Paranormal operator on a Hilbert space

In this thesis an extensive study is made of the set P of all paranormal operators in B(H), the set of all bounded endomorphisms on the complex Hilbert space H. T ϵ B(H) is paranormal if for each z contained in the resolvent set of T, d(z, σ(T))//(T-zI)^-1 = 1 where d(z, σ(T)) is the distance from z to σ(T), the spectrum of T. P contains the set N of normal operators and P contains the set of hyponormal operators. However, P is contained in L, the set of all T ϵ B(H) such that the convex hull of the spectrum of T is equal to the closure of the numerical range of T. Thus, N≤P≤L.

If the uniform operator (norm) topology is placed on B(H), then the relative topological properties of N, P, L can be discussed. In Section IV, it is shown that: 1) N P and L are arc-wise connected and closed, 2) N, P, and L are nowhere dense subsets of B(H) when dim H ≥ 2, 3) N = P when dimH ˂ ∞ , 4) N is a nowhere dense subset of P when dimH ˂ ∞ , 5) P is not a nowhere dense subset of L when dimH ˂ ∞ , and 6) it is not known if P is a nowhere dense subset of L when dimH ˂ ∞.

The spectral properties of paranormal operators are of current interest in the literature. Putnam [22, 23] has shown that certain points on the boundary of the spectrum of a paranormal operator are either normal eigenvalues or normal approximate eigenvalues. Stampfli [26] has shown that a hyponormal operator with countable spectrum is normal. However, in Theorem 3.3, it is shown that a paranormal operator T with countable spectrum can be written as the direct sum, N ⊕ A, of a normal operator N with σ(N) = σ(T) and of an operator A with σ(A) a subset of the derived set of σ(T). It is then shown that A need not be normal. If we restrict the countable spectrum of T ϵ P to lie on a C²-smooth rectifiable Jordan curve G_o, then T must be normal [see Theorem 3.5 and its Corollary]. If T is a scalar paranormal operator with countable spectrum, then in order to conclude that T is normal the condition of σ(T) ≤ G_o can be relaxed [see Theorem 3.6]. In Theorem 3.7 it is then shown that the above result is not true when T is not assumed to be scalar. It was then conjectured that if T ϵ P with σ(T) ≤ G_o, then T is normal. The proof of Theorem 3.5 relies heavily on the assumption that T has countable spectrum and cannot be generalized. However, the corollary to Theorem 3.9 states that if T ϵ P with σ(T) ≤ G_o, then T has a non-trivial lattice of invariant subspaces. After the completion of most of the work on this thesis, Stampfli [30, 31] published a proof that a paranormal operator T with σ(T) ≤ G_o is normal. His proof uses some rather deep results concerning numerical ranges whereas the proof of Theorem 3.5 uses relatively elementary methods.

Nd3+螯合物的含氢有机溶液光谱性能研究

Tris-thenoyltrifluroacetonate of Nd3+ has been prepared and dissolved in DMF solation with very high concentration, and the contained hydrogen has not been substituted by deuterium. The absorption spectrum, emission spectrum, and fluorescence lifetime of the solution were measured. Very obvious characteristic fluorescence peaks were observed at 898 and 1058 nm. Based on Judd-Ofelt theory, three intensity parameters were obtained: Omega(2) = 4.9 x 10(-20) cm(2), Omega(4) = 5.1 x 10(-20) cm(2) and Omega(6) = 2.5 x 10(-20) cm(2). Line strengths S-cal, oscillator strengths f(cal), radiative transition probabilities A(ed), radiative lifetimes tau(r) and branch ratios beta were calculated too. The measured lifetime tau of 1058 nm peak is 460 mu s, and that of 898 nm 505 mu s. Comparison between theoretically computed radiative lifetime tau(r)(682 mu s) and the measured lifetime indicates that the non-radiative transition probability of the solution is very low and the fluorescence quantum efficiency very high. High values of three intensity parameters prove the high asymmetric surroundings of Nd3+, which is important for Nd3+ to absorb the excitation energy. Spectropic quality factor Omega(4)/Omega(6) > 1 makes radiation at 898 nm stronger than at 1058 nm.

