非傍轴矢量异常空心光束的传输特性

 将Cai提出的异常空心光束的理论模型推广到非傍轴范畴,推导出非傍轴矢量异常空心光束传输的解析表达式,用以研究它在自由空间中的传输特性。研究表明,异常空心光束在传输过程中光束形状会发生变化。与高斯光束不同,非傍轴异常空心光束傍轴近似成立条件依赖于传输距离,这与异常空心光束光强分布随传输距离的变化有关。非傍轴异常空心光束远场的光束质量可用桶中功率来描述,桶中功率随f参数(波长与束腰宽度的比值)的增大而减小。     

Propagation of elegant Hermite cosine Gaussian laser beams

In this paper, a more generalized beam containing an elegant Hermite Gaussian beam and a cosine Gaussian beam, which is called elegant Hermite cosine Gaussian (EHcoG) beam, is introduced and studied. The propagation properties of the EHcoG laser beams through a first-order paraxial optical system are demonstrated analytically and numerically. The recurrence propagation equations of the EHcoG beams through a first-order paraxial optical system with and without aperture are derived, from which the analytical propagation expression for EHcoG beams of any order can be obtained by means of the recursive procedures. The validity of the analytical results is confirmed by the numerical results.     

Propagation properties of partially polarized Gaussian Schell-model beams through an axis-unsymmetric paraxial ABCD system

By using the beam coherence-polarization (BCP) matrix approach, analytical propagation equations of partially polarized Gaussian Schell-model (PGSM) beams through an axis-unsymmetric paraxial optical ABCD system are derived, which enable us to study the propagation-induced polarization changes and irradiance distributions at any propagation distance of PGSM beams through axis-unsymmetric systems within the framework of the paraxial approximation. Detailed numerical results for a PGSM beam passing through a bifocal lens are presented to illustrate the propagation properties of PGSM beams. A comparison with the previous work is also made.     

New Expressions for Dark-Hollow Light Beams

A class of new light beams of dark-hollow beams, named sinusoidal dark-hollow beams, is introduced. The propagation formula for a sinusoidal dark-hollow beam through a paraxial ABCD optical system is derived. The propagation properties of the sinusoidal dark-hollow beam are comparatively studied and illustrated with numerical examples.     

Polarization properties of nonparaxial partially polarized Gaussian Schell-model beams

The polarization properties of nonparaxial partially polarized Gaussian Schell-model (PGSM) beams are studied. Based on the beam coherence-polarization matrix, the propagation formula of the degree of polarization for the nonparaxial PGSM beams is derived. The paraxial approximation is dealt with as special cases of our general results. Some conditions that limit the choice of the parameters are established. The sufficiency condition of polarization invariance in propagation for the nonparaxial PGSM beams is derived. By using the derived formulae, the propagation properties of the degree of polarization for the nonparaxial PGSM beam in free space are illustrated and analyzed with numerical examples. Some detailed comparisons of the obtained results with the paraxial results are made.     

Nonparaxial propagation of phase-flipped Gaussian beams

This paper derives the closed-form expressions for nonparaxial phase flipped Gaussian （PFG） beams propagating in free space, through a knife edge and an aperture, which enable us to study nonparaxial propagation properties of PFG beams and to compare nonparaxial results with paraxial ones. It is found that the f parameter, offsetting distance of the knife edge and truncation parameter affect the nonparaxial beam propagation properties. Only under certain conditions the paraxial approximation is applicable. The results are illustrated by numerical examples.     

Propagation properties of partially polarized Gaussian Schell-model beams through an astigmatic lens

Based on the beam coherent-polarization (BCP) matrix approach and propagation law of partially coherent beams, analytical propagation equations of partially polarized Gaussian Schell-model (PGSM) beams through an astigmatic lens are derived, which enables us to study the propagation-induced polarization changes and irradiance distributions at any propagation distance of PGSM beams through an astigmatic lens within the framework of the paraxial approximation. Detailed numerical results for a PGSM beam passing through an astigmatic lens are presented. A comparison with the aberration-free case is made, and shows that the astigmatism affects the propagation properties of PGSM beams.     

