Spectroscopic properties of Nd<Superscript>3+</Superscript>:CaNb<Subscript>2</Subscript>O<Subscript>6</Subscript> crystal

The absorption spectra, fluorescence spectrum and fluorescence decay curve of Nd³⁺ ions in CaNb₂O₆ crystal were measured at room temperature. The peak absorption cross section was calculated to be 6.202×10⁻²⁰ cm² with a broad FWHM of 7 nm at 808 nm for E//a light polarization. The spectroscopic parameters of Nd³⁺ ions in CaNb₂O₆ crystal have been investigated based on Judd-Ofelt theory. The parameters of the line strengths Ω _t are Ω ₂=5.321×10⁻²⁰ cm²,Ω ₄=1.734×10⁻²⁰ cm²,Ω ₆=2.889×10⁻²⁰ cm². The radiative lifetime, the fluorescence lifetime and the quantum efficiency are 167 μs, 152 μs and 91%, respectively. The fluorescence branch ratios are calculated to be β ₁=36.03%,β ₂=52.29%,β ₃=11.15%,β ₄=0.533%. The emission cross section at 1062 nm is 9.87×10⁻²⁰ cm².     

Thulium doped monoclinic KLu(WO<Subscript>4</Subscript>)<Subscript>2</Subscript> single crystals: growth and spectroscopy

This paper presents the crystal growth and optical characterization of thulium-doped KLu(WO₄)₂ (KLuW). Thulium-doped KLuW macrodefect-free monoclinic single crystals (a^*×b×c≈10×7×15 mm³) were grown by the top seeded solution growth slow cooling method with dopant concentrations of 0.5%, 1%, 3% and 5% atomic in solution. The evolution of unit cell parameters in relation with thulium doping was studied by X-ray powder patterns. Thulium energy levels in the KLuW host were determined by 6 K polarized optical absorption. The Judd–Ofelt parameters determined were Ω₂=9.01×10^-20 cm², Ω₄=1.36×10^-20 cm² and Ω₆=1.43×10^-20 cm². The maximum emission cross section for the 1.9 μm emission, calculated by Füchtbauer–Ladenburg method, is 1.75×10^-20 cm², at 1845 nm with E//N_m. The intensity decay time from the emitting levels ¹ G ₄ and ³ H ₄ levels in relation to the concentration were studied. For the lowest thulium concentration, the measured decay times from ¹ G ₄ and ³ H ₄ emitting levels are 140 μs and 230 μs, respectively. PACS 42.55.Rz; 78.20.-e; 78.55.-m     

Spectroscopic properties of Er<Superscript>3+</Superscript> ions in LiNbO<Subscript>3</Subscript> crystals codoped with HfO<Subscript>2</Subscript>

The results of the spectroscopic analysis of transition strengths for Er³⁺ ions in a series of Hf:Er:LiNbO₃ crystals with variable Hf content and fixed Er content are reported. Unpolarized UV-VIS-NIR absorption spectra, upconversion fluorescence spectra excited at 800 nm, and microsecond time-resolved spectra excited at 400 nm and 800 nm by 800 nm femtosecond laser were measured at room temperature. The HfO₂ incorporation has influence on Er³⁺ radiative lifetimes, and fluorescence branching ratios. For Hf(4 mol %):Er(1 mol %):LiNbO₃, Ω₂=2.63×10^-20 cm², Ω₄=2.86×10^-20 cm², and Ω₆=0.72×10^-20 cm². Ω₂<Ω₄ is contrary to the Er³⁺ general trend of Ω₂>Ω₄>Ω₆ when the Hf content is below its threshold concentration. In addition, the sum of Ω increases with the Hf content when the HfO₂ content below 6 mol % is unfamiliar. The upconversion mechanism is discussed in this work. PACS 71.20.Eh; 77.84.Dy; 42.62.Fi; 42.65.Ky     

Study of spectroscopic characteristics of holmium-doped double sodium-yttrium fluoride crystals Na<Subscript>0.4</Subscript>Y<Subscript>0.6</Subscript>F<Subscript>2.2</Subscript>:Ho<Superscript>3+</Superscript>

