Standard Judd Ofelt Research Articles

Absorption intensities and emission cross sections of Tb3+ (4f8) in TbAlO3

Trivalent terbium absorption intensities in single-crystal TbAlO3 are analyzed using the Judd-Ofelt model to assess the crystal’s potential as a solid state laser system. The standard Judd-Ofelt model was applied to the room temperature absorption intensities of Tb3+ (4f8) to determine the phenomenological intensity parameters Ω2, Ω4, and Ω6. Seven multiplet manifolds are identified and the absorption intensities of these manifolds are least-squares fitted to the calculated intensities to obtain the intensity parameters: Ω2=40.52×10−20cm2, Ω4=8.74×10−20cm2, and Ω6=2.26×10−20cm2 in TbAlO3. These intensity parameters are then applied to determine the radiative decay rates and branching ratios of Tb3+ transitions from the D45 to the FJ′7 multiplet manifolds. Based on the results, the radiative lifetime of the excited state manifold D45 is determined from the radiative decay rates and found to be 3.5ms. The calculated lifetime is longer than the measured lifetime, reflecting the nonradiative interactions between the Tb3+ ions and the lattice in the pure compound. The intensity parameters, radiative lifetime, and emission cross sections are then compared to those reported in other laser hosts. The quantum efficiency of the laser transition D45→F57 of Tb3+ is approximately 57.0% in TbAlO3.

Spectroscopic investigation of 2.0 µm emission in Ho3+-doped fluoroindate glasses

In this paper we report the optical characterization of Ho3+-doped fluoroindate glasses with the following composition (40 − x)InF3–20SrF2–16BaF2–20ZnF2–2GdF3–2NaF–xHoF3 with x = 1.0, 2.0, 2.5, 3.0, 4.0, 5.0, 6.0, 8.0 and 9.0 mol%. This investigation was done by means of absorption, fluorescence and lifetime measurements. The phenomenological intensity parameters Ωλ (λ = 2, 4, 6) were calculated using the standard Judd–Ofelt theory. In order to evaluate potential applications of the 5I7 → 5I8 Ho3+ emission at 2.0 µm, the radiative lifetime, total transition rate and emission cross section were determined. The effect of Ho3+ concentration on the fluorescence intensity and lifetimes was analysed. It was concluded that the non-radiative losses of the 5I7 level are mainly due to energy migration among Ho3+ ions followed by energy transfer to quenching impurities.

Concentration effect of Er3+ ion on the spectroscopic properties of Er3+ and Yb3+/Er3+ co-doped phosphate glasses

Abstract Spectroscopic properties of Er 3+ and Er 3+ –Yb 3+ co-doped phosphate glass matrix have been analyzed by fitting the experimental data with the standard Judd–Ofelt theory. Various spectroscopic parameters were obtained to evaluate their dependence and the potential of the samples as a laser material in the eye-safe laser wavelength (1.53 μm) as a function of the Er 3+ and Yb 3+ concentration. Results indicate that the increment in the active ion concentration and the small variation in the Ba content in phosphate matrix reduce the Ω t parameters and modify the fluorescence spectral properties of Er 3+ ion. The fluorescence decay time range from 3 to 8.5 ms depending on the ionic concentration and the maximum quantum efficiency for the 1.53 μm was 86% for 0.25 mol% of Er 3+ with 2.5 mol% of Yb 3+ . The effect of Er 3+ concentration on the quantum efficiency was discussed in terms of the cluster formation of the active ion and by the dynamics change induced by the presence of Yb 3+ . Calculated and measured parameters are in agreement with others results reported recently.

Absorption intensities and emission cross sections of principal intermanifold and inter-Stark transitions of Er3+(4f11) in polycrystalline ceramic garnet Y3Al5O12

A comparative spectroscopic study is performed on Er3+(4f11) ions doped in polycrystalline ceramic garnet Y3Al5O12 (YAG) and single-crystal laser rod, both containing nominal 50 at. % of Er3+. The standard Judd–Ofelt (JO) model is applied to the room-temperature absorption intensities of Er3+(4f11) transitions in both hosts to obtain the phenomenological intensity parameters. These parameters are subsequently used to determine the radiative decay rates, radiative lifetimes, and branching ratios of the Er3+ transitions from the upper multiplet manifolds to the corresponding lower-lying multiplet manifolds LJ2S+1 of Er3+(4f11) in these garnet hosts. The emission cross sections of the intermanifold Er3+I13∕24→I15∕24 (1.5 μm) transition as well as the principal inter-Stark transition Y1→Z4 (1550 nm) within the corresponding multiplet manifolds have been determined. The room-temperature fluorescence lifetimes of the I13∕24→I15∕24 (1.5 μm) transition in both polycrystalline ceramic and single-crystal YAG samples were measured. From the radiative lifetimes determined from the JO model and the measured fluorescence lifetimes, the quantum efficiencies for both samples were determined. The comparative study of Er3+(4f11) ions performed suggests that polycrystalline ceramic YAG is an excellent alternative to single-crystal YAG rod for certain applications.

