Nonparaxial propagation properties of the chirped Airy Gaussian vortex beams in uniaxial crystals orthogonal to the optical axis

In this article, we investigate the nonparaxial propagation properties of the chirped Airy Gaussian vortex（CAiGV）beams in uniaxial crystals orthogonal to the optical axis analytically and numerically. We discuss how the linear chirp parameters, the quadratic chirp parameters, and the Gaussian factors influence the nonparaxial propagation dynamics of the CAiGV beams. The intensity, the energy flow, the beam center, and the angular momentum of the CAiGV beams are deeply investigated. It is shown that the Gaussian factors have a great effect on the intensity and the centroid positions of the CAiGV beams. With the Gaussian factors increasing, the intensity of CAiGV beams decreases rapidly. The main lobes of the transverse intensity distribution of the CAiGV beams are similar to triangles.

Partially coherent nonparaxial modified Bessel-Gauss beams

The concept of partially coherent nonparaxial modified Bessel Gauss （MBG） beams is proposed. Based on the generalized Rayleigh-Sommerfeld diffraction integral, the analytical propagation equations of nonparaxial MBG beams in free space are derived and analysed, and some special cases are discussed. In particular, under the paraxial approximation our results reduce to the corresponding paraxial ones. Numerical calculation examples are given to illustrate the dependence of intensity and spectral degree of coherence on the beam order m, ζ and f parameters, and to compare the difference between the paraxial and nonparaxial results.

Nonparaxial propagation of Hermite-Laguerre-Gaussian beams in uniaxial crystal orthogonal to the optical axis

Analytical expressions for the three components of the nonparaxial propagation of a Hermite-Laguerre-Gaussian （HLG） beam in uniaxial crystal orthogonal to the optical axis are derived. The intensity distribution of an HLG beam and its three components propagating in a uniaxial crystal orthogonal to the optical axis are demonstrated by numerical examples. Although the y and z components of an HLG beam in the incident plane are both equal to zero, they emerge upon propagation inside the uniaxial crystal. Moreover, the beam profile of the x component is relatively stable and the beam profiles of the y and z components have the same evolution law. If the ratio of the extraordinary refractive index to the ordinary refractive index is larger than unity, the beam profile of the HLG beam is elongated in the x direction and generally rotates clockwise. Otherwise, the beam profile of the HLG beam is elongated in the y direction and generally rotates anticlockwise. This research is beneficial to the optical trapping and nonlinear optics involved in the rotation of a beam profile.

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.

Nonparaxial propagation of a super-Lorentz-Gauss SLGmode beam

Based on the vectorial Rayleigh-Sommerfeld integral formulae, this paper derives the analytical nonparaxial propagation equation of a super-Lorentz-Gauss （SLG） SLGo1 mode beam in free space. The far field expression and the scalar paraxial result are treated with special cases of the general formulae. According to the obtained analytical representation, the nonparaxial propagation properties of the SLG01 mode beam are illustrated and analysed with numerical examples. This research provides an approach to investigate the propagation of the SLG01 mode beam within the framework of the nonparaxial regime.

Nonparaxial propagation of a vectorial apertured off-axis Lorentz beam

Based on the vectorial Ftayleigh-Sommerfeld integral formula and the complex Gaussian expansion of the hardedge aperture function, an analytical propagation expression for a nonparaxial vectorial off-axis Lorentz beam passing through a rectangular aperture is derived. The unapertured case, the far field expression and the scalar paraxial result are also presented as special cases of the general formulae, respectively. Some numerical examples are also given to show the propagation characteristics of a nonparaxial vectorial off-axis Lorentz beam through a rectangular aperture. It is indicated that the f parameter, the off-axis displacement and the truncation parameter all play an important role in determining nonparaxial propagation behaviour.

Nonparaxial propagation of radially polarized chirped Airy beams in uniaxial crystal orthogonal to the optical axis

The nonparaxial propagation of radially polarized chirped Airy beams(RPCAiBs) in uniaxial crystal orthogonal to the optical axis is analytically studied. The effects of the first and the second order chirp factors, and the ratio of the extraordinary refractive index to the ordinary refractive index on the nonparaxial evolution of RPCAi Bs in different observation planes are investigated in detail. The results show that when one parameter changes, different components behave differently, and even the same component has various behavior in different directions. The initial slope of RPCAi Bs in the x-direction varies more with the first order chirp factor than that in the y-direction. Meanwhile, with the second order chirp factor becoming larger, the depth of the focus of the y-component in the x-direction decreases while that in the y-direction has no difference. In addition, the different ratios of the extraordinary refractive index to the ordinary refractive index change the difference of the depth of the focus between the x-and the y-components.