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.     

Nonparaxial propagation of a cylindrical beam with Lanczos reduction

We discuss a numerical method based on Lanczos reduction of modeling nonparaxial propagation of a cylindrical symmetric beam. To illustrate the performance and demonstrate the significant difference between nonparaxial and paraxial beams, we consider Gaussian beam propagation in two different settings.     

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。     

复宗量双曲余弦高斯光束的束腰及其位置

 由复宗量双曲余弦高斯光束通过近轴-ABCD-光学系统传输公式，推导出了基于二阶矩定义的光斑尺寸的解析表达式，给出了复宗量双曲余弦高斯光束在自由空间传输和通过薄透镜时的光斑尺寸、束腰宽度及其位置的解析表达式，并进行了数值计算，对计算结果进行了分析和讨论，该方法可用于其它光束通过近轴ABCD光学系统的类似计算。     

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

1　Ｉｎｔｒｏｄｕｃｔｉｏｎ　　Ｒｅｃｅｎｔｌｙ ,Ｃａｓｐｅｒｓｏｎ ｅｔａｌ.[1,2 ]ｒｅｐｒｅｓｅｎｔｅｄａｓｏ ｃａｌｌｅｄＨｅｒｍｉｔｅ ｓｉｎｕｓｏｉｄａｌ Ｇａｕｓｓｉａｎｂｅａｍｓ (ＨＳＧＢｓ)ａｎｄ ｐｒｏｖｅｄｔｈａｔｔｈｅｙａｒｅｓｔｉｌｌｓｏｌｕｔｉｏｎｓｏｆｔｈｅｗａｖｅｅｑｕａｔｉｏｎｕｎｄｅｒｔｈｅ ｐａｒａｘｉａｌａｐｐｒｏｘｉｍａｔｉｏｎａｎｄｔｈｅｉｒｃｏｍｐｌｅｘｒａｄｉｕｓｏｆｃｕｒｖａｔｕｒｅａｎｄｍｅａｎｒａｙｐａｒａｍｅｔｅｒｓｏｂｅｙｔｈｅｗｅｌｌ ｋｎｏｗｎＡ…     

Structure of a nonparaxial gaussian beam near the focus: III. Stability,eigenmodes, and vortices

Exact analytical structurally stable solutions of the Maxwell equations for singular mode beams propagating in free space or a uniform isotropic medium are obtained. Approximate boundary conditions are chosen in the form of the requirement that in the paraxial approximation the fields of nonparaxial mode beams in the waist plane are transformed into the fields of eigenmodes and vortices of weakly guiding optical fibers with the axial symmetry of refractive index. It is shown that optical vortices, in spite of a rather complex structure of field distribution, do not experience substantial changes in the beam form and reproduce, in general features, the field of paraxial vortices. Linear perturbations of the characteristic parameters of mode beams do not change the structure of their electromagnetic field. Nonparaxial singular beams have one more important property, in addition to the fact that the structure of these beams in the paraxial approximation is similar to the structure of the fields of eigenmodes in a fiber. The propagation constants of eigenmodes of a fiber exactly coincide (in the first approximation of perturbation theory) with the projection of the wave vector of a mode beam on the optical axis (an analog of the propagation constant). The possibility of the paraxial transition for nonparaxial mode beams with arbitrary values of azimuthal and radial indices is shown. The properties of nonparaxial modes are illustrated by numerous examples. The solutions obtained and the results of their analysis can be used for exact matching optical fibers and laser beams in various applications.     

