1. Introduction

Ultrafast and high power lasers have attracted great interests due to their wide applications in fusion energy, high energy nuclear physics and attosecond chemistry [1], et al. The ultrafast and ultraintense lasers have been moving towards all-solid-state, high repetition rate, and new wavelength bands [2]. Presently, the ultrafast and ultraintense laser technologies in the near infrared bands are the most mature ones. However, the poor thermal conductivities in the conventionally adopted laser gain materials made the laser repetition rate be low even in the near infrared bands, hence new laser materials were essentially needed to develop high repetition frequency pulses.

Recently, the neodymium doped calcium fluoride crystals have played a more crucial role in ultrafast and high power lasers. The crystals have excellent performance for both the high thermal conductivity (10 W·m^-1·K^-1) and the broad photoluminescence band (20∼30 nm). Besides, they exhibit low phonon energy, moderate emission cross-section (3∼6 × 10⁻²⁰ cm²), high upper level lifetime (300-480 µs) and small nonlinear refractive index as low as 0.43 esu [3–5]. Qin et al. achieved the shortest mode-locked pulses of 103 fs by Nd,Y:CaF₂ crystal, which was the first time to realize 100-fs level pulses in Nd-doped laser crystals [6]. The maximum output pulse energy of 5.1 mJ was accomplished with 5 Hz repetition in Nd,Y:SrF₂ crystals [7]. The Nd,Y:CaF₂ crystals was available for the gain medium of Inertial Confinement Fusion (ICF) laser drivers and a small signal gain of 2.7 is achieved which was nearly twice as that of Nd-glass [8]. These results indicated clearly that Nd-doped alkaline earth fluoride laser crystals are promising candidates for generation of high repetition frequency, ultrafast and high power lasers.

In fact, Nd:CaF₂ crystal was studied shortly after the first realization of ruby lasers, and the laser resonant was greatly limited due to the serious luminescence quenching. In order to break the coherent dipolar-dipolar interactions among Nd³⁺ ions, Kaminskii et al. firstly introduced La³⁺, Gd³⁺, Y³⁺, Lu³⁺ in Nd³⁺-doped fluoride crystals, then the photoluminescence intensity was improved significantly [9–12]. With deeper research, the line characteristics of the spectra were found to be varied with the codopant species, which was supposed to be connected with the rare earth clusters [3,13–15]. Catlow et al. reported that the rare earth ions tend to agglomerate together, then dimers, trimers and even hexamers could be formed in the crystals by means of empirical potential simulation [16]. Subsequently, Su et al. investigated the rare earth doped fluorides by using the density functional theory based first principles calculation [17,18]. The cluster features of the rare earth ions were found to be different, which depended on the rare earth ions and matrix crystals, as well as the doping concentrations [19–21]. They demonstrated the rare earth clusters in SrF₂ crystal as an example, which showed that the cluster structures relied on the size of rare earth ions and evolved with the doping concentrations [22].

Compared with SrF₂, the initial clustering concentration in CaF₂ crystals was two orders of magnitude lower [23,24]. The spectral properties in CaF₂ crystals were also different. Since the rare earth clusters are intimately related with the spectroscopic properties [25–27], however, there are rare reports on how the codopant species impact the cluster structure and the spectra properties of the crystals. By systematic research, this work focus on the clusters and spectra of La³⁺/Gd³⁺/Y³⁺/Lu³⁺ codoped Nd:CaF₂. The results show that the cluster structures varied with the codoped ions, which contribute to the differed spectral properties.

2. Methodology

2.1 First principles calculation

The calculations of trivalent rare earth clusters in CaF₂ crystal were carried out by using the VASP codes [28,29]. The projector augmented wave (PAW) potential was utilized. The formalism for the calculations is related to the Perdew-Burke-Ernzerhof (PBE) function within the generalized gradient approximation (GGA) [30,31]. And the spin polarization was included in all calculations. The Ca 3p⁶4s², F 2s²2p⁵, La 5s²5p⁶5d¹6s², Nd 5s²5p⁶5d¹6s², Gd 5s²5p⁶5d¹6s², Y 4s²4p⁶4d²5s¹, Lu 5s²5p⁶5d¹6s² states were considered as valence electrons. Due to interactions among the ions, the plane wave basis has set the cut off energy as 550 eV. To obtain sufficient accuracy, the 2 × 2 × 2 supercell and 1 × 1 × 1 Gamma k-meshes were considered. The converged energy gap was 10⁻⁵ eV and force on individual atoms reached 0.01 eV·Å⁻¹.