Optical intensities of Pr3+ ions in transparent oxyfluoride glass and glass–ceramic. Applications of the standard and modified Judd–Ofelt theories

The optical characterisation of Pr3+ ions in transparent SiO2–Al2O3–CdF2–PbF2–YF3 based glass and glass–ceramic have been performed. From absorption and emission spectra the oscillator strengths of the 4f2–4f2 electronic transitions have been obtained. The intensity parameters have been calculated using both the Judd–Ofelt theory and the modified theory developed by Kornienko, Kaminskii and Dunina. A comparison of the experimental oscillator strengths, the spontaneous emission probabilities and the lifetimes of the 3P0 level and those calculated using the above theoretical procedures has been performed for both samples. The root mean square deviation found using the standard Judd–Ofelt theory is larger than the value obtained with the modified treatment.

Optical transitions, absorption intensities, and intermanifold emission cross sections of Pr3+(4f2) in Ca5(PO4)3F crystal host

A spectroscopic Judd–Ofelt investigation has been performed on Pr3+ ions doped in calcium fluorapatite, Ca5(PO4)3F, belonging to the apatite structure family. The standard Judd–Ofelt analysis was applied to the room temperature absorption intensities of Pr3+ transitions to determine the phenomenological intensity parameters: Ω2, Ω4, and Ω6. Values of the intensity parameters were subsequently used to determine the decay rates (emission probabilities), radiative lifetimes, and branching ratios of the principal intermanifold transitions of Pr3+ from the P23, D21, and P03 manifold states to the lower-lying manifolds. In addition, the room temperature fluorescence lifetimes and emission cross sections of the P23→H53, D21→H43, and P03→F23 transitions were measured; these values were compared with those of Nd3+:yttritium–aluminum–garnet and Pr3+:Sr5(PO4)3 (known as S–FAP).

Optical intensities of Pr3+ ions in transparent oxyfluoride glass and glass?ceramic. Applications of the standard and modified Judd?Ofelt theories

The optical characterisation of Pr 3+ ions in transparent SiO 2 –Al 2 O 3 –CdF 2 –PbF 2 –YF 3 based glass and glass–ceramic have been performed. From absorption and emission spectra the oscillator strengths of the 4f 2 –4f 2 electronic transitions have been obtained. The intensity parameters have been calculated using both the Judd–Ofelt theory and the modified theory developed by Kornienko, Kaminskii and Dunina. A comparison of the experimental oscillator strengths, the spontaneous emission probabilities and the lifetimes of the 3 P 0 level and those calculated using the above theoretical procedures has been performed for both samples. The root mean square deviation found using the standard Judd–Ofelt theory is larger than the value obtained with the modified treatment.

Judd–Ofelt analysis of the Er3+(4f11) absorption intensities in phosphate glass: Er3+, Yb3+

A spectroscopic Judd–Ofelt investigation has been performed on Er3+ in the doubly doped phosphate glass:Er3+, Yb3+ in order to assess its potential as a laser system. The standard Judd–Ofelt model was applied to the room-temperature absorption intensities of Er3+(4f11) transitions to determine the intensity parameters: Ω2=6.28×10−20 cm2, Ω4=1.03×10−20 cm2, and Ω6=1.39×10−20 cm2 in the phosphate glass host. The intensity parameters are used to determine the radiative decay rates (emission probabilities of transitions) and branching ratios of the Er3+ transitions from the excited-state J manifolds to the lower-lying J′ manifolds. The radiative lifetimes of these excited states are determined from the radiative decay rates. The predicted decay rates and radiative lifetimes are compared to those of Er3+ transitions in other glass hosts. The quantum efficiency of the eye-safe laser transition I13/24→4I15/2 (1.54 μm) of Er3+ is approximately 80% in the phosphate glass host.

