f4—f7的波函数

本文用算子L⁺,S⁺,Q,R求得了f^4-7的波函数。并讨论了通过表象变换计算库仑能、自旋轨道作用和晶场,以及使希土离子能量矩阵对角化的方案。     

Intracavity frequency-doubled diode-pumped Nd : LaSc3(BO3)4 lasers

 An intracavity frequency-doubled 10%Nd : LaSc₃(BO₃)₄ (Nd : LSB) laser was investigated in different resonator configurations and in different operation modes under continuous wave (cw) and quasi-cw laser-diode pumping. With a Cr⁴⁺ : YAG passive modulator and a KTP crystal the second-harmonic output power at 531 nm amounted to 190 mW in Q-switched TEM₀₀ mode at 750 mW of pump power. In a sandwich resonator, when all the optical elements were in direct contact with each other, 0.8 W of green output power was obtained in cw mode under 2.7 W of pump power with a slope efficiency of 44%. In the same setup under fiber-coupled diode-laser array pumping (5.6 W of incident power), 1.2 W of green output power was achieved in cw mode and 1.4 W in quasi-cw mode. Received: 30 April 1996/Revised version: 1 July 1996     

New green self-frequency-doubling diode-pumped Nd:Ca4GdO(BO3)3 laser

3+ :Ca₄GdO(BO₃)₃ (Nd:GdCOB). 21 mW of green cw laser emission for an absorbed pump power of 820 mW were achieved under laser diode-pumping. 64 mW of green cw laser output were obtained with 1 W of absorbed pump power under titanium-sapphire pumping. Its availability in large-size crystals with good optical quality makes Nd:GdCOB a true challenger to the best SFD laser crystal reported so far: Nd:YAl₃(BO₃)₄ (Nd:YAB or NYAB). Received: 2 March 1998/Revised version: 20 May 1998     

Type-I non-critically phase-matched second-harmonic generation in Gd1-xYxCa4O(BO3)3

Second-harmonic generation was z-cut observed Gd_1-xY_xCa₄O(BO₃)₃ (Gd_1-xY_xCOB) and the dependence of the phase-matching wavelength on the mixing ratio x has been investigated. The dependence on both temperature and angle tuning was examined as well. We found the suitable composition for noncritical frequency doubling at 930 nm, which is the lasing wavelength of Nd:YAlO₃ on the ⁴F_3/2?⁴I_9/2 transition. Received: 19 April 1999 / Published online: 5 May 1999     

Gd1-xEuxAl3(BO3)4纳米晶的合成及其发光性能

以高温固相反应法合成了Gd_1-xEu_xAl₃(BO₃)₄:Eu³⁺纳米荧光粉。使用XRD分析确定了样品的物相,并根据谢乐公式计算出其微晶的纳米粒度。采用了“粉末悬浮法”以甘油为分散介质,在RF540荧光光度计上测试了纳米晶荧光粉的激发光谱和发射光谱。GdAl₃(BO₃)₄基质本身发光,GdAl₃(BO₃)₄:Eu纳米荧光粉表现了Eu³⁺的特征发射光谱,其中最强峰为⁵D₀→⁷F₂发射,表明晶体结构中没有对称中心格位。实验表明在GdAl₃(BO₃)₄:Eu纳米晶荧光粉中,存在Gd³⁺对Eu³⁺发光的基质敏化作用。     

Generation of tunable 187.9-196-nm radiation in beta-Ba(2)BO(4)

Tunable 187.9-196-nm vacuum-ultraviolet radiation was generated at room temperature in a beta barium borate crystal by sum-frequency mixing of Nd:YAG laser radiation and the second harmonic of a dye laser pumped by the second harmonic of the same Nd:YAG laser. By use of the advantageous noncollinear phase-matching configuration, a peak power of 1.3 kW was obtained at 194 nm with input power densities as low as 79MW/cm(2) for 1064-nm and 0.65MW/cm(2) for 237.3-nm radiation.     