The symbol i₁i₂|v|d|s_r-O/A/T/Cn was applied to describe the rare earth clusters based on Refs. [16,20]. i₁ and i₂ represent the number of Nd and second kind of codoped rare earth atoms, respectively; v is the number of lattice fluorine vacancies; d is the number of lattice fluorines that deviated from the normal site; and s means the number of interstitial fluorines (F_i^-); r = 1 and 2 point to that the interstitial fluorines located at the nearest and next nearest site of rare earth ion, respectively; O, A, T, C respectively refer to the shape of the cluster resembling a circle (O), an armchair (A in abbreviation), a crescent moon (C) and a tack nail (T), respectively. The suffix n means the serial number to supplement the insufficient notation. The formation energy of the cluster was calculated by Eq. (1):

In Eq. (2), g is the scaling factor of -0.34 for face-centered cubic structure [34]; q is the net charge, α is the Madelung constant of 5.0388 for fluorite [35]; ε and L respectively denote to the static dielectric constant and supercell dimension (2 × 2 × 2), ε equals to 6.812 at 300 K [36], and L equals to 10.9 Å. Hence for a 2 × 2 × 2 supercell, the correction energy of CaF₂ with a net charge was 0.323 eV [37].

The partial Density of States (pDOS) calculations were performed based on the optimized structures. The 4 × 4 × 4 Gamma k-meshes was adopted to sampling the first Brillouin zone. The LSDA + U method by Dudarev was considered for pseudopotential corrections and Coulomb onsite interactions [38]. In the work U = 0.5, 6 and 1 were respectively utilized for lanthanum, neodymium and yttrium. It is noted that the Nd 4f³5s²5p⁶5d¹6s² with 4f electrons unfreezing was adopted in the the Partial Density of States(pDOS).

2.2 Sample preparation and characterization

Four groups of single crystals Nd³⁺,R³⁺:CaF₂ (R = La, Gd, Y, Lu) were grown by temperature gradient technique method. The concentrations of Nd³⁺ is around 0.5 at.% measured by Inductive Coupled Plasma Optical Emission Spectrometer (ICP-OES). The doping concentrations of R³⁺ were 0.5, 2, 5 and 8 at.% in four classes of crystals. The sample of 0.5% Nd³⁺,8%Ce³⁺:CaF₂ was also grown as a comparison with other crystals. 1 wt.% PbF₂ was added as oxygen scavenger. Raw materials of NdF₃, LaF₃, GdF₃, YF₃, LuF₃, CaF₂ and PbF₂ were used with purity of 99.99%. All raw materials were weighted stoichiometrically and well-mixed, and then loaded into a graphite crucible. The growth program wasn’t started to run until the vacuum reached 10⁻³ Pa. The crystal growth was followed with rate of 1.5 K/h, as described in Ref. [39]. After the growth process, the as grown crystals were prepared with dimension of Φ11 × 2 mm³ for spectral measurement. The samples were polished double faces.

Room temperature absorption spectra were tested by Cary 5000 UV-Vis-NIR Spectrophotometer, with step of 1 nm, spectral band width (SBW) of 2 nm and dwell time of 0.1 s. The fluorescence spectra were recorded by FLS980 time-resolved fluorimeter with a thermoelectric (TE) cooled InGaAs detector. The fluorescence decay curves were measured by using a TDS 3052 oscilloscope following excitation at 794 nm by Xenon flashlamp. In addition, the detection wavelength for the decay lifetime measurement is 1060 nm. If the curves are nonexponential, then the following equation is used to calculate the average lifetime.

Based on these parameters, the peak emission cross sections are calculated by Eq. (4).