Stimulated emission and radiative properties of Nd 3+ ions in barium fluorophosphate glass containing sulphate

Spectroscopic properties of Nd 3+ in barium fluorophosphate glassy matrix containing sulphate have been analysed by fitting the experimental data with the standard Judd–Ofelt theory. Various spectroscopic parameters viz. radiative transition probabilities, radiative decay time, fluorescence branching ratios, electric dipole line strengths, stimulated emission cross sections and optical gain of the principal fluorescence transition from the 4F 3/2 metastable level are obtained. Results show that addition of sulphate to the fluorophosphate matrix will enhance the fluorescence spectral properties of Nd 3+ considerably. Quantum efficiency of the 4F 3/2 emission is found to be higher than that of fluorophosphate glasses and stimulated emission cross section of the 4F 3/2→ 4I 11/2 transition is the highest among all reported values. Quantitative estimation of the non-radiative processes such as multiphonon relaxation and quenching by water content was carried out and the results show that the water content is below the critical level for optimum laser performance.

Influence of borate content on the radiative properties of Nd3+ ions in fluorophosphate glasses

Spectroscopic properties of Nd3+ in barium fluoroborophosphate glassy matrix have been analyzed by fitting the experimental data with the standard Judd–Ofelt theory. Various spectroscopic parameters viz. radiative transition probabilities, radiative decay time, fluorescence branching ratios, electric dipole line strengths, stimulated emission cross-sections and optical gain of the principal fluorescence transitions from the 4F3/2 metastable level are obtained. Results show that addition of borate content to the fluorophosphate matrix will reduce the fluorescence spectral properties of Nd3+. However, the radiative properties of the present fluoroborophosphate glassy matrix are found to be well improved over that of pure borate and phosphate matrix and is attributed to the influence of fluorine content in the glassy matrix. The changes in the position and the Judd–Ofelt intensity parameters are correlated with the structural changes in the host glass matrix. The shift of the hypersensitive band shows that the covalency of the rare earth to oxygen bond increases with the increase of Na2O content. This covalency effect and the formation of the BO4 groups with the addition of Na2O content are responsible for the increase in the radiative properties of the present system. Quantitative estimation of the non-radiative processes such as multiphonon relaxation and quenching by water content was carried out and the results show that both are below the critical level for optimum laser performance.

Characterization of spectroscopic and laser properties of Pr3+ in Sr5(PO4)3F crystal

Spectroscopic and laser properties have been characterized for Pr3+ incorporated into Sr5(PO4)3F crystal belonging to the apatite structure family. The standard Judd–Ofelt analysis has been applied to the measured optical absorption intensities to determine the radiative decay rates, branching ratios, and emission cross sections of principal intermanifold transitions of Pr3+ from the D21 and P03 states to the lower-lying manifolds in the visible region. The measured room temperature fluorescence lifetimes of the D21→3H4 (594 nm) and P03→3F2 (625 nm) transition are 325 and 105 μs, respectively, while the Judd–Ofelt analysis predicts the radiative lifetimes for the D21 and P03 states to be 822 and 116 μs, respectively. The room temperature emission cross sections of the D21→3H4 and P03→3F2 intermanifold transitions have been also determined to be 0.54×10−20 and 4.15×10−20 cm2, respectively.

Direct calculation of optical absorption amplitudes for trivalent rare-earth ions inLiYF4

The approximations within the Judd-Ofelt theory are eliminated by an explicit reformulation of the absorption amplitude for $f\ensuremath{\leftrightarrow}f$ dipole transitions in terms of determinantal product states and perturbed functions. By considering the crystal-field and spin-orbit perturbations we obtain expressions for amplitudes of the type $〈{\ensuremath{\varphi}}_{\mathrm{cf}}^{1}|{d}_{q}^{1}|{\ensuremath{\varphi}}^{0}〉,$ $〈{\ensuremath{\varphi}}_{\mathrm{cf}}^{1}|{d}_{q}^{1}|{\ensuremath{\varphi}}_{\mathrm{so}}^{1}〉,$ and $〈{\ensuremath{\varphi}}_{\mathrm{cf}}^{1}|{d}_{q}^{1}|{\ensuremath{\varphi}}_{\mathrm{cf}}^{1}〉.$ The latter two are third-order results, going beyond the standard Judd-Ofelt theory. There are no experimentally fitted parameters used in the amplitude calculations. Crystal-field parameters ${A}_{\mathrm{tp}}$ needed for the intensity calculations are calculated using the self-consistent electrostatic model. Polarized absorption spectra are calculated for ${\mathrm{Nd}}^{3+},$ ${\mathrm{Ho}}^{3+},$ ${\mathrm{Er}}^{3+},$ or ${\mathrm{Tm}}^{3+}$ in ${\mathrm{LiYF}}_{4}.$ Very good agreement with experiment is, in general, observed. The contribution from the third-order terms $〈{\ensuremath{\varphi}}_{\mathrm{cf}}^{1}|{d}_{q}^{1}|{\ensuremath{\varphi}}_{\mathrm{so}}^{1}〉$ and $〈{\ensuremath{\varphi}}_{\mathrm{cf}}^{1}|{d}_{q}^{1}|{\ensuremath{\varphi}}_{\mathrm{cf}}^{1}〉$ are seen to be small in comparison with $〈{\ensuremath{\varphi}}_{\mathrm{cf}}^{1}|{d}_{q}^{1}|{\ensuremath{\varphi}}^{0}〉.$

