The derivation of the relationship between the paraxial wave equation and the complex source points is given and proved.
推导并证明了旁轴波动方程的解与复源点方法之间的一致性关系。
Laguerre-Gaussian mode is the solution of Hemoltze Equation in the cylindrical coordinate under paraxial condition.
Laguerre-Gaussian模是傍轴近似条件下亥姆霍兹方程在柱坐标系中的解，波前位相成螺旋形状，光子携带的轨道角动量不为零。
Paraxial approximation absorption boundary condition based on acoustic wave equation can obtain better absorption results by increasing paraxial approximation order of Taylor series. However, this kind of operation will increase the complexity of difference computation, and result in instability of computation process.
基于声波波动方程的旁轴近似吸收边界条件可以通过提高泰勒级数展开的旁轴近似阶数获得更好的吸收效果，但这样不仅增加了差分计算的复杂性，同时还导致计算过程不稳定。
In order to eliminate boundary reflection, the absorbing boundary conditions of Clayton Engquist paraxial wave equation are introduced to frequency domain. The stiffness matrix and mass matrix of finite element are compressed for storing. The forward solutions are obtained by using conjugate gradient algorithm.
为了消除边界反射，将ClaytonEngquist旁轴波动方程吸收边界条件引入频率域，并对有限元刚度矩阵和质量矩阵进行压缩存储，利用广义共轭梯度法求解有限元方程获得正演解。
By using the complex analytic signal representation and the method of stationary phase, the propagation equation of ultrashort pulses in the far-field has been derived beyond the paraxial approximation, which allows for large angles in the far-field.
使用复解析信号法和稳相法推导出了等衍射长度超短脉冲高斯光束在自由空间远场非近轴传输方程，可用来处理自由空间远场大角度的传输。
Starting from the Rayleigh diffraction integral and using analytic signal complex representation, the propagation equation of ultrashort pulses in free space has been derived in the near-field beyond the paraxial approximation, which is consistent with the paraxial results in previous literatures if the paraxial approximation is made.
从瑞利衍射积分公式出发，利用复解析信号法推导出了等衍射长度超短脉冲高斯光束在自由空间近场非近轴传输方程，在近轴近似条件下与文献已有的近轴结果一致。
Three-dimensional paraxial approximate equation with optimized coefficientscan be obtained by using conjugate gradient method under least square premise.
本文在最小二乘意义下用共轭梯度方法导出优化系数的三维傍轴近似方程。
An approximate solution of the paraxial ray equation for cylindrical dense electron beams was obtained by means of the Taylor expansion.
本文提出圆柱形强流电子束的傍轴轨迹方程，可以用台劳展开求出它的近似解。
Three dimensional one-pass migration using paraxial approximate equation with optimized coefficients Fussell's approximate method.
优化系数傍轴近似方程三维一步法偏移Fussell近似方法计算了该系统的可用度、失效期望值、平均修复时间等可靠性参数。
We describe a class of closed-form solutions of the paraxial wave equation, the elegant cosh-squared-Gaussian (EchSG) beams whose parameter related with cosh function part is complex number.
本文引入了近轴近似下波动方程的解&复变量双曲余弦平方-高斯光束，该光束与双曲余弦函数项相关的参数为复数。
Using Helmholtz equation and Fourier transform, the approximate formulas and numerical results have been obtained under paraxial approximation.
在傍轴条件下导出了相应的近似公式，并给出了数值计算结果。
Based on the definition of complex wave number and the generalized Huygens-Fresnel diffraction integral, the closed-form propagation equation of Hermite-Gaussian (HG) beams passing through a paraxial optical ABCD system without aperture, in which the linear gain and absorption media are included, is derived.
从复数波数定义和广义惠更斯-菲涅耳积分出发，推导出厄米-高斯（HG）光束在介质中通过傍轴ABCD光学系统后的一般传输公式。
In this work, the equations describing circular Gaussian beams propagating inside absorptive Keer medium have been derived from nonlinear paraxial equation. Based on the equations, an evolution equation of beam waist lias been obtained.
本文从非线性近轴波方程出发，导出了在吸收克尔介质中具有二次位相因子的圆对称高斯光束的传输方程，得到了光束束腰的演化方程。
Based on the nonlinear paraxial wave equation, the propagation equation of small-scale perturbation of divergent beams has been deduced with a coordinate transformation. The evolvement law of the growth critical frequency of small-scale perturbation, maximum growth frequency and relative B integral is obtained.
从非线性傍轴波动方程出发，利用坐标变换，推导出发散光束小尺度扰动的传输方程，进而得到小尺度扰动增长的临界频率、最大增长频率和相应B积分值的变化规律。
It is proved in a complicated optical system that the diffraction integration in terms of ray matrix element is the right solution'for paraxial equation.
对复杂光学系统证明了光线矩阵元表达的衍射积分是旁轴波动方程的准确解。
Based on the Collins formula and Sylvester theorem, the propagation equation of Gaussian beams passing through a multi-Gaussian apertured paraxial optical ABCD system is derived.
对高斯光束通过有硬边光阑近轴ABCD光学系统的传输进行了研究，采用将矩形函数展开为复高斯函数的技巧，推导出了近似的解析传输公式。
From paraxial ray equation, the collimation application for selfoc lenses are researched.
根据近轴子午光线方程，研究了自聚焦透镜准直应用。
Based on paraxial meridian-ray equation, the principle of fibre accelerometer using self-focussing lens is studied;
本文根据近轴子午光线方程，研究了自聚焦透镜光纤加速度计的工作原理；
The laser propagation is governed by the paraxial wave equation, which is solved by the FFT method.
激光传播由近轴波方程描述，用快速傅里叶变换技术求解；
The parabolic equation method, which is an efficient and fast numerical approach based on paraxial approximation of the wave equation, models energy propagation in a cone centered on the paraxial direction.
抛物线方程算法是建立在波动方程轴向近似基础上的一种数值方法，该方法假设电磁波能量沿抛物线轴向的锥形区域传播。