3. Results and discussion

3.1 Rare earth clusters simulation

When the rare earth ions are introduced in CaF₂, it will replace the Ca²⁺ and interstitial F_i^- work as charge compensation. There are several nonequivalent sites for the charge compensation F_i^- to occupy. Then the 1₁|0|0|1₁ and 1₁|0|0|1₂ with F_i^- at the nearest and next nearest sites of rare earth ions respectively are emerged. These monomers would be further aggregated to be clusters and about twenty kinds of rare earth centers are observed in Er³⁺:CaF₂ [40]. Herein, the rare-earth clusters in CaF₂ crystal are modeled based on Ref. [21], and then totally relaxed. The potential thermodynamic stable clusters are shown in Fig. 1 and Table 1. The thermodynamic stable centers are classified into three stages. The first stage consists of monomers containing only one rare earth ions; the second stage consists of clusters with more than one rare earth ions and the ionic sublattice within the cluster is remained to be cubic, and the third stage points to square antiprism ionic sublattice. It can be seen in Fig. 1 that, from La³⁺, Nd³⁺, Gd³⁺, Y³⁺ to Lu³⁺, formation energy of the first stage monomer center 1₁|0|0|1₁ increases while that of 1₁|0|0|1₂ decreases. It means that the charge compensation F_i^- tends to occupy the next nearest site of rare earth ions as the ionic radius decreases. At the same time, one more lattice fluorine departs from the normal site in the second stage dimers 2₁|0|1|2₁ and 2₁|0|1|3₁ of large size La³⁺ ion clusters. Then 2₁|0|2|2₁ and 2₁|0|2|3₁ centers were generated for small size ion such as Y³⁺. The cubic center 4₁|1|0|4₁ is thermodynamic stable in large size La³⁺ and Nd³⁺ doped CaF₂, and it becomes unstable for Y³⁺ and Lu³⁺. There are two lattice fluorines deviating in the cubic cluster 3₁|0|2|4₁-T for Nd³⁺ and Gd³⁺. While for Y³⁺ and Lu³⁺, five and six more normal fluorines relaxed, respectively. More importantly, the ionic sublattice varied from cubic to square antiprism structure. As for the third stage clusters, there shows no stable centers in large radius ions like La³⁺ and Nd³⁺ and the stability was significantly improved in small size ions Lu³⁺ and Y³⁺. As to Gd³⁺, the number of cubic stable clusters account for a large propotion while there is only a small percentage stable centers in the third stage. These results clearly suggest that the characters of centers change with the radius of rare-earth ions. The second stage cubic sublattice clusters are more stable in large size ions La³⁺, Nd³⁺ and Gd³⁺, while the third stage square antiprism clusters are more stable for small size ions Y³⁺ and Lu³⁺. Accordingly, cluster characters of La³⁺, Nd³⁺ and Gd³⁺ were classified as one category and that of Y³⁺ and Lu³⁺ as another category.

 

Fig. 1. The thermodynamic stable clusters in La³⁺-, Nd³⁺-, Gd³⁺-, Y³⁺-, Lu³⁺-doped CaF₂ crystals, these centers are divided into three groups, “1”, “2” and “3” represent the cubic monomers, cubic sublattice clusters and square antiprism structure clusters, respectively.

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Table 1. Formation energy of the thermodynamic stable rare earth clusters in CaF₂ crystal.

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The number of rare earth ions dependent formation energy is also depicted. It can be seen in Fig. 2 that, as the number of rare earth ions within the same doping center increases, the formation energy reduces linearly. It indicates that the clusters would be more stable when the rare earth ions agglomerate together, which is in line with the reported results [37]. The energy slopes for La³⁺, Nd³⁺, Gd³⁺, Y³⁺ and Lu³⁺ are -1.54, -1.54, -1.71, -1.61 and -1.74 eV, respectively. As the formation slopes become steeper, the stabilities of clusters are enhanced. Thus the magnitude of energy slopes reflects the difficulty of aggregating. Hence the smaller values observed in small size rare earth ions mean, that it is easier for not only the process of aggregating, but also the transforming of ionic sublattice from cubic to square antiprism structure. Subsequently, the lattice mismatch was significantly alleviated. Thus the formation energy and slopes are further reduced for smaller size rare-earth ions Y³⁺ and Lu³⁺.

