RE3+-Doped Ca3(Nb,Ga)5O12 and Ca3(Li,Nb,Ga)5O12 Crystals (RE = Sm, Dy, and Pr): A Review of Current Achievements

Spectroscopic characteristics of RE3+ ions (RE = Sm, Dy, and Pr) doped in partially disordered Ca3Nb1.6875Ga3.1875O12-CNGG and Ca3Li0.275Nb1.775Ga2.95O12-CLNGG crystals are reviewed in detail to assess their prospects as laser crystals with emission in the visible spectral domain. All investigated crystals were grown using the Czochralski crystal growth technique. High-resolution absorption and emission measurements at different temperatures, as well as emission dynamics measurements, were performed on the grown crystals. The spectroscopic and laser emission characteristics of the obtained crystals were determined based on the Judd-Ofelt parameters. The obtained results indicate that CNGG:RE3+ and CLNGG:RE3+ (RE = Sm, Dy, and Pr) crystals can be promising materials for lasers in the visible range.


Introduction
A natural limitation of solid-state lasers due to the nature of the quantum processes underlying their operation is the existence of well-specified laser emission wavelengths determined by both the laser active ion and the host material. This situation requires further identification of new laser materials or emission schemes. One of the most viable solutions is to use host crystals with partially disordered structures determined by the mixed occupation of the host cationic sites with different ions. One of the most viable solutions is the use of host crystals with a partially disordered structure caused by the simultaneous occupation of some of the host cationic sites with different ions. Partial compositional disorder preserves the global crystallographic structure and symmetry of the crystal, but influences properties dependent on the local composition, such as the crystal field in the position of the laser active ion. Significant in this respect is the possibility of controlling the host disordering by producing manageable effects on the dopant ion spectra (especially the absorption and emission linewidths) through suitable control of the crystal field distribution in a compositionally disordered crystal. In the case of intrinsically disordered crystals in which certain crystallographic sites are filled with different types of cations with varying valences, the charge compensation induced by doping is achieved by changing the amounts of host cations. Due to the disorder in the close vicinity of the dopant ion, a multicenter structure and an inhomogeneous widening of the absorption and emission lines occur. Controlling the compositional disordering of the host laser material and a proper selection of the materials with an intrinsic disorder, are essential for identifying new laser materials or emission regimes.
Many families of disordered crystals such as aluminates, niobates, borates, double tungstates, etc., are currently known [1][2][3][4][5][6][7], but most of them are of low symmetry. Over recent years, trivalent rare earth ions (RE 3+ ) doped in intrinsically disordered calciumniobium-gallium-garnet (CNGG) and calcium-lithium-niobium-gallium-garnet (CLNGG) XRPD spectra on the SmGG, DyGG, PrGG, SmLNGG, DyLNGG, and PrLNGG sintered compounds revealed a dominant garnet-type cubic phase (space group Ia3d) and some residual phases like Ga 2 O 3 , SmNbO 4 , LiGa 5 O 8 , DyNbO 4 , and PrGaO 3 . According to Rietveld analysis, the majority garnet phase was found to be in the range of 85-91 wt.%, while the total of minor secondary phases was quantified to be less than 15 wt.% in each sintered compound [47]. The relationships between interplanar spacings and Miller indices, as well as the lattice constants for the garnet phase in each sintered compound, are presented in Reference [47]. Figure 1 shows the CNGG:RE and CLNGG:RE grown crystals. As can be observed, they have very good transparency, are free of macroscopic defects, and are of high optical quality. The grown crystal sizes are approximately 12 and 25-30 mm in diameter and length, respectively. The grown crystals present good mechanical properties, being hard enough for cutting and polishing. and a tunable OPOTEK RADIANT 355 LD laser (Opotek LLC., California, CA, USA) in the range of 410-2500 nm or the third harmonic at 355 nm of an Nd:YAG Quantel laser was utilized as an excitation source.

Crystals Growth and Structural Characterization
XRPD spectra on the SmGG, DyGG, PrGG, SmLNGG, DyLNGG, and PrLNGG sintered compounds revealed a dominant garnet-type cubic phase (space group Ia3d) and some residual phases like Ga2O3, SmNbO4, LiGa5O8, DyNbO4, and PrGaO3. According to Rietveld analysis, the majority garnet phase was found to be in the range of 85-91 wt.%, while the total of minor secondary phases was quantified to be less than 15 wt.% in each sintered compound [47]. The relationships between interplanar spacings and Miller indices, as well as the lattice constants for the garnet phase in each sintered compound, are presented in Reference [47]. Figure 1 shows the CNGG:RE and CLNGG:RE grown crystals. As can be observed, they have very good transparency, are free of macroscopic defects, and are of high optical quality. The grown crystal sizes are approximately 12 and 25-30 mm in diameter and length, respectively. The grown crystals present good mechanical properties, being hard enough for cutting and polishing. The XRPD patterns on the CNGG:RE and CLNGG:RE grown crystals are shown in Figure 2. The patterns are very well indexed by the garnet-type structure (space group Ia3d) and no residual phases could be found. The lattice parameters were determined and are given in Table 1 together with those of the undoped host. The determined lattice parameters match very well with the ionic radii of Ca 2+ (1.12 Å), Pr 3+ (1.126 Å), Sm 3+ (1.079 Å), and Dy 3+ (1.027 Å) ions in 8-fold oxygen coordination, thus proving the insertion of RE 3+ ions into the dodecahedral c-sites of the obtained crystals. Moreover, the elemental compositions of the crystals with a measurement error of ± 0.2% are given in Table 1. The effective segregation coefficients (keff) of RE 3+ ions in the CNGG host crystal were evaluated to be keff (Sm) = 0.69, keff (Dy) = 0.84, and keff (Pr) = 0.36, being similar to those obtained in the case of the CLNGG host crystal. Thus, the concentration of RE 3+ dopant ions in CNGG:RE and CLNGG:RE crystals was determined as being 3.4 at.%, 4.2 at.%, and 1.8 at.% for Sm 3+ , Dy 3+ , and Pr 3+ , respectively. The cation densities of RE 3+ ions were calculated to be NA = 4.236 × 10 20 ions/cm 3 (CNGG:Sm), NA = 5.14 × 10 20 ions/cm 3   The XRPD patterns on the CNGG:RE and CLNGG:RE grown crystals are shown in Figure 2. The patterns are very well indexed by the garnet-type structure (space group Ia3d) and no residual phases could be found. The lattice parameters were determined and are given in Table 1 together with those of the undoped host. The determined lattice parameters match very well with the ionic radii of Ca 2+ (1.12 Å), Pr 3+ (1.126 Å), Sm 3+ (1.079 Å), and Dy 3+ (1.027 Å) ions in 8-fold oxygen coordination, thus proving the insertion of RE 3+ ions into the dodecahedral c-sites of the obtained crystals. Moreover, the elemental compositions of the crystals with a measurement error of ± 0.2% are given in Table 1

