渐变折射率介质中标准矢量波函数的构成

研究了在渐变折射率介质中构成标准矢量波函数的必要条件。研究结果表明在渐变折射率介质中构成标准矢量波函数除了仍需遵循Morse-Feshbach判据外，领示矢量仅能选取与折射率变化方向一致的那根坐标轴的单位矢量。     

矢量贝塞尔涡旋波束在均匀单轴各向异性介质中的传输

基于电磁场的矢量波函数展开方法和不同坐标系中矢量波函数转化关系,得到了圆对称矢量贝塞尔涡旋波束的圆柱矢量波函数展开系数;结合电磁场边界条件,获得了圆对称矢量贝塞尔涡旋波束以任意方向照射均匀单轴各向异性介质层的反射场、透射场和内部场的展开系数;数值计算了沿波束传播方向横截面上的入射、反射和透射电场强度分布以及xOz平面内传播路径方向的总电场强度分布。结果表明,圆对称贝塞尔涡旋波束入射单轴各向异性介质的反射场基本保持同心圆环结构,但强度分布不再呈圆对称;透射场出现两束交错折射光,总电场强度轮廓显著扭曲。     

矩孔光栅的矢量模式理论

本文引入满足均匀矢量亥姆霍兹（Ｈｅｌｍｈｏｌｔｚ）方程的矢量波函数作为基矢，对矩孔光栅的孔内外光场分别进行矢量模式展开和矢量平面波展开，并由耦合条件导出了求解展开系数的方程组，从方程组中求解出相应的振幅系数，可研究光栅的衍射场分布，该方法可研究入入射扬方向和偏振任意时的衍射效率和偏振特性等问题。     

对称型闪耀光栅的矢量模态理论

本文将满足均匀矢量亥姆霍兹方程的标准矢量波函数作为基矢对对称型闪耀光栅槽内、外的电磁场分别进行矢量模式和矢量平面波展开。然后通过在槽内外分界面上的场耦合条件得到一组振幅系数方程组。从方程组中求解出相应的振幅系数,就可研究光栅的衍射场分布。该方法适用于对称型闪耀光栅对任意入射方向、任意偏振态入射场衍射问题的研究。在K_2=0入射情况下,其振幅方程组与已发表的文献[6]相同。     

非均匀散射层矢量辐射传输(VRT)方程高阶散射解的迭代法

将散射介质层在z轴方向划分成薄层，用薄层的一阶散射强度、Fourier变换和迭代方法求解散射介质整层的矢量辐射传输(VRT)方程的高阶散射解.该方法将一阶散射与高阶散射迭代结合起来，计算公式简明，可计算高阶迭代解，计算时间少.计算结果与一层均匀散射介质的VRT方程一阶Mueller矩阵解、半空间均匀散射介质二阶Mueller矩阵解、以及离散坐标-特征值特征矢量法的VRT热辐射的数值解作了全面的比较.提出并讨论了非均匀散射层主动与被动VRT方程的高阶解.本计算程序可以通用于非球形粒子多层结构及非均匀介质的散射和热辐射计算. 关键词： VRT方程 分层 迭代解     

厄米-高斯光束对手征介质球的远场散射

利用复源点方法将厄米-高斯光束展开为球矢量波函数的形式。基于广义洛伦兹米氏理论,应用手征介质球与自由空间分界面处电磁场切向连续的边界条件以及球矢量波函数的正交性,得到手征介质球远区散射场展开系数。研究了厄米-高斯光束对手征介质球的散射特性。数值计算了厄米-高斯光束对手征介质球的远区散射场分布,分析了波束模式、手征参数和手征球尺寸等对散射特性的影响。     

平面上方分层小球的光散射计算

本文基于扩展的Mie理论方法求解平面上方分层小球的散射问题。通过建立小球和平面的模型,解决小球和平面的边界条件问题,并利用矢量波函数展开的方法求得了散射场。强调了小球与表面的相互作用。利用Mie理论方法得到了分层小球的散射场系数,通过计算平面上小球的散射模型,得到了平面上分层小球的散射场分布。结论给出了分层介质小球的微分散射截面图。     

一维均匀势场中含时薛定谔方程的求解

本文详细讨论了一维均匀势场中含时薛定谔方程的求解.求解的思想是以均匀势场中经典粒子的运动作为参考，从经典粒子的运动轨迹出发，构建出量子情形下描述粒子运动的高斯波包形式的演化波函数，进而借助含时薛定谔方程确定波函数的具体形式.在上述思想指导下，推导得出了坐标表象和动量表象下均匀势场内一维粒子的传播子函数.同时，作为比较，狄拉克态矢量符号提供了另一种得到上述传播子函数的途径.     

矩形槽光栅的矢量模式理论

本文引进满足均匀矢量Helmholtz方程的矢量波函数作为基矢,对矩形槽光栅的槽内和槽外的光场分别进行矢量平面波展开和矢量模式展开,并由耦合条件导出了求解展开系数的方程组,可进行数值计算.该方法可研究入射场的方向和偏振任意时的衍射效率、偏振特性变化等问题.在p偏振和s偏振的特殊情况下所得到的公式与用标量模式理论得到的结果一致.     