一种新型芴类衍生物的光谱性质研究

合成了具有大π共轭性的对称型芴类衍生物9，9-二（2-乙基已基）-2，7-（2-（4-甲氧基）苯-2，1-乙烯基）芴（简写为MO-F1u—MO）。通过元素分析、质谱、紫外-可见光谱和红外光谱对其进行了表征。测试了该染料在乙腈、二氯甲烷、四氢呋喃和正己烷4种不同极性溶剂中的线性吸收光谱和单光子荧光谱。结果发现溶剂效应对吸收光谱和荧光光谱表现出不同程度的影响，对产生这些光谱行为的主要原因进行了讨论。

杂质对掺钕磷酸盐激光玻璃光谱性质的影响

综述了过渡金属杂质（Cu，Fe）和稀土杂质（Dy，Pr，Sm，Ce）对掺钕磷酸盐激光玻璃吸收损耗及Nd^3＋荧光猝灭影响的研究状况。

Infrared-to-visible upconversion emissions in Er3+ doped TeO2-based oxyhalide glasses

The fluorescence and up-conversion spectral properties of Er3+-doped TeO2-ZnO and TeO2-ZnO-PbCl2 glasses suitable for developing optical fiber amplifier and laser have been fabricate and characterized. Strong green (around 527-550 nm) and red (around 661 nm) up-conversion emissions under 977 nm laser diode excitation were investigated, corresponding to H-2(11/2), S-4(3/2), --> I-4(15/2) and F-4(9/2) --> I-4(15/2) transitions of Er3+ ions respectively, have been observed and the involved mechanisms have been explained. The dependence of up-converted fluorescence intensity versus laser power confirm that two-photons contribute to up-conversion of the green-red emissions. The novelty of this kind of optical material has been its ability in resisting devitrification, and its promising optical properties strongly encourage for their further development as the rare-earth doped optical fiber amplifiers and upconversion fiber laser systems.

Effects of Yb3+ in Er3+/Yb3+ codoped fluorophosphate glasses

For the Er3+/Yb3+ codoped fluorophosphate glasses, Judd-Ofelt theory is used to analyse the influence of YbF3 as not a sensitizer but an average component on the spectroscopic properties around 1530 nm emission. The double roles of Yb3+, as a sensitizer and as an average component, are discussed. It is found that Yb3+ as an average component contributes to the increase of fluorescence lifetime, and Yb3+ as a sensitizer has the best sensitization when its concentration is 2.4 mol%.

碱金属氟化物对掺Yb~(3+)氟磷酸盐玻璃析晶稳定性和光谱性质的影响

研究了碱金属氟化物对掺Yb3+氟磷玻璃的光谱性质和析晶稳定性能的影响。运用倒易法计算了Yb3+的发射截面。结果显示,LiF的引入对吸收和发射截面的提高作用较大并出现最佳引入量极值,其次为KF。碱金属氟化物的引入可提高二元体系的析晶稳定性能,使玻璃网络结构得到改善;拉曼光谱显示二元体系中引入YbF3后玻璃网络结构得到增强,而在引入碱金属氟化物的三元体系中掺杂YbF3后破坏了网络完整性,降低系统析晶稳定性能。

荧光俘获效应对掺铒氧化物玻璃光谱性质的影响

测试了不同掺杂浓度和样品厚度下掺铒磷酸盐和碲酸盐玻璃的吸收光谱、荧光光谱和荧光寿命，计算了Er^3＋离子在1．53μm处的吸收截面（σa）、发射截面（σe）、自发辐射跃迁概率（Arad）、辐射跃迁寿命（τrad）、以及辐射跃迁量子效率（η）等光谱参数．讨论了荧光俘获效应对掺铒磷酸盐和碲酸盐玻璃光谱性质及光谱参数的影响．结果表明即使在铒离子低掺杂浓度（0．1mol％Er2O3）下，荧光俘获效应也普遍存在于掺铒玻璃材料中，使得荧光寿命（τt）和荧光半高宽（FWHM）随样品的厚度和铒离子掺杂浓度增加而增大，导致

UV-blue upconverted emission from Nd3+-doped InF3-based heavy-metal fluoride glasses for blue upconversion fibre laser

We report spectral properties and thermal stability of Nd3+-doped InF3-based heavy-metal fluoride glasses. Fluoroindate glasses in the chemical compositions (in mol%) of (38-x)InF3-16BaF(2)-20ZnF(2)-20SrF(2)-3GdF(3)-1GaF(3-)2NaF-xNdF(3) (x = 0.1, 0.5, 1, 2, 3) have been prepared under a controlled atmosphere in a dry box. Strong UVblue upconversion emission from a green excitation wavelength has been observed and the involved mechanisms have been explained. Near-infrared emission occurs simultaneously upon excitation of the UV-blue upconversion emissions with a cw Ar(+)laser. The upconversion spectra have revealed four dominant emissions at 354, 380, 412 and 449 nm, which belong to the transitions of D-4(3/2) -> I-4(9/2), D-4(3/2) -> I-4(11/2) and P-2(3/2) -> I-4(9/2), D-4(3/2) -> I-4(13/2) and P-2(3/2) -> I-4(11/2), D-4(3/2) -> I-4(15/2) and P-2(3/2) -> I-4(13/2), respectively.