 

Fig. 2. The number of rare earth ions dependent formation energy of the thermodynamic stable centers.

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The rare earth cluster structures in singly-doped calcium fluorite are already figured out. However, clusters in the rare earth codoped crystals remain unclear. Since the codoped fluorites, especially Nd³⁺ and R³⁺ codoped crystals are potential candidates for generation of high repetition rate high power lasers, the cluster structures in the codoped crystals are also vital. Referring to the characters of rare earth clusters stated above, it was assumed that the structures of mixed [Nd³⁺-La³⁺] are similar with that of [Nd³⁺-Gd³⁺], and of [Nd³⁺-Y³⁺] resemble that of [37] [37]. The centers of [Nd³⁺-La³⁺] and [Nd³⁺-Y³⁺] were therefore chosen in order to simplify the calculation. The mixed clusters were then modeled and relaxed. The thermodynamic stable clusters are shown in Fig. 3 and Tables 2–3. As can be seen that only the cubic sublattice centers are thermodynamically stable in [Nd³⁺-La³⁺] mixed clusters. The structure characters are similar with that of Nd³⁺ or La³⁺ singly-doped crystals in which the cubic sublattice centers are stable. Compared with [Nd³⁺-La³⁺], however, the proportion of cubic sublattice centers decrease in the Nd³⁺ and Y³⁺ codoped crystals. There is quite amount of cubic sublattice [Nd³⁺-Y³⁺] clusters were converted to square antiprism structure centers. It is in line with the structure characters of Y³⁺-doped CaF₂. Therefore, the mixed cluster structures depend on the compositions and structural features of the rare earth centers.

 

Fig. 3. Thermodynamic stable centers of the mixed [Nd³⁺-La³⁺] and [Nd³⁺-Y³⁺] clusters in CaF₂ crystal.

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Table 2. The formation energy (FE), averaged bond length (ABL), coordination number (CN) and the ionic sublattice (SBL) around Nd³⁺ in [Nd³⁺-La³⁺] centers, the SAP means square antiprism sublattice.

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Table 3. The formation energy (FE), averaged bond length (ABL), coordination number (CN) and the ionic sublattice (SBL) around Nd³⁺ in [Nd³⁺-Y³⁺] centers, the SAP means square antiprism sublattice.

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According to Tables 2–3, the number of rare earth ions dependent formation energy is illustrated. As for [Nd³⁺-La³⁺] clusters (m = 0 ∼ 4), the formation energy decreases linearly with the number of La³⁺ atoms rising, as the solid lines shown from Fig. 4. The slopes of clusters with m = 0, 1 and 2 are approximately the same, and the value is around -1.56 eV, agrees well with that of La³⁺ or Nd³⁺ singly doped crystals. Besides, as the dotted lines show, the formation energy of the [Nd³⁺-La³⁺] clusters are dropped when compared with that of pure Nd³⁺ or La³⁺ centers. These are strong evidence that the introduction of La³⁺ into Nd³⁺ clusters contribute to a more stable framework and two possible reasons should be responsible. First, the different radius sizes of La³⁺ and Nd³⁺ ions would probably bring a large reduction of lattice mismatch. Second, the centers of Nd³⁺ or La³⁺ singly doped crystals are thermodynamic stable with cubic sublattice structures which are also expected in Nd³⁺ and La³⁺ codoped sample.

 

Fig. 4. Number of R³⁺ ions dependent formation energy of the mixed [Nd³⁺-R³⁺] clusters in CaF₂ crystal, R = La (a) and Y (b), respectively, the m and n represent number of Nd³⁺ and R³⁺ atoms in the clusters, respectively.