The influence of nonparaxiality on the spectral behavior in Young's experiment illuminated by partially coherent light

Starting from the Rayleigh-Sommerfeld diffraction integral, this paper studies the spectral behavior in Young＇s experiment illuminated by nonparaxial partially coherent light and compares with the paraxial case, where the influence of nonparaxiality of partially coherent light on the spectral shifts and spectral switches is stressed. It is shown that there is a spectral shift in the nonparaxial case relative to the paraxial one and the critical position changes, at which the spectral switch occurs. The ratio of the waist width to the central wavelength ω0/λ0 and relative spatial correlation length △ affect the spectral difference. The smaller ω0/λ0 is, the larger the difference between the nonparaxial and paraxial results appears. The effect of relative spatial correlation length △ is relatively small.

Propagation and focusing characteristics of the Bessel-Gaussian beam with the spiral phase term of new power-exponent-phase

A new type of beam called the NPEP-BG(a Bessel-Gaussian(BG)beam with a spiral phase term of a new powerexponent-phase(NPEP))is theoretically studied in this paper.The results show that the number of singularities of the phase and side lobes of the intensity of this beam were equal to the topological charges(TCs)and the beam has the characteristics of self-healing during propagation.The NPEP-BG beam combined the partial characteristics of the new power-exponentphase vortex(NPEPV)and the Bessel-Gaussian beam.At the focus of the beam,the characteristic like a perfect vortex beam was present,in which the focal radius is stable and independent of the topological charge.There are multi-focal spots around a ring in the focal plane,meaning that the NPEP-BG beam has a potential for application in multi-particle manipulation.

The Wigner distribution functions of coherent and partially coherent Bessel-Gaussian beams

Based on the integral representation of the Bessel functions and the generating function of the Tricomi function, an analytical expression of the Wigner distribution function （WDF） for a coherent or partially coherent Bessel Gaussian beam is presented. The reduced two-dimensional WDFs are also demonstrated graphically, which reveals the dependence of the reduced WDFs on the beam parameters.

Electron acceleration by two crossed Bessel-Gaussian beams in vacuum

The direct acceleration of electrons by using two linearly polarized crossed Bessel-Gaussian （BG） beams with equal frequency and amplitude in vacuum is proposed and studied. It is shown that two linearly polarized BG beams of the same order （0 or 1） with a π-rad phase difference have a resultant non-zero longitudinal electric field on the z-axis and can be used, in principle, to accelerate electrons.

Propagation of Modified Bessel-Gaussian Beams in a Misaligned Optical System

The formalism of generalized diffraction integral for paraxial misaligned optical systems is used to investigate the propagation of the Modified Bessel-Gaussian (MBG) beam through a misaligned thin lens. The properties of the propagation of MBG beam traveling through this misaligned ABCD optical system are discussed. A special case of misaligned circular thin lens is illustrated analytically and numerically. The shape of the MBG beam at the exit of the misaligned optical system is unchanged;however the center of the beam is shifted from the propagation axis in correlated manner with the design parameters of the optical system.

Vectorial Hermite-Laguerre-Gaussian beams beyond the paraxial approximation

Starting from the vectorial Rayleigh-Sommerfeld integrals, the free-space propagation expressions for vectorial Hermit-Lagucrre-Gaussian （HLG） beams beyond the paraxial approximation are derived. The far-field expressions and the scalar paraxial results are given as special cases of our general expressions. The intensity distributions of vectorial nonparaxial HLG beams are studied and illustrated with numerical examples.

Walk-off reduction,using an external optical plate and Bessel-Gaussian interaction

To reduce the walk-off angle of the extraordinary third-harmonic ultraviolet wave at 355 nm generated by type ⅡKTiOPO4 and type I β-BaB2O4 optical crystals,and the Gaussian output beam of a Q-switched Nd：YAG laser,a simple theoretical model was developed based on a rotatable BK7 plate of variable thickness.By rotating the plate up to 35°along the beam direction,we reduced the walk-off angle up to ~ 13%.The same phenomenon is predicted by the model,confirming the performance of the model.It is found that,due to the walk-off effect,the intensity profile of the thirdharmonic generation beam is slightly degraded.To compensate for the observed phenomena and further reduce the walkoff,we used a combination of a convex lens and an axicon to transform the beam profile of the interacting fundamental and second-harmonic generation waves to the zero-order Bessel-Gaussian form.As a result,the walk-off is decreased to~ 48.81 mrad,providing ~ 30%relative reduction.By using the same BK7 plate rotated up to 35° along the third-harmonic beam direction,the walk-off angle is further reduced to 38.9 mrad.Moreover,it is observed that the beam profile of the emerged Bessel-Gaussian third-harmonic generation beam remains unchanged with no degradation.

