Propagation of partially coherent beams carrying an edge dislocation through atmospheric turbulence along a slant path

This paper derives the explicit expressions for the average intensity, beam width and angular spread of Gaussian Schell-model (GSM) beams with edge dislocation propagating through atmospheric turbulence along a slant path. The propagation of GSM beams with edge dislocation through horizontal atmospheric turbulence can be treated as a special case through a slant one. The propagation properties of GSM beams with edge dislocation through slant atmospheric turbulence are studied, where the influence of edge dislocation parameters including the slope p and off-axis distance d on the spreading of GSM beams with edge dislocation in atmospheric turbulence is stressed. It shows that the spreading of the intensity profile of GSM beams with edge dislocation along a slant path is smaller than that along a horizontal path in the long-distance atmospheric propagation. The larger the slope vert pvert and the smaller the off-axis distance vert dvert are, the less the beam-width spreading and angular spread of GSM beams with edge dislocation are affected by turbulence. The GSM beams with edge dislocation is less affected by turbulence than that of GSM beams without edge dislocation. The results are illustrated numerically and their validity is interpreted physically.     

空心高斯涡旋光束的远场特性

基于角谱法和稳相法,推导出了空心高斯涡旋光束的TE波和TM波在自由空间远场传输和能流密度的解析表达式,研究了其相位奇点和能流密度分布。结果表明,空心高斯涡旋光束的远场特性主要跟控制参数有关。改变光束中的涡旋离轴量,光涡旋和能流密度黑核会发生移动。圆刃型位错线的半径和能流密度暗环位置跟束腰宽度有关,而能流密度的对称性主要受涡旋离轴量的影响。     

Cross focusing of two coaxial cosh-Gaussian laser beams in a parabolic medium

In this paper authors have presented the cross focusing of two coaxial cosh-Gaussian laser beams of different frequencies in a parabolic medium. Starting from the expression for field distribution of cosh-Gaussian beams, differential equations for beam-width parameters of two beams have been established through parabolic wave equation approach and analytical solution for weak beam has been obtained. The effect of decentred parameter of strong beam on the behavior of beam-width parameter with the normalized distance of propagation for weak beam has been specifically considered. The results have been presented graphically and discussed.     

拉盖尔-高斯模叠加而成的部分相干光的相干涡旋

对Bogatyryova等人近来提出的一种可分离位相的部分相干光的相干涡旋作了详细研究.这类新的光束由相同角向指数的拉盖尔-高斯(LG)模非相干叠加而成.研究表明，叠加LG模式的模指数，权重因子和参考点位置的选择都会影响圆刃型位错出现的位置，使得涡旋消失或出现多个相干涡旋.而且，LG模叠加而成的位相不可分离的部分相干光也存在相干涡旋. 关键词： 奇点光学 一类新的部分相干光束 相干涡旋 圆刃型位错     

Induced focusing and conversion of a Gaussian beam into an elliptic Gaussian beam

We have presented an investigation of the induced focusing in Kerr media of two laser beams, the pump beam and the probe beam, which could be either Gaussian or elliptic Gaussian or a combination of the two. We have used variational formalism to derive relevant beam-width equations. Among several important findings, the finding that a very week probe beam can be guided and focused when power of both beams are well below their individual threshold for self-focusing, is a noteworthy one. It has been found that induced focusing is not possible for laser beams of any wavelength and beam radius. In case both beams are elliptic Gaussian, we have shown that when power of both beams is above a certain threshold value then the effective radius of both beams collapses and collapse distance depends on power. Moreover, it has been found that induced focusing can be employed to convert a circular Gaussian beam into an elliptic Gaussian beam.     

Two orthogonally polarized optical beams in a family of Kerr-law nonlinear shifted parabolic graded-index rod lenses

The field, the propagation and the imaging characteristics of two Gaussian optical beams with orthogonal polarization passing through a family of Kerr-law nonlinear shifted parabolic graded-index rod lenses are investigated. The coupled differential equations of the dimensionless beam-width parameters of two Gaussian optical beams are derived by using a variational approach and then solved. It is concluded that there are two regimes of propagation and that the power, the incident waist radius and the position of one beam have large effects on the field, the propagation and the imaging characteristics of the other beam.     

湍流大气中高斯谢尔光束的波前位错

在Rytov近似下,通过引入短期统计平均位错位置的概念,研究了高斯谢尔光束通过近地面弱湍流大气传播时,波前圆形位错形成和位错位置与湍流大气起伏强度和传播距离等参数间的关系.基于湍流大气中平行和交叉双光束的简化近似传输模型,研究了湍流大气中传播高斯谢尔光束波前位错位置与大气湍流强度、传输距离等参数间的相关机制.在远小于光波位相起伏周期的条件下,分别得出了束径不同同轴双光束和交叉双光束传播情况下波前圆位错位置的湍流系综统计平均理论关系.所得结果表明,同轴平行光束干涉和交叉光束干涉所产生的光束波前位错受大气湍流强度、传输距离等参数调制的规律是不同的.     