We have grown crystals Na_0.4Y_0.6F_2.2:Ho³⁺ (NYF:Ho³⁺) by the Bridgman-Stockbarger method. The optical spectra and luminescence kinetics of NYF:Ho³⁺ crystals have been studied. Based on the analysis of low-temperature absorption spectra, we determine the structure of the Stark splitting of holmium levels in NYF:Ho³⁺ crystals. From absorption spectra examined at T = 300 K, we calculate absorption cross-section spectra and oscillator strengths of transitions from the ground state of holmium to excited multiplets. We show that the absorption spectra of NYF:Ho³⁺ crystals consist of broad bands that lie in the UV, visible, and near-IR ranges. The most intense bands are observed in the visible range, they correspond to transitions ⁵ I ₈ → (⁵ F ₁, ⁵ G ₆) and ⁵ I ₈ → (⁵ F ₄, ⁵ S ₂), and their maximal absorption cross sections are σ_abs^max (λ = 450.3 nm) = 1.16 × 10⁻²⁰ cm² and σ_abs^max (λ = 535.1 nm) = 0.9 × 10⁻²⁰ cm². The intensity parameters Ω _t have been calculated by the Judd-Ofelt method taking into account 10, 12, and 20 transitions from the ⁵ I ₈ ground state to excited multiplets. We show that, with an increasing number of transitions taken into account in the calculation, the parameters Ω _t somewhat increase. For 20 transitions, we have obtained the following intensity parameters: Ω₂ = 0.97 × 10⁻²⁰, Ω₄ = 1.74 × 10⁻²⁰, and Ω₆ = 1.15 × 10⁻²⁰ cm². With these parameters, we have calculated the probabilities of radiative transitions, the radiative lifetimes, and the branching ratios. The rates of multiphoton nonradiative transitions have been estimated. The luminescence decay kinetics from excited holmium levels ⁵ F ₃ (⁵ F ₄, ⁵ S ₂) and ⁵ F ₅ have been studied upon selective excitation in the range of 490 nm, and the lifetimes of these levels have been experimentally determined. We find that the calculated and experimental rates of radiative and nonradiative relaxation from excited holmium levels agree well with each other. We show that, upon pumping in the range of 490 nm, the multiplet (⁵ F ₄, ⁵ S ₂) is populated as a result of the radiative and nonradiative excitation relaxation from the ⁵ F ₃ level, while the lower-lying ⁵ F ₅ level is populated due to direct radiative transitions ⁵ F _{3, 2} → ⁵ F ₅, obviating the cascade scheme ⁵ F ₃ → (⁵ F ₄, ⁵ S ₂) ↝ ⁵ F ₅. We conclude that NYF:Ho³⁺ crystals are processable; admit doping by holmium in high concentrations (up to 100%); and, with respect to all their radiative characteristics, can be considered as potential active media for solid-state continuously tunable lasers in the IR and visible ranges.     

Mid-Infrared Emission Characteristic and Energy Transfer of Ho<Superscript>3+</Superscript>-Doped Tellurite Glass Sensitized by Tm<Superscript>3+</Superscript>

We report on 2.0-μm emission characteristic and energy transfer of Ho³⁺-doped tellurite glass sensitized by Tm³⁺ upon excitation of a conventional 808 nm laser diode. The Judd-Ofelt strength parameters, spontaneous radiative transition probabilities and radiative lifetime of Ho³⁺ have been calculated from the absorption spectra by using the Judd-Ofelt theory. Significant enhancement of 2.0-μm emission of Ho³⁺ has been observed with increasing Tm³⁺ doping up to 0.7 mol%. The energy transfer coefficient of the forward Tm³⁺→Ho³⁺ is approximately 17 times larger than that of the backward Tm³⁺←Ho³⁺ energy transfer. Our result indicates that the maximum gain of 2.0-μm emission, assigned to the transition of ⁵I₇→⁵I₈ of Ho³⁺, might be achieved from the tellurite glass at the concentration of 0.5 mol% of Tm₂O₃ and 0.15 mol% of Ho₂O₃. The high gain coefficient and quantum efficiency (1.16) along with the large value of the product of the stimulated emission cross-section and the measured radiative lifetime (4.12×10⁻²⁷ m²s) of the Ho³⁺/Tm³⁺-codoped tellurite glasses might find potential applications in efficient 2.0-μm laser.     

