Comparison of the Luminescence Properties of Dy3+ in α-Sialon and Oxynitride Glass

Dy-α-sialon and β-Si₃N₄ materials containing Dy-oxynitride glass were hot pressed at 1800°C for 1 h. The luminescence spectra of Dy³⁺ in these samples were compared when excited at 350 nm. The results showed that two strong emission bands in the region 470–500 nm and 570-600 nm, associated with the ⁴F_9/2→⁶H_15/2 and ⁴F_9/2→⁶H_13/2 transitions of Dy³⁺ ions, were observed in Dy-α-sialon. However, no emission peak was detected from the β-Si₃N₄ sample, despite it containing the same amount of Dy³⁺ cations. This proved that only the Dy³⁺ cations in the α-sialon structure, not those in the oxynitride glass, produce the luminescence spectrum.     

Judd-Ofelt Parameters, Hypersensitivity, and Emission Characteristics of Ln3+ (Nd3+, Ho3+, and Er3+) Ions Doped in PbO-PbF2 Glasses

The Judd–Ofelt parameters, Ω₂ and ΣΩ_λ (λ= 2, 4, 6), for Nd³⁺, Ho³⁺, and Er³⁺ doped in the oxyfluoride glass 30PbO70PbF₂ lie intermediate between fluoride glasses and oxide glasses such as borate and phosphate glasses, providing evidence for the sensitivity of these parameters to the bonding environment. The variation of Ω₂ unlike Ω₄ and Ω₆ for the lanthanide series is qualitatively different for glass matrices compared to crystalline matrices. Plots of oscillator strengths of hypersensitive transitions for these ions against ΣΩ_λ (λ= 2, 4, 6) are found useful in discerning the degree of hypersensitivity of these transitions due to change in the host matrix. The ⁵F₂³K₈⁵G₆←⁵I₈ transition of Ho³⁺ is found to be the most hypersensitive. The radiative parameters for the oxyfluoride glasses are close to fluoride glasses and the branching ratio of the important lasing transition, viz., ⁴F_3/2→⁴I_11/2, of Nd³⁺ is higher for the present case compared to fluoride glass. The results suggest that the oxyfluoride glasses may be used as hosts in the place of fluoride glasses wherever suitable as they are more stable and easy to prepare and have similar radiative properties.     

Energy Transfer and Population Inversion in Heavy Metal Oxide Glasses Doped with Tm3+ and Tb3+

Emission properties and energy transfer of PbO–Bi₂O₃–Ga₂O₃–GeO₂ glasses codoped with Tm³⁺ and Tb³⁺ ions were investigated. The 1.48-μm emission due to the Tm³⁺:³H₄→³F₄ transition can be used to amplify the S-band (1460–1530-nm) signal light. With Tb³⁺ addition, the lifetime and emission intensity of the Tm³⁺:³F₄ level decreased sharply via the Tm³⁺:³F₄→Tb³⁺:⁷F_0,1,2 energy transfer. Population densities of the ³F₄ and ³H₄ levels in Tm³⁺ calculated from rate equations clearly verified that population inversion in Tm³⁺ ions became possible with as little as 0.1 mol% of Tb³⁺ addition.     

Compositional Dependence of Infrared-to-Visible Upconversion in Yb3+- and Er3+-Codoped Germanate, Gallate, and Tellurite Glasses

Upconversion fluorescences of the green ⁴S_3/2→⁴I_15/2 and red ⁴F_9/2→⁴I_15/2 transitions of the Er³⁺ ion are studied for Yb³⁺- and Er³⁺-codoped sodium germanate, potassium tantalum gallate, and barium tellurite glasses by InGaAs laser-diode pumping. The phonon energies of the host glasses are determined by infrared-reflection measurements. Compositional effects on the Judd—;Ofelt parameters for the Er³⁺ ion, the spontaneous emission probability (SPE) of the ²F_5/2→²F_7/2 transition for the Yb³⁺ ion, and the phonon energy of the glass network are discussed in terms of glass structure. The factors that affect the upconversion fluorescence intensities of the Er³⁺ ion are discussed, using the phonon energy of the host glass and the SPE for the Yb³⁺ ion in the germanate, gallate, and tellurite glasses.     

