Open Access
Add to BibSonomyAbstract
We report on the crystal growth, structural and spectroscopic investigation of a novel trigonal calcium vanadate crystal, Tm3+:Ca9La(VO4)7. Polarized absorption, stimulated-emission and gain cross-section spectra are determined for this material. The maximum σSE corresponding to the 3F4 → 3H6 transition amounts to 1.28 × 10−20 cm2 at 1854 nm for σ-polarization. The measured lifetime of the Tm3+ ions in the 3F4 state is 1.19 ms. The Judd-Ofelt analysis performed yielded intensity parameters of Ω2 = 4.682, Ω4 = 0.659 and Ω6 = 0.475 [10−20 cm2]. The polarized Raman spectra indicate a strong and broad band centered at 867 cm−1. Owing to the disordered nature of Ca9La(VO4)7, the Tm3+ ions exhibit a broad and smooth gain profile at ~2 μm. The spectroscopic properties of Tm3+:Ca9La(VO4)7 are very promising for broadly tunable and ultrashort pulse lasers near 2 µm.
© 2017 Optical Society of America
1. Introduction
Vanadate crystals represent an important class of host materials for doping with laser-active trivalent lanthanide ions, Ln3+ = Yb3+, Nd3+, Tm3+, Ho3+, etc. A well-known example is the family of the tetragonal zircon-type REVO4 crystals where RE stands for Y, Gd or Lu [1]. In recent years, REVO4 crystals doped with Yb3+ and Tm3+ ions were used in efficient and broadly tunable continuous-wave (CW), Q-switched and mode-locked (ML) lasers operating at ~1 and 2 μm [2–6]. Additional broadening of the spectral bands of the Ln3+ ions enables shorter pulses to be generated by ML lasers. For this reason “mixed” YxGdyLuzVO4 crystals doped with Yb3+ were also studied [7,8].
There is a different crystal family of trigonal calcium vanadates, with the chemical formula Ca9RE3+(VO4)7 where RE = La, Y, Gd, Lu or Bi [9–11]. The first studies of these non-centrosymmetric (point group: 3m) crystals were focused on their nonlinear properties for second-harmonic generation (SHG) [12]. In recent years, they are being studied as laser host materials for Ln3+ dopants [13–15]. A partially disordered structure of the Ca9RE(VO4)7 crystals promotes broadening of the spectral bands of the active ions [11] which is of interest for tunable operation and the generation of ultrashort pulses. The Ca9RE(VO4)7 crystals are uniaxial [16] and they can provide naturally polarized laser output. These materials possess relatively low anisotropy of the thermal expansion (αa/αc ~1.5...2) and they are expected to feature “athermal” thermo-optic behavior [11] which may overcome the disadvantage of its low thermal conductivity (~1 W/mK). The Ca9RE(VO4)7 compounds melt congruently and large-volume crystals can be grown by the Czochralski method [10]. Spectroscopic properties of some of the Ln3+ ions in the Ca9RE(VO4)7-type crystals have been studied [11,13–15].
Thulium (Tm3+) ions are attractive for laser operation around 2 μm. Such an emission is eye-safe and absorbed in water in the atmosphere and bio-tissues. Tm lasers are thus used in range-finding, remote sensing and medicine. To date, the Tm3+ ions have been doped into numerous oxide and fluoride host materials, e.g. Y3Al5O12, Lu2O3, YVO4, KLu(WO4)2, YAlO3, LiYF4, etc., and efficient and wavelength-tunable laser operation in the 1.8...2.1 μm spectral range (depending on the host) has been achieved. In the present work, we report on the crystal growth and a detailed spectroscopic study of a novel trigonal crystal, Tm:Ca9La(VO4)7. Its properties designate Tm:Ca9La(VO4)7 for applications in broadband tunable and ultrashort pulse lasers at ~2 μm.