The transformation of an edge dislocation in atmospheric turbulence

The explicit expression for the cross-spectral density of partially coherent elliptical Gaussian beams carrying an edge dislocation propagating through atmospheric turbulence along a slant path is derived, and used to study the transformation of the edge dislocation in atmospheric turbulence. We find that the edge dislocation disappears and transforms to a noncanonical coherence vortex, when partially coherent elliptical Gaussian beams with edge dislocation propagate through atmospheric turbulence. The inversion of the topological charge of the coherence vortex may take place. The ellipticity of the beam and slope of the edge dislocation play a dominant role in the evolution of the coherence vortex. In the coherent limit the coherence vortex in turbulence becomes an intensity vortex, however, differing from the case in free-space propagation, the position of the intensity vortex depends on the choice of the reference point. The results are illustrated analytically and numerically.     

Dynamic evolution of Riemann–Silberstein vortices for Gaussian vortex beams

The dynamic evolution of Riemann–Silberstein (RS) vortices for Gaussian vortex beams with topological charges m = ± 1 in free space is studied. It is shown that for Gaussian on-axis vortex beams there exist both RS vortex with m = + 2 and circular edge dislocation. For Gaussian off-axis vortex beams the circular edge dislocation splits into two RS vortices with opposite topological charges m = ± 1 and the RS vortex with m = + 2 decays into two vortices with same topological charges m = + 1. The motion of RS vortices takes place by varying the propagation distance, waist width, off-axis parameter, or topological charge. RS vortices for Gaussian vortex-free beams can be treated as a special case. The results are illustrated analytically and numerically.     

Propagation properties of partially coherent Hermiteben Gaussian beams through non-Kolmogorov turbulence

The propagation properties of partially coherent Hermite—Gaussian beams through non-Kolmogorov atmospheric turbulence are studied. The effects of non-Kolmogorov turbulence and beam nonparaxiality on the average intensity evolution and the beam-width spreading are stressed. It is found that the evolution of the average intensity distribution and the beam-width spreading depends on the generalized exponent factor, namely, on the non-Kolmogorov turbulence strength for the paraxial case. For the non-paraxial case the effect of the turbulence is negligible, while the beam-width spreading becomes very large. The analytical results are illustrated numerically and interpreted physically.     

Propagation properties of partially coherent Hermite–cosh-Gaussian beams through atmospheric turbulence

The analytical expression of partially coherent Hermite–cosh-Gaussian (HChG) beams propagating through atmospheric turbulence is derived and used to study their propagation properties through atmospheric turbulence. It is shown that partially coherent HChG beams propagating through atmospheric turbulence undergo several stages of evolution and a decrease of the spatial correlation length speeds up the evolution process. The smaller the spatial correlation length and the larger the beam orders are, the less the beam-width spreading of partially coherent HChG beams is affected by turbulence. At a sufficiently long propagation distance the beam-width spreading of partially coherent HChG beams with smaller Ch-part parameter and smaller waist width is less affected by turbulence. The results are illustrated by numerical examples, and the validity of the results is interpreted physically.     

部分相干刃型位错光束的谱Stokes奇点

利用交叉谱密度函数的传输公式,推导出部分相干刃型位错光束在自由空间中传输的解析表达式.结合谱Stokes参数,详细讨论了其Stokes场的奇点变化规律.结果表明,部分相干刃型位错光束在自由空间传输过程中存在谱s12,s23和s31奇点.改变刃型位错的离轴量、斜率、空间相关长度等光束参数以及随着传输距离的变化,会有谱Stokes奇点的移动、产生和湮没,也会有V点的产生和C点旋性的反转.     

Effect of Non-Kolmogorov Turbulence on the Spreading of Polychromatic Partially Coherent Hermite–Gaussian Array Beams

Based on the extended Huygens–Fresnel principle, we derive an analytical expression for the beam width of polychromatic partially coherent Hermite-Gaussian array (PPCHGA) beams propagating through non-Kolmogorov turbulence and study in detail the effect of bandwidth, array parameters, and non-Kolmogorov turbulence on the beam-width spreading. We show that the beam width of PPCHGA beams increases with increase in the bandwidth, beam number, and relative distance of beam separation. The spreading of polychromatic array beams with increasing generalized exponent parameter is smaller than that of monochromatic array beams under the same conditions. The results are illustrated by numerical examples.     