Enhanced broadband near-infrared luminescence in transparent silicate glass ceramics containing Yb3+ ions and Ni2+-doped Li Ga5 O8 nanocrystals

Spectral properties of Yb3+/Ni2+ codoped transparent silicate glass ceramics containing LiGa5O8 nanocrystals were investigated. The near-infrared emission intensity of Ni2+ was largely increased with Yb3+ codoping due to Yb3+-> Ni2+ energy transfer. The qualitative calculation of the energy transfer constant Cs-a and rate Ps-a showed that the Yb3+-> Ni2+ energy transfer was much greater than in the opposite direction. Yb3+/Ni2+ codoped glass ceramics with 0.75 mol % Yb2O3 exhibited a near-infrared emission with full width at half maximum of 290 nm and fluorescent lifetime of 920 mu s. The glass ceramics are promising for broadband optical amplification.

γ-辐照对纯Y2SiO5和Eu^3＋：Y2SiO5晶体光谱性能的影响

研究了γ-辐照前后纯Y2SiO5和Eu^3＋掺杂的Y2SiO5晶体吸收光谱的变化，辐照后，未退火和氢气退火的纯Y2SiO5晶体在260-270nm和320nm波段产生了附加吸收峰，分别是由F心和O^-心的吸收引起的；经过空气退火的纯YSO晶体中，由于消除了氧空位，因此辐照后没有出现色心吸收峰。在Eu^3＋；Y2SiO5晶体中，不但有相同的F心和O心吸收峰，而且还有Eu^2＋离子在300nm和390nm的吸收峰。随着辐照剂量的增加，色心附加吸收峰增强。空气退火能减少Eu^3＋：Y2SiO5晶体中的色心，而氢

Study on the growth, etch morphology and spectra of Y2SiO5 crystal

Undoped Y2SiO5 single crystal was grown by the Czochralski method. The samples were optically polished after orienting and cutting. The rhombus and quadrangular dislocation etching pits, the low-angle grain boundaries and the inclusions in the samples were observed using optical microscope and scanning electron microscope. The absorption spectra were measured before and after H-2 annealing or air annealing. The absorption edge of Y2SiO5 crystal was determined to be about 202 nm. The absorption coefficient of Y2SiO5 crystal decreased after H-2 annealing and obviously increased after air annealing. (C) 2005 Elsevier B.V. All rights reserved.

Cr^3＋：Al2O3透明多晶陶瓷光谱特性分析

对透光性良好的Cr^3＋：Al2O3透明多晶陶瓷的光谱性能进行了研究，其吸收光谱中吸收峰与单晶红宝石相一致，按吸收光谱和Tanabe-Sugano能级图，算出其晶场强度参数Dq及Racah参数B分别为1792cm^-1，689cm^-1，Dq／B=2．6，陶瓷中Cr^3＋离子所处格位的晶体场强比单晶弱一些，但Cr^3＋：Al2O3透明陶瓷仍属于强场晶体材料；当Cr^3＋掺杂浓度到达0．8wt％时，陶瓷的发射谱仍保持较好的R线发射；随Cr^3＋掺杂浓度的增大，激发峰位发生“红移”．在Cr^3＋：Al2O3透

大尺寸高浓度掺杂Nd：GGG和Nd：YAG晶体的光谱性质(英文)

由于Nd^3＋离子半径0．112nm和Y^3＋离子半径0．101nm相差10．9％，使得Nd^3＋离子非常难于进入YAG晶体中。我们用温度梯度法生长了大尺寸高浓度（2．8 at％）的Nd：YAG晶体，同时与用提拉法Nd：GGG晶体进行了比较。分析了高浓度掺杂Nd：GGG和Nd：YAG晶体浓度猝灭问题。研究了不同浓度掺杂的猝灭效应。在同样的掺杂浓度下，我们发现它们的猝灭程度不同，其原因是两种晶体中△Emism（-）和（＋） △Emism（＋） 不同。

A comparison between TGT and Cz grown Nd : YAG

Large sized neodymium-doped Y3Al5O12 (Nd:YAG) laser crystals have been grown by temperature gradient technique (TGT) method and compared with Czochralski (Cz) method. The comparison of these two crystal growth methods has been listed. The results showed that the TGT method has many advantages over the Cz method. The concentration distribution of Nd ions in the crystals was determined and the absorption spectra of these crystals have been investigated and compared. The TGT grown highly doped Nd:YAG crystal has a larger absorption FWHM than that of Cz grown Nd:YAG crysral. Highly doped Nd:YAG (similar to 2.8 at. pct) crystals could be obtained by TGT.