Tellurite Glasses for Broadband Amplifiers and Integrated Optics

The present investigation discusses the advantage of using RE-ion-doped (Nd³⁺, Tm³⁺, and Er³⁺) TeO₂ glasses for developing fiber and planar broadband amplifiers and lasers. The spectroscopy of RE-ion-doped fibers and glasses is discussed along with the thermal properties of glass hosts. The results of emission from the ³H₄ level in single-mode Tm³⁺-doped tellurite fiber show that the emission band overlaps with Er³⁺ emission from the ⁴I_13/2 level and Nd³⁺ emission from the ⁴F_3/2 level in silicate and tellurite glasses, thereby enabling the development of amplifiers and lasers between 1350 and 1650 nm. Recent results using Z-scan measurements of nonlinear refractive index and absorption demonstrate that the third-order nonlinearity in undoped TeO₂ glasses is of the order of 2 × 10⁻¹⁵ to 3 × 10⁻¹⁵ cm²·W⁻¹ between 1300 and 1550 nm. These results are briefly discussed in view of an amplifier operation combined with ultrafast all-optical switching.     

Compositional Dependence of Judd-Ofelt Parameters in Silicate, Borate, and Phosphate Glasses

Judd-Ofelt parameters Ω _t with t = 2,4, 6 for the rare-earth ions Pr³⁺, Nd³⁺, Sm³⁺, Tb³⁺, Dy³⁺, Ho³⁺, Er³⁺, and Tm³⁺ in alkali and/or alkaline-earth silicate, borate, and phosphate glasses have been determined. The variations of Ω _t with the number of 4 f electrons of the rare-earth ions are demonstrated, and factors affecting the Judd-Ofelt parameter Ω₆are discussed. The intensity parameter Ω₆ depends on the ionic packing ratio of the glass host by changing modifier type in silicate and borate glasses, and it is independent of that in a series of borate glasses as a function of modifier content and phosphate glasses. The peak wavenumbers of the transitions whose intensities are determined mainly by the Ω₆<| U ⁽⁶⁾|>² term—where <| U ⁽⁶⁾|> is one of the reduced matrix elements—shift systematically with the values of Ω₆ for all the rare-earth ions.     

Dy:YAG Phosphor Coating Using the Solution Precursor Plasma Spray Process

Dy:YAG phosphor coatings were deposited using the solution precursor plasma spray process. The phase composition, microstructure, and photoluminescent properties of the as-deposited coatings were investigated. X-ray diffraction analysis confirmed that the coating is mainly composed of the YAG phase with a small amount of an intermediate YAP phase. Scanning electron microscopy micrograph revealed that the as-sprayed coating has columnar structures with a thickness of ∼60 μm. The measurement of photoluminescent properties indicated that the phosphor coating exhibits two predominant emission regions: a blue region (470–500 nm) and a yellow region (560–600 nm), which are assigned to ⁴F_9/2–⁶H_15/2 and ⁴F_9/2–⁶H_13/2 transitions, respectively.     

Correlation between Radiative Transition Probabilities of Nd3+ and Composition in Silicate, Borate, and Phosphate Glasses

Compositional dependence of spontaneous emission probabilities between initial ⁴ F _3/2 and terminal ⁴ I _J J = 9/2, 11/2, 13/2, 15/2) levels of Nd³⁺ were studied for about 90 samples of silicate, borate, and phosphate glasses using the Judd–Ofelt theory. The effect of the covalency of the Nd–O bond on the magnitude of intensity parameters was estimated from the variation of spectral profiles of the ⁴ I _9/2→⁴ G _5/2, ² G _7/2 and ⁴ F _7/2, ⁴ S _3/2 transitions. Intensity parameters Ω₄ and Ω₆ and the spontaneous emission probabilities were strongly affected by the ionic packing ratio of the glass host. The results were discussed in terms of the site selectivity of Nd³⁺ ions in glasses.     