Experimental verification of Foreman dislocation model

We present a strain analysis of an edge dislocation core, and a detailed discussion of the Foreman dislocation model. In order to examine the model, the quantitative measurement of strain field around an edge dislocation in aluminum is performed, and high-resolution transmission electron microscopy and geometric phase analysis are employed to map the strain field of the edge dislocation core in aluminum. The strain measurements are compared with the Foreman dislocation model, showing that they are in good agreement with each other when 0.7 ≤ a ≤ 1.5.     

晶体缺陷规范场中的刃位错

本文用位错连续分布方法表出了刃位错所产生的应变和应力场,得到了刃位错芯区内、外的应力场,位错芯区的无限小位错分布用缺陷规范场表出,并在一定规范条件下求解了位错规范场,在刃位错芯区外,其应力场与Volterra位错的应力场完全一样,而在芯区内,当r趋于零,刃位错的应力场为有限,消除了应力的奇异性。 关键词：     

Coherence vortices of partially coherent beams in the far field

Based on the propagation law of cross-spectral density function, studied in this paper are the coherence vortices of partially coherent, quasi-monochromatic singular beams with Gaussian envelope and Schell-model correlator in the far field, where our main attention is paid to the evolution of far-field coherence vortices into intensity vortices of fully coherent beams. The results show that, although there are usually no zeros of intensity in partially coherent beams with Gaussian envelope and Schell-model correlator, zeros of spectral degree of coherence exist. The coherence vortices of spectral degree of coherence depend on the relative coherence length, mode index and positions of pairs of points. If a point and mode index are kept fixed, the position of coherence vortices changes with the increase of the relative coherence length. For the low coherent case there is a circular phase dislocation. In the coherent limit coherence vortices become intensity vortices of fully coherent Laguerre--Gaussian beams.     

Circular beams

A very general beam solution of the paraxial wave equation in circular cylindrical coordinates is presented. We call such a field a circular beam (CiB). The complex amplitude of the CiB is described by either the Whittaker functions or the confluent hypergeometric functions and is characterized by three parameters that are complex in the most general situation. The propagation through complex ABCD optical systems and the conditions for square integrability are studied in detail. Special cases of the CiB are the standard, elegant, and generalized Laguerre-Gauss beams; Bessel-Gauss beams; hypergeometric beams; hypergeometric-Gaussian beams; fractional-order elegant Laguerre-Gauss beams; quadratic Bessel-Gauss beams; and optical vortex beams.     

Possible Mechanism of Plasticity Influenced by Magnetic Field

The strain energy of an edge dislocation in an external static magnetic field is determined by the theory of elasticity and electrodynamics according to the Volterra dislocation model for continuous media. The results show that the strain energy of the edge dislocation in paramagnetic states is increased due to static magnetic field and the increase in the energy of the dislocation is capable of influencing the dislocation depinning which leads to the change of plasticity. This gives an explanation on plasticity induced by magnetic field.     

Wavefront motion in the vicinity of a phase dislocation: “optical vortex”

In the scalar approximation, an analysis is made of the light field structure in the vicinity of a line of the ring phase dislocation corresponding to the zero value of the field formed by the interference of two uniaxial Gaussian beams. The formation of an “optical vortex” or the toroidal motion of a portion of a light flow around a ring phase dislocation is shown.     

Direct laser patterning of self-assembled monolayer using elliptical laser beams: A theoretical parametric study

A theoretical quantitative analysis of processing parameters for application of an elliptical laser beam to achieve maximum patterning area is the focus of this study. Direct laser patterning (DLP) of self-assembled monolayers (SAM) is achieved by localized heating of the sample above the SAM desorption temperature. Through use of elliptical laser beams in the present work, three goals are achieved by analyzing the heat diffusion model and related thermo-kinetics model: (1) optimal working conditions (combination of laser power, scanning velocity and aspect ratio) for DLP to produce maximum feature size, or highest processing velocity at a given power; (2) identification of conditions that reduces the potential thermal damage to the substrate; (3) shedding light on issues related to uniformity or homogeneity of heating a substrate using an elliptical laser beam. A heat diffusion model is employed to provide the resulting surface temperature caused by elliptical laser beams, and the coupled thermo-kinetics model is used to determine the final SAM coverage generated by DLP. Parametric analysis revealed that 70–150 mW can be used to pattern feature sizes in the range of 2–10 times of equivalent circular beam size. It is also found that each elliptical laser beam has a unique optimal aspect ratio to result in the widest feature size for a given laser power and scanning velocity. The edge transition width increases with an increase of the aspect ratio. Keeping the aspect ratio of elliptical laser beam small (i.e. β<20), a sharp edge definition could be obtained; if an aspect ratio larger than 30 is used, a surface with gradual edge definition could be obtained.