附加球面相位引致Airy光束在单轴晶体传输时的两次镜像演化

利用单轴晶体光束传输理论,求得了具有附加球面相位Airy光束在单轴晶体中的传输公式.数值模拟计算结果表明,线偏振附加球面相位Airy光束在晶体中传输时仍为线偏振,但不是传输不变的.粗略地讲,具有附加球面相位的Airy光束在晶体中传输时,近场是传输不变的;而在由晶体寻常与非寻常折射率和球面半径共同确定的两个特定传输距离处,传输光束转换成了取向不同的Gaussian-Airy光束,且高斯依赖的束宽度敏感地与截断因子相关;而当光束依次穿过此两位置时光斑花样先后相对于两横向轴平面做镜像演化,且镜像演化顺序也与晶体寻常和非寻常折射率相对大小密切相关,其总的效果是远场强度花样能恢复原样但花样取向产生了关于对过横平面二、四象限平分平面的镜像演化.这些结果表明,通过恰当选择晶体材料(即折射率)和附加球面相位的半径R,可以调控光束花样的形状、取向及表征各向异性材料的相关性质.     

Propagation of confluent hypergeometric beam through uniaxial crystals orthogonal to the optical axis

Based on the theory of paraxial electromagnetic beams in anisotropic medium, propagation properties of a linearly polarized confluent hypergeometric (HyG) beam through uniaxial crystals orthogonal to the optical axis are investigated. Analytical expressions are derived for the resultant optical field components. Effects of separate beam parameters together with the ratio of refractive indices of crystals on transversal intensity distributions are revealed by numerical calculations, respectively. It is shown that the beam profile finally converts into an elliptical shape due to influences of anisotropic crystals. Moreover, it is also indicated that through suitable selection of parameters, types of the optical vortices of resultant field would change from a central dark spot to a slight dark ring or an axial shadow during the propagation. These numerical results may provide alternative advantages to the trapping of tiny particles by utilizing HyG beams in practical experiments.     

一维线阵离轴高斯光束通过湍流大气的传输特性

研究了一维(1D)线阵离轴高斯光束通过湍流大气的传输特性，推导出了其光强传输方程. 研究表明，1D线阵离轴高斯光束通过湍流大气传输经历了三个阶段，即在近场其光强分布为类似于入射光的锯齿状分布，随着传输距离的增加逐渐变为平顶分布，最后在远场成为类高斯分布. 湍流的增强会使光束传输经历三阶段的进程加快. 并且，湍流使得不同子光束数的1D线阵离轴高斯光束的归一化光强分布相接近. 此外，子光束数越多的1D线阵离轴高斯光束受到湍流的影响越小；1D线阵离轴高斯光束较高斯光束受到湍流的影响要小. 关键词： 一维(1D)线阵离轴高斯光束 湍流大气 传输特性     

椭圆高斯光束在单轴晶体中垂直于光轴的传输特性

基于光束在各向异性介质中的傍轴矢量传输理论,导出了椭圆高斯光束在各向异性单轴晶体中垂直于光轴的传输公式,并利用此解析式进行数值计算和分析,研究了各向异性介质对x方向偏振的椭圆高斯光束偏振特性的影响. 研究表明,晶体的各向异性对光束的偏振和对称性有较大影响. 关键词： 椭圆高斯光束 单轴晶体 各向异性 传输     

Diffraction properties of four-petal Gaussian beams in uniaxially anisotropic crystal

Propagation properties of polarized four-petal Gaussian beams along the optical axis of uniaxially anisotropic crystals were investigated. Based on the paraxially vectorial theory of beam propagation, analytic expressions of the diffraction light field were obtained. The effects of the anisotropy on the polarization properties of the diffracted four-petal Gaussian beams have also been explained by numerical method. The results elucidate that the linear polarization state and the symmetry of the incident beams cannot be kept during propagation in anisotropic crystals.     

Propagation of a twisted anisotropic Gaussian Schell-model beam beyond the paraxial approximation

With the help of a tensor method, an analytical nonparaxial propagation formula for a twisted anisotropic Gaussian Schell-model (GSM) beam in free space is derived based on the generalized Raleigh-Sommerfeld diffraction integral. The far-field nonparaxial propagation expression for a twisted anisotropic GSM beam is also derived. The paraxial approximation is dealt with as a special case of our general result. Our numerical results show that the nonparaxial propagation properties of a twisted anisotropic GSM beam are closely related to the initial beam parameters (i.e., twist factor, transverse spot width matrix, coherence width matrix and wavelength) and the propagation distance. Our formulae provide a convenient and powerful way for studying the paraxial and nonparaxial propagation of an isotropic or anisotropic GSM beam with or without twist phase in free space.     