Four-petal Gaussian beams and their propagation

A new form of laser beams called four-petal Gaussian beams is introduced. Based on the Collins integral, two kinds of analytical propagation expressions for this new kind of beams through a paraxial ABCD optical system are derived. The propagation properties of the four-petal Gaussian beams are studied and illustrated with numerical examples. At the source plane the beam has four-petals; the space among the petals is determined by the beam order. In the far field the beam evolves into a number of mirror symmetric petals and the petals of higher order beams can be equally spaced.     

部分相干双曲余弦-高斯光束的传输特性和空间整形

 通过加入高斯项的空间相干度，引入部分相干双曲余弦-高斯（ChG）光束，推导出部分相干ChG光束通过近轴ABCD光学系统传输的解析表达式，并用以研究其传输特性和空间整形。结果表明，部分相干ChG光束的光强分布不能保持传输不变性，其光强分布不仅与传输距离和离心参数有关，而且还与空间相干参数有关。在传输距离固定时，适当改变部分相干ChG 光束的离心参数和空间相干参数，可实现光束的空间整形。光束质量因子随空间相干性的增大和离心参数的减小而减小。高斯-谢尔模型光束和完全相干ChG光束可作为部分相干ChG光束的特例处理。     

经光阑衍射的高阶贝塞耳光束位相奇点演化特性

推导出了高阶贝塞耳光束通过有光阑近轴ABCD光学系统传输的解析公式,用以研究了高阶贝塞耳光束被光阑衍射位相奇点的演化特性.结果表明:高阶贝塞耳光束经光阑系统衍射后,中心光涡旋始终存在,拓扑电荷守恒,但涡旋核大小会随光阑半径、传输距离和光束阶数而变化;随光阑半径和传输距离变化,圆刃型位错会消失或产生.     

Flat-topped Mathieu-Gauss beam and its transformation by paraxial optical systems

In order to avoid the severe axial intensity oscillations which appear when an ideal Mathieu beam is truncated, we propose to modulate it by a flattened multi-Gaussian envelope. The obtained beam, which is referred as flattened Mathieu-Gauss (FTMG) beam, can be expanded into a finite series of Mathieu-Gauss beams with various waists. The propagation study of this beam reveals that the axial intensity is unchanged within a certain propagation distance as for super-Gaussian-Bessel beams or Gori’s flattened Bessel beams. By using Collins formula, we derive closed-form expressions of FTMG beam propagating through a paraxial axisymmetric ABCD optical system. Some numerical calculations and discussions are also given.     

Off-Axis Astigmatic Gaussian Beam Combination Beyond the Paraxial Approximation

Taking the off-axis astigmatic Gaussian beam combination as an example, the beam-combination concept is extended to the nonparaxial regime. The closed-form propagation expressions for coherent and incoherent combinations of nonparaxial off-axis astigmatic Gaussian beams with rectangular geometry are derived and illustrated with numerical examples. It is shown that the intensity distributions of the resulting beam depend on the combination scheme and beam parameters in general, and in the paraxial approximation （i.e., for the small f-parameter） our results reduce to the paraxial ones.     

Propagation properties of high order axially symmetric polarized beams

The paraxial and non-paraxial propagation properties of high order axially symmetric polarized beams are theoretically studied. The mathematical expressions of the propagation fields for such beams are derived based on vectorial Rayleigh–Sommerfeld formulas. Simulation results are presented for different dimensionless perturbation parameters, which shows the beam propagation intensity distribution and evolution behavior are affected largely by the polarization property of such beams, especially in the non-paraxial regime.     

Hollow Gaussian Schell-model beam and its propagation

In this paper, we present a new model, hollow Gaussian Schell-model beams (HGSMBs), to describe the practical dark hollow beams. An analytical propagation formula for HGSMBs passing through a paraxial first-order optical system is derived based on the theory of coherence. Based on the derived formula, an application example showing the influence of spatial coherence on the propagation of beams is illustrated. It is found that the beam propagating properties of HGSMBs will be greatly affected by their spatial coherence. Our model provides a very convenient way for analyzing the propagation properties of partially coherent dark hollow beams.