Specific heat of YFe3(BO3)4, Y0.5Gd0.5Fe3(BO3)4, and GdFe3(BO3)4

The specific heat was measured in the range 0.4–300 K in YFe₃(BO₃)₄, Y_0.5Gd_0.5Fe₃(BO₃)₄, and GdFe₃(BO₃)₄ single crystals. Sharp anomalies were found at temperatures of first-order structural, second-order antiferromagnetic, and first-order spin-reorientational transitions. A Néel temperature of about 37 K was found to be virtually independent of presence of rare-earth ions, indicating rather weak coupling of Gd and Fe subsystems. The contribution of the magnetic system to specific heat was separated through the scaling procedure allowing determination of the magnetic entropy of Fe and Gd subsystems. At the lowest temperatures, the specific heat in GdFe₃(BO₃)₄ exhibits a Schottky-type anomaly, which is due to Gd³⁺ eightfold degenerate ground-level splitting by the internal magnetic field of the Fe subsystem of about 7 T. The text was submitted by the authors in English.     

Linear electro-optic properties of YCa4O(BO3)3

We have characterized the effective linear electro-optic coefficients of YCa4O(BO3)3 (YCOB) relative to KH2PO4 and KD2PO4 at 632.8 nm. We measured a maximum r(eff) value of 10.8 +/- 1.4 pm/V for YCOB in a transverse electric field configuration for propagation along the X or the alpha dielectric axis, with the electric field applied along the Z or the gamma dielectric axis. We also found effective coefficients of 10.7 +/- 1.0 and 3.4 +/- 0.4 pm/V for YCOB in longitudinal configurations. The remaining values of r(eff) for various transverse applied voltages were found to be less than 3 pm/V. The excellent thermomechanical properties of this crystal, coupled with moderate electro-optic coefficients, make YCOB and its isomorphs potential candidates for use as high-average-power electro-optic switches.     

6 MHz BAW resonators fabricated using new piezoelectric crystals PrCa4O(BO3)3 and NdCa4O(BO3)3

Thickness shear mode Bulk Acoustic Wave (BAW) resonators with frequency of 6 MHz, were fabricated using monoclinic piezoelectric crystals PrCa₄O(BO₃)₃ (PrCOB) and NdCa₄O(BO₃)₃ (NdCOB). Zero temperature coefficient of frequency (TCF) characteristics were achieved over the temperature range of –140 °C to 200 °C for (YXt)–1.5° cut PrCOB and (YXt)15° cut NdCOB, with the turnover temperature at 20 °C. The electromechanical coupling factor k₂₆ and the piezoelectric coefficient d₂₆ were determined to be 30.2% and 15.8 pC/N for PrCOB, 29.0% and 15.1 pC/N for NdCOB resonators, respectively. The temperature independent frequency behavior, large coupling factor, high piezoelectric coefficient, together with noticeable mechanical quality factors (Q > 2,500), make PrCOB and NdCOB crystals good candidates for sensing applications with expanded temperature usage range. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Spectroscopic properties and structure of the ErFe3(BO3)4 single crystal

Single crystals of the ErFe₃(BO₃)₄ borate were synthesized and their structure was studied. Absorption spectra of the Er³⁺ ion in σ- and π-polarizations of f-f transitions ⁴ I _15/2 → ⁴ I _13/2, ⁴ I _11/2, ⁴ I _9/2, ⁴ F _9/2, ⁴ S _3/2, ² H _11/2, and ⁴ F _7/2 were measured. The refractive index and birefringence were measured as a function of the wavelength. The transition intensities were analyzed within the Judd-Ofelt theory, and the following parameters of the theory were obtained: Ω₂ = 7.056 × 10^?20 cm², Ω₄ = 1.886 × 10^?20 cm², and Ω₆ = 2.238 × 10^?20 cm². Using these parameters, the radiative transition probabilities, luminescence branching ratios, and radiative lifetimes of multiplets were calculated.     