Pr3+/Er3+ Codoped Ge-As-Ga-S Glasses as Dual-Wavelength Fiber-optic Amplifiers for 1.31 and 1.55 μm Windows

Fluorescence emissions at both 1.31 and 1.55 μm communication windows were observed from Pr³⁺/Er³⁺ codoped Ge-As-Ga-S glasses with a single wavelength pumping at 986 nm. The lifetime of the Er³⁺:⁴ I _11/2 level decreased as the Pr³⁺ concentration increased, and that of the Pr³⁺:¹ G ₄ level increased as the Er³⁺ concentration increased. Energy transfer from the Er³⁺:⁴ I _11/2 level to the Pr³⁺:¹ G ₄ level was responsible for emission of the 1.31 μm fluorescence from the Pr³⁺:¹ G ₄ level. Ge-As-Ga-S glasses that have been doped with Pr³⁺ and Er³⁺ cations are promising amplifier materials for both 1.31 and 1.55 μm communication windows.     

Populations and Emission Properties of the 5I6 and 5I7 Levels in Ho3+ Doped into PbO–Bi2O3–Ga2O3 Glasses

Emission properties of PbO–Bi₂O₃–Ga₂O₃ glasses doped with Ho³⁺ were investigated for fiber-optic amplification at the 1.18 μm wavelength region. When the glasses were doped with Ho³⁺ ions only, there was a weak emission at 1.18 μm with a lifetime of ∼200 μs. However, when Yb³⁺ ions were codoped, the lifetime of the 1.18 μm emission increased to 630 μs together with a significant increase in intensity. A similar enhancement in the intensity and lifetimes was realized for the 2.05 μm emission. These effects are due to energy transfer from the Yb³⁺:²F_5/2 to the Ho³⁺:⁵I₆ level. Devitrification of the ternary PbO–Bi₂O₃–Ga₂O₃ glasses was efficiently suppressed by adding 10 mol% GeO₂. Optimum Ho³⁺ concentration was ∼0.4 mol%, whereas Yb³⁺ ions can be added up to the solubility limit.     

Conduction and Dielectric Loss Mechanisms in β-Alumina and Glass: A Discussion Based on the Paired Interstitialcy Model

A paired interstitialcy model is used as a basis for qualitative comparisons of conductivity and dielectric phenomena in β-alumina crystals and in glass. Thus, the increase in the conductivity of sodium silicate glasses with increasing Na₂O activity can be explained if the concentration of (Na₂*)²⁺ interstitial pairs increases with increased polarizability of O^2- ions, expressed in terms of the optical basicity parameter, Δ. Similarly, the occurrence of the pronounced minima in conductivity isotherms (the mixed-alkali effect in glass) is attributed to disappearance of mobile interstitial pairs, e.g. (Li₂*)²⁺ or (K₂*)²⁺, and the stabilization (by polarization interactions) of apparently immobile mixed-alkali pairs, (LiK*)²⁺. The phenomenon of coionic conduction in certain β-alumina crystals is an interesting departure from this general pattern. The orientation dependence of the electrical modulus spectrum of monocrys-talline β-alumina highlights the presence of a bimodal distribution of relaxation times, in which the low-frequency component ( v ₀=10¹¹ Hz) may arise from the rearrangement of interstitial pairs and the high-frequency component ( v ₀=2×10¹² Hz) may arise from less hindered ionic motions. It is suggested that the motions of interstitial pairs and surrounding cations are mutually catalytic and that some form of combined motion is responsible for both the electrical and mechanical relaxations in β-alumina and glass.     