Spectroscopic Investigations
The room temperature absorption spectra of CNGG:RE and CLNGG:RE crystals (RE 3+ = Pr 3+ , Sm 3+ , Dy 3+ ) were registered and analyzed within the Judd-Ofelt (JO) theory [48,49] to calculate the oscillator strengths and transition probabilities of the 4f 2 , 4f 5 , and 4f 9 electronic configurations of the Pr 3+ , Sm 3+ , and Dy 3+ ions, respectively. The JO theory is described in detail in References [21,23,24], and the most important formulas are given below. The electric dipole line strength (Smeas) of a transition can be determined from the absorption measurements as: where c is the speed of light, h is the Planck constant, n is the bulk index of refraction, NA is the RE 3+ ion concentration, is the mean wavelength of the absorption band that corresponds to the J→J' transition, ∫ ( ) is the integrated absorption coefficient, and k() is the absorption coefficient which depends on the wavelength. Based on several values of the refractive indices at various wavelengths of undoped CNGG [50,51] and CLNGG [17] crystals and a least-squares fitting program for the Sellmeier equations, dispersion

Spectroscopic Investigations
The room temperature absorption spectra of CNGG:RE and CLNGG:RE crystals (RE 3+ = Pr 3+ , Sm 3+ , Dy 3+ ) were registered and analyzed within the Judd-Ofelt (JO) theory [48,49] to calculate the oscillator strengths and transition probabilities of the 4f 2 , 4f 5 , and 4f 9 electronic configurations of the Pr 3+ , Sm 3+ , and Dy 3+ ions, respectively. The JO theory is described in detail in References [21,23,24], and the most important formulas are given below. The electric dipole line strength (S meas ) of a transition can be determined from the absorption measurements as: where c is the speed of light, h is the Planck constant, n is the bulk index of refraction, N A is the RE 3+ ion concentration, λ is the mean wavelength of the absorption band that corresponds to the J→J' transition, k(λ)dλ is the integrated absorption coefficient, and k(λ) is the absorption coefficient which depends on the wavelength. Based on several values of the refractive indices at various wavelengths of undoped CNGG [50,51] and CLNGG [17] crystals and a least-squares fitting program for the Sellmeier equations, dispersion curves of refractive indices were determinate and further used to calculate S meas for each transition. The theoretical (S theor ) [52] and measured (S meas ) oscillator strengths of the absorption transitions were obtained and used to determine the Ω t (t = 2, 4, 6) intensity parameters.
The root-mean-square (rms) deviation ∆S rms = (q − p) −1 ∑ (∆S) 2 1/2 , where q is the number of the analyzed transitions, p is the number of parameters, and ∆S = S theor -S meas , represents the matching error.
Other spectroscopic parameters such as spontaneous emission probabilities (A JJ' ), branching ratios (β), and radiative lifetimes (τ r ), were determined based on JO intensity parameters. The total spontaneous electric dipole emission transition probabilities from the excited state J to the lower state J' are given by the formula: The radiative lifetime τ r for an excited state J and the luminescence branching ratios β(J→J') for the various emission transitions from this state can be then calculated as: From room temperature emission spectra originating from 1 D 2 (Pr 3+ ), 4 G 5/2 (Sm 3+ ), and 4 F 9/2 (Dy 3+ ) manifolds, stimulated emission cross-sections (σ em ) were calculated by using the Fuchtbauer-Ladenburg (FL) equation [53]: where A (J→J') is the spontaneous emission probability from the excited state J to the terminal state J', I(λ) is the emission intensity at wavelength λ, n is the refraction index, c is the speed of light, and λI(λ)dλ is the integrated emission intensity. The energy transfer (ET) processes induced by the static interactions between the dopant ions strongly influence the excitation flow between the energy levels of the active ion. The interionic process represents the direct transfer of excitation between two ions without the absorption or emission of photons. The ions involved (donors D and acceptors) are connected through the multipolar, exchange, or super-exchange interactions explained by the theory developed by Förster [54] and Dexter [55]. The ET from the donor to the acceptor, in addition to radiative and non-radiative de-excitation, represents a process of de-excitation of the donor. This transfer modifies the excited level lifetime of the donor. Depending on the dopant concentration, the kinetics of the emission level can be described by an exponential or non-exponential function. At very low dopant concentration, the measured lifetime is likely to be the radiative lifetime if there is no non-radiative contribution to the decay curve. For higher dopant concentration, the non-exponential luminescence decays can be evaluated using the formula τ av = ∞ 0 tI(t)dt/ ∞ 0 I(t)dt and extracting an average lifetime for the emitting level. At high doping concentrations, the type of interaction between RE 3+ ions, such as dipole-dipole (DD), dipole-quadrupole (DQ), or quadrupole-quadrupole (QQ) interaction, can be determined from the non-exponential profile of the luminescence decay. In this case, the Inokuti-Hirayama (IH) energy transfer model [56] was employed to analyze the emission decay by using the following equation for the luminescence intensity, Φ(t): where A is the amplitude, τ 0 is the lifetime of isolated RE 3+ ions, Γ is Eulers' function (Γ is 1.77, 1.43, and 1.3 for s = 6, 8, and 10, respectively), s is the mechanism of multipolar interaction (6 for DD, 8 for DQ, 10 for QQ), N A is the concentration of RE 3+ ions, and R 0 is the critical transfer distance between two neighboring RE 3+ ions. When non-radiative losses through cross-relaxation processes between two neighboring dopant ions are present, the microparameter of donor-acceptor interaction (C DA ) and the transfer rates (W DA ) can be calculated by the following equations, C DA = R s 0 τ −1 0 and W DA = C DA /R s 0 , respectively. The energy transfer rate (W ET ) through cross relaxation [57], as well as quantum efficiency , can be also calculated by the formulas W ET = 1 τ − 1 τ rad and ( = τ/τ rad ), respectively.