Spectroscopic characterization of Nd3+ ions in barium fluoroborophosphate glasses

Abstract Spectroscopic properties of Nd3+ in barium fluoroborophosphate glassy matrix have been analyzed by fitting the experimental data with the standard Judd–Ofelt theory. Various spectroscopic parameters, viz. radiative transition probabilities, radiative decay time, fluorescence branching ratios, electric dipole line strengths, stimulated emission cross-sections and optical gain of the principal fluorescence transition from the 4 F 3/2 metastable level were obtained to evaluate the potential of the samples as laser material. Results show that addition of borate content to the fluorophosphate matrix will reduce the fluorescence spectral properties of Nd3+. However, the radiative properties of the fluoroborophosphate glassy matrix are found to be well improved over those of pure borate and pure phosphate matrix and are attributed to the influence of fluorine content in the glassy matrix. Quantitative estimation of the non-radiative processes such as multiphonon relaxation and quenching by water content shows that the first process is absent in our sample while the water content is found to be below the critical level for optimum laser performance.

Judd–Ofelt theory in a new light on its (almost) 40th anniversary

The standard Judd–Ofelt theory of one photon electric dipole transitions in f N systems is discussed in the language of the one particle parametrization scheme. An overview of various physical mechanisms that contribute to the Judd–Ofelt intensity parameters is performed. The analysis of the morphology of these parameters is based on the static model of their original derivation, dynamic model, electron correlation third order approach, spin–orbit interaction influence, and an exotic perturbation caused by a specific mass shift. As a new aspect of the investigations on the physical nature of f↔f transitions, a transformation of the Judd–Ofelt effective operators to their relativistic version is presented. In this approach the transition amplitude is expressed by the effective double tensor operators, acting within the 4f N shell, and effectively representing relativistic contributions. In particular, the relativistic form of the crystal field potential is employed, and in addition, the interactions through the crystal field potential within the spin–orbital space are included.

Relativistic f↔f transitions in crystalfields

A relativistic model of f↔f transitions based on thetransformation of all intershell tensor operators to effectiverelativistic double tensor operators is developed. Thetransition amplitude is expressed in terms of effectiveoperators acting within the fN shell due to a partialclosure performed upon the relativistic intershell operators.The final expression is discussed in the light of its reductionto the non-relativistic case that describes f↔ftransitions in the language of the standard Judd-Ofelt theory.

4f–4f intensities of the Tm3+ ions in fluoroindate glasses: the influence of third-order effects through odd intensity parameters

In this work an analysis of the phenomenological Ωλ intensity parameters for the Tm3+ ion in fluoroindate glass is made using the standard Judd–Ofelt theory, and a modified oscillator strength taking into account odd-order contributions is utilized. Different sets of phenomenological intensity parameters Ωλ (λ=1,2,3,4,5,6) are discussed. The set of better quality is used to analyze the influence of third-order effects through odd intensity parameters in the new approximation. Fluoroindate glasses of compositions (40−x)InF3–20ZnF2–20SrF2–16BaF2–2GdF3–2NaF–xTmF3 with x=1, 2 and 3 mol% were prepared, and the absorption spectra at room temperature in the spectral range from 300 to 2500 nm were obtained. The experimental oscillator strengths determined from the area under the absorption band are compared to the calculated ones.

