具有突变结构开放腔的矩阵分析

利用模式展开与场匹配原理，建立了突变波导的散射矩阵(S参数矩阵)，在此基础上分析研究了具有突变结构的波导开放式谐振腔，并由矩阵级联建立了开放腔总的S参数矩阵.通过Matlab编制计算程序对具有多级突变结构的开放式输出腔进行了数值计算和分析，并通过与实验数据和软件模拟的结果比较对该方法得到的数据结果进行了验证. 关键词： 回旋管 开放式谐振腔 突变结构 S参数矩阵     

Surface relief resonant Brewster filters with multiple channels

In this paper, a new type of resonant Brewster filters （RBF） with surface relief structure for the multiple channels is first presented by using the rigorous coupled-wave analysis and the S-matrix method. By tuning the depth of homogeneous layer which is under the surface relief structure, the multiple channels phenomenon is obtained. Long range, extremely low sidebands and multiple channels are found when the RBF with surface relief structure is illuminated with Transverse Magnetic incident polarization light near the Brewster angle calculated with the effective media theory of sub wavelength grating. Moreover, the wavelengths of RBF with surface relief structure can be easily shifted by changing the depth of homogeneous layer while its optical properties such as low sideband reflection and narrow band are not spoiled when the depth is changed. Furthermore, the variation of the grating thickness does not effectively change the resonant wavelength of RBF, but have a remarkable effect on its line width, which is very useful for designing such filters with different line widths at desired wavelength.     

阿达玛变换成像光谱术的研究

本文论述了阿达玛变换成像光谱仪的基本原理,探讨了工作模式和若干设计问题,利用自行研制的实验装置,在可见波段获得了各种透明字形的成像光谱图。采用对称π变换和快速δ阿达玛变换,改善了实验数据的处理方法。     

Reaction matrix for Dirichlet billiards with attached waveguides

The reaction matrix of a cavity with attached waveguides connects scattering properties to properties of a corresponding closed billiard for which the waveguides are cut off by straight walls. On the one hand, this matrix is directly related to the S-matrix, on the other hand it can be expressed by a spectral sum over all eigenfunctions of the closed system. However, in the physically relevant situation where these eigenfunctions vanish on the impenetrable boundaries of the closed billiard, the spectral sum for the reaction matrix, as it was used before, fails to converge and does not reliably reproduce the scattering properties. We derive here a convergent representation of the reaction matrix in terms of eigenmodes satisfying Dirichlet boundary conditions and demonstrate its validity in the rectangular and the Sinai billiards.     

S-矩阵猜想的几个特殊情形

利用矩阵分块技术、矩阵Frobenius范数的性质以及矩阵的极分解,对SLOANE等在1976年提出的一个关于〖WTHX〗S〖WTBZ〗\|矩阵的猜想进行了讨论. 对于一些特殊矩阵,这个猜想被证明是成立的.     

Investigations on compton scattering: New directions

Although inelastic (Compton) scattering of a photon off a free electron was well understood about 80 years ago, inelastic scattering off bound electrons remains an incompletely understood process. The availability of synchrotron light sources has led a great enhancement in the precision of experimental measurements involving this process. As a result, approximations made in obtaining numerical predictions of physical observables are being reexamined by theorists. In this article, we present a comparison of experimental measurements to theoretical predictions to assess the need for future advances in both experiment and theory.     

The S-matrix version of the Hulthén-Kohn variational principle for quantum scattering: Finite element calculations for state-to-state reaction probabilities

Summary The finite element (FE) method can be applied to solve the reactive scattering problem of the A + BC AB + C type. We are using the S-matrix version of the Hulthén-Kohn variational principle for the two-dimensional collinear problem. The asymptotic wavefunction is described by analytical functions and the interaction part by FE functions.Two approaches are used and compared to each other: 1) FE functions are employed as the basis functions for the interior part of the potential; 2) the FE method is used in order to calculate eigenfunctions for the interior region of the potential and then these eigenfunctions are used as a new basis. In the second case two ways of choosing grid points are applied. First a grid is built that covers both reaction channels, secondly we considered the two reactions channels separately and two basis sets are used in the scattering calculations. This last version would be more helpful from the point of application to three-dimensional non-collinear problems. Results obtained by raising the number of elements, or by increasing the polynomial order, are compared. General formulas for the formfunctions in case of arbitrary order of the polynomials will be presented.Dedicated to the 60th birthday of Prof. Jan Linderberg (Aarhus)     

反应碰撞的动力学李代数描述

提出一种李代数方法描述分子反应碰撞问题．给出了含有主要动力学参量的S-矩阵元、分子碰撞跃迁几率以及反应体系能量统计平均值随时间演化的解析表达式．讨论了一个简单排斥势场中的原子-双原子分子共线反应体系，以阐明这种新方法的要点。     

When hadrons become unstable: A novel type of non-analyticity in chiral extrapolations

Hadron masses show a specific dependence on the quark masses. Therefore, the variation of these masses can cause a resonance in a hadronic scattering amplitude to become a bound state. Consequently, the amplitude exhibits a non-analytic behavior at this transition. Crossed amplitudes, where the resonance can be exchanged in the t-channel, can be shown to exhibit the same phenomenon by s→t analytic continuation. This entails possible kinks in lattice quark-mass extrapolations needed to compute hadronic observables.