非均匀平板波导的色散方程

利用转移矩阵理论分析了任意折射率分布平板波导的传输特性，导出了非均匀平板波导的近似解析色散方程，并指出了ＷＫＢ近似的局限性，数值比较的结果表明，文中所得公式的精确度优于传统的ＷＫＢ方法和其它近似方法。     

改进WKB方法与相移值的修正

利用非均匀波导的多层分割法,对传统ＷＫＢ法的相称值进行修正,导出了改进的ＷＫＢ计算公式,并给出相移修正值的计算公式。对常见的典型折射率剖面（指数型、高斯型、余误差型、截断线型）的数值计算表明,该方法所得公式的精度远高于传统的ＷＫＢ近似,在接近截止时仍与精确数值十分吻合。     

基于等效衰减矢方法的非均匀光波导色散方程

利用转换矩阵理论和等效衰减矢的概念，以此为根据分析了任意折射率分布平板波导的模式传输特性，导出了意义明确的非均匀平板波导的色散方程的严格的解析解，并指出了ＷＫＢ法的局限性，数值计算的结果表明本文所得公式的结果和严格的数值解非常接近，表明本文所得的公式是严格的。     

光程,费马原理和光纤的模式色散

利用光程概念和费马原理，对光波导理论中的光纤模式色散问题给出了一种新的处理方法，它比起传统的ＷＫＢＪ法，不仅数学处理简单，而且物理意义更突出，结合该问题的讨论，本还对普通物理课内容设置提出了一些建议。     

水平缓变声道中的WKBZ绝热简正波理论

本文利用具有海面相移修正的本征函数的ＷＫＢＺ近似，并同时考虑波导简正波和海底反射简正波的贡献，提出了适合于水平缓变水下声道的ＷＫＢＺ绝热简正波理论。数值结果表明，会聚区声场主要由波导简正波决定，而影区声场主要由海底反射简正波决定。在菲律宾海中，频率范围在１０９ＨＺ至８６０ＨＺ，距离至２５０ｋｍ范围时，用ＷＫＢＺ绝热简正波理论计算的结果与实验数据符合得很好。     

WKB波函数连接公式的初等推导与一维势阱势垒的WKB近似解

本文用初等方法导出ＷＫＢ波函数的连接公式，其要点是在转折点邻近，用阶跃型势能曲线代替真实的势能曲线。给出了求一维势阱能级及一维势垒穿透因子的方法与结果。方法简便，可供初等量子力学与普通物理教学参考。     

硅键合SOI平面光波导探索

本文分析了ＳＩＭＯＸ／ＳＯＩ和ＤＷＢ／ＳＯＩ结构的性能特点。尝试用ＤＷＢ／ＳＯＩ材料制备不同波导层厚度的平面光波导样品，并测试了１．１５μｍ和１．５２３μｍ激光的ＴＥ和ＴＭ模的传输损耗。１．５２３μｍ光的ＴＥ模的最小传输损耗已达０．２７ｄＢ／ｃｍ。说明ＤＷＢ／ＳＯＩ材料是一种有潜力的光波导材料。     

水下声道中脉冲传播的WKBZ简正波方法

本文将ＷＫＢＺ简正波方法应用于水下声道中的脉冲能量和波形传播。文中分别给出在两种不同水下声道中的数值结果，并与精确简正波数值解进行了比较。数值模拟结果表明，ＷＫＢＺ简正波方法能精确地计算水下声道中脉冲声信号的波形，计算速度比传统的简正波方法提高近两个数量级。     

齐次函数分析在WKB近似中的应用

本文对处于幂函数型、对数型和其他某些有心势场中的粒子，给出一个仅通过齐次函数分析就可以得到粒子ＷＫＢ能级构造式的简便方法．此法不仅适用于ｓ态，也适用于非ｓ态．     

水平不变海洋声道中的WKBZ简正波方法

本文利用本征函数的ＷＫＢＺ近似和海面相移修正发展了一种新的计算海洋声场的数值方法，该方法具有形式简明、易于计算、精度满足实用要求的优点．本文给出了ＷＫＢＺ方法应用于北太平洋声道中声传播的一些数值结果，这些结果表明该方法是一种计算分层海洋声道会聚区声场的快速而精确的数值方法．     

迭代法重建平板光波导折射率分布

提出了一种用于重建渐变折射率平板光波导折射率分布的方法,这种方法通过数值法求解亥姆霍兹方程．从光波导的低阶模开始采用迭代法顺次对各个模式对应的“转折点”位置进行校正．并多次重复迭代以消除“转折点”外折射率分布的变化对相应模式“转折点”位置的影响。借助WKB近似原理说明了这种方法迭代过程中“转折点”坐标的收敛性。对折射率按照指数规律变化的平板光波导的折射率分布重建结果证明这种方法具有较高的精度。分析表明：这种方法克服了WKB法固有的缺陷,即忽略模式“转折点”外折射率分布对相应模式传输常鞋的影响和“转折点”处相移的不确定性,因而比逆WKB法具有更好的自洽性和精确性。     

