有增益及损耗的平板波导导模的精确微扰分析

给出求含有增益层与损耗层的突变与渐变折射率剖面多层平板波导导模的微扰与解析计算公式。举例讨论了导模模式的增益（或损耗）与结构参数和偏振的关系，本文方法较求解复本征值的打靶法等简便且节省机时，对于（半导体激光器与半导体激光放大器等）实际遇到的波导结构能给出精确数值结果，并可用以分析材料的增益系数或损耗对ＴＥ和ＴＭ模式及其增益的影响等问题。     

强场物理中定态Schr(o)dinger方程的辛算法

简述了一维定态Schr(o)dinger方程的辛形式、求解本征值问题的辛-矩阵法和辛-打靶法及在充分远空间计算线性无关解的保Wronskian算法.     

改进打靶法求解Gross-Pitaevskii方程及三个凝聚体的干涉

用改进的打靶法求解零温简谐势阱中中性原子玻色-爱因斯坦凝聚的一维Gross-Pitaevskii方程,给出不同非线性参数时凝聚体基态的本征值.用辛算法研究三个凝聚体在撤掉陷俘势后产生的干涉,和三个凝聚体处于同-陷俘势中的干涉及周期性演化,讨论不同的相对相位对凝聚体干涉的影响.     

求解含温Thomas—Fermi方程的打靶法

提出一种直接求解在某温度，密度条件下Ｔｈｏｍａｓ－Ｆｅｒｍｉ（以下简称ＴＦ）方程的数值计算方法－打靶法。同时介绍了为使打靶法收敛而采用的调节试探值的方法，最后给出一些元素的计算结果。     

金属覆层保偏光纤偏振器的五层波导模型及理论分析

对金属履层保偏光纤偏振器建立了五层波导变参量物理模型,设计了自适应套孔爬山法的数值计算方法求解含多层波导本征值的复超越方程,计算结果揭示了金属覆层偏光纤偏振器的物理机制,并对器件进行了优化设计,给出了实验结果。     

体积算符对任意价顶角的本征作用与本征值谱

利用体积算符所含抓三元组对自旋网任意价顶角中圈线作用的反称化和双元恒等式，证明了这种作用均为本征作用，本征值为-2.用代数方法给出了对任意价顶角求体积算符本征值的系统程式，得到了普遍情况下的3，4，5和6顶角体积本征值的具体代数表式. 关键词： 体积算符 任意价顶角 本征作用证明 本征值谱     

用科尔-霍普夫变换法求非均匀光波导导模本征方程的严格解

采用科尔-霍普夫(Cole-Hopf)变换法，将渐变折射率波导导模的本征值方程变换为里卡提(Riccati)方程，通过较简洁的数学演算导出导模的传播常量与模场分布的解析解，给出了平方律分布、对称爱泼斯坦(Epstein)分布、爱泼斯坦层的平板波导与平方律分布圆光纤4种折射率分布的计算公式。     

半径渐变同轴波导模式耦合系数研究

 为了用耦合波理论研究一些同轴结构的高频特性，推导了半径渐变同轴波导内模式耦合系数的计算公式，发现半径渐变圆波导模式耦合系数只是同轴波导模式耦合系数的特例。对同轴波导中的模式及其本征方程根的特点进行了讨论，通过建立同轴波导模式和矩形波导模式之间的对应关系，给出了同轴波导模式本征方程根的快速计算方法。对所给模式耦合系数公式进行了验证，耦合波理论计算结果与有限元方法计算结果吻合良好。     

远红外波导自由电子激光器的新性能

提出了用波导本征模展开的方法计算射频调制的短脉冲电子束在矩形波导中的自发辐射，模展开系数决定了辐射进入ＴＥ０ｎ模的功率，将短脉冲理想化为时间上的δ函数，可以发现辐射频率正好等于用来调制电子束的射频的整数倍时，辐射模式表现为“纯”的波导本征模，此时辐射功率最强，用此方法估算了设计中的上海远外波导出自由电子激光器的辐射功率。     

离子交换KTP晶体光波导及其各向异性波导性能研究

采用离子交换法制备了Ｒｂ：ＫＴＰ晶体光波导，在不同波长的耦合光下测量了ＴＥ和ＴＭ偏振波导模式的有效折射率，拟合了波导层折射率的余误差函数分布，证明了波导折射率增量的各向异性，给出了其色散关系；最后计算并讨论了Ｒｂ：ＫＴＰ波导的扩散特性。     

Transfer matrix of conical waveguides with any geometric parameters for increased precision in computer modeling

The existing formula for the transfer matrix of conical elements assumes constant wave number, which is only valid for sufficiently short conical elements. In acoustic waveguides, the phase velocity, attenuation constant, and hence complex wave number depend on frequency and cross-section radius. As for conical waveguides, the cross-section radius is position dependent, the transfer matrix must allow for a position-dependent wave number. Taking this into account, this letter presents an analytic derivation of the transfer matrix for conical waveguides with any geometric parameters, which can be utilized to improve the method of computer modeling of complex waveguides.     