Convergence of general beams into Gaussian intensity profiles after propagation in turbulent atmosphere

It is shown that a general shaped laser beam will eventually approach a Gaussian average intensity profile after propagation in turbulent atmosphere. In our formulation, source field at the exit plane of the laser is taken as the product of arbitrary functions of source transverse coordinates with Gaussian exponential modulations. Following the expansion of the arbitrary functions in terms of Hermite polynomials, the average receiver intensity expression is derived using the extended Huygens-Fresnel principle and the conditions for the intensity profile to assume a Gaussian shape are stated. The results are illustrated by simulating various source field distributions.     

Transverse Effects in Slow Light Propagation

The effect of finite control beam on the transverse spatial profile of the slow light propagation in an electromagnetically induced transparency medium is studied. From the second-order wave equation and linear response of an EIT medium to the signal field, we find it is possible to produce an effective waveguide for the signal field. The existence and properties of a set of localized, stationary transverse modes are demonstrated. Especially, by carefully manipulating the profile of the control beam, we can realize single-mode propagation for the signal field, which may be important for potential applications.     

Kerr非线性介质中聚焦像散高斯光束的传输特性

当高功率激光通过Kerr非线性介质传输时,Kerr效应会严重影响激光的传输特性.实际应用中常遇到像散光束.迄今为止,像散光束传输特性的研究大都局限于在线性介质中的传输,而在非线性介质中传输的研究较少,且还未涉及像散激光束通过含光学系统的Kerr非线性介质传输变换的研究.本文主要研究Kerr效应对聚焦光束像散特性和焦移特性的影响,以及聚焦像散高斯光束的自聚焦焦距和光束焦点调控.在光束扩展情况下,推导出了聚焦像散高斯光束在Kerr非线性介质中传输的束宽、束腰位置和焦移的解析公式,研究表明:在自聚焦介质中,随着自聚焦作用增强(如光束功率增强),光束像散越强,但焦移越小;在自散焦介质中,随着自散焦作用增强(如光束功率增强),光束像散越弱,但焦移越大.另一方面,在光束自聚焦情况下,推导出了自聚焦焦距的解析公式,研究表明利用光束像散可以调控光束焦点个数.     

Propagation aspects of Mathieu–Gaussian beams in turbulence

Based on our recent source plane formulation, the propagation characteristics of Mathieu–Gaussian beams in turbulent atmosphere are investigated. In this connection, the average receiver plane intensity expression is deduced using the Huygens–Fresnel integral. Our results offered in the form of graphical illustrations reveal that, for some settings of source and propagation parameters, the center of the source beam is evacuated after propagation, while the initially smaller side lobes begin to grow. In a parallel development, the angular distribution of the beam also changes. At small Gaussian source sizes and transverse components of the wave vector, the source beam profile remains almost invariant throughout the propagation. The larger refractive index structure constant values cause the final Gaussian beam profile to be attained at earlier propagation distances. Smaller refractive index structure constants, on the other hand, do not change the beam profile substantially from that of free space.     

光束偏转器传输特性对系统定向准确度的影响

基于光束在单轴晶体交界面处的折射理论和单轴晶体中的矢量传播理论,研究了基模高斯光束通过铌酸锂光束偏转器后的电场变化,计算得到了光束定向系统探测器输出的中频电流与光束失配角之间的关系曲线.结果表明:通过铌酸锂光束偏转器后的基模高斯光束的电场分布发生了细微的变化,这种细微的电场变化将改变输出中频电流与光束失配角之间的对应关系.借助该修正的数学模型,可提高光束定向系统的角度测量准确度.     

高斯光束通过非线性介质层的限幅效应

本文用数值分析的方法研究了两维高斯光束通过一定厚度的非线性折射介质后在线性空间传播的状态,分析了光束的近场和远场横向强度分布及通过一定孔径光阑的功率.结果表明,在考虑到光束经过非线性介质时,相位与横向分布都会发生变化后,仅在非线性折射效应作用下,在远场就存在限幅效应.在一定的强度范围之内,近场也存在限幅利用的可能性.     

Profile of radial inhomogeneity for stationary self-trapped propagation of laser beams in a non-linear absorbing/amplifying medium with arbitrary non-linearity

Summary This paper presents an analysis of stationary self-trapped propagation of a Gaussian laser beam in radially inhomogeneous absorbing/amplifying medium with saturating non-linearity. Using the paraxial theory, the profile of radial inhomogeneity corresponding to stationary self-trapped propagation has been evaluated.     