Spectroscopic properties of Er<Superscript>3+</Superscript> in Sc:LiNbO<Subscript>3</Subscript> crystal

The results of Er³⁺ ion spectroscopic analysis in Sc:LiNbO₃ crystals were reported. The line strengths from the ground state to the excited state were evaluated from the measured unpolarized absorption spectrum and analyzed by using standard Judd–Ofelt theory. For Sc(3 mol. %):Er (1 mol. %):LiNbO₃ crystal, the obtained intensity parameters are: Ω₂=3.72×10^-20 cm², Ω₄=1.07×10^-20 cm², and Ω₆=0.98×10^-20 cm². The fluorescence spectra and microsecond time-resolved spectra were investigated in the visible region. The excited state absorption transition strengths at 800 nm excitation were evaluated based on Judd–Ofelt theory. The results obtained here were compared to results from other research on Er:LiNbO₃ crystals. PACS 71.20.Eh; 77.84.Dy; 42.70.Hj; 42.62.Fi; 42.65.Ky     

Spectroscopy and laser properties of Tm<Superscript>3+</Superscript>:KY(WO<Subscript>4</Subscript>)<Subscript>2</Subscript> crystal

The polarized absorption spectra of Tm³⁺-doped potassium yttrium tungstate (Tm:KY(WO₄)₂) crystal at room temperature were measured. The emission spectrum and lifetime of the ³ F ₄ excited state were determined. Using standard and modified Judd–Ofelt theories, the intensity parameters and the radiative lifetimes were calculated and good agreement with the experimental results was obtained for both theories. Continuous-wave laser operation in Tm:KYW crystal under laser diode pumping at 802 nm and 1750 nm was demonstrated with slope efficiency of 53% and 28% and output power of about 555 mW and 86 mW, respectively. PACS 42.55.Xi; 42.60.Pk; 42.70.Hj     

Spectroscopic Properties and Energy Transfer Analysis of Tm<Superscript>3+</Superscript>-Doped BaF<Subscript>2</Subscript>-Ga<Subscript>2</Subscript>O<Subscript>3</Subscript>-GeO<Subscript>2</Subscript>-La<Subscript>2</Subscript>O<Subscript>3</Subscript> Glass

This paper reports on the spectroscopic properties and energy transfer analysis of Tm³⁺-doped BaF₂-Ga₂O₃-GeO₂-La₂O₃ glasses with different Tm₂O₃ doping concentrations (0.2, 0.5, 2.0, 2.5, 3.0, 3.5, 3.5, 4.0 wt%). Mid-IR fluorescence intensities in the range of 1,300 nm−2,200 nm have been measured when excited under an 808 nm LD for all the samples with the same pump power. Energy level structure and Judd-Ofelt parameters have been calculated based on the absorption spectra of Tm³⁺, cross-relaxation rates and multi-phonon relaxation rates have been estimated with different Tm₂O₃ doping concentrations. The maximum fluorescence intensity at around 1.8 μm has been obtained in Tm₂O₃-3 wt% sample and the maximum value of calculated stimulated emission cross-section of Tm³⁺ in this sample is about 0.48 × 10⁻²⁰ cm² at 1,793 nm, and there is not any crystallization peak in the DSC curve of this sample, which indicate the potential utility of Tm³⁺-doped BaF₂-Ga₂O₃-GeO₂- La₂O₃ glass for 2.0-μm optical fiber laser.     

Optical properties of Tm,Mg:LiTaO3 laser crystal

A Tm, Mg co-doped LiTaO₃ crystal has been grown by Czochralski method. Room temperature polarized absorption spectra and fluorescence spectrum of the Tm, Mg:LiTaO₃ crystal were measured and analyzed. The maximum absorption cross-section is 6.0791 × 10⁻²⁰ cm² at around 790 nm with full width at half maximum of 5 nm. The emission cross-section of ³ F ₄ manifold was 2.2 × 10⁻²⁰ cm². The spectroscopic parameters of Tm³⁺ ion were calculated by applying the Judd-Ofelt approach, and the intensity parameters Ω₂, Ω₄, and Ω₆ were obtained to be 7.71 × 10⁻²⁰, 1.09 × 10⁻²⁰, and 1.16 × 10⁻²⁰ cm², respectively. The branching ratios and radiative lifetimes were also presented and the radiative lifetime of Tm^{3+ 3} F ₄ → ³ H ₆ transition is 968.3 μs. The results were also analyzed and compared with other Tm³⁺ doped hosts.     

