (N0) in each as-grown crystal was calculated, and the results are listed in Table 3. It can see that the values of N0 range from 0.81110 × 1021 ion·cm−3 for 7.5 at.% Yb3+ to 3.60307 × 1021 ion·cm−3 for 30 at.% as the Yb3+ concentration increases. As shown in Fig. 5, the RT absorption spectrum of Yb:GSGG for several doping levels was measured in the range from 800 to 1100 nm, showing only one broad absorption band with a peak at 943~945 nm, corresponding to the Yb3+: 2F7/2→2F5/2 transition. Each absorption band has a very large full width at half maximum (FWHM) value, with values of 37.4, 35.1 35.4, 35.3 nm, respectively, for the 7.5, 10, 15 and 30 at.% Yb3+ concentrations. It should be noted that such a broad absorption band is quite suitable for efficient LD pumping. From Table 3, the values of the largest absorption cross-section at this wavelength for Yb:GSGG crystals are 0.61 × 10−20, 0.60 × 10−20, 0.57 × 10−20, 0.57 × 10−20 cm2, for the 7.5, 10, 15 and 30 at.% Yb3+, respectively. In addition, the value of the absorption cross-section at 968~970 nm for the Yb:GSGG crystals corresponding to the zero-phonon line (ZL) transition between the lowest levels of the 2F7/2 and 2F5/2 manifolds are also listed in this table, which indicates that the crystals are well suited for pumping by a commercial InGaAs laser. Compared with other Yb-doped garnet crystals, we know that the absorption cross-section in the strongest band of the Yb:GSGG crystals is similar to those of Yb:GGG (7.5 at.%, σabs = 0.66 × 10−20 cm2) [13] and Yb:YAG (8 at.%, σabs = 0.7 × 10−20 cm2) [41], confirming that there is an effective absorption of pump light at this wavelength [42].
Table 3. Spectroscopic parameters for Yb-doped GSGG crystals
Owing to the simple energy level scheme and the effect of radiation trapping [41], the stimulated emission cross-sections σems(λ) of the Yb3+ ions is generally obtained by the RM, as derived from the absorption spectrum:
where σabs (λ) is the absorption cross-section at wavelength λ, and Zl and Zu are the lower and upper manifold partition functions [43], respectively, which are calculated to be 1.4519 and 1.4101. The quantity h is the Planck constant, k is the Boltzmann constant, T is the absolute temperature, c is the velocity of light, and EZl is the zero phonon line energy, which is defined as the energy separation between the lowest Stark levels of the two energy states (2F5/2 and 2F7/2). The calculated emission spectra of Yb:GSGG crystals are shown in Fig. 6. An overlap of the fluorescence and absorption spectra is detected at 969.9 nm, which can be attributed to the self-absorption of Yb3+ ions. The strongest emission peak (λpeak) for Yb:GSGG crystals was located around 1024~1025 nm with σems = 1.66 × 10−20, 1.83 × 10−20, 1.73 × 10−20 and 1.80 × 10−20 cm2, respectively, for 7.5, 10, 15 and 30 at.% Yb3+ concentration. This peak displays a blue shift compared with corresponding emission peak located at 1030 nm for Yb:YAG, with an emission cross-section of 2.03 × 10−20 cm2 [41]. There is another emission peak located at 968~970 nm. However, this emission band is little practical importance for laser operation due to the presence of strong absorption at the same wavelength. Moreover, the largest σems value observed at λpeak is in the 10 at.% Yb:GSGG crystal, which is lower than those for Yb:GGG (2.0 × 10−20 cm2), Yb:YGG (2.56 × 10−20 cm2) and Yb:LuAG (2.6 × 10−20 cm2) [13, 25, 44], suggesting that the Yb:GSGG crystals will behave good performance because of the larger absorption cross-section and smaller stimulated emission cross-section. The FWHM at λpeak for the Yb:GSGG crystals was calculated, and the results are summarized in Table 3. As shown in Table 3, all the FWHM values of the Yb:GSGG crystals are larger than that of Yb:YAG (10 nm) and Yb:GGG (10 nm) [13]. It is especially note that the FWHM of 7.5 at.% Yb:GSGG is up to 12 nm. In recent year, it is demonstrated that the Yb:YAG has an excellent mode-locking laser property [45, 46], assuming that the Yb:GSGG is very suitable for the generation of ultrashort pulses, and the pulse width of the Yb:GSGG should be smaller than that of Yb:YAG.For a laser crystal, the fluorescence lifetime (τ) is an important parameter for judging the energy storage capacity. Four curves of the luminescence decay kinetics of Yb:GSGG crystals are shown in Fig. 7. From the curves, we deduced the fluorescence lifetimes to be 1.29, 1.37, 1.27 and 0.68 ms, respectively, for Yb3+ doping levels over the range from 7.5 to 30 at.%. We see that the RT fluorescence lifetime increases in crystals with a doping concentration between 7.5 at.% and 10 at.%, while for the 15 at.% and 30 at.% crystals it drops dramatically. This discrepancy is mainly caused by the decrease of Yb−Yb ions separation distances in the Yb:GSGG crystals, which can easily increase the density of quenching centers in the highly doped crystals and lead to energy migration among the Yb3+ ions [47, 48]. As observed in the inset of Fig. 7, the value of 1.37 ms for the 10 at.% Yb3+-doped crystal, is larger than that of Yb:YAG (0.95 ms [49],) or Yb:GGG (0.8 ms [50],). For the high concentration Yb3+-doped crystals, the short fluorescence lifetime is not favorable for storing the thermal population at the upper laser level, and strong re-absorption at the emission wavelength also weakens the output laser intensity, which has been demonstrated in other garnets such as Yb:YAG and Yb:GGG [51–53]. Taking into account the smaller emission cross-section and a relatively long fluorescence lifetime, we can infer that the 10 at.% Yb:GSGG crystal is a more suitable candidate for Q-switched and mode-locked application.
