Geometry of 2 × 2 hermitian matrices

LetD be a division ring which possesses an involution a → α . Assume that is a proper subfield ofD and is contained in the center ofD. It is pointed out that ifD is of characteristic not two, D is either a separable quadratic extension of F or a division ring of generalized quaternions over F and that if D is of characteristic two,D is a separable quadratic extension ofF. Thus the trace map Tr:D → F, a → a + a is always surjective, which is formerly posed as an assumption in the fundamental theorem of n×n hermitian matrices overD when n ≥ 3 and now can be deleted. WhenD is a field, the fundamental theorem of 2 × 2 hermitian matrices overD has already been proved. This paper proves the fundamental theorem of 2×2 hermitian matrices over any division ring of generalized quaternions of characteristic not two This research was completed during a visit to the Academy of Mathematics and System Sciences, Chinese Academy of Sciences.     

LD-end-pumped Nd:YAP laser operating at 1341.4 nm and doubling of its frequency

We report an LD-end-pumped linearly-polarized continuous-wave (CW) Nd:YAP laser operating at 1341.4 nm. Making use of the plane-concave resonator (T = 2.4%) and the plane-plane resonator (T = 2.6%), we obtain linearly-polarized laser radiation at 1341.4 nm with a power of 3.15 and 2.86 W and corresponding optical slope efficiency of 18.4 and 17.5%, respectively. The effect of the laser oscillation mode on the output is analyzed. An experiment on the intra-cavity frequency doubling with an LBO crystal has been performed, and a laser power of 431 mW in one direction at 670.7 nm was obtained.     

On the division of polynomial matrices

The main purpose of this paper is to determine two new algorithmsfor the division of the polynomial matrix B(s) R[s]^pxq by A(s) R[s]^pxp (a) based on the Laurent matrix expansion at s = =of the inverse of A(s), i.e. A(s)^–1, and (b) in a waysimilar to the one presented by Gantmacher (1959).     

InGaAsSb/AlGaAsSb长波长多量子阱激光器有源区的优化设计

系统地研究了波长为2.7μm的InGaAsSb/AlGaAsSb多量子阱激光器中有源区的优化设计.分别用含应变势的6带KP模型和抛物带模型计算价带和导带的能带结构，并得到薛定谔方程和泊松方程的自洽解，由此计算量子阱在载流子注入时的增益谱.研究表明制约量子阱增益的主要因素不是跃迁矩阵元，而是粒子数反转程度，尤其是空穴填充HH1子带的概率.增加压应变或减小阱宽都会提高量子阱增益.前者降低了价带HH1子带空穴的平面内有效质量；后者拉大了价带子带间距，尽管它同时略微增加了空穴有效质量.这两种因素都导致价带顶空穴态     

光交叉连接节点的功能结构

光交叉连接(OXC)是未来波分复用光传送网实现交换与选路功能的核心部件.目前,OXC节点的物理结构得到深入研究,已经提出了一些采用不同光子器件的OXC实现方案.本文从描述光交叉连接功能的角度出发,给出一种分析OXC节点功能结构的模型,并比较各种OXC方案在功能结构上的差异。     

Propagating beam analysis of fiber wavelength filters with a depressed-index section

A wavelength filter consisting of single-mode and few-mode fibers is investigated numerically. A simple finite-difference beam-propagation method, in which a transparent boundary condition can be imposed, is developed for circularly symmetric waveguides. After confirming the validity of the numerical method by the mode-mismatch loss, we calculate the propagating field in the fiber wavelength filter, in which interference between LP₀₁, and LP₀₂ modes occurs. To improve the filtering operation, a depressed-index fiber is employed for the few-mode fiber. The effects of the radius and refractive index of the depressed section on the transmission power are revealed and discussed. Power is suppressed to less than 0.1% at 1.3 μm, while maintaining power transmission of more than 85% at 1.55 μm. It is also found that the filtering operation shifts to higher wavelengths as the input power is increased when we choose a self-focusing nonlinear material in the depressed section.     

1.55-μm InGaAs/InGaAlAs MQW vertical-cavity surface-emitting lasers with InGaAlAs/InP distributed Bragg reflectors

High-performance InGaAs/InGaAlAs multiple-quantum-well vertical-cavity surface-emitting lasers (VCSELs) with InGaAlAs/InP distributed Bragg reflectors are proposed for operation at the wavelength of . The lasers have good heat diffusion characteristic, large index contrast in DBRs, and weak temperature sensitivity. They could be fabricated either by metal-organic chemical vapor deposition (MOCVD) or by molecular beam epitaxy (MBE) growth. The laser light-current characteristics indicate that a suitable reflectivity of the DBR on the light output side in a laser makes its output power increase greatly and its lasing threshold current reduce significantly, and that a small VCSEL could output the power around its maximum for the output mirror at the reflectivity varying in a broader range than a large VCSEL does.     

Commutativity of rings through a Streb's result

In this paper we investigate commutativity of rings with unity satisfying any one of the properties:

Trees and valuation rings

A subring of a division algebra is called a valuation ring of if or holds for all nonzero in . The set of all valuation rings of is a partially ordered set with respect to inclusion, having as its maximal element. As a graph is a rooted tree (called the valuation tree of ), and in contrast to the commutative case, may have finitely many but more than one vertices. This paper is mainly concerned with the question of whether each finite, rooted tree can be realized as a valuation tree of a division algebra , and one main result here is a positive answer to this question where can be chosen as a quaternion division algebra over a commutative field.

     

Broadband arrayed waveguide gratings on InP

Broadband arrayed waveguide gratings on InP are presented using a novel S-shape design. This design was utilized to accommodate the large free spectral range required for broadband operation. Four and eight channel AWGs with a wavelength channel spacing of 18 nm are discussed. The output peaks of the AWGs have a wide FWHM of 11 nm which provides insensitive operation to polarization, temperature fluctuations, and chromatic dispersion.