Spectroscopic study of thulium-activated double sodium yttrium fluoride Na<Subscript>0.4</Subscript>Y<Subscript>0.6</Subscript>F<Subscript>2.2</Subscript>:Tm<Superscript>3+</Superscript> crystals: I. Intensity of spectra and luminescence kinetics

Na_0.4Y_0.6F_2.2:Tm³⁺ crystals with a thulium content from 1 to 100 at % have been grown by the Stockbarger-Bridgman method. The optical spectra of Na_0.4Y_0.6F_2.2:Tm³⁺ crystals were investigated in detail at room and low (10 K) temperatures, and the luminescence kinetics was analyzed using different excitation methods. The structure of the Stark splitting of thulium levels as “quasi-centers,” characterized by inhomogeneous broadening of the Stark components, is determined from analysis of the absorption spectrum at 10 K. The oscillator strengths of the transitions from the ground state to excited multiplets are determined from the absorption cross-section spectra at 300 K for ten transitions in the range 5000–38 500 cm^?1 and seven transitions in the range 5000–28 500 cm^?1. The transition intensity parameters Ω _t , obtained by the Judd-Ofelt method from the spectra due to the transitions to ten and seven excited levels, were found to be, respectively, (i) Ω₂ = 1.89 × 10^?20, Ω₄ = 2.16 × 10^?20, and Ω₆ = 1.40 × 10^?20 cm² and (ii) Ω₂ = 2.04 × 10^?20, Ω₄ = 2.01 × 10^?20, and Ω₆ = 1.44 × 10^?20 cm². These values of the intensity parameters were used to calculate the radiative transition probabilities and branching ratios and to estimate the multiphonon nonradiative transition probabilities for NYF:Tm. The luminescence decay kinetics from thulium radiative levels upon their selective excitation by nanosecond laser pulses has been studied and the lifetimes of thulium radiative levels in NYF crystals have been found.     

Optical spectra and excited state relaxation dynamics of Sm<Superscript>3+</Superscript> in Gd<Subscript>2</Subscript>SiO<Subscript>5</Subscript> single crystal

Single crystals of gadolinium orthosilicate Gd₂SiO₅ containing 0.5 at% and 5 at% of Sm³⁺ were grown by the Czochralski method. Optical absorption spectra, luminescence spectra and luminescence decay curves were recorded for these systems at 10 K and at room temperature. Comparison of optical spectra recorded in polarized light revealed that the anisotropy of this optically biaxial host affects the intensity distribution within absorption and emission bands related to transitions between multiplets rather than the overall band intensity. It has been found that among four bands of luminescence related to the ⁴G_5/2→⁶H_J (J=5/2–11/2) transitions of Sm³⁺ in the visible and near infrared region the ⁴G_5/2 →⁶H_7/2 one has the highest intensity with a peak emission cross section of 3.54×10⁻²¹ cm² at 601 nm for light polarized parallel to the crystallographic axis c of the crystal. The luminescence decay curve recorded for Gd₂SiO₅:0.5 at% Sm³⁺ follows a single exponential time dependence with a lifetime 1.74 ms, in good agreement with the ⁴G_5/2 radiative lifetime τ _rad=1.78 ms calculated in the framework of Judd-Ofelt theory. Considerably faster and non-exponential luminescence decay recorded for Gd₂SiO₅:5 at% Sm³⁺ sample was fitted to that predicted by the Inokuti-Hirayama theory yielding the microparameter of Sm³⁺–Sm³⁺ energy transfer C _da=1.264×10⁻⁵² cm⁶×s⁻¹.     

Polarized spectral properties of Er<Superscript>3+</Superscript> ions in NaGd(WO<Subscript>4</Subscript>)<Subscript>2</Subscript> crystal

Polarized spectral properties of Er³⁺:NaGd(WO₄)₂ single crystal are reported. The crystal was grown by the Czochralski method. The Judd–Ofelt theory was applied to analyze the polarized absorption spectra and then calculate the spontaneous emission probabilities, radiative lifetimes, and branching ratios. Fluorescence decay curves of the ⁴ I _13/2, ⁴ I _11/2, and ⁴ S _3/2 multiplets for the Er³⁺ ions were measured. Stimulated emission cross-sections of the ⁴ I _13/2→⁴ I _15/2 transition obtained by the Fuchtbauer–Ladenberg formula and the reciprocity method were compared. Multi-phonon relaxation rates of the crystal were estimated. Green up-conversion fluorescence around 531 and 552 nm was observed, and the possible up-conversion mechanisms were proposed. PACS 78.20.-e; 42.70.Hj     

Growth,spectroscopic and laser properties of Yb<Superscript>3<Emphasis Type="Bold">+</Emphasis></Superscript>-doped GdAl<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript> crystal: a candidate for infrared laser crystal