Comparison Between Standard and Modified Judd-Ofelt Theories in a Pr3+-Doped Fluoride Glass

Α method which takes into account normalized oscillator strengths is detailed for the calculation of parameters in Judd-Ofelt theory (B.R. Judd, Phys. Rev. 127, 750 (1962), G.S. Ofelt, J. Chem. Phys. 37, 511 (1962)). In the case of a Pr3+ -dopaed fluorozirconate glass, the Judd-Ofelt parameters obtained in this way do not depend strongly on the transitions included in the frt. Particularly, it is no longer necessary to exclude the 3H4 → 3Ρ2 transition from tle analysis. Three modifred theories (F. Auzel, S. Hubert, P. Delamoye, J. Lumin. 26, 251 (1982), A.A. Kornienko, A.A. Kaminskii, E.B. Dunina, Phys. Status Solidi B 157, 267 (1990)) are also considered but do not improve the calculated intensities when the energy of the 5d level is set to its experimentally determined value. Finally, in connection with 1.3 μm amplification, the 1.3 hn1 reabsorption ( 1i.4 → 1D2) oscillator strength is computed from the various models as well as the 1.3 /im emission branching ratio ( 1G4 --> 3H5/ 1G4 — 3H6). The best agreement with experiment is obtained with the standard Judd-Ofelt theory.

Application of standard and modified Judd–Ofelt theories to a praseodymium-doped fluorozirconate glass

A method which takes into account normalized oscillator strengths is detailed for the calculation of parameters in Judd–Ofelt theory (B. R. Judd, Phys. Rev. 127, 750 (1962), G. S. Ofelt, J. Chem. Phys. 37, 511 (1962)). In the case of a Pr3+-doped fluorozirconate glass, the Judd–Ofelt parameters obtained in this way do not depend strongly on the transitions included in the fit. Particularly, it is no longer necessary to exclude the 3H4→3P2 transition from the analysis. Two modified theories [F. Auzel, S. Hubert, and P. Delamoye, J. Lumin. 26, 251 (1982), and A. A. Kornienko, A. A. Kaminskii, and E. B. Dunina, Phys. Stat. Solidi. 157, 267 (1990)] are also considered but do not improve the calculated intensities when the energy of the 5d level is set to its experimentally determined value. Finally, in connection with 1.3 μ amplification, the 1.3 μ reabsorption (1G4→1D2) oscillator strength is computed from the various models as well as the 1.3 μ emission branching ratio (1G4→3H5/1G4→3H6). The best agreement with experiment is obtained with the standard Judd–Ofelt theory.

An alternative formulation of the Judd-Ofelt theory of f ↔ f transitions

A contribution is made to the discussion about the choice between length and velocity formulae which describe the interaction between matter and a radiation field. The analysis is illustrated by the Judd-Ofelt theory of one-photon electric dipole transitions between the levels of 4f N configuration of rare earth ions in crystals. The standard effective operators which contribute to the transition amplitude are one-particle tensor operators of even rank and are defined within the electric gauge of an electromagnetic field. When the radiation gauge is applied, the transition amplitude is determined by new effective operators which are of odd rank. The latter are one-, two- and three-particle objects and are caused by the non-local character of the Hartree-Fock potential of the zeroth-order hamiltonian defined within the central field approximation. The new effective operators are expressed in terms of the so-called perturbed functions; it is demonstrated that their angular factors and radial terms are of the same general structure as in the case of effective operators of the standard Judd-Ofelt theory.

Theoretical intensities of 4f-4f transitions between stark levels of the Eu 3+ ion in crystals

We report a theoretical calculation of the intensities of the 4f-4f transitions between Stark levels of the Eu 3+ ion in KY 3F 10, LiYF 4 and LaOCl hosts. A ligand field Hamiltonian, described by a simple overlap model, is initially applied to oxychlorides, oxybromides and fluorides doped with the Eu 3+ ion. Since for the even rank ligand field parameters, there is a significant improvement with respect to the crude electrostatic approximation, this model is also used in the evaluation of the odd rank parameters required in the intensity calculations. The average energy denominator method used by Bebb and Gold to treat multi-photon ionization processes in hydrogen and rare gas atoms is used here as an alternative procedure to evaluate the electric dipole matrix elements. The results are in good agreement with those given by the standard Judd-Ofelt theory. Only the forced electric dipole mechanism up to second order and the dynamic coupling are taken into account. Emphasis is given to the fact that these two mechanisms should contribute with the same sign to the B λtp intensity parameters, in contrast with theoretical calculations currently found in the literature. Comparison with experimental values points to the neglect of higher order corrections to these two mechanisms, and the use of a still incomplete representation of the ligand field as the reason for the discrepancies between theory and experiment.