• Sm 3+ ions The absorption spectra of 3.4 at.% Sm 3+ ions in CNGG:Sm and CLNGG:Sm crystals were measured at 300 K in the spectral range of 350-3000 nm and analyzed within the JO theory [48,49]. The obtained spectra are shown in Figure 3. Twelve absorption lines of Sm 3+ ions were identified and analyzed to determine the JO parameters [21]. microparameter of donor-acceptor interaction (CDA) and the transfer rates (WDA) can be calculated by the following equations, CDA = and WDA = CDA/ , respectively. The energy transfer rate (WET) through cross relaxation [57], as well as quantum efficiency ɳ, can be also calculated by the formulas = 1 − 1 and ɳ (ɳ = τ/τrad), respectively.
The absorption spectra of 3.4 at.% Sm 3+ ions in CNGG:Sm and CLNGG:Sm crystals were measured at 300 K in the spectral range of 350-3000 nm and analyzed within the JO theory [48,49]. The obtained spectra are shown in Figure 3. Twelve absorption lines of Sm 3+ ions were identified and analyzed to determine the JO parameters [21]. Based on measured and calculated line strengths [21], the Ωt (t = 2, 4, 6) parameters of CNGG:Sm and CLNGG:Sm crystals were obtained and are listed in Table 2. The order Ω4 > Ω2 > Ω6 of the parameters is in trend with that obtained for different Sm 3+ -doped crystals with similar structures [57][58][59][60]. The significance of each JO parameter was studied [61][62][63] and it was established that Ω2 is an intensity parameter very sensitive to the crystal field asymmetry in the RE 3+ ion site, the covalency of the RE 3+ ion, as well as to any modification in the energy gap between the 4f n and 4f n−1 5d states of the RE 3+ ion. Ω6 is a parameter that reacts more to any variation in the electron density of the 4f and 5d configurations. Any alteration of the Ω2 and Ω6 parameters have an impact on the Ω4 parameter, which frequently complicates the establishment of the real factors that influence its modification. The values of spontaneous emission probabilities (AJJ'), branching ratios (βJJ'), and radiative lifetimes (τr) for the 4 G5/2 excited level were determined based on the Ωt (t = 2, 4, 6) parameters [21], and are given in Table 3. The radiative lifetime values of the 4 G5/2 level were found to be 1.58 ms and 1.5 ms, for CNGG:Sm and CLNGG:Sm crystals, respectively.  Based on measured and calculated line strengths [21], the Ω t (t = 2, 4, 6) parameters of CNGG:Sm and CLNGG:Sm crystals were obtained and are listed in Table 2. The order Ω 4 > Ω 2 > Ω 6 of the parameters is in trend with that obtained for different Sm 3+ -doped crystals with similar structures [57][58][59][60]. The significance of each JO parameter was studied [61][62][63] and it was established that Ω 2 is an intensity parameter very sensitive to the crystal field asymmetry in the RE 3+ ion site, the covalency of the RE 3+ ion, as well as to any modification in the energy gap between the 4f n and 4f n−1 5d states of the RE 3+ ion. Ω 6 is a parameter that reacts more to any variation in the electron density of the 4f and 5d configurations. Any alteration of the Ω 2 and Ω 6 parameters have an impact on the Ω 4 parameter, which frequently complicates the establishment of the real factors that influence its modification. The values of spontaneous emission probabilities (A JJ' ), branching ratios (β JJ' ), and radiative lifetimes (τ r ) for the 4 G 5/2 excited level were determined based on the Ω t (t = 2, 4, 6) parameters [21], and are given in Table 3. The radiative lifetime values of the 4 G 5/2 level were found to be 1.58 ms and 1.5 ms, for CNGG:Sm and CLNGG:Sm crystals, respectively. Table 2. JO intensity parameters for Sm 3+ in different oxide crystals with partially disordered structure (Reprinted with permission from Ref. [21], copyright 2017, Elsevier).
Crystal  Table 3. Spontaneous emission probabilities (A JJ' ), branching ratios (β JJ' ), and radiative lifetimes (τ r ) of Sm 3+ ions in CNGG:Sm and CLNGG:Sm crystals. (Reprinted with permission from Ref. [21], copyright 2017, Elsevier).  Figure 4a shows the excitation spectra of CNGG and CNLGG host crystals obtained by observing the blue emission line at 450 nm (Nb 5+ ). The spectra exhibit a charge transfer (CT) band in the UV range positioned at 272 nm and 280 nm for CLNGG and CNGG, respectively, assigned to the Nb 5+ -O 2− interactions into the [NbO 4 ] tetrahedrons of the host lattices [17]. Compared to CNGG, the shift to the higher energy of the CT band peak for CLNGG is due to the insertion of Li + ions into the CNGG structure which practically removes the vacancies producing a slight distortion of the [NbO 4 ] tetrahedrons. The emission spectra under 280 nm and 272 nm excitation wavelengths of the CNGG and CLNGG hosts, respectively, are shown in Figure 4b. As can be seen, both crystals display a wide emission band in the VIS range with a peak located at about 450 nm. Figure 4c shows the excitation spectra of Sm 3+ ions in CNGG:Sm and CLNGG:Sm crystals by observing the emission line of Sm 3+ ions in orange at 615 nm attributed to the 4 G 5/2 → 6 H 7/2 transition. The spectra present the CT bands from 200 to 300 nm assigned to the Nb 5+ -O 2− interactions into the [NbO 4 ] tetrahedrons of the host lattices, and a group of narrow lines in the UV-VIS region assigned to the 4f 5 electronic configuration of Sm 3+ ions.