Spectroscopic Properties and Thermal Stability of Er3+-Doped Germanotellurite Glasses for Broadband Fiber Amplifiers

The thermal stability and spectroscopic properties of Er₂O₃-doped TeO₂–GeO₂–ZnO–Na₂O–Y₂O₃ glasses for 1.5 μm fiber amplifiers were investigated. The thermal stability of the 75TeO₂·20ZnO· 5Na₂O glass was improved by introducing GeO₂ and Y₂O₃. The radiative transition and the nonradiative transition have a dominant influence on the ⁴I_13/2 level lifetime of Er³⁺ in high- and low-GeO₂ regions, respectively. Adding Y₂O₃ increases the ⁴I_13/2 level lifetime of Er³⁺ significantly. The Judd–Ofelt (J-O) parameter Ω₆ shows a strong correlation with the 1.5 μm emission bandwidth; and the larger the Ω₆, the wider the bandwidth.     

Refractive-Index Dispersion of Tellurite Glasses in the Region from 0.40 to 1.71 μm

The refractive index of binary tellurite glasses with various modifiers was measured down to the fifth decimal place in the wavelength range of 0.40–1.71 μm using the minimumedeviation method. An empirical equation based on the single-oscillator Drude–Voigt dispersion equation. n _d²= A·Nf λ₀²+ B , is obtained, where n _d is the refractive index at 0.5876 μm, N is the number of molecules in a unit volume, f is the average oscillator strength, λ₀ is the average resonance wavelength, and A and B are constants. The refractive index n _d of tellurite glasses is substantially determined by the resonance wavelength at the ultraviolet region, which is affected by the main constituent, TeO₂.     

Energy Transfer Process for the Blue Up-Conversion in Calcium Aluminate Glasses Doped with Tm3+ and Nd3+

Excitation of Tm³⁺ to ³ H ₄ using the 791 nm pump source showed the frequency up-converted blue emission (∼480 nm) due to the Tm³⁺:¹ G ₄→³ H ₆ transition in Tm³⁺/Nd³⁺ codoped CaO·Al₂O₃ glasses. Intensity and lifetime changes with rare-earth concentrations suggested the efficient energy transfer of Tm³⁺:³ H ₄→ Nd³⁺:⁴ F _5/2 and Nd³⁺:⁴ F _3/2→ Tm³⁺:¹ G ₄. The latter transfer enabled Tm³⁺ to reach its ¹ G ₄ level, and the blue emission became possible through the ¹ G ₄→³ H ₆ transition. Quantitative analysis with rate equations proved that these two transitions were the most efficient among all the possible energy transfer routes between Tm³⁺ and Nd³⁺. Calculated up-conversion efficiency of the Tm³⁺/Nd³⁺ combination in CaO·Al₂O₃ glass was 6.6 × 10⁻³, and it was ∼4 orders of magnitude larger than those reported for other oxide glasses.     

Compositional Dependence of Absorption and Fluorescence of b3+ in Oxide Glasses

The integrated absorption cross section, the spontaneous emission probability, and the stimulated emission cross section of Yb³⁺ were determined in silicate, phosphate, borate, germanate, aluminate, gallate, and ZBLAN host glasses. The compositional dependence of the stimulated emission cross section of the ²F_5/2→²F_7/2 transition is determined mainly by the integrated absorption cross section in the glasses. A peak stimulated emission cross section above 1 pm², which is the highest value in glasses, was obtained in a gallate glass with a composition of 40K₂O·20Ta₂O₅. 40Ga₂O₃. The factors affecting the integrated absorption cross section are discussed using the Judd-Ofelt parameters of Er³⁺ calculated in previous studies.     