Yb³⁺:GdAl₃(BO₃)₄ (hereafter Yb³⁺:GAB) crystals with large sizes and good optical quality have been grown by the top-seed solution growth (TSSG) method. The polarized absorption and emission spectra have been investigated at room temperature. For the σ-polarization, the intensities of both absorption and emission spectra are stronger than those for the π-polarization, the σ-absorption cross section of Yb³⁺ in GAB being 3.43×10^-20 cm² at 977 nm, and the σ-emission cross section being 0.98×10^-20 cm² at 1045 nm. The fluorescence lifetime of the ² F _5/2→² F _7/2 transition was measured to be 800 μs in the 5% doped sample used for our laser experiments, 993 μs in a 10% doped sample and 569 μs in a 0.5% doped sample. The laser parameters were estimated as: β_min=0.022, I_sat=10.4 kW/cm² and I_min=0.23 kW/cm². About 0.4 W laseroutput at the wavelength of 1043 nm was achieved when the Yb³⁺:GAB crystal was pumped by a 974 nm laser diode, with 27.4% slope efficiency. PACS 42.55.-f; 42.70.Hj; 78.20.-e; 81.10.Dn     

Crystal growth,spectroscopic characterization and laser performance of Nd:Lu<Subscript>0.33</Subscript>Y<Subscript>0.36</Subscript>Gd<Subscript>0.3</Subscript>VO<Subscript>4</Subscript> crystal

A new three-matrix mixed vanadate crystal Nd:Lu_0.33Y_0.36Gd_0.3VO₄ (Nd:LuYGdVO₄) crystal was grown by the Czochralski method. Room temperature absorption and fluorescence spectra of the Nd:LuYGdVO₄ crystals were measured and the spectroscopic parameters were calculated by the Judd-Ofelt theory. The intensity parameters of the Nd:LuYGdVO₄ crystal were Ω₂ = 9.736 × 10⁻²⁰ cm², Ω₄ = 4.179 × 10⁻²⁰ cm², Ω₆ = 8.020 × 10⁻²⁰ cm² and the stimulate emission cross section was 5.3 × 10⁻¹⁹ cm². Diodepumped actively Q-switched and passively Q-switched Nd:LuYGdVO₄ and Nd:Lu_0.14Y_0.86VO₄ lasers at 1.06 μm were demonstrated. The results indicate that, for both actively and passively Q-switched lasers, the Nd:LuYGdVO₄ lasers can generate shorter pulse width with higher peak power than the Nd:Lu_0.14Y_0.86VO₄ lasers at the same cavity conditions.     

Growth and optical properties of Pr<Superscript>3+</Superscript>:KLu(WO<Subscript>4</Subscript>)<Subscript>2</Subscript> laser crystal: a candidate for red emission laser

A Pr³⁺:KLu(WO₄)₂ crystal with dimension of 30 × 30 × 15 mm³ was grown in the K₂W₂O₇ flux. A slice was cut from the crystal, and the polarized absorption and fluorescence spectra were measured at room temperature. Based on the J-O theory, the oscillator intensity parameters Ω _t (t = 2, 4, 6), spontaneous emission probabilities and branch ratios were estimated and good results had been obtained. Furthermore, the crystal has a relatively large emission cross-section in the region of 615–630 nm with the highest value of 14.5 × 10^?20 cm², which indicates that the crystal is good for the application in red emission laser. The emission decay time for ¹D₂ and ³P₀ multiplets was discussed. By adapting the I-H model to fit the emission decay curves, the lifetime for ¹D₂ at 607 nm and ³P₀ at 615 nm are 19.72 μs and 8.95 μs, respectively. Then the corresponding fluorescence quantum efficiencies of the two multiplets reach 83.7 % and 87.9 %, respectively. All the studies illustrate that this crystal is potential in red emission laser application.     

Green,blue, red,near-infrared up-conversion luminescence of Yb<Superscript>3+</Superscript>/Er<Superscript>3+</Superscript>/Tm<Superscript>3+</Superscript> co-doped YVO<Subscript>4</Subscript> nanoparticles