The emission spectra of Sm 3+ ions in CNGG:Sm and CLNGG:Sm crystals under 270 nm and 405 nm excitations were recorded at room temperature ( Figure 5). Sm 3+ ion has an intense absorption band around 405 nm attributed to the 6 H 5/2 → 6 P 3/2 , 6 P 5/2 transitions, which is very appropriate for the efficient pumping with InGaN laser diodes at~405 nm. The values of the absorption cross-sections for the peaks at 404.9 nm and 405.6 nm were determined to be 2.1 × 10 −20 cm 2 and 2.3 × 10 −20 cm 2 , respectively, for CNGG:Sm, and 2.2 × 10 −20 cm 2 and 2.8 × 10 −20 cm 2 , respectively, for the CLNGG:Sm crystal [21]. Under both excitation wavelengths (270 nm and 405 nm), the emission spectra of Sm 3+ ions exhibit three emission bands centered at 567 nm, 615 nm, and 662 nm corresponding to the 4 G 5/2 → 6 H 5/2 , 4 G 5/2 → 6 H 7/2 , and 4 G 5/2 → 6 H 9/2 transitions, respectively. Under 270 nm excitation, a low-intensity emission band around 450 nm attributed to the host emission can be observed (Figure 5a). The emission line at 615 nm assigned to the 4 G 5/2 → 6 H 7/2 transition is the most intense line observed for both CNGG:Sm and CLNGG:Sm crystals, under both 270 nm and 405 nm excitation wavelengths. The emission cross sections were calculated for each emission band corresponding to the transitions from the 4 G 5/2 level to 6 H 5/2 , 6 H 7/2 , and 6 H 9/2 lower levels of Sm 3+ ions in CNGG:Sm and CLNGG:Sm crystals.
The highest values of the emission cross-sections were obtained for the CLNGG:Sm crystal at 615 nm ( 4 G 5/2 → 6 H 7/2 ) and 662 nm ( 4 G 5/2 → 6 H 9/2 ). All obtained values are presented and compared with other similar materials in Table 4. The values of Sm 3+ emission crosssections at 615 nm suggest that CNGG:Sm and CLNGG:Sm are potential laser crystals with orange emission at 615 nm. Figure 4a shows the excitation spectra of CNGG and CNLGG host crystals obtained by observing the blue emission line at 450 nm (Nb 5+ ). The spectra exhibit a charge transfer (CT) band in the UV range positioned at 272 nm and 280 nm for CLNGG and CNGG, respectively, assigned to the Nb 5+ -O 2interactions into the [NbO4] tetrahedrons of the host lattices [17]. Compared to CNGG, the shift to the higher energy of the CT band peak for CLNGG is due to the insertion of Li + ions into the CNGG structure which practically removes the vacancies producing a slight distortion of the [NbO4] tetrahedrons. The emission spectra under 280 nm and 272 nm excitation wavelengths of the CNGG and CLNGG hosts, respectively, are shown in Figure 4b. As can be seen, both crystals display a wide emission band in the VIS range with a peak located at about 450 nm. Figure 4c shows the excitation spectra of Sm 3+ ions in CNGG:Sm and CLNGG:Sm crystals by observing the emission line of Sm 3+ ions in orange at 615 nm attributed to the 4 G5/2→ 6 H7/2 transition. The spectra present the CT bands from 200 to 300 nm assigned to the Nb 5+ -O 2interactions into the [NbO4] tetrahedrons of the host lattices, and a group of narrow lines in the UV-VIS region assigned to the 4f 5 electronic configuration of Sm 3+ ions.  The emission spectra of Sm 3+ ions in CNGG:Sm and CLNGG:Sm crystals under 270 nm and 405 nm excitations were recorded at room temperature ( Figure 5). Sm 3+ ion has an intense absorption band around 405 nm attributed to the 6 H5/2 → 6 P3/2, 6 P5/2 transitions, which is very appropriate for the efficient pumping with InGaN laser diodes at ~405 nm. The values of the absorption cross-sections for the peaks at 404.9 nm and 405.6 nm were determined to be 2.1 × 10 −20 cm 2 and 2.3 × 10 −20 cm 2 , respectively, for CNGG:Sm, and 2.2 × 10 −20 cm 2 and 2.8 × 10 −20 cm 2 , respectively, for the CLNGG:Sm crystal [21]. Under both excitation wavelengths (270 nm and 405 nm), the emission spectra of Sm 3+ ions exhibit three emission bands centered at 567 nm, 615 nm, and 662 nm corresponding to the 4 G5/2  6 H5/2, 4 G5/2  6 H7/2, and 4 G5/2  6 H9/2 transitions, respectively. Under 270 nm excitation, a lowintensity emission band around 450 nm attributed to the host emission can be observed ( Figure 5a). The emission line at 615 nm assigned to the 4 G5/2  6 H7/2 transition is the most intense line observed for both CNGG:Sm and CLNGG:Sm crystals, under both 270 nm and 405 nm excitation wavelengths. The emission cross sections were calculated for each emission band corresponding to the transitions from the 4 G5/2 level to 6 H5/2, 6 H7/2, and 6 H9/2 lower levels of Sm 3+ ions in CNGG:Sm and CLNGG:Sm crystals. The highest values of the emission cross-sections were obtained for the CLNGG:Sm crystal at 615 nm ( 4 G5/2→ 6 H7/2) and 662 nm ( 4 G5/2→ 6 H9/2). All obtained values are presented and compared with other similar materials in Table 4. The values of Sm 3+ emission cross-sections at 615 nm suggest that CNGG:Sm and CLNGG:Sm are potential laser crystals with orange emission at 615 nm.  The partial energy levels and the multiplet barycenter (Bc) of Sm 3+ ions in CNGG:Sm The partial energy levels and the multiplet barycenter (B c ) of Sm 3+ ions in CNGG:Sm and CLNGG:Sm crystals were identified based on absorption and emission spectra at 10 K [21]. The energy levels involved in the main Sm 3+ emission transitions are given and compared with those for the YAG:Sm crystal [57] in Table 5, to highlight the effect of partial structural disorder on the energy levels of Sm 3+ in CNGG:Sm and CLNGG:Sm compared to the structurally ordered YAG:Sm crystal. The main crystal field effects are given by the perturbations of the crystal field induced by the disorder through the mixed occupation of the cationic sublattices, charge difference, and size mismatch effects. All these facts lead to the formation of multiple Sm 3+ centers, a low local crystal field, as well as changes in the spectral properties of the Sm 3+ ions by modifying the emission wavelengths. The luminescence kinetics of the 4 G 5/2 level of Sm 3+ ions in CNGG:Sm and CLNGG:Sm at room temperature were recorded by observing the emission line at 615 nm under 405 nm excitation. To find out the lifetime of isolated Sm 3+ ions, CNGG:Sm and CLNGG:Sm sintered ceramics doped with 0.1 at.