Virtual sources for a cosh-Gaussian beam

On the basis of superposition of beams, a group of virtual sources that generate a cosh-Gaussian wave is identified. A closed-form expression is derived for this cosh-Gaussian wave, which, in the appropriate limit, yields the paraxial approximation for the cosh-Gaussian beam. From this expression, the paraxial approximation and the nonparaxial corrections of all orders for the corresponding paraxial cosh-Gaussian beam are determined.     

Propagation of Lorentz–Gaussian Beams in Strongly Nonlocal Nonlinear Media

In this paper the propagation of Lorentz-Gaussian beams in strongly nonlinear nonlocal media is investi- gated by the ABCD matrix method. For this purpose, an expression for field distribution during propagation is derived and based on it, the propagation of Lorentz-Gaussian beams is simulated in this media. Then, the evolutions of beam width and curvature radius during propagation are discussed.     

Beam Propagation Factor and Generation of Cosh-squared-Gaussian Beams

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Beam Propagation Factor and Generation of Cosh-squared-Gaussian Beams

A new light beam termed as a cosh-squared-Gaussian beam (ChSGB) which may be one of solutions of the paraxial wave equation for propagation in complex optical systems has been introduced. Their beam propagation factor (M2-factor) is derived and schemes to generate this light beams are proposed.     

Virtual source for a Hermite-Gauss beam

A virtual source that generates a Hermite-Gauss wave of mode numbers m and n is introduced. An expression is obtained for this Hermite-Gauss wave. From this expression, the paraxial approximation and the first 3 orders of nonparaxial corrections for the corresponding paraxial Hermite-Gauss beam are determined. When both m and n are even, leading to maximum amplitude along the axis, the number of orders of nonvanishing nonparaxial corrections is found to be equal to (m + n)/2.     

非稳腔傍轴波动方程高斯球面波修正方法的数值研究

在分析用差分方法求解虚共焦非稳腔三维傍轴波动方程,及用数值积分方法与快速付氏变换(FFT)方法求解三维菲涅耳积分方程优缺点的基础上,从激光束在虚共焦非稳腔中以修正高斯球面波形式传输的特征出发,经坐标变换把发散(或会聚)的光束拉直成平行光束,然后用FFT方法求解了在新坐标系中修正函数满足的傍轴波动方程.把相同条件下得到的结果与国内外文献给出的结果进行了比较;计算COIL实验非稳腔给出的近远场结果图象合理正确.     

非傍轴双光束势阱产生的辐射力

分析了两束相对传输的非傍轴高斯光束相干叠加形成的双光束势阱对瑞利粒子产生的辐射力,并作了数值计算,结果表明,与傍轴双光束势阱相比,非傍轴双光束势阱的辐射力有明显的不同,纵向辐射力和横向辐射力都增大,y方向平衡点数目由一个增加到多个,且势阱更深,横向辐射力变化趋势更陡,更有利于微粒的精确定位,与非傍轴单光束势阱相比,势阱更深,所产生的辐射力更大,因而更利于控制瑞利粒子。     

Virtual source for a Laguerre-Gauss beam

A virtual source that generates a cylindrically symmetric Laguerre-Gauss wave of radial mode number n is introduced. An expression is derived for this Laguerre-Gauss wave that in the appropriate limit yields the corresponding Laguerre-Gauss beam. From the spectral representation of the Laguerre-Gauss wave, the first three orders of nonparaxial corrections for the paraxial Laguerre-Gauss beam are determined. On the beam axis, the number of orders of nonvanishing nonparaxial corrections is found to be equal to n .     

洛伦兹-高斯光束在梯度折射率介质中的传输

导出了洛伦兹-高斯光束在梯度折射率介质中传输的光场分布,给出了二阶矩定义下的光束半宽度及其变化率的解析表达式,重点分析了梯度折射率系数对洛伦兹-高斯光束传输性能的影响。结果表明,梯度折射率介质中的归一化光强分布和光束半宽度等呈周期性变化,周期为梯度折射率系数的"倍,轴上最大光强出现在半周期处。梯度折射率系数除影响周期性外,对归一化光强分布和光束半宽度无明显影响,但影响光束半宽度变化率。     

Scalar field of nonparaxial Gaussian beams

A family of closed-form expressions for the scalar field of strongly focused Gaussian beams in oblate spheroidal coordinates is given. The solutions satisfy the wave equation and are free from singularities. The lowest-order solution in the far field closely matches the energy density produced by a sine-condition, high-aperture lens illuminated by a paraxial Gaussian beam. At the large waist limit the solution reduces to the paraxial Gaussian beam form. The solution is equivalent to the spherical wave of a combined complex point source and sink but has the advantage of being more directly interpretatable.     