也论电位移矢量D仅与自由电荷分布有关的条件

电位移矢量是一辅助矢量，它的引入为计算一些介质问题提供了方便．但由于普物中的静电场介质问题，绝大多数为均匀介质问题，这就使学生常常产生“电位移矢量仅与自由电荷分布有关”的误解．文献［１］对此问题作了说明，但其推导和结论都有些不足．本文试图给出Ｄ仅与电荷分布有关的一般条件式，并对各种电介质进行分析，最后对有关问题做出简略说明．     

Phase and group velocity considerations for dynamic modulus measurement in anisotropic media

In anisotropic media, the direction of energy propagation does not necessarily coincide with the wave normal, i.e. the energy flux vector does not coincide with the wave normal. Since, experimentally, one measures group velocity not phase velocity, one must therefore be careful in interpreting ultrasonic wave speed measurements in anisotropic media. This is of particular importance in elastic property reconstruction where acoustic velocity measurements are used as the basis for determining anisotropic material properties. In this work, the consequences of energy flux deviation from the wave normal are considered for typical experimental geometries. Particular attention is devoted to developing appropriate relationships between the phase velocity and ultrasonic transit time measurements, as these relations are most useful for elastic property reconstruction. In all the cases considered, it is shown that the phase velocity can be directly calculated from appropriate time delay measurements.     

On resolving the refractive index and the wave vector

The identification of the refractive index and the wave vector for general (possibly active) linear, isotropic, homogeneous, and nonspatially dispersive media is discussed. Correct conditions for negative refraction necessarily include the global properties of the permittivity and permeability functions epsilon=epsilon(omega) and mu=mu(omega). On the other hand, a necessary and sufficient condition for left handedness can be identified at a single frequency (Re epsilon/|epsilon|+Re mu/|mu|<0). At oblique incidence to semi-infinite, active media, it is explained that the wave vector generally loses its usual interpretation for real frequencies.     

Regular and Chaotic Spatial Distribution of Bose-Einstein Condensed Atoms in a Ratchet Potential

We study the regular and chaotic spatial distribution of Bose-Einstein condensed atoms with a space-dependent nonlinear interaction in a ratchet potential. There exists in the system a space-dependent atomic current that can be tuned via Feshbach resonance technique. In the presence of the space-dependent atomic current and a weak ratchet potential, the Smale-horseshoe chaos is studied and the Melnikov chaotic criterion is obtained. Numerical simulations show that the ratio between the intensities of optical potentials forming the ratchet potential, the wave vector of the laser producing the ratchet potential or the wave vector of the modulating laser can be chosen as the controlling parameters to result in or avoid chaotic spatial distributional states.     

Highly symmetric discrete breather in a two-dimensional Morse crystal

It has been shown recently that a moving discrete breathers localized in one close-packed atomic row can be excited in a two-dimensional monoatomic crystal with Morse interaction. In this work, a motionless discrete breathers having the threefold symmetry axis has been excited in the same crystal. The initial conditions for the excitation of such discrete breathers are set by the superposition of a bell-shaped function on a planar nonlinear phonon mode with the wave vector lying at the edge of the Brillouin zone. In addition, the displacement of the centers of atomic oscillations from the center of the discrete breathers owing to the asymmetry of the Morse potential is taken into account. The results obtained make it possible to approach the search for highly symmetric discrete breathers in three-dimensional crystals.     

Analytical solution of the inverse spectroscopic problem: Determination of electron moments of vibrational transitions of diatomic molecules by their probabilities

The inverse problem of spectroscopy of vibrational transitions of diatomic molecules was analytically solved on the basis of wave functions of the Morse oscillator. An example of the determination of the transition dipole-moment function by intensities of several lines of molecule vibrational-rotational spectra measured experimentally was considered. A similar approach based on simple expressions for matrix elements can be applied to consider optimal lasing conditions of the CO electronic transition laser.     

Relativistic Treatment of Spinless Particles Subject to a q-Deformed Morse Potential

The approximate analytical solutions of the Klein-Gordon equation with equal scalar and vector q-deformed Morse potential are presented for arbitrary e-states by using Laplace integral transform. The energy eigenvalues and corresponding wave functions are obtained for n and e values. In this study, in the non-relativistic limit c→∞, it has been also provided that the energy eigenfunctions for Klein-Gordon system turn into those for Schrdinger one.     

Analogien zwischen außerordentlichen und ordentlichen Wellen nach nichtorthogonaler Koordinatentransformation und die parabolischen Näherungsgleichungen

Within the limits of Linear Optics we treat analogies between ordinary and extraordinary waves in uniaxial media which become conspicuous through a nonorthogonal transformation of coordinates. To any ordinary wave solution in unbounded uniaxial media we can construct a corresponding extraordinary wave solution by interchanging electrical and magnetical field components. Boundary conditions for instance for ideal conducting plane surfaces approximately preserve their original form, if the optical axis or the middle wave vector are normal to the surface. The parabolic approximative equations for slowly varying amplitudes are derived, the polarisation of these waves being considered as a slowly varying quantity. Further these approximative equations are expanded to include frequency dispersion. Through the specified transformation we can simplify problems with extraordinary waves.