2. Crystal growth and structure
The Tm:Ca9La(VO4)7 crystal was grown by the Czochralski method. The raw materials used for crystal growth were synthesized by traditional high temperature solid-state reaction method. The chemicals CaCO3, V2O5 (analytical reagent grade), and La2O3, Tm2O3 with 4N purity, were weighed according to the 9CaCO3 + 0.47La2O3 + 0.03Tm2O3 + 3.5V2O5 → Ca9La0.94Tm0.06(VO4)7 + 9CO2↑ reaction. The mixtures were ground in an agate mortar for blending well, and extruded to form pellets. Then, these pellets were placed into an alumina crucible and sintered in a muffle furnace at 1000 °C for 48 h. These processes were repeated, and the sintering temperature was raised to 1200 °C to ensure complete reaction. The formation of the trigonal Ca9La(VO4)7 phase was confirmed by X-ray power diffraction (XRD).
The crystal was grown in an iridium crucible with dimensions of Ø27 × 26 mm3, in a 25 kHz mid-frequency induction furnace (DJL-400) in a N2 atmosphere, with a pulling rate of 1-1.5 mm/h and a rotation rate of 8-12 rpm. A [001] oriented Ca9La(VO4)7 crystal was used as a seed. When the growth process ended, the grown crystal was pulled slowly out of the melt, and cooled to room temperature at a rate of 15-30 °C/h. Large-volume boules of Tm:Ca9La(VO4)7 30 mm in length and 25 mm in diameter were obtained, Fig. 1(a). The coloration of the as-grown crystals ranged from dark-yellow to green. This is an indication of the presence of color centers which is typical for disordered Ca vanadates grown in anoxic conditions [13]. The formation of color centers is due to the reduction of the V5+ ions to V4+ and V3+ and the appearance of oxygen vacancies. In order to eliminate these effects which will be detrimental for potential laser applications, and to reduce the thermal stress, the grown crystal was annealed at 1200 °C for 24 h in air. This improved the transparency of the crystal and its coloration changed to yellowish, Fig. 1(b).
Fig. 1 (a) As-grown Tm:Ca9La(VO4)7 boule; (b) annealed in air and polished 1 mm-thick plate cut from this boule; XRD pattern of the powdered Tm:Ca9La(VO4)7 crystal.
The XRD data for the grown crystal were collected at room temperature in the 2θ = 10-80° range with a step of 0.02° and a scan speed of 0.13°/min, using a Desktop X-ray diffractometer (Rigaku, Miniflex 600) equipped with Cu Kα radiation. The XRD pattern of the powdered as-grown crystal is shown in Fig. 1(c). The diffraction peaks match perfectly the standard pattern of undoped Ca9La(VO4)7 (ICSD card #85104). The concentration of the Tm3+ ions in the grown crystal NTm was measured by an Inductively Coupled Plasma OES spectrometer (HORIBA Jobin Yvon, Ultima 2), resulting in a value of NTm = 0.88 × 1020 at/cm3 or 5.72 at.%. Consequently, the segregation coefficient of Tm3+ ions is KTm = 0.95 which indicates that they can easily substitute the “passive” La3+ ions.
The Ca9RE(VO4)7 vanadates are isostructural to the double calcium vanadate, Ca3(VO4)2 or Ca10.5(VO4)7 (sp.gr. R3c), which is considered as a parent compound [17]. The trigonal whitlockite-like structure of Ca9La(VO4)7 is formed as a result of a distortion of the Ca3(VO4)2 one when the La3+ ions partially occupy the cationic positions of the Ca2+ ions [9,18], see Fig. 2(a). Since the difference of the ionic radii of the La3+ and Ca2+ ions is relatively small, the Ca9La(VO4)7 structure is isomorphic to that of Ca3(VO4)2 while disordering of the cationic positions occurs. The Ca9RE(VO4)7 structure has four cationic sites with different occupancy numbers [9,17,18]: three low-symmetry sites (point group C1): Me(1), Me(2) and Me(3) with coordination numbers 9, 8, and 7, respectively, and a 6-fold coordinated (octahedral) cationic site Me(4), as shown in Fig. 2(b). For an undoped Ca9La(VO4)7, the Ca2+ and La3+ ions occupy randomly the same Me(1) – Me(4) sites in an overall proportion of 9:1 (the occupancy number for the Me(4) site is close to 1 for the Ca2+ ions). In the Ln3+-doped Ca9La(VO4)7 crystals, the Ln3+ and La3+ ions are randomly distributed over the Me(1) – Me(3) cationic positions without inversion symmetry (together with the Ca2+ ions). For the Me(1), Me(2) and Me(3) sites, the average Ln3+/La3+/Ca2+–O2- distances are ~2.4, 2.5, and 2.6 Å, respectively. The shortest Ln3+ – Ln3+ distance is ~3.6 Å. Based on the XRD analysis, we determined the lattice constants for Tm:Ca9La(VO4)7 as a = b = 10.846 Å, c = 37.901 Å (V = 3861.2 Å3 and Z = 6), slightly shorter than for the undoped crystal (a = 10.8987 Å, c = 38.1470 Å) [9]. This is attributed to the difference in ionic radii of the dopant Tm3+ and the substituted La3+ ions (0.994 Å and 1.160 Å, respectively, e.g., for the 8-fold O2--coordination). The calculated density of Tm:Ca9La(VO4)7 is ρ = 3.746 g/cm3.