Vibrational spectra and elastic,piezoelectric, and magnetoelectric properties of HoFe3(BO3)4 and HoAl3(BO3)4 crystals

Raman spectra of light are obtained for HoFe₃(BO₃)₄ and HoAl₃(BO₃)₄ crystals at various temperatures and are used for determining the frequencies of crystal lattice vibrations at the center of the Brillouin zone. It is also found that the HoFe₃(BO₃)₄ crystal exhibits a phase transition at T _c ≈ 366 K. The magnetoelectric effect in the paramagnetic phase of these compounds is studied experimentally. The lattice vibration frequencies, elastic and piezoelectric moduli, Born dynamic charges, and the high-frequency permittivity are calculated using the density functional method. A peculiar behavior of the transverse acoustic vibration branch is observed in the Γ → Z direction of the Brillouin zone of the HoFe₃(BO₃)₄ crystal. The electric polarization induced by an external field is estimated using the calculated values of piezoelectric moduli and experimental values of magnetostriction.     

Thermo-optic characterization of Yb:YAl3(BO3)4 laser crystal

Principal thermo-optic coefficients, dn _o/dT and dn _e/dT, are determined for 7at.%Yb: YAl₃(BO₃)₄ crystal by the use of a minimum deviation method, modified for anisotropic, optically uniaxial crystals. Direct measurements are accompanied by modeling of the dn/dT versus light wavelength dependence, yielding analytic thermo-optic dispersion formulae for the spectral range of 0.4–1.6 μm. At the wavelength of 1030 nm, dn _o/dT = 3.5 and dn _e/dT = 6.0 [10^?6 K^?1]. Sellmeier formulas are evaluated for the principal refractive indices n _o and n _e. The thermal coefficients of the optical path are determined for the principal crystal cuts of Yb:YAl₃(BO₃)₄, a-cut and c-cut, and light polarizations, π or σ. Finally, thermal lens parameters are evaluated for Yb:YAl₃(BO₃)₄ crystals on the basis of measured material parameters.     

Theoretical Studies of Energy Spectra and g Factors of Cr3+-Doped YAl3(BO3)4

With the strong-field scheme and trigonal bases, by diagonalizing the complete d³ energy matrix in a trigonally distorted cubic-field, the energy spectra and wavefunctions of YAl₃(BO₃)₄:Cr³⁺ have been calculated. The rates of change of levels with respect to various parameters and the contributions to levels from various parameters are calculated, and the physical origins of various levels or splittings have been clearly and quantitatively shown. By using the wavefunctions obtained from diagonalizing the complete energy matrix, the g factors of the ground state of YAl₃(BO₃)₄:Cr³⁺ have been evaluated. The calculated results are in good agreement with the optical-spectral and EPR experimental data. It is demonstrated that the bonding between Cr³⁺ and ligands (O^2-) is ionic.     

Investigation of intracavity third-harmonic generation at 1.06 μm in YCa4O(BO3)3 crystals

Intracavity sum-frequency mixing of 1.06 μm and 532 nm in YCa₄O(BO₃)₃ (YCOB) crystals cut for different type-I phase-matching directions of (θ,ϕ)=(106°,77.2°), (111°, 79.6°) and (65°, 82.8°) was investigated in a compact diode-end-pumped acousto-optical Q-switched Nd:YVO₄/KTP laser formed with a three-mirror folded resonator. The maximum 355-nm average output power of 124 mW was obtained in the phase-matching direction of (106°, 77.2°) with a pump-to-ultraviolet conversion efficiency of 3.3% at the repetition frequency of 20 kHz. Received: 17 September 2001 / Revised version: 27 November 2001 / Published online: 17 January 2002     

Intracavity second-harmonic generation of 1.06 μm in GdCa4O(BO3)3 crystals

The characteristics of intracavity second-harmonic generation (SHG) at 1.06 μm in GdCa₄O(BO₃)₃ (GdCOB) crystals cut for different type I phase-matching (PM) directions of (θ,φ)=(66.8°, 132.3°); (19.4°, 0°); (90°, 46°) have been investigated. It was found that the intracavity SHG was significantly efficient in the PM direction of (66.8°, 132.3°), and that the intrinsic lower effective nonlinear coefficient (d_eff) was responsible for the less-efficient SHG in the other two directions. A maximum CW SHG output power of 2.81 W was obtained with an optical conversion efficiency of 18.7%, while the corresponding effective intracavity SHG efficiency was determined to be 41.3%. The intracavity SHG efficiency of GdCOB has been found to reach two-thirds of that obtained with type II phase-matching KTiOPO₄ (KTP). Received: 26 April 2000 / Revised version: 3 July 2000 / Published online: 5 October 2000     