YVO₄:Yb³⁺,Er³⁺; YVO₄:Yb³⁺,Tm³⁺; and YVO₄:Yb³⁺,Er³⁺,Tm³⁺ were all synthesized via sol-gel method with a subsequent thermal treatment. Specifically, YVO₄:Yb³⁺,Er³⁺,Tm³⁺ phosphors were prepared with different annealing temperatures to study the influence of temperature. The transmission electron microscope (TEM), scanning electron microscope (SEM), X-ray diffractometer (XRD), and photoluminescent (PL) spectrofluorometer were used to investigate the morphology, crystal structure, and up-conversion luminescent properties of all samples. In summary, all samples were granular-like nanoparticles and well crystallized with the same tetragonal phase as YVO₄. Under the irradiation at 980 nm, YVO₄:Yb³⁺,Er³⁺ phosphors can generate green emission at 525 and 553 nm and red emission at 657 nm, while YVO₄:Yb³⁺,Tm³⁺ phosphors can generate blue emission at 476 nm, red emission at 648 nm, and near-infrared emission at 800 nm. Notably, YVO₄:Yb³⁺,Er³⁺,Tm³⁺ samples can exhibit green emission, blue emission, red emission, and near-infrared emission at the same time, which might endow the as-prepared samples with potential applications in many fields, such as luminous paint, infrared detection, and biological label.     

Upconversion blue emission dependence on the pump mechanism for Tm<Superscript>3+</Superscript>-heavy-doped NaY(WO<Subscript>4</Subscript>)<Subscript>2</Subscript> crystal

Upconversion blue emissions of Tm³⁺-ion-heavy-doped NaY(WO₄)₂ crystals are investigated with three different near-infrared pump mechanisms. The dependence of upconversion efficiency on the pump mechanism is analyzed from the scope of the concentration quenching effect. Three cross-relaxation processes, , , and , which influence the upconversion dominantly in the Tm³⁺-heavy-doped system, are demonstrated theoretically and experimentally. The results indicate that Yb³⁺ ions can weaken the concentration quenching effect of Tm³⁺ ions significantly so that the blue emission efficiency can be enhanced by one order of magnitude. At the same time, the wavelength of the pump source also has considerable influence on both the population of some crucial energy levels and the upconversion mechanism. Experiments show that the upconversion blue emission in Tm³⁺/Yb³⁺ co-doped NaY(WO₄)₂ crystal under 980-nm laser diode excitation is the most intensive of these three different near-infrared pump mechanisms. The conclusions are confirmed by spectra measurements and calculations of Judd–Ofelt theory and Miyakawa–Dexter theory. PACS 42.70.Hj; 78.55.-m     

Thermo-optic coefficients of monoclinic KLu(WO<Subscript>4</Subscript>)<Subscript>2</Subscript>

The three thermo-optic coefficients of the biaxial laser host KLu(WO₄)₂ are measured at 633 nm by a deflection method. Their values at 300 K amount to ∂ n _g /∂ T=−7.4×10⁻⁶ K⁻¹; ∂ n _m /∂ T=−1.6×10⁻⁶ K⁻¹ and ∂ n _p /∂ T=−10.8×10⁻⁶ K⁻¹. Nearly athermal propagation directions are found for polarizations along the N _m and N _p dielectric axes.     

Spectroscopic characteristics of Pr<Superscript>3+</Superscript> in biaxial La<Subscript>2</Subscript>(WO<Subscript>4</Subscript>)<Subscript>3</Subscript> crystal

A Pr³⁺-doped La₂(WO₄)₃ crystal grown by the Czochralski method has been investigated as a promising laser material. The principal axes of the optical indicatrix and Pr³⁺ concentration of the crystal were determined. The polarized absorption, fluorescence spectra and fluorescence decay curves of the main emission multiplets of the crystal were measured at room temperature. The spectroscopic parameters were obtained by the modified Judd–Ofelt theory combined with the normalized method. The peak stimulated emission cross-sections of the major emission lines were estimated. The good spectroscopic properties imply that the Pr³⁺:La₂(WO₄)₃ crystal is a potential laser gain medium for solid-state laser and self-stimulated Raman laser applications. PACS 78.20.-e; 42.70.Hj     

Direct calculation of transition intensities in LiYF<Subscript>4</Subscript>: Nd<Superscript>3+</Superscript>

Duan’s simple model is extended to analyze the mixing of the 4f ^{N − 1}5d configuration with the 4f ^N states. The explicit static coupling and traditional dynamic coupling are considered, and the parameters are fitted according to the absorption spectrum in LiYF₄: Nd³⁺. The parameter values obtained are as follows: T ₃₂ = −28i × 10⁻⁷, T ₅₂ = −1151i × 10⁻⁷, A ₃₂² = 192i × 10⁻¹² cm, A ₅₂⁴ = i × 10⁻¹² cm, A ₇₂⁶ = 54i × 10⁻¹² cm, and A ₇₆⁶ = −680i × 10⁻¹² cm. Compared to the experimental measurements, the present model yields better results than those obtained from the Judd-Ofelt theory. The text was submitted by the authors in English.