Fig. 2 (a) Fragment of the structure of the Tm:Ca9La(VO4)7 crystal within one unit-cell; (b) oxygen coordination of metal ions in the four possible sites.
The vibrational properties of the Tm:Ca9La(VO4)7 crystal were studied with polarized Raman spectroscopy. The Raman spectra recorded for the x'(xy)y' geometries with x, y = π or σ and x' = y' = a are shown in Fig. 3. The excitation wavelength was 514 nm. Here we use standard notations where x' and y' represent the direction of propagation of the excitation and scattered light, and x and y stand for the polarization of the excitation and scattered light, respectively. The Raman bands are observed in two separate ranges: 200–470 cm−1 and 740–930 cm−1 which are similar to the Raman spectrum of the parent compound, Ca3(VO4)2 [19]. The Raman bands in the low-frequency range are assigned to the O–V–O bending modes and to the Ca2+ cation displacements. The high-frequency Raman bands are attributed to the V–O stretching modes and possible vibrations of the V–O–...La/Tm chain [20]. The strongest Raman signal is observed for the a(πσ)a geometry. The most intense band is at 867 cm−1 with a full width at half maximum (FWHM) of 26.6 cm−1. This stretching mode is assigned as ν(A1). The broadening of the Raman bands is due to the disordered nature of the material. The parent compound, Ca3(VO4)2, has been used for stimulated Raman scattering (SRS) of picosecond pulses [21]. The broad and intense Raman bands of Tm:Ca9La(VO4)7 make it also interesting for self-SRS. In addition, the low-energy bands around ~350 cm−1 can provide vibronic Tm laser operation as further extension of the tuning capability [22].
Fig. 3 Raman spectra for an a-cut Tm:Ca9La(VO4)7 crystal excited at 514 nm: (a) polarization dependence in the a(xy)a geometry; (b) details of the spectrum for the a(πσ)a geometry.
3. Spectroscopic characterization
The Ca9La(VO4)7 crystal is an optically uniaxial birefringent crystal (point group R3c). Its optical axis is parallel to the c-axis. At ~1.85 μm, the two principal refractive indices of Ca9La(VO4)7 are no = 1.841 and ne = 1.808 [16] (positive uniaxial crystal). The spectral properties are described for the two principal light polarizations, E || c (π) and E ⊥ c (σ).
The absorption spectrum of the Tm:Ca9La(VO4)7 crystal for the π- and σ-polarizations is shown in Fig. 4(a). It was measured at room temperature. For the absorption band related to the 3H6 → 3H4 transition of the Tm3+ ion which is suitable for pumping at around 800 nm with commercial AlGaAs laser diodes, the maximum absorption cross-section is 1.5 × 10−20 cm2 at 791.3 nm for σ-polarization, determined as σabs = α/NTm where α is the absorption coefficient. The FWHM of the local peak is 8.2 nm. For π-polarization, σabs is ~3 times lower. The UV absorption edge for the Tm:Ca9La(VO4)7 crystal is at λg = 0.44 μm (Eg = 2.82 eV).