Divergence-free WKB theory

We present a divergence-free WKB theory, which is a new semiclassical theory modified by nonperturbative quantum corrections. Conventionally, the WKB theory is constructed upon a trajectory that obeys the bare classical dynamics expressed by a quadratic equation in momentum space. Contrary to this, the divergence-free WKB theory is based on a higher-order algebraic equation in momentum space, which represents a dressed classical dynamics. More precisely, this higher-order algebraic equation is obtained by including quantum corrections to the quadratic equation, which is the bare classical limit. An additional solution of the higher-order algebraic equation enables us to construct a uniformly converging perturbative expansion of the wavefunction. Namely, our theory removes the notorious divergence of wavefunction at a turning point from the WKB theory. Moreover, our theory is able to produce wavefunctions and eigenenergies more accurate than those given by the traditional WKB method. In addition, the divergence-free WKB theory that is based on the cubic equation allows us to construct a uniformly valid wavefunction for the nonlinear Schrödinger equation (NLSE). A recent short letter [T. Hyouguchi, S. Adachi, M. Ueda, Phys. Rev. Lett. 88 (2002) 170404] is the opening of the divergence-free WKB theory. This paper presents full formalism of this theory and its several applications concerning wavefunction and eigenenergy to show that our theory is a natural extension of the traditional WKB theory that incorporates nonperturbative quantum corrections.     

WKB approximation in complex time

The WKB approximation to the one particle Schrödinger equation in time is used to obtain the wavefunction at a given point as a sum of semiclassical terms, each corresponding to a different classical trajectory (real or complex) but ending up at the same point. A method to find out reflection coefficient for processes involving one and two turning points is developed and it is shown that the semiclassical complex analysis reproduces exactly the reflection coefficient that is obtained through the exact solution of the problem. The connection between pair production and reflection amplitude is also shown. The pair production amplitude in a time dependent gravitational background is calculated and it is shown that the vacuum considered in complex trajectory WKB analysis refers to adiabatic vacuum.     

一种简单精准的渐变折射率分布光波导分析方法

渐变折射率分布的光波导分析对光波导器件的设计和研究至关重要, 近年来已提出了多种分析方法, 然而在简便性或准确性上都存在着不足. 为此, 提出了一种分析渐变折射率分布光波导的方法, 能够结合现有的Wentzel-Kramers-Brillouin近似法和离散化的波动方程, 构建模场分布, 再结合变分运算方程和修正的模式本征方程, 计算出较为精确的有效折射率. 与其他分析方法相比, 该方法较为简单, 而且有一定的精度.     

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从Braginskii冷离子流体模型出发,利用准环坐标系,导出了轴对称(环向模数为零的)扰动密度和扰动电位所服从的两个二维线性偏微分本征波方程。采用WKB法及Langer变换,解出了测地声模过转向点一致有效的整体模结构和分立本征频率谱;论述了不存在连续谱解的原因;指出Schrödinger意义下的径向高激发态对应了近零频模;论证了与测地声模定级分析的自洽性将导致“蝌蚪”定域化;并讨论了“蝌蚪”定域化理论与实验上所观察到的“多个测地声模共存”现象之间的关係。     

Multidimensional WKB Approximation for Tunneling Along Curved Escape Paths

Asymptotics of the perturbation series for the ground state energy of the coupled anharmonic oscillators for the positive coupling constant is related to the lifetime of the quasistationary states for the negative coupling constant. The latter is determined by means of the multidimensional WKB approximation for tunneling along curved escape paths. General method for obtaining such approximation is described. The cartesian coordinates (x,y) are choosen in such a way that the x-axis has the direction of the probability flux at large distances from the well. The WKB wave function is then obtained by the simultaneous expansion of the wave function in the coordinate y and the parameter γ determining the curvature of the escape path. It is argued, both physically and mathematically, that these two expansions are mutually consistent. Several simplifications in the integrations of equations are pointed out. It is shown that to calculate outgoing probability flux it is not necessary to deal with inadequacy of the WKB approximation at the classical turning point. The WKB formulas for the large-order behavior of the perturbation series are compared with numerical results and an excellent agreement between the two is found.     

变波长逆WKB方法确定单模渐变平面光波导的折射率轮廓

将渐变波导模式方程(WKB积分方程)化为分段积分,以波导某一模式在不同波长下的转折点为分段点,当波长相差很小时,相应的转折点相差也很小,可在各个分段积分中作折线近似,从而从理论上推出确定波导轮廓数据的递推式.以所得轮廓必须满足光滑条件为判据,最后定出波导的轮廓.该方法尤其适用于单模渐变波导,而且无需事先假设待定轮廓的函数形式.本文对双曲止割和抛物线轮廓的理想波导进行了计算机模拟,结果证明该方法的精度达到10~(-3)甚至于更高.而且理论上具有分割愈密,精度愈高的优点.     

Analysis of planar waveguides with index discontinuity or index slope discontinuity

In this paper, we propose a novel analytic transfer matrix method (ATMM) to the analysis of planar waveguides with index discontinuity or index slope discontinuity, for the cases when the conventional WKB method is no longer valid. We also analyze the physical insight of the approximations in WKB theory, and according to our research, the phase shift at the turning point is not /2, but exactly . Test calculations are done for an index profile with a known solution and the comparison shows that our method gives extremely accurate propagation constant.     

Second-order semiclassical calculations for diatomic molecules

The second-order WKB quantization condition is used to derive expressions for the second-order contributions to the vibrational energy levels and the rotational and centrifugal constants of a diatomic molecule. The second-order corrections to the RKR (Rydberg-Klein-Rees) turning points are also calculated. These second-order quantities are related to the quantities calculated from Kaiser's modified first-order quantization condition. Numerical calculations for the ground electronic state of carbon monoxide are compared with quantum-mechanical values obtained by numerical solution of the Schrödinger equation. In general, the second-order semiclassical values are in good agreement with the quantum-mechanical values, and can be computed by the present methods in a small fraction of the time.