% Sm 3+ ions were also measured. The normalized decay curves are shown in Figure 6a,b. For 0.1 at. % Sm, the decay curves are nearly exponential, and the measured lifetimes were determined to be τ 0 = 1.483 ms for CNGG:Sm and τ 0 = 1.44 ms for CLNGG:Sm. The values obtained for isolated Sm 3+ ions (τ 0 ) are near to the values determined by the JO method, as being τ r = 1.58 ms for the CNGG:Sm crystal and τ r = 1.5 ms for the CLNGG:Sm crystal. This fact indicates that the values of τ 0 can be considered as the radiative lifetimes, since that the energy gap between the 4 G 5/2 level and the next lower level is about 7200 cm −1 and the maximum phonon energy in the hosts is about 750 cm −1 [12], thus resulting in a negligible non-radiative contribution to the luminescence decay. For 3.4 at.% Sm, the decay curves present a non-exponential shape. The average luminescence lifetimes were estimated to be τ av =1 ms and τ av = 0.95 ms for CNGG:Sm and CLNGG:Sm crystals, respectively. Employing the Inokuti-Hirayama (IH) model, the non-exponential decay curves were evaluated, and the experimental transfer functions were determined (Figure 6c). From the fitting of the 4 G 5/2 decay curve, the critical distance (R 0 ), microparameter of donor-acceptor interaction (C DA ), transfer rates (W DA ), energy transfer rate (W ET ), and quantum efficiency () were determined (   The emission quenching of the 4 G5/2 level with Sm concentration could be mostly due to the energy transfer (ET) by cross-relaxation [57]. The ET rate (WET) is 325 s −1 and 358 s −1 for the CNGG:Sm and CLNGG:Sm crystals, respectively. The quantum efficiency ɳ of the 4 G5/2 level, which is defined as the ratio of the number of photons emitted to the number of photons absorbed, was estimated to be ~66 % for both crystals. This shows that the multiphonon relaxations and the ET processes of the 4 G5/2 level are negligible, which is advantageous for lasers and photonic devices.

 Dy 3+ ions
The absorption spectra of 4.2 at.% Dy 3+ ions in CNGG:Dy and CLNGG:Dy crystals were recorded in the extended spectral domain of 330-2000 nm at room temperature (Figure 7a) [23]. The absorption spectra were analyzed within the JO theory [48,49] to evaluate the intensity parameters Ωt (t = 2, 4, 6) contributing to the determination of the electric and magnetic dipole spontaneous emission probabilities (AJJ'), spectroscopic quality factor (χ = Ω4/Ω6), branching ratios (βJJ'), and the radiative lifetime (τr) of the 4 F9/2 Dy 3+ emitting manifold [23]. Table 7 summarizes all the results obtained.  The emission quenching of the 4 G 5/2 level with Sm concentration could be mostly due to the energy transfer (ET) by cross-relaxation [57]. The ET rate (W ET ) is 325 s −1 and 358 s −1 for the CNGG:Sm and CLNGG:Sm crystals, respectively. The quantum efficiency of the 4 G 5/2 level, which is defined as the ratio of the number of photons emitted to the number of photons absorbed, was estimated to be~66 % for both crystals. This shows that the multiphonon relaxations and the ET processes of the 4 G 5/2 level are negligible, which is advantageous for lasers and photonic devices.
The absorption spectra of 4.2 at.% Dy 3+ ions in CNGG:Dy and CLNGG:Dy crystals were recorded in the extended spectral domain of 330-2000 nm at room temperature ( Figure 7a) [23]. The absorption spectra were analyzed within the JO theory [48,49] to evaluate the intensity parameters Ω t (t = 2, 4, 6) contributing to the determination of the electric and magnetic dipole spontaneous emission probabilities (A JJ' ), spectroscopic quality factor (χ = Ω 4 /Ω 6 ), branching ratios (β JJ' ), and the radiative lifetime (τ r ) of the 4 F 9/2 Dy 3+ emitting manifold [23]. Table 7 summarizes all the results obtained.   Figure 7b shows the excitation spectra of Dy 3+ ions in CNGG:Dy and CLNGG:Dy crystals [23] obtained by observing the yellow line at 579 nm assigned to the 4 F9/2→ 6 H13/2 transition. For both crystals, the spectra present a CT band in the UV range of 200-300 nm assigned to the Nb 5+ -O 2interactions into the [NbO4] tetrahedrons of the host lattices, and a group of narrow lines in the UV-VIS domain assigned to the 4f 9 electronic configuration of Dy 3+ ions. Being positioned at wavelengths shorter than 200 nm according to Reference [68], the CT band due to the Dy 3+ −O 2− interaction could not be highlighted.
The emission spectra of Dy 3+ ions in CNGG:Dy and CLNGG:Dy crystals (Figure 8a,b) were recorded at 300 K under different excitation wavelengths of λex = 272, 280, and 352 nm. The obtained spectra show emission bands in the blue, yellow, and red spectral regions, assigned to the 4 F9/2  6 H15/2, 4 F9/2  6 H13/2, and 4 F9/2  6 H11/2 transitions, respectively,    Figure 7b shows the excitation spectra of Dy 3+ ions in CNGG:Dy and CLNGG:Dy crystals [23] obtained by observing the yellow line at 579 nm assigned to the 4 F 9/2 → 6 H 13/2 transition. For both crystals, the spectra present a CT band in the UV range of 200-300 nm assigned to the Nb 5+ -O 2− interactions into the [NbO 4 ] tetrahedrons of the host lattices, and a group of narrow lines in the UV-VIS domain assigned to the 4f 9 electronic configuration of Dy 3+ ions. Being positioned at wavelengths shorter than 200 nm according to Reference [68], the CT band due to the Dy 3+ −O 2− interaction could not be highlighted.