Fig. 4 (a) Absorption spectrum of the 5.72 at.% Tm:Ca9La(VO4)7 crystal; (b) absorption cross-sections σabs for the 3H6 → 3H4 transition of the Tm3+ ion.
The absorption oscillator strengths for the Tm3+ ion in Ca9La(VO4)7 were determined from the measured absorption spectrum:
where me and e are the electron mass and charge, respectively, c is the speed of light, Г(JJ') is the integrated absorption coefficient within the absorption band and ‹λ› is the “center of gravity” of the absorption band. The experimental absorption oscillator strengths were averaged over the principal light polarizations, 1/3 × (2fσ + fπ). The results are shown in Table 1.
Table 1. Experimental and Calculated Absorption Oscillator Strengths for the Tm:Ca9La(VO4)7 Crystal
The values of fexp were used to determine the intensity parameters, Ω2, Ω4 and Ω6, within the standard Judd-Ofelt (J-O) theory [23,24], Ω2 = 4.682, Ω4 = 0.659 and Ω6 = 0.475 [10−20 cm2]. Using these parameters, the absorption oscillator strengths were also calculated:
Here, Scalc are the line strengths, h is the Planck constant, n is the refractive index of the crystal and U(k) are the squared reduced matrix elements [25]. The J-O theory describes electric-dipole (ED) transitions. The contribution of magnetic-dipole (MD) transitions with J–J’ = 0, ± 1, fMD, was taken from the literature [26].The probabilities of spontaneous radiative transitions were calculated from the corresponding line strengths which, in turn, are derived from the J-O parameters Ωk and squared reduced matrix elements U(t), see Eq. (2)b):
The MD contributions AMD were taken from [26]. On the basis of the probability of spontaneous transitions for the separate emission channels J→J’, we calculated the total probability, Atot, the corresponding radiative lifetime of the excited-state, τrad, and the luminescence branching ratios for the emission channels, B(JJ’): The results are summarized in Table 2. In particular, the radiative lifetime of the lowest excited-state, τrad(3F4) = 2.02 ms.Table 2. Calculated Emission Probabilities for the Tm3+ Ion in Ca9La(VO4)7 Crystal
The photoluminescence (PL) spectra for the Tm3+-doped Ca9La(VO4)7 crystal were measured with unpolarized light under excitation to the 3H4 state at ~0.79 μm using a tunable Ti:Sapphire laser, see Fig. 5. The PL from the excited level is observed at 0.78-0.82 μm (3H4 → 3H6 transition) and at 1.4-1.55 μm (3H4 → 3F4 transition). A broad band spanning from 1.6 to 2.05 μm is due to the 3F4 → 3H6 transition from the upper laser level. In addition, several emissions in the visible (centered at ~0.48 μm and at ~0.7 μm) and near-IR (at ~1.07 μm) are detected which are related to the radiative transitions from the higher-lying 1G4 and 3F2,3 states of Tm3+. These states are populated by the excited-state absorption (ESA) process 3H5 → 1G4 (for the 1G4 state) and the same ESA with a subsequent non-radiative relaxation (for the 3F2,3 states). A weak PL of Er3+ impurity is also observed at ~0.52, 0.54 and 1 μm. The presence of Er3+ in the studied crystal may be due to impurities in the Tm2O3 reagent. Then, the Er3+ ions are excited by an energy-transfer process Tm3+(3H4) → Er3+(4I9/2) which is very probable because these two states are resonant in energy. The green emission from Er3+ originates from the 4S3/2 + 2H11/2 → 4I15/2 transition and the near-IR emission from the 4I11/2 → 4I15/2 one. As a result, visible PL from the Tm:Ca9La(VO4)7 crystal has a green-bluish color.
Fig. 5 PL spectra for Tm3+-doped Ca9La(VO4)7 crystal (unpolarized light, excitation wavelength is 0.79 μm): (a) visible and (b-d) near-IR emissions.