Fig. 7 Fluorescence lifetimes of Yb:GSGG crystals. (Inset) Fluorescence lifetime values for different Yb3+ concentrations.
It is reasonable to assume that the RM method can only be used if there is significant absorption, i.e. only in the vicinity of the fundamental transition. That is to say, the RM method is not accurate at long wavelengths. Thus, the emission cross-section of Yb:GSGG crystals can also be calculated using the F−L equation:
where I(λ) is the emission spectral intensity of the Yb3+ ion as a function of wavelength, τ is the fluorescence lifetime of the upper laser level, c is the velocity of light in vacuum, and n is the refractive index at the emission wavelength. During the process of calculation, the dispersion parameters of the Yb:GSGG crystals were assumed to be the same as for Nd:GSGG [18] as follows:The calculated emission cross-sections from the measured fluorescence spectra by the F−L formula are also shown in Fig. 6. It can be seen that the values of the largest emission cross-section at 1024~1025 nm are about 1.20 × 10−20, 1.22 × 10−20, 0.96 × 10−20 and 0.95 × 10−20 cm2, respectively, for 7.5 at.%, 10 at.%, 15 at.% and 30 at.%, from which it can be concluded that the emission cross-sections calculated by the F−L formula differ from those obtained by the RM. The former is greater than the latter at shorter wavelengths, while the situation is reversed at longer wavelengths, which is mainly caused by the effect of self-trapping.In order to get an accurate result for the fluorescence lifetime, the radiative lifetime τr can be obtained using the following equation [54]:
where n is the refractive index of the medium, c is the speed of light, and the integration is performanced over the entire transition centered at nm. Thus, the radiative lifetime of the Yb:GSGG crystals are calculated, and the results was also listed in Table 3. The fluorescence lifetime is longer than the radiative lifetime, which is caused by the re-absorption of the Yb3+ ion fluorescence. The re-absorption reduces the possibility of photon transition from the metastable level to the ground state, so the fluorescence lifetime is longer than the real fluorescence lifetime of the 2F5/2 level. The discrepancy becomes larger with increasing Yb3+ concentration. On the basis of the above analysis, the concentration of the doped ion is an important factor for determining the fluorescence lifetime. As is well known, a broadened emission band is a fundamental condition for generating femtosecond laser emission. Therefore, it should be easier for Yb:GSGG to absorb the output of an ultrashort pulsed laser than for the other reported Yb3+-doped crystals that have been studied.4. Conclusions
In summary, a series of Yb:GSGG single crystals with different Yb3+ ion concentrations (7.5, 10, 15 and 30 at.%) was successfully grown for the first time by the OFZ method. The phase purity, crystal structures, effective elemental segregation coefficient and chemical composition were studied by XRPD and XRF. The formation of a continuous series of solid solutions was confirmed. The thermal properties of Yb:GSGG, including specific heat, thermal expansion coefficient, thermal diffusion coefficient and thermal conductivity, were systematically investigated. The absorption and fluorescence spectra, and the fluorescence lifetime were measured at RT. Moreover, the stimulated emission cross-section of Yb:GSGG crystals was calculated by both the RM and F−L formula. The effect of radiation trapping on the spectroscopic properties was discussed, considering that the Yb3+ concentration is an important factor for measuring the fluorescence lifetime. The spectroscopic results allow one to assume that Yb:GSGG crystals could well be promising laser materials for the generation of ultra-short, mode-locked laser pulses, owing to the high thermal conductivity, large bandwidth and long fluorescence lifetime.
Acknowledgments
Financial support from Innovative Cooperation Fund, Institute of Chemical Materials of China Academy of Engineering Physics, China (Nos. kjcx-201202, 201203) and the National Science Foundation of China (Nos. 51025210, 51102156, 51272131, 51032004) are gratefully acknowledged. All the authors would like to thank Professor R.I. Boughton, Department of Physics and Astronomy of Bowling Green State University, for linguistic polish.
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