The emission spectra of Dy 3+ ions in CNGG:Dy and CLNGG:Dy crystals (Figure 8a,b) were recorded at 300 K under different excitation wavelengths of λ ex = 272, 280, and 352 nm. The obtained spectra show emission bands in the blue, yellow, and red spectral regions, assigned to the 4 F 9/2 → 6 H 15/2 , 4 F 9/2 → 6 H 13/2 , and 4 F 9/2 → 6 H 11/2 transitions, respectively, but the most intense emission line is in the yellow domain at 579 nm for both CNGG:Dy and CLNGG:Dy crystals. Under the host excitations of λ ex = 272 and 280 nm ( Figure 8), it can be seen that the emission lines of Dy 3+ ions have low intensity suggesting that the energy transfer from the host to Dy 3+ ions is weak in both investigated crystals. The value of the emission cross-section for yellow emission at 579 nm was calculated to be σ em = 0.33×10 −20 cm 2 , being similar in both CNGG:Dy and CLNGG:Dy crystals. Moreover, other laser parameters such as branching ratios (β JJ' ) and Y/B (yellow/blue) ratio, required for efficient lasing in the yellow domain, were determined to have similar or even higher values compared to other crystals (Table 8). Therefore, CNGG:Dy and CLNGG:Dy crystals are promising yellow gain media.  (Figure 8), it can be seen that the emission lines of Dy 3+ ions have low intensity suggesting that the energy transfer from the host to Dy 3+ ions is weak in both investigated crystals. The value of the emission cross-section for yellow emission at 579 nm was calculated to be σem = 0.33×10 −20 cm 2 , being similar in both CNGG:Dy and CLNGG:Dy crystals. Moreover, other laser parameters such as branching ratios (βJJ') and Y/B (yellow/blue) ratio, required for efficient lasing in the yellow domain, were determined to have similar or even higher values compared to other crystals (Table 8). Therefore, CNGG:Dy and CLNGG:Dy crystals are promising yellow gain media.  The partial energy levels and the multiplet barycenter (Bc) of Dy 3+ ions in the CNGG:Dy and CLNGG:Dy crystals were determined by using the absorption and emission spectra at 10 K [23]. The energy levels involved in the yellow emission transition of Dy 3+ compared with those of the Dy:YAG crystal [73] are given in Table 9.  The partial energy levels and the multiplet barycenter (Bc) of Dy 3+ ions in the CNGG:Dy and CLNGG:Dy crystals were determined by using the absorption and emission spectra at 10 K [23]. The energy levels involved in the yellow emission transition of Dy 3+ compared with those of the Dy:YAG crystal [73] are given in Table 9.
The luminescence decays of the 4 F 9/2 level of Dy 3+ ions in CNGG:Dy and CLNGG:Dy crystals at room temperature were measured by observing the yellow line at 579 nm under the excitation wavelength of 355 nm. To find out the lifetime of isolated Dy 3+ ions, sintered ceramic samples of CNGG:Dy and CLNGG:Dy doped with 0.1 at.% Dy were also measured. The normalized luminescence decays are shown in Figure 9. The decay curve is exponential for the low concentration of 0.1 at.% Dy in the CNGG:Dy ceramic, with a measured lifetime of τ 0~5 43 µs (Figure 9a), while in the case of the CLNGG:Dy ceramic, the decay has a non-exponential profile (Figure 9b) indicating the presence of ET processes at the doping concentration of 0.1 at.% Dy. In this case, the average lifetime was determined to be τ av = 405 µs.   The absorption spectra of the 1.8 at.% Pr 3+ ions in CNGG:Pr and CLNGG:Pr crystals ( Figure 10) were measured in the 400-2750 nm domain at room temperature [24] and analyzed within the JO theory [48,49]. For the estimation of JO parameters, seven absorption bands of Pr 3+ ions were considered. Generally, the traditional Judd-Ofelt theory supposes that the 4f5d configurations are situated at higher energies than the 4f n configuration. For the Pr 3+ ions, the difference between the 4f 2 configuration and 4f 1 5d 1 level is only about −1 For the 4.2 at.% Dy concentration, the decay curves present a non-exponential shape (Figure 9), and the average luminescence lifetimes were estimated to be τ av =229 µs and τ av = 143 µs for the CNGG:Dy and CLNGG:Dy crystals, respectively. Using the IH model, the non-exponential decay curves were evaluated, and the experimental transfer functions were determined. From the fitting of the 4 F 9/2 luminescence decay, the critical distance (R 0 ), microparameter of donor-acceptor interaction (C DA ), transfer rates (W DA ), energy transfer rate (W ET ), and quantum efficiency () were determined (Table 10) and compared with other Dy 3+ -doped crystals in Table 10 [57][58][59]. The analysis of the decay curves highlighted the efficient ET between Dy 3+ ions in the CNGG:Dy and CLNGG:Dy crystals. The high values of the quantum efficiency of the 4 F 9/2 level, ~73 %, coupled with the favorable emission cross-sections at 579 nm, σ em = 0.33 × 10 −20 cm 2 , indicate that Dy 3+ ions doped in CNGG:Dy and CLNGG:Dy are potential laser crystals in yellow at 579 nm.