The stimulated-emission (SE) cross-section, σSE, spectra corresponding to the 3F4 → 3H6 transition of the Tm3+ ion in Ca9La(VO4)7 were calculated using the modified reciprocity method [27]:
Here, σiSE and σiabs (i = π or σ) are the SE and absorption cross-sections for the i-th principal light polarization, respectively, τrad is the radiative lifetime of the emitting state (3F4 state of Tm3+) determined with the J-O theory. The results on the SE cross-sections are shown in Fig. 6(a). The maximum value of σSE is 1.28 × 10−20 cm2 at 1854 nm for σ-polarization. This value is ~3 times larger than for π-polarized light, 0.38 × 10−20 cm2 at 1858 nm. The strong polarization-anisotropy of σSE was observed by direct measurement of the luminescence intensity for the two polarizations.Fig. 6 (a) Absorption, σabs, and stimulated-emission, σSE, cross-sections for the 3H6 ↔ 3F4 transition of the Tm3+ ion in Ca9La(VO4)7 crystal for the π- and σ-polarizations; (b) measured decay of luminescence from the 3F4 upper laser level (at 1.85 μm) and the 3H4 pump state (at 0.8 μm); the excitation wavelength is ~0.79 μm.
The results on the luminescence decay for the Tm:Ca9La(VO4)7 crystal are presented in Fig. 6(b). By exciting the Tm3+ ions at 0.79 μm, we monitored the decay from the 3F4 upper laser level (at 1.85 μm) and the 3H4 pump state (at 0.8 μm). The sample was powdered and immersed in glycerin (10 wt.% of powder in the solution) in order to prevent the effect of reabsorption on the measured lifetime. The decay curves are clearly single-exponential. The determined lifetimes are τexp(3F4) = 1.19 ms and τexp(3H4) = 122 μs. The shortening of the experimental lifetime of the upper laser level with respect to the radiative lifetime, expressed by a quantum yield of luminescence of ηq = τexp/τrad = 59%, is partially attributed to the non-radiative relaxation probably related to the color centers which are not completely eliminated even after crystal annealing, to the concentration quenching which is also rather strong in, cf. Tm:REVO4 crystals [28], and to the excitation transfer to the Er3+ impurities.
An important parameter for quasi-three-level laser materials, e.g. Tm3+-doped ones, is the gain cross-section, σg = βσSE – (1 – β)σabs where β = N2/NTm is the inversion ratio and N2 is the population of the upper laser level, 3F4. The results on σg for the Tm:Ca9La(VO4)7 crystal are shown in Fig. 7.
Fig. 7 Gain cross-sections, σg = βσSE – (1 – β)σabs, for the 3F4 → 3H6 transition of the Tm3+ ion in Ca9La(VO4)7 crystal for the π- (a) and σ- (b) polarizations; β = N2(3F4)/NTm is the inversion ratio.
The gain cross-sections are much higher for σ-polarization as compared with π-polarization. The uniaxial crystals offer two principal orientations of the laser elements, denoted as a-cut and c-cut. For a laser based on an a-cut Tm:Ca9La(VO4)7 crystal and containing no polarizing elements, we expect linearly (σ-) polarized laser output; and for a c-cut crystal, it will be unpolarized. For the σ-polarization at low β < 0.05, a broad gain spectrum spanning from 1.9 to 2.05 μm is observed. With an increase of β, a local peak is formed in the gain spectra shifting from ~1.93 μm (β ~0.1) to 1.86 μm (β >0.1). In contrast, the π-polarization impresses by a broad gain smoothness up to high inversion levels of β ~0.3. In general, the gain spectra for Tm:Ca9La(VO4)7 are broad and structureless. Thus, one can expect broad tuning of the laser emission from ~1.8 to 2.05 μm.