Electronic and magnetic properties of the iron borate Fe2BO4

Polycrystalline Fe₂BO₄ was prepared by solid state reactions and its electronic and magnetic properties were investigated by Mössbauer spectroscopy and magnetization measurements. The Mössbauer spectra of Fe₂BO₄ below 270 K indicate the presence of Fe²⁺ and Fe³⁺ sites in the structure, in a ratio 1 : 1. Above this temperature electron delocalization sets in between the divalent and trivalent iron ions and Fe^2.5+ states are observed. The temperature dependence of the Mössbauer spectra and magnetization measurements clearly show the onset of magnetic order below 155 K.     

Excited state absorption and stimulated emission of Nd3+ in crystals III: LaSc3(BO3)4, CaWO4, and YLiF4

3+ ions in CaWO₄, LaSc₃(BO₃)₄, and YLiF₄ crystals are presented. The spectra were measured by a continuous-wave pump and probe technique. It is shown that ESA is a negligible loss mechanism in cw lasers emitting at 1.06 μm. In contrast, the effective emission cross sections in Nd:CaWO₄ and Nd:LaSc₃(BO₃)₄ around 1.35 μm are considerably diminished. Received: 8 May 1998/Revised version: 7 September 1998     

Photothermally Induced Bistability of Emission of Yb-doped Ca4NdO(BO3)3 Single Crystals

We report on studies of changes in the emission spectra (excited at 808 nm) of the Yb-doped Ca₄NdO(BO₃)₃ single crystals due to the photothermal effects caused by the pulsed Nd:YAG laser. Increase of the sample's surface temperature after laser treatment leads to significant enhancement of the 1040 to 1060 nm emission (ascribed to the Nd^{3+ 4}F_3/2 → ⁴I_9/2, ⁴I_11/2 transitions) and simultaneous decrease of the 975 to 1050 nm emission (corresponding to the Yb^{3+ 2}F_5/2 → ²F_7/2 transition). We explain such an increase of the Nd³⁺ luminescence by thermally activated Yb³⁺ → Nd³⁺ energy transfer.     

Short-pulse generation from a resonantly pumped NdAl3(BO3)4 microchip laser

We report on continuous-wave and subnanosecond passively Q-switched laser oscillation from a NdAl3(BO3)4 microchip laser operating at 1.06 microm. Efficient and stable laser operation is possible only when resonant pumping (4I9/2-->4F3/2 at 882 nm) is used instead of the traditional 4I9/2-->4F5/2 (808 nm) pumping. The improvement in laser performance is caused by a strong reduction in the pump-induced thermal loading, which is achieved by pumping directly into the emitting level.     

Magnetic properties of HoFe3(BO3)4

The magnetic properties of an antiferromagnet with trigonal symmetry, namely, HoFe₃(BO₃)₄, have been investigated theoretically. The calculations have been performed in the molecular field approximation and in the framework of the crystal field model for the rare-earth subsystem. Extensive experimental data on the magnetic properties of HoFe₃(BO₃)₄ have been interpreted and good agreement between theory and experiment has been achieved using the obtained theoretical dependences. The spontaneous spin-reorientation transition and the spin-reorientation transition induced by a magnetic field B ‖ a from the easy-axis to easy-plane state, as well as the spin-flop transition in a magnetic field B ‖ c, have been described. It has been shown that the spontaneous spin-reorientation transition is a magnetic analog of the Jahn-Teller effect. The temperature dependences of the initial magnetic susceptibility at temperatures ranging from 2 to 300 K, the nonlinear curves of magnetization for B ‖ c and B ⊥ c in a magnetic field up to 1.2 T (which indicate the occurrence of first-order phase transitions), and their evolution with variations in the temperature have been described, as well as the temperature and field dependences of the magnetization in a magnetic field up to 9 T. The parameters of the trigonal crystal field for the rare-earth ion Ho³⁺ and the parameters of the Fe-Fe and Ho-Fe exchange interactions have been determined in the course of interpretation of the experimental data.