•
Pr 3+ ions The absorption spectra of the 1.8 at.% Pr 3+ ions in CNGG:Pr and CLNGG:Pr crystals ( Figure 10) were measured in the 400-2750 nm domain at room temperature [24] and analyzed within the JO theory [48,49]. For the estimation of JO parameters, seven absorption bands of Pr 3+ ions were considered. Generally, the traditional Judd-Ofelt theory supposes that the 4f 5d configurations are situated at higher energies than the 4f n configuration. For the Pr 3+ ions, the difference between the 4f 2 configuration and 4f 1 5d 1 level is only about ∆E~15000 cm −1 , implying the existence of significant mixing between these two configurations. Therefore, a large difference between the calculated and theoretical results is usually obtained, particularly when the 3 H 4 → 3 P 2 transition is considered in the JO parameters calculation [74]. These incompatibilities are generated by the theoretical characteristics of the standard JO model and can be eliminated by removing the 3 H 4 → 3 P 2 transition or by employing a modified JO analysis. The modified OJ theory proposed by Kornienko et al. [74] assumes that the transition probabilities from the ground level to the 4f 1 5d 1 state are higher than those calculated by standard JO theory, and therefore the energy difference between the 4f 2 and 4f 1 5d 1 configurations is taken into account, and the absorption oscillator strength is expressed as: where Sstandard is the standard oscillator strength and Ei, E5d, and are the energies of the final state, the 4f 1 5d 1 state, and the mean energy of the 4f 2 configuration, respectively. For our crystals, the mean energy of the 4f 2 configuration was determined to be = 10578 cm −1 for the CNGG:Pr crystal and = 10660 cm −1 for the CLNGG:Pr crystal. Based on the absorption and excitation spectra, the energy of the 4f 1 5d 1 lower level of the 4f5d configuration was found to be E5d = 31348 cm −1 (319 nm) in both CNGG:Pr and CLNGG:Pr crystals. Consequently, the modified JO analysis excluding the 3 H4 → 3 P2 + 1 I6 transitions The modified OJ theory proposed by Kornienko et al. [74] assumes that the transition probabilities from the ground level to the 4f 1 5d 1 state are higher than those calculated by standard JO theory, and therefore the energy difference between the 4f 2 and 4f 1 5d 1 configurations is taken into account, and the absorption oscillator strength is expressed as: where S standard is the standard oscillator strength and E i , E 5d , and E 0 f are the energies of the final state, the 4f 1 5d 1 state, and the mean energy of the 4f 2 configuration, respec-tively. For our crystals, the mean energy of the 4f 2 configuration was determined to be E 0 f = 10578 cm −1 for the CNGG:Pr crystal and E 0 f = 10660 cm −1 for the CLNGG:Pr crystal. Based on the absorption and excitation spectra, the energy of the 4f 1 5d 1 lower level of the 4f 5d configuration was found to be E 5d = 31348 cm −1 (319 nm) in both CNGG:Pr and CLNGG:Pr crystals. Consequently, the modified JO analysis excluding the 3 H 4 → 3 P 2 + 1 I 6 transitions was applied, and the obtained Ω t mod (t = 2, 4, 6) intensity parameters are given in Table 11. The values of spontaneous emission probabilities (A JJ' ), branching ratios (β JJ' ), and radiative lifetimes (τ r ) for the excited levels of Pr 3+ ions in CNGG:Pr and CLNGG:Pr crystals [24] were determined based on the values of Ω t mod parameters, and are also shown in Table 11. Table 11. Spontaneous emission probabilities (A JJ' ), branching ratios (β JJ' ), and radiative lifetimes (τ r ) of the 3 P 0 and 1 D 2 excited levels of Pr 3+ ions in CNGG:Pr and CLNGG:Pr crystals. The excitation spectra of the 1.8 at.% Pr 3+ ions in CNGG:Pr and CLNGG:Pr crystals were recorded by observing the emission line at λ em = 606 nm assigned to the 1 D 2 → 3 H 4 transition ( Figure 11). The obtained spectra present a wide UV band in the 200-400 nm spectral range and a group of narrow lines in the 420-490 nm spectral domain assigned to the 4f 2 electronic configuration of Pr 3+ ions. The wide bands in the UV domain contain two types lines: the first one is associated with the CT bands assigned to the Nb 5+ −O 2− interactions into the [NbO 4 ] tetrahedrons of the host lattices (peaks at 272 nm for CLNGG and 280 nm for CNGG), while the second type are the peaks placed at λ = 319 nm and attributed to the 4f 1 5d 1 lower level of the 4f 5d configuration of Pr 3+ ions. transition ( Figure 11). The obtained spectra present a wide UV band in the 200-400 nm spectral range and a group of narrow lines in the 420-490 nm spectral domain assigned to the 4f 2 electronic configuration of Pr 3+ ions. The wide bands in the UV domain contain two types lines: the first one is associated with the CT bands assigned to the Nb 5+ −O 2− interactions into the [NbO4] tetrahedrons of the host lattices (peaks at 272 nm for CLNGG and 280 nm for CNGG), while the second type are the peaks placed at λ = 319 nm and attributed to the 4f 1 5d 1 lower level of the 4f5d configuration of Pr 3+ ions.  However, when the Pr 3+ and Nb 5+ ions are both contained in a material, a photoinduced redox process Pr 3+ +Nb 5+ →Pr 4+ + Nb 4+ takes place, leading to the formation of an intervalence charge transfer (IVCT) band. If the IVCT band is located at low energies, it can interact with the 3 P 0,1,2 manifolds of the Pr 3+ ions leading to the emission quenching of these manifolds. The quenching of emission from the 3 P 0 level in materials containing M 4+ or M 5+ metal ions (M = Ti, V, Nb, and Ta) was intensively studied [24,[75][76][77][78]. When the IVCT band is positioned at higher energies, there is no influence on the 3 P 0 level emissions and intense emissions from the 3 P 0 level can be obtained, especially a strong emission in the blue domain attributed to the 3 P 0 → 3 H 4 transition [24,77]. Therefore, the UV line situated around 319 nm can contain both the 4f 1 5d 1 lower level of 4f 5d configuration and the IVCT band.