From the point of view of the spectroscopic properties, both a- and c-cut Tm:Ca9La(VO4)7 crystals are attractive for laser operation as they offer access to the high-gain σ-polarization. Under laser-pumping, the same pump polarization is preferable for high pump efficiency. The thermo-optic coefficients are negative for the Ca9La(VO4)7 crystal: dno/dT = −13.2 and dne/dT = −12.4 × 10−6 K−1 at ~1.85 μm [11]. However, for an a-cut crystal, one can expect a positive thermal lens due to an “athermal” compensation of the negative contribution of dne/dT and the positive contribution of the large thermal expansion along the a-axis, αa = 17.5 × 10−6 K−1 [11]. This may potentially enable microchip laser operation where the positive thermal lens plays a key role in the mode stabilization in a plano-plano laser cavity [29]. For a c-cut crystal, the thermal lens is expected to be negative due to much weaker thermal expansion along this direction, as αa/αc ~1.9. Thus, one can conclude that a-cut Tm:Ca9La(VO4)7 crystals are more attractive for laser operation.
4. Conclusion
We report on the Czochralski growth and detailed spectroscopic characterization (including study of absorption, emission and Raman spectra, luminescence decay, transition cross-sections and Judd-Ofelt modeling) of a novel trigonal crystal, Tm3+:Ca9La(VO4)7. This work represents the first description of the optical properties of the Tm3+ ion in calcium vanadate single crystals. The disordered multi-site structure of Ca9La(VO4)7 results in broad and structureless absorption and emission bands of the Tm3+ ions while preserving the polarization anisotropy of the optical properties. According to the analysis of the spectroscopy and thermo-optics of Tm:Ca9La(VO4)7, the preferred orientation for laser operation is a-cut (σ-polarization). The maximum SE cross-section corresponding to the 3F4 → 3H6 transition is 1.28 × 10−20 cm2 at 1854 nm for the σ-polarization. According to the gain spectra in both polarizations, broadband tunable laser emission at 1.8-2.05 μm and ultrashort pulse generation may be achieved. Tm:Ca9La(VO4)7 possesses relatively long storage time in the upper laser level, ~1.2 ms for 5.72 at.% Tm doping, which is beneficial for passive Q-switching. Future work on Tm:Ca9La(VO4)7 should be focused on the reduction of non-radiative quenching via proper annealing and purification of the raw materials which may provide higher luminescence quantum yield. In addition, Tm:Ca9La(VO4)7 crystals are promising Raman and self-Raman frequency shifters.
Funding
The National Natural Science Foundation of China (11404332, 61575199, 21427801); Key Project of Science and Technology of Fujian Province (2016H0045); the Strategic Priority Research Program of the Chinese Academy of Sciences (XDB20000000); the National Key Research and Development Program of China (2016YFB0701002); the China Scholarship Council (CSC, 201504910418 and 201504910629); the Instrument project of Chinese Academy of Sciences (YZ201414); Spanish Government (MAT2016-75716-C2-1-R, MAT2013-47395-C4-4-R, TEC 2014-55948-R); Generalitat de Catalunya (2014SGR1358); Government of the Russian Federation (Grant 074-U01); ICREA (2010ICREA-02); European Union's Horizon 2020 (654148); Marie Skłodowska-Curie (657630).
Acknowledgments
P. Loiko acknowledges financial support from the Government of the Russian Federation (Grant 074-U01) through ITMO Post-Doctoral Fellowship scheme. F.D. acknowledges additional support through the ICREA academia award 2010ICREA-02 for excellence in research. This work has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 654148 Laserlab-Europe and under the Marie Skłodowska-Curie grant agreement No 657630.