Changes in the statistical properties of stochastic anisotropic electromagnetic beams propagating through the oceanic turbulence

On the basis of the extended Huygens?CFresnel principle, an analytical propagation expression for the elements of the cross-spectral density matrix of a stochastic anisotropic electromagnetic beam through oceanic turbulence is derived. From this formula the spectral density, spectral degree of coherence, spectral degree of polarization, orientation angle and the degree of ellipticity of such a beam on propagation are determined. Some numerical calculations are illustrated relating to the anisotropic electromagnetic Gaussian Schell-model beams propagating through oceanic turbulence. The results indicate that the spectral degree of coherence of stochastic anisotropic electromagnetic beams tends to zero with increasing propagation distance through oceanic turbulence, which is in agreement with results previously reported for turbulent atmosphere. It is also found that the changes in the statistical properties of the anisotropic source on propagation are qualitatively different from those of the isotropic source.     

Propagation of Gaussian beam array through an optical system in?turbulent atmosphere

The propagation of Gaussian beam array through an optical system in turbulent atmosphere is studied in this paper. Analytical propagation formulas for the propagation of a Gaussian beam array through an optical system in turbulent atmosphere are derived based on the extended Huygens–Fresnel diffraction principle. Numerical examples are provided to illustrate the propagation property. It is shown that the intensity profile at the receiving plane is significantly affected by the optical system, turbulence intensity and the propagation distance.     

Transformation and shift of a Gaussian light beam upon reflection from a resonant medium

The specific features of the transformation and shift of a Gaussian beam reflected from a resonant absorbing medium are analyzed numerically. The study is based on the expansion of the field of the incident Gaussian beam into plane-wave components by using the Fourier integral transform. The calculations are performed for a frequency range covering the resonance region. The conditions for the splitting of the profile of the reflected beam and for its negative shift are established.     

椭圆平顶高斯光束及其传输特性

 用张量光学方法定义了三维不可分离变量的椭圆平顶高斯光束(EFGB),导出了这种光束经过非轴对称光学系统的传输公式及相应的张量ABCD定律, 并对EFGB经过自由空间的传输作了数值计算。结果表明, EFGB的传输特性依赖于阶次, 而且耦合EFGB的光强分布在传输过程中会发生旋转。     

Propagation Characteristics of a Partially Coherent Gaussian Schell-model Array Vortex Beam in the Joint Turbulence Effect of a Jet Engine and Atmosphere

This work investigates the joint effects of jet engine exhaust-induced turbulence and atmospheric turbulence on the propagation of a partially coherent Gaussian Schell-model Array (GSMA) vortex beam. Using the two-process propagation method, analytical formulae are derived for the cross-spectral density, spectral density, degree of coherence, and beam width of the considered beam. The results show that the considered beam takes different shapes; when the spatial coherence is large, the spectral density of the GSMA vortex beam takes an elliptical shape, whereas when the spatial coherence is smaller, the spectral density remains a Gaussian shape. The evolution profile of the degree of coherence weakens gradually when the propagation distance, topological charge, and turbulence strength increase. Moreover, the profile of the degree of coherence takes the Gaussian profile when the propagation distance is longer or turbulence atmospheric is stronger. Furthermore, the results reveal that the corresponding beam spreads faster with a larger propagation distance, lower spatial coherence, and high-strength turbulence. This study also concludes from the results that the beam is affected more when its propagation is near the jet engine exhaust, which means that this latter has a significant impact.     

Field correlations of flat-topped Gaussian and annular beams in turbulence

Starting from the second order moment formulation for multi-beam incidence, field correlations at the receiver plane of flat-topped Gaussian and annular beams are found in turbulence. Reflecting the information on both the randomness due to turbulence and the field profile of the incident field, field correlations of the flat-topped Gaussian beams are found to become larger at larger source size, smaller flatness parameters and smaller turbulence strengths. For the annular beam structures, field correlations are larger for thicker beams. Field correlations of larger primary beam sized annular incidences are smaller at smaller diagonal distances and larger at larger diagonal distances. As expected, annular beam field correlations are found to be larger at smaller structure constants and at smaller wavelengths. However, at large link lengths, field correlations could be larger than at smaller link lengths due to fact that for annular beams, the field at the centre of the receiver attains very small value at smaller link lengths, however, on propagation in turbulence, receiver field distribution changes to a Gaussian profile.