The emission spectra of Pr 3+ ions in CNGG:Pr and CLNGG:Pr crystals in the VIS (Figure 12a,b) and near-infrared spectral ranges (Figure 12c,d) were registered under UV (275-375 nm) and 450 nm excitation wavelengths at room temperature [24]. Under UV excitation, the spectra exhibit very low intensities for the emission lines arising from the 3 P J (J=0,1,2,) manifolds, while the emission lines arising from the 1 D 2 manifold are intense and well-structured in both spectral domains. Under UV excitation, the electrons migrate from the (4f 1 5d 1 level + IVCT) band passing through the 3 P J (J = 0,1,2,) manifolds to the 1 D 2 multiplet, thus leading to obtaining a dominating 1 D 2 → 3 H 4 emission [79]. A total quenching of the 3 P 0 level emission was observed for the NaYTiO 4 :Pr phosphor [80], where the energy gap between the 3 P 0 level and the IVCT band is less than 7400 cm −1 . For the CNGG:Pr and CLNGG:Pr crystals [24], this energy gap is around 11827 cm −1 , thus explaining the partial quenching of emission from the 3 P 0 level. Under direct excitation at 450 nm in the 3 P 2 level, the obtained spectra show more intense emission lines from both 3 P J (J = 0,1,2,) and 1 D 2 manifolds compared with those obtained under 275-375 nm UV excitation. Table 12 shows the stimulated emission cross-sections corresponding to the 3 P 0 → 3 H 4 , 1 D 2 → 3 H 4 , and 3 P 0 → 3 F 2 transitions obtained for the investigated crystals in comparison with other similar crystals. The high values of the emission cross-sections indicate that the CNGG:Pr and CLNGG:Pr are potential laser crystals in the blue, red, and orange domains.  The partial energy level scheme and the manifold barycenter (Bc) of Pr 3+ ions are presented in detail in Reference [24]. The levels involved in the blue, orange, and red emissions assigned to the 3 P0 → 3 H4, 1 D2 → 3 H4, and 3 P0 → 3 F2 transitions, respectively, of the Pr 3+ ions in CNGG:Pr and CLNGG:Pr are given and compared with those of the Pr: YAG crystal [84] in Table 13.  The partial energy level scheme and the manifold barycenter (B c ) of Pr 3+ ions are presented in detail in Reference [24]. The levels involved in the blue, orange, and red emissions assigned to the 3 P 0 → 3 H 4 , 1 D 2 → 3 H 4 , and 3 P 0 → 3 F 2 transitions, respectively, of the Pr 3+ ions in CNGG:Pr and CLNGG:Pr are given and compared with those of the Pr: YAG crystal [84] in Table 13. The emission kinetics of 1 D 2 level of Pr 3+ ions in CNGG:Pr and CLNGG:Pr crystals were measured at room temperature by observing the emission line at 606 nm under direct excitation at 590 nm [24]. To obtain the lifetime of isolated Pr 3+ ions, ceramic samples of CNGG:Pr and CLNGG:Pr doped with 0.01 at.% Pr were also sintered and measured. The normalized luminescence decays are presented in Figure 13. The luminescence decay is exponential for the low concentration of 0.01 at.% Pr in the CNGG:Pr ceramic, with a measured lifetime of τ 0~1 28 µs (Figure 13a), while in the case of the CLNGG:Pr ceramic, the decay has a non-exponential profile (Figure 13b) indicating the presence of ET processes at the doping concentration of 0.01 at.% Pr. In this case, the average lifetime was determined to be τ av = 110 µs. For the doping concentration of 1.8 at.% Pr, the decay curves have a non-exponential shape, and the measured lifetime decrease drastically to τ av = 18 µs and τ av = 15 µs, respectively. The quenching emission of the 1 D 2 level at room temperature can increase due to the increase of the Pr 3+ -Pr 3+ non-radiative interactions if the resonance between levels is fulfilled or the ET process is phonon-assisted. Due to the presence of Pr 3+ multicenters, the application of the IH model does not seem appropriate since the analysis of the 1 D 2 decay profiles may lead to inaccurate results. (Reprinted with permission from Ref. [24], copyright 2019, Elsevier).

Conclusions
The growth and spectroscopic characteristics of RE 3+ ions (RE = Sm, Dy, Pr) doped in partially disordered Ca3Nb1.6875Ga3.1875O12 -CNGG and Ca3Li0.275Nb1.775Ga2.95O12 -CLNGG crystals were reviewed. High-quality CNGG:RE and CLNGG:RE crystals were grown using the Czochralski crystal growth technique. The JO model was employed to determine the Ωt (t = 2, 4, 6) intensity parameters and to evaluate the spectroscopic properties and laser emission features of the Pr 3+ , Sm 3+ , and Dy 3+ ions, respectively, doped in the grown crystals. The partial energy levels of each dopant ion were determined. The luminescence decays of the 4 G5/2 (Sm 3+ ) and 4 F9/2 (Dy 3+ ) levels were evaluated within the IH theory, and the ET parameters were determined. For the Pr 3+ ion, the emission decays of the 1 D2 level show a drastic decrease of the lifetime values at high doping concentrations due to the cross-relaxation processes, and the application of the IH model does not seem appropriate because may lead to inaccurate results. The high values obtained for the stimulated emission cross-sections indicate that CNGG and CLNGG crystals doped with Sm 3+ , Dy 3+ , and Pr 3+ ions could be promising materials to achieve laser emission in the orange (Sm 3+ ), yellow (Dy 3+ ), and blue, orange, and red (Pr 3+ ) domains.

Conclusions
The growth and spectroscopic characteristics of RE 3+ ions (RE = Sm, Dy, Pr) doped in partially disordered Ca 3 Nb 1.6875 Ga 3.1875 O 12 -CNGG and Ca 3 Li 0.275 Nb 1.775 Ga 2.95 O 12 -CLNGG crystals were reviewed. High-quality CNGG:RE and CLNGG:RE crystals were grown using the Czochralski crystal growth technique. The JO model was employed to determine the Ω t (t = 2, 4, 6) intensity parameters and to evaluate the spectroscopic properties and laser emission features of the Pr 3+ , Sm 3+ , and Dy 3+ ions, respectively, doped in the grown crystals. The partial energy levels of each dopant ion were determined. The luminescence decays of the 4 G 5/2 (Sm 3+ ) and 4 F 9/2 (Dy 3+ ) levels were evaluated within the IH theory, and the ET parameters were determined. For the Pr 3+ ion, the emission decays of the 1 D 2 level show a drastic decrease of the lifetime values at high doping concentrations due to the cross-relaxation processes, and the application of the IH model does not seem appropriate because may lead to inaccurate results. The high values obtained for the stimulated emission cross-sections indicate that CNGG and CLNGG crystals doped with Sm 3+ , Dy 3+ , and Pr 3+ ions could be promising materials to achieve laser emission in the orange (Sm 3+ ), yellow (Dy 3+ ), and blue, orange, and red (Pr 3+ ) domains.