References and links
1. A. A. Kaminskii, “Laser crystals and ceramics: recent advances,” Laser Photonics Rev. 1(2), 93–177 (2007). [CrossRef]
2. J. Petit, B. Viana, P. Goldner, D. Vivien, P. Louiseau, and B. Ferrand, “Laser oscillation with low quantum defect in Yb:GdVO4, a crystal with high thermal conductivity,” Opt. Lett. 29(8), 833–835 (2004). [CrossRef] [PubMed]
3. J. Liu, V. Petrov, H. Zhang, J. Wang, and M. Jiang, “High-power laser performance of a-cut and c-cut Yb:LuVO4 crystals,” Opt. Lett. 31(22), 3294–3296 (2006). [CrossRef] [PubMed]
4. Yu. D. Zavartsev, P. A. Studenikin, V. A. Mikhailov, A. I. Zagumennyi, G. Huber, E. Heumann, V. G. Ostroumov, and I. A. Shcherbakov, “Tm3+:GdVO4 – a new efficient medium for diode-pumped 2-μm lasers,” Quantum Electron. 27(1), 13–14 (1997). [CrossRef]
5. X. Mateos, J. Liu, H. Zhang, J. Wang, M. Jiang, U. Griebner, and V. Petrov, “Continuous-wave and tunable laser operation of Tm:LuVO4 near 1.9 µm under Ti:sapphire and diode laser pumping,” Phys. Status Solidi203(4), R19–R21 (2006) (a). [CrossRef]
6. S. Rivier, X. Mateos, J. Liu, V. Petrov, U. Griebner, M. Zorn, M. Weyers, H. Zhang, J. Wang, and M. Jiang, “Passively mode-locked Yb:LuVO(4) oscillator,” Opt. Express 14(24), 11668–11671 (2006). [CrossRef] [PubMed]
7. V. E. Kisel, N. A. Tolstik, A. E. Troshin, N. V. Kuleshov, V. N. Matrosov, T. A. Matrosova, M. I. Kupchenko, F. Brunner, R. Paschotta, F. Morier-Genoud, and U. Keller, “Spectroscopy and femtosecond laser performance of Yb3+:Gd0.64Y0.36VO4 crystal,” Appl. Phys. B 85(4), 581–584 (2006). [CrossRef]
8. J. Liu, W. Han, H. Zhang, X. Mateos, and V. Petrov, “Comparative study of high-power continuous-wave laser performance of Yb-doped vanadate crystals,” IEEE J. Quantum Electron. 45(7), 807–815 (2009). [CrossRef]
9. A. A. Belik, V. A. Morozov, R. N. Kotov, S. S. Khasanov, and B. I. Lazoryak, “Crystal structures of double vanadates Ca9R(VO4)7: I. R= La, Pr, and Eu,” Crystallogr. Rep. 42(5), 751–757 (2000).
10. M. V. Dobrotvorskaya, Yu. N. Gorobets, M. B. Kosmyna, P. V. Mateichenko, B. P. Nazarenko, V. M. Puzikov, and A. N. Shekhovtsov, “Growth and characterization of Ca9Ln(VO4)7 crystals (Ln = Y, La, or Gd),” Crystallogr. Rep. 57(7), 959–961 (2012). [CrossRef]
11. P. A. Loiko, A. S. Yasukevich, A. E. Gulevich, M. P. Demesh, M. B. Kosmyna, B. P. Nazarenko, V. M. Puzikov, A. N. Shekhovtsov, A. A. Kornienko, E. B. Dunina, N. V. Kuleshov, and K. V. Yumashev, “Growth, spectroscopic and thermal properties of Nd-doped disordered Ca9La(VO4)7 and Ca10(Li/K)(VO4)7 laser crystals,” J. Lumin. 137, 252–258 (2013). [CrossRef]
12. Z. Lin, G. Wang, and L. Zhang, “Growth of a new nonlinear optical crystal YCa9(VO4)7,” J. Cryst. Growth 304(1), 233–235 (2007). [CrossRef]
13. L. Li, G. Wang, Y. Huang, L. Zhang, Z. Lin, and G. Wang, “Crystal growth and spectral properties of Nd3+:Ca9Gd(VO4)7 crystal,” J. Cryst. Growth 314(1), 331–335 (2011). [CrossRef]
14. P. N. Hu and G. F. Wang, “Growth and spectral properties of Er3+:Ca9La(VO4)7 crystal,” Mater. Res. Innov. 15(1), 75–77 (2011). [CrossRef]
15. F. F. Yuan, W. Zhao, Y. S. Huang, L. Z. Zhang, S. J. Sun, Z. B. Lin, and G. F. Wang, “Growth and optical properties of a new promising laser material Er3+/Yb3+:Ca9Y(VO4)7,” Opt. Commun. 328, 62–66 (2014). [CrossRef]
16. L. Huang, N. Zhuang, G. Zhang, J. Chen, C. Huang, B. Zhao, Y. Wei, X. Hu, and M. Wei, “Accurate measurement of refractive indices of Ca9La(VO4)7 crystal,” Opt. Mater. 31(2), 372–374 (2008). [CrossRef]
17. R. Gopal and C. Calvo, “The structure of Ca3(VO4)2,” Z. für Kristallographie-Crystalline Materials 137(1–6), 67–85 (1973).