An Extension of the Effective Index Method to Analyze Leakage Losses in Rib Type Waveguides

An extension of the effective index method is proposed as a tool to investigate leakage losses in two-dimensional waveguides. The above method, referred to as the Extended Effective Index Method (EEIM), utilizes the Transfer Matrix Technique (TMT) for the calculation of the complex propagation constants. The results show that the EEIM can be applied to conventional rib leaky waveguides as well as to rib ARROW leaky waveguides. The results for rib ARROW waveguides show excellent agreement when compared to those obtained with Finite Element Method.     

New method for calculating the spectra and radiation losses of leaky waves in multilayer optical waveguides

The efficiency of a new method for calculating the spectrum and attenuation coefficient of leaky electromagnetic modes is demonstrated with multilayer planar optical waveguides the guiding properties of which are determined by antiresonant reflection from the multilayer cladding (antiresonant reflecting optical waveguides) rather than by total internal reflection from the core-cladding interface as in standard optical waveguides. The new method applies to calculation of both electromagnetic modes in dielectric waveguides and electron quantum states in multibarrier semiconductor heterostructures. The characteristics of multilayer waveguides calculated by the new method are compared with published data obtained from a complex dispersion relation by the transfer matrix method. As an example, the wavelength dependence of the radiation losses for the first TE mode of a planar optical waveguide containing 52 pairs of layers is calculated.     

任意截面波导中截止波长测试的一种新方法

 提出了一种测试任意复杂截面波导截止波长的新方法。该方法利用波导及谐振腔的有关理论,把任意复杂截面波导的截止频率测试问题转化为对波导谐振腔的测试,因而不但在测试中回避了匹配和过渡等难题,而且达到较高精度,非常适合于微波工程设计使用。还提出了对波导衰减以及模式场分布的测试方法。     

有损耗波导中非线性TE波的数值模拟

本文发展了一种以有限元技术为基础的数值方法,用它分析有损耗波导中的非线性TE模。在这种方法中,非线性有损耗波导中TE波与功率有关的复传播常数和局城电场分布,可从这种波导直接得到,没有任何近似。作为这种方法的应用,计算了非线性有损耗波导系统中TE0模的功率色散关系和电场分布。     

用松弛法解薛定谔方程

求解定态薛定谔方程常常会涉及到常微分方程的本征值问题.目前解常微分方程本征值用的比较多的方法是以龙格-库塔方法为基础的打靶方法.打靶方法常用,但是计算时间长.当边界条件比较复杂或比较敏感的时候,用松弛法会有更好的效果.本文用松弛法解薛定谔方程,并和理论解进行比较.发现松弛法得到的数值解和理论解符合度很高,而且使用松弛法能够很快得到符合要求的解.     

Mixed finite elements used to analyze the real and complex modes of cylindrical waveguides

The application of the mixed finite-element method for the analysis of dispersion curves of the cylindrical waveguides with a gradient loading is considered. The test results of the algorithm and the calculations of systems with a variable refractive index are presented. The initiation of complex waves in layered waveguides is shown.     

Complex angle of incidence for planar optical waveguide analysis

We propose the concept of an incident angle in the form of complex number and analyse planar optical waveguides by applying the concept. The complex angle of incidence is concerned with the modelling of prism–gap–waveguide structures. It is shown that, when optical waveguides are analysed by means of the transfer matrix method, the proposed concept enables us to find solutions faster and more accurately than by using the method utilizing the leaky structure. This revised version was published online in November 2006 with corrections to the Cover Date.     

Calculation of parameters of plane-transverse inhomogeneities in waveguides with complex cross sections in the multimode regime

We present a method for studying plane-transverse inhomogeneities in waveguides with complex cross sections in the regime of incidence of several propagating and nonpropagating waves on an inhomogeneity. Vector eigenfunctions and critical wave numbers of waveguides with complex cross section have been determined using the method of partial regions allowing for a singularity on the edge. State University, Rostov-on-Don, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 40, No. 10, pp. 1286–1301, October, 1997.