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The formation energy of [Nd³⁺-Y³⁺] centers is presented as a comparison. It can be seen from the solid lines, that formation energies are also reduced linearly. The slope values are similar to that of pure Y³⁺ centers, especially in the centers with more Y³⁺ ions. The lower slope of [Nd³⁺-Y³⁺] centers than that of [Nd³⁺-La³⁺] indicate that it is easier to be clustering for Nd³⁺ and Y³⁺ [37]. For the dotted lines, formation energy of the cubic sublattice centers with m + n = 2 and 3 increase as the number of Y³⁺ boosts up, while that of square antiprism structure clusters with m + n = 4, 5 and 6 slightly decrease. These results clearly demonstrate that stabilities of the cubic structure centers are weakened and they tend to shift towards square antiprism centers with addition of Y³⁺. The cluster characters of La³⁺ and Y³⁺ are different, which then contributes to the varied structure characteristics of [Nd³⁺-La³⁺] and [Nd³⁺-Y³⁺] mixed centers.

The bonding characters are further analyzed to confirm the varied cluster structures. Given that the relative stabilities of 1₁|0|0|1₁ and 1₁|0|0|1₂ corresponding to that of second and third stage centers depend on the 1₁|0|0|1₁ [17], the pDOS of 1₁|0|0|1₁ center in La³⁺, Nd³⁺ and Y³⁺ doped CaF₂ is therefore calculated. As is shown in Fig. 5(a), the f orbital of La³⁺ locates at 6.5 eV in the conduction band, which is the lowest when compared with that of f states in Nd³⁺ and d states in Y³⁺. It would be easier for the nonbonding charges of interstitial F_i^- moving towards the lowest unoccupied states in La³⁺. The connection between La³⁺ and F_i^- was then strengthened. For Nd³⁺, although the energy of 4f states in conduction band is higher than that of d states in Y³⁺, however, the much more intense bonding was observed near the top of the valence band. In terms of interstitial F_i^-, as can be seen in Fig. 5(b) that the intensity of 2p states at about 0 eV in Y³⁺ is the highest. It means that there are more charges located at the F_i^-, which would give a strong repulsion to the lattice fluorines around. The cubic sublattice then became unstable and it alters to be square antiprism structure. The bonding characters match well with the structure characters of rare earth centers and the mixed.

 

Fig. 5. pDOS of the lanthanide and interstitial fluorine in 1₁|0|0|1₁ center of CaF₂. (a) The states of La³⁺ (4f), Nd³⁺ (4f) and Y³⁺ (4d); (b) the 2p states of the F_i^-.

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3.2 Spectral properties of Nd³⁺,R³⁺:CaF₂ crystals

On the basis of the aforementioned results, the cubic sublattice clusters prefer to be formed in Nd³⁺,La³⁺:CaF₂ and Nd³⁺,Gd³⁺:CaF₂ crystals. While as the codopant changes to be Y³⁺ and Lu³⁺, the square antiprism clusters are emerged. With the results in mind, the spectral properties of Nd³⁺,R³⁺:CaF₂ (R = La, Gd, Y, Lu) crystals were compared to confirm the viewpoint.

The room temperature absorption and emission spectra as well as decay curves of Nd³⁺,R³⁺:CaF₂ are presented in Fig. 6 and the spectra are all normalized for comparison. Since the clustering of the codopant would be more expressed in the mixed centers when the concentration of R³⁺ is substantially higher than that of Nd³⁺, the crystals codoped with 8% R³⁺ were selected. As can be seen in Fig. 6(a) that, there are two absorptions peaking at 790 and 796 nm, which corresponds to the ⁴I_9/2 → ⁴F_5/2 + ²H_9/2 transition. When using La³⁺ and Gd³⁺ as the codopant, the highest peak emerges at 790 nm while the intensity of 796 nm absorption is relatively weak, which agrees well with the crystal codoped with large size Ce³⁺. However, the absorption intensity of 796 nm is much stronger than that at 790 nm as codopants switch to be Y³⁺ and Lu³⁺ [13].

 

Fig. 6. Comparison of area normalized absorption (a), intensity normalized emission spectra (b) and (c) decay curves of Nd³⁺,R³⁺:CaF₂ crystal.