18. L. Liu, R. Xie, N. Hirosaki, Yu. Li, T. Takeda, C. Zhang, J. Li, and X. Sun, “Crystal structure and photo-luminescence properties of red-emitting Ca9La1-x(VO4)7:xEu3+ phosphors for white light-emitting diodes,” J. Am. Ceram. Soc. 93(12), 4081–4086 (2010). [CrossRef]
19. A. Grzechnik, “High-temperature transformations in calcium orthovanadate studied with Raman scattering,” Chem. Mater. 10(4), 1034–1040 (1998). [CrossRef]
20. M. B. Kosmyna, B. P. Nazarenko, V. M. Puzikov, A. N. Shekhovtsov, W. Paszkowicz, A. Behrooz, P. Romanowski, A. S. Yasukevich, N. V. Kuleshov, M. P. Demesh, W. Wierzchowski, K. Wieteska, and C. Paulmann, “Ca10Li(VO4)7:Nd3+, a promising laser material: growth, structure and spectral characteristics of a Czochralski-grown single crystal,” J. Cryst. Growth 445, 101–107 (2016). [CrossRef]
21. P. G. Zverev, A. Ya. Karasik, T. T. Basiev, L. I. Ivleva, and V. V. Osiko, “Stimulated Raman scattering of picosecond pulses in SrMoO4 and Ca3(VO4)2 crystals,” Quantum Electron. 33(4), 331–334 (2003). [CrossRef]
22. P. Loiko, X. Mateos, S. Y. Choi, F. Rotermund, J. M. Serres, M. Aguiló, F. Díaz, K. Yumashev, U. Griebner, and V. Petrov, “Vibronic thulium laser at 2131 nm Q-switched by single-walled carbon nanotubes,” J. Opt. Soc. Am. B 33(11), D19–D27 (2016). [CrossRef]
23. B. R. Judd, “Optical absorption intensities of rare-earth ions,” Phys. Rev. 127(3), 750–761 (1962). [CrossRef]
24. G. S. Ofelt, “Instensities of crystal spectra of rare-earth ions,” J. Chem. Phys. 37(3), 511–520 (1962). [CrossRef]
25. B. M. Walsh, N. P. Barnes, and B. Di Bartolo, “Branching ratios, cross sections, and radiative lifetimes of rare earth ions in solids: Application to Tm3+ and Ho3+ ions in LiYF4,” J. Appl. Phys. 83(5), 2772–2787 (1998). [CrossRef]
26. C. M. Dodson and R. Zia, “Magnetic dipole and electric quadrupole transitions in the trivalent lanthanide series: Calculated emission rates and oscillator strengths,” Phys. Rev. B 86(12), 125102 (2012). [CrossRef]
27. A. S. Yasyukevich, V. G. Shcherbitskii, V. E. Kisel, A. V. Mandrik, and N. V. Kuleshov, “Integral method of reciprocity in the spectroscopy of laser crystals with impurity centers,” J. Appl. Spectrosc. 71(2), 202–208 (2004). [CrossRef]
28. R. Lisiecki, P. Solarz, G. Dominiak-Dzik, W. Ryba-Romanowski, M. Sobczyk, P. Černý, J. Šulc, H. Jelínková, Y. Urata, and M. Higuchi, “Comparative optical study of thulium-doped YVO4, GdVO4, and LuVO4 single crystals,” Phys. Rev. B 74(3), 035103 (2006). [CrossRef]
29. J. M. Serres, X. Mateos, P. Loiko, K. Yumashev, N. Kuleshov, V. Petrov, U. Griebner, M. Aguiló, and F. Díaz, “Diode-pumped microchip Tm:KLu(WO4)2 laser with more than 3 W of output power,” Opt. Lett. 39(14), 4247–4250 (2014). [CrossRef] [PubMed]