双层界面下非近轴近似多元高斯模型的相控阵声场模拟

非近轴近似多元高斯模型克服了近轴近似条件的限制,能保证较大偏转角度下模拟声场的精确度和效率。根据双层介质的瑞利积分模型和单层介质的非近轴近似多元高斯模型,推导出双层介质中基于非近轴近似多元高斯模型的单阵元辐射声场计算模型。并在得到各阵元声束偏转聚焦的延迟时间基础上,累加得到基于非近轴近似高斯模型的超声相控阵横波检测辐射声场计算模型。模拟计算带丙烯酸树脂楔块的超声相控阵探头在钢中横波检测的声束偏转与偏转聚焦辐射声场,并与近轴近似多元高斯模型的横波检测声束的偏转聚焦辐射声场进行比较分析。对比分析结果表明非近轴近似多元高斯模型计算速度更快,用时约为近轴近似多元高斯模型的1/13。此外,非近轴近似高斯模型方法横波检测的聚焦声束覆盖区域更大,能量更集中,更适于远场区域检测。      

Radiation pattern of cylindrically symmetric scalar Laguerre-Gauss beams

The exact full-wave generalization of the cylindrically symmetric scalar real-argument Laguerre-Gauss beam is determined. The radiation intensity of the resulting Laguerre-Gauss wave is deduced, and the main characteristics of the radiation intensity pattern are described. The total power P(n) is evaluated, where n is the radial mode number. By the use of 1/P(n) as the quality parameter, the characteristics of the quality of the paraxial beam approximation to the full Laguerre-Gauss wave are discussed.     

Vectorial Nonparaxial Four-Petal Gaussian Beams and Their Propagation in Free Space

The vectorial nonparaxial four-petal Gaussian beam （FPGB） is introduced. The closed-form propagation expressions for the free-space propagation of FPGBs are derived and their more general applicable advantages are illustrated analytically and numerically. Some special interesting cases, in particular the paraxial one, are discussed. It is found that the parameter f = 1/kwo with the k being the wave number and wo being the waist width plays a crucial role in determining the nonparaxiallity of FPGBs. For small values of the f parameter the paraxial approximation is allowable. In the nonparaxial regime the beam order n additionally affects the vectorial and nonparaxial behaviour of FPGBs.     

Dynamics of topological multipoles: I. High-order nonparaxial singular beams

Approximate boundary conditions for matching the high-order nonparaxial and paraxial singular beams propagating through free space or through a homogeneous isotropic medium are formulated. It is found that the nonparaxial and paraxial beams have almost the same structure both in the vicinity of the focal caustic and away from it. In the intermediate zone, the beam profiles are distorted, and a phase mismatch arises and increases with increasing mode order. The combined nonparaxial singular beams are devised, and their dynamics is studied. It is shown that the problem of matching the paraxial and nonparaxial wave functions may be reformulated as a problem of the phase matching for nonparaxial wave function. Such a problem is similar to the mode-dispersion problem and is unsolvable in terms of a linear problem for the entire optical axis. Thus, it makes sense to discuss either the precise matching of the paraxial and nonparaxial beams within small spatial zones or an approximate matching away from the focal plane but at long distances along the optical axis.     

一类新平顶光束的束传播因子

 基于迭加原理，引入了利用双曲余弦-高斯光束的相干迭加而得的新光束，结果表明这类迭加光场的场强分布在适当参数条件下可具有平顶结构，并且分析了这类迭加所得的平顶光束的束传播因子与束参数的关系。     

光在类锥形梯度折射率纤维中的传播——波动光学研究

本文从近轴波动方程出发,寻求光在类锥梯度折射率纤维中传播的解析解。研究了在纤维中传播的高斯光束光斑半径、波面曲率半径、光束强度分市的变化规律,并讨论了准锥形近似及准几何光学传播条件。     

Influence of the cladding layer field of fiber on beam parameters

Beam parameters, including mode-field radius, divergence half-angle and beam propagation factor are studied and relations among them are derived under the condition of paraxial approximation. Several formulas of the beam parameters for end diffraction-limited from the fundamental mode of fiber are given based on the normalized standing wave parameter, normalized evanescent wave parameter and radii of core layer and circular aperture. Moreover, influence of change of the near-field on beam parameters is researched and the results show that the cladding layer field has determinant effect and cannot be neglect. These conclusions may provide theoretical foundation for further researching the beam parameters.