THIRD-ORDER ASYMPTOTIC PROPERTIES OF ESTIMATORS IN GAUSSIAN ARMA PROCESSES WITH UNKNOWN MEAN

Abstract. This paper deals with the third-order asymptotic theory for Gaussian autoregressive moving-average (ARMA) processes with unknown mean μ. We are interested in the estimation of ρ = ( α₁…, α_p, β₁…, β_q ), where α ₁…, α_ρ and β ₁…, β_q are the coefficients of the autoregressive part and the moving-average part, respectively. First, we investigate the third-order asymptotic optimality of the bias adjusted maximum likelihood estimator (MLE) of ρ in the presence of the nuisance parameters μ and ² (innovation variance). Next, for a Gaussian AR(1μ μ, ²), we propose a mean corrected estimator α_c1c2 of the autoregressive coefficient. We make a comparison between the bias adjusted estimator α_c1c2* and the bias adjusted MLE, in terms of their probabilities of concentration around the true value, or equivalently, in terms of their mean squared errors. Finally some numerical studies are provided in order to verify the third-order asymptotic theory.     

Effect of Network Modifier on Spontaneous Emission Probabilities of Er3+ in Oxide Glasses

Compositional dependence of spontaneous emission probabilities of Er₃₊ was studied for silicate, borate, and phosphate glasses using the Judd–Ofelt theory. Through all of the glass systems, spontaneous emission probabilities of the ⁴ I _13/2→⁴ I _15/29→⁴ I _9/2→⁴ I _J, and ⁴ S _3/2→⁴ I _J ( J = 9/2, 11/2,13/2,15/2) transitions increased with increased ionic packing ratio of the glass host, which varied markedly with the type of network modifier. The effect of Er–O covalency on the transition probabilities was discussed from the spectral profile of the ⁴ I _15/2→⁴ I _3/2transition in terms of nephelauxetic effect.     

Upconversion Luminescence in γ-AlON:Yb3+,Tm3+ Ceramic Phosphors

Upconversion emission properties of γ-AlON:Yb³⁺,Tm³⁺ phosphors were investigated under single-wavelength diode laser excitation of 980 nm. Blue (479 nm) and red (653 nm) emission bands were observed which correspond to the transitions of ¹G₄→³H₆ and ¹G₄→³F₄ of Tm³⁺ ions, respectively. The upconversion spectra show a concentration-dependent luminescence intensity, reaching its peak at a concentration of 1.2 mol% Yb and 0.5 mol% Tm. Pump power dependence of the upconversion emission intensity ( P – I ) revealed that a two-photon process was involved in the blue and red emissions.     

Structure and Nonlinear Optical Properties of Lanthanide Borate Glasses

The third–order nonlinear optical susceptibility, χ⁽³⁾, of lanthanide (lanthanum, praseodymium, neodymium, and samarium) borate glasses has been measured by the third harmonic generation method. The structure of the present glass system has been studied by infrared and Raman spectroscopic methods. The network structures of the present Ln₂O₃–B₂O₃ glasses have been confirmed to be basically similar to each other. Praseodymium, neodymium, and samarium borate glasses exhibit χ⁽³⁾ values that are larger than lanthanum borate glasses, because of the optical resonance effect, in accordance with the f – f transition. Especially, the χ⁽³⁾ value for 30Pr₂O₃·70B₂O₃ glass is 1.8 × 10⁻¹² esu, which is a factor of ∼60 larger than that of SiO₂ glass. This striking enhancement of χ⁽³⁾ is mainly attributed to the large transition moment to the first excitation state.     

Estimation in nonstationary random coefficient autoregressive models

Abstract.  We investigate the estimation of parameters in the random coefficient autoregressive (RCA) model X _k  = ( φ  +  b _k ) X _{k −1} +  e _k , where ( φ ,  ω ²,  σ ²) is the parameter of the process,     ,     . We consider a nonstationary RCA process satisfying E  log | φ  +  b ₀| ≥ 0 and show that σ ² cannot be estimated by the quasi-maximum likelihood method. The asymptotic normality of the quasi-maximum likelihood estimator for ( φ ,  ω ²) is proven so that the unit root problem does not exist in the RCA model.