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As displayed in Fig. 6(b), the emission spectra are also illustrated. The emission band corresponds to the ⁴F_3/2 → ⁴I_11/2 transition. The line characters of emission spectra in Nd³⁺,La³⁺/Ce³⁺/Gd³⁺:CaF₂ crystals are quite similar and two peaks are observed. The stronger emission is at 1065 nm and the weaker is at 1049 nm. When Y³⁺ and Lu³⁺ are introduced in the crystals, the emissions at 1049 and 1065 nm disappear and the intensity at 1054 nm boosts up. Hence, as additional information, the spectrum of Nd³⁺,Ce³⁺:CaF₂ crystal further demonstrates that similar spectrum are related to the size of ion radius. In addition, the decay curve of Nd³⁺,La³⁺:CaF₂ is nearly the same with Nd³⁺,Gd³⁺:CaF₂, and that of Nd³⁺,Y³⁺:CaF₂ and Nd³⁺,Lu³⁺:CaF₂ resemble with each other in Fig. 6(c). Specifically, the decay values of Nd³⁺,La³⁺/Gd³⁺:CaF₂ crystals are 481.7 and 566.5 µs, which is relatively high. While the lifetime values of Nd³⁺,Y³⁺/Lu³⁺:CaF₂ crystals are 401.0 and 362.7 µs, which are almost the same and shorter. The results of emissions and decays agree well with the absorption spectra. Combined with the calculated results, the absorption of 790 nm and the emissions of 1049 and 1064 nm could be connected with the cubic sublattice centers. While the 796 nm absorption and the 1054 nm emission are bounded with the square antiprism clusters [41].

Furthermore, the codopant concentrations dependent spectral parameters of Nd³⁺,R³⁺:CaF₂ crystals are summarized and depicted in Fig. 7. As for the quantum efficiencies, they are all improved when the doping concentration increases in Fig. 7(a). The quantum efficiencies are related with the broken of [Nd³⁺-Nd³⁺] clusters [15]. As discussed before, the introduced R³⁺ ions would agglomerate with Nd³⁺ efficiently as the amount of [Nd³⁺-R³⁺] nonquenching clusters increases, which contributes to the enhanced quantum efficiencies. Additionally, the quantum efficiency is connected with the number of photons of absorption and emission. While the local structures impact both the characteristics of absorption and emission spectrum, thus the effects might be neutralized. In respect of the lifetimes, there is a positive correlation between the values and the codopant concentrations. In particular, the lifetimes of Nd³⁺,La³⁺:CaF₂ and Nd³⁺,Gd³⁺:CaF₂ crystals are higher than Nd³⁺,Y³⁺:CaF₂ and Nd³⁺,Lu³⁺:CaF₂. The variation trends of the concentration dependent lifetimes in Nd³⁺,La³⁺:CaF₂ and Nd³⁺,Gd³⁺:CaF₂ exhibited to be the same in Fig. 7(b). As can be seen the trends in Nd³⁺,Y³⁺:CaF₂ and Nd³⁺,Lu³⁺:CaF₂ are also approximately the same. It is similar with the concentrations dependent emission cross sections of the codoped crystals in Fig. 7(c). Therefore, the varied photoluminescence parameters of Nd³⁺,R³⁺:CaF₂ crystals are in accord with the altered rare earth cluster structures.

 

Fig. 7. The codopant concentrations dependent photoluminescence parameters of Nd³⁺,R³⁺:CaF₂ crystals, (a) the quantum efficiencies, (b) the fluorescence lifetimes, (c) the peak emission cross sections.

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It should be noted here that the longer lifetimes and smaller emission cross sections were collected in Nd³⁺,La³⁺:CaF₂ when compared with that of Nd³⁺,Y³⁺:CaF₂. The averaged bond length, coordination number and polyhedrons around the active Nd³⁺ in the mixed clusters were collected in Tables 2 and 3. It shows that a wider span of averaged bond lengths were observed in Nd³⁺,La³⁺:CaF₂ crystals. While for Nd³⁺,Y³⁺:CaF₂, span of the averaged bond lengths declines. As can be seen the averaged bond lengths range from 2.38 to 2.49 Å in the La³⁺-codoped crystal. Similar spanning was observed in the cubic sublattice centers of Nd³⁺,Y³⁺:CaF₂ crystal. However, it altered to be spanning 2.39 to 2.41 Å in the high order clusters. The longer averaged bond lengths, dispersal distribution of bond lengths and larger coordination numbers as well as the higher symmetric cubic polyhedrons lead to the longer lifetimes and smaller emission cross sections. When the codoped rare-earth ions alter from La³⁺, Gd³⁺, Y³⁺ to Lu³⁺, the cluster structures shift from cubic to square antiprism, attributing to the shorter lifetime and larger emission cross section. The relationship of cluster structures and photoluminescence parameters were then depicted in Fig. 8. As the local structures varied from cubic to square antiprism, the emission cross sections were improved and simultaneously the lifetimes decrease. The relationship provides a methodology for designing new laser materials by regulating the local structures of rare earth ions.

 

Fig. 8. The local structures dependent peak emission cross sections and lifetimes in 0.5%Nd³⁺,8%R³⁺:CaF₂ crystals.

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The photoluminescence parameters and thermal conductivities of Nd³⁺,R³⁺:CaF₂ crystals were also listed and compared with other famous Nd³⁺-doped laser materials, such as Nd:YAG, Nd:YVO₄, Nd:YLF, Nd:Ca₃La₂(BO₃)₄ and Nd:glass. It can be seen in Table 4, that the bandwidths of Nd,R:CaF₂ crystals are comparable with Nd:Ca₃La₂(BO₃)₄ and Nd:glass, and is much broader than that in Nd:YAG, Nd:YVO₄ and Nd:YLF. The thermal conductivities in Nd,R:CaF₂ are much higher than that in Nd:Ca₃La₂(BO₃)₄ and Nd:glass, which supports the high repetition rate ultrafast lasers. More importantly, a lifetime near 600 µs was achieved in Nd³⁺,Gd³⁺:CaF₂ crystal. The high energy storage ability means that the LD-pumped lasers were highly expected in the crystals.

Table 4. Comparison of the photoluminescence parameters and thermal conductivities at room temperature of the neodymium-doped laser materials.

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4. Conclusion

In summary, we have in this work prepared for four kinds of Nd³⁺,R³⁺:CaF₂ crystals. As to the simple-doped calculation results, the stabilities of cubic sublattice clusters declined and that of square antiprism clusters strengthened when the codopant varied from La³⁺, Gd³⁺, Y³⁺ to Lu³⁺. The mixed rare earth clusters calculation indicates, that the cluster characters in Nd³⁺,La³⁺:CaF₂ and Nd³⁺,Gd³⁺:CaF₂ crystals are nearly the same and could be classified into one category, correspondingly the Nd³⁺,Y³⁺:CaF₂ and Nd³⁺,Lu³⁺:CaF₂ crystals are as another one. The pDOS analysis supplements the reason for different cluster structures from the view of binding characteristics. The local structure dependent spectral properties and the concentration dependent photoluminescence parameters results show that the similar line characters were collected in Nd³⁺,La³⁺:CaF₂ and Nd³⁺,Gd³⁺:CaF₂. Subsequently, the Nd³⁺,Y³⁺:CaF₂ and Nd³⁺,Lu³⁺:CaF₂ possess almost the same spectral features, which agrees with the calculated results. Accordingly, the 790 and 796 nm absorptions were ascribed to the cubic and square antiprism sublattice centers, respectively. And the cubic sublattice centers result in the emissions at 1049 and 1064 nm, while the square antiprism clusters cause the 1054 nm emission. The higher local symmetries around the active ions in cubic sublattice centers contribute to the longer lifetimes (∼ 600 µs) and moderate emission cross sections (∼ 2.5 × 10⁻²⁰ cm²) in the crystals codoped with large size rare earth ions. The ultralong lifetime and appropriate emission cross sections make the crystals be potential candidates for generation of laser diode-pumped ultrafast pulses.