Talbot effect in nonparaxial self- accelerating beams with electromagnetically induced transparency

In this study,we report on the fractional Talbot ffect of nonpar axial self-accelerating beams in a multilevel electromagnetically induced transparency(EIT)atomic configuration,which,to the best of our knowledge,is the first study on this subject.The Tallbot ffect originates from superposed eigenmodes of the Helmholtz equation and forms in the EIT window in the presence of both linear and cubic susceptibilities.The Talbot ffect can be realized by appropriately selecting the cofficients of the beam components.Our results indicate that the larger the radial difference between beam components,the stronger the interference between them,the smaller the Tallbot angle is.The results of this study can be useful when studying optical imaging.optical measurements,and optical computing.

The nonparaxial property of chirped pulsed beam

The nonparaxial property of the chirped pulsed beam is analyzed both quantitatively and qualitatively. Through the qualitative investigation of the paraxial approximation condition, we show there are chirp-induced changes in the nonparaxial propagation of the chirped pulsed beam. A quantitative nonparaxial correction was developed by use of the perturbational technic and the Fourier transform for a few-cycle chirped pulsed beam with relative small chirp parameter. It was shown that the nonparaxial corrections were enhanced near the leading or trailing edge of pulse depending on weather the chirp parameter is positive or negative. An example for pulsed Gaussian beam driven by a chirped Gaussian pulse is shown in the numerical result to confirm our analysis.

旋转双棱镜光束指向解析解

光束指向机构实现光束指向调整时,需要搞清两棱镜的方位与出射光束指向位置之间的关系。本文采用一级近轴近似方法和非近轴光线追迹方法研究了旋转双棱镜指向系统的光束指向机制,由两棱镜的旋转角度推算出了出射光束指向的解析公式。对比分析了两种方法的研究结果并设计旋转双棱镜光束指向实验进行了验证。结果显示,非近轴光线追迹方法能准确地描述系统光束偏转机制,而传统的一级近轴近似方法的分析结果与实验值存在偏差,且光束的偏转角越大,偏转角的一级近轴近似解与实验值的差异越明显。当两棱镜旋转角之差为90°时,光束方位角的一级近轴近似解与实验值的差异最大。实验表明,对于大偏转角度旋转双棱镜光束指向系统,应采用非近轴光线追迹方法来探讨其光束偏转机制。

对激光光束质量一些问题的认识

从对激光光束质量研究进展开始,讨论了在傍轴和非傍轴范畴内激光光束质量的一些问题,主要是非傍轴光束的光束质量评价。光束传输的非傍轴矢量二阶矩理论可用于计算多种非傍轴光束的M2因子,但对M2因子的物理解释却有困难。例如,在非傍轴范畴,M2因子依赖于束腰宽度与波长之比,并可小于1。但远场发散角之值可趋于90,°这将导致很大的M2因子值。另一方面,若将公式中的光强用时间平均坡印廷矢量z分量代替,桶中功率(PIB),或等价地,!参数可推广用于评价非傍轴光束的远场光束质量。PIB表征了光束功率的可聚焦能力,是一种简明、直观评价不同激光光束的方法。然而,在!参数的公式中的束宽是按功率含量百分比定义的,因此双曲线传输规律不再严格成立。

旋转双棱镜光束指向的反向解析解

用旋转双棱镜系统控制光束指向时,需要由光束的目标指向位置推算两棱镜的旋转角度(称为反向问题)。本文采用一阶近轴近似方法和非近轴光线追迹方法探讨了旋转双棱镜系统反向问题的完整解析解。首先,基于一阶近轴理论,利用中心算法分析了反向问题的近似解。然后,基于矢量形式的斯涅尔定律对系统进行非近轴光线追迹,用两步算法推算出反向问题的精确解。对比分析两种方法所得的反向解差异并设计实验对结果进行了比较和验证。结果表明,针对一个确定的光束目标指向位置,存在两套反向解。相对一阶近轴近似方法,非近轴光线追迹法推算的反向解更加准确。对于大偏转角度的旋转双棱镜光束指向系统,非近轴光线追迹法是推算其精确反向解的有效方法。

非傍轴截断平顶光束的质量因子

使用功率密度的二阶矩方法和Li提出的平顶光束模型,推导出了非傍轴截断平顶光束的束腰宽度、远场发散角和光束质量因子的解析表达式。计算结果表明:非傍轴截断平顶光束的质量因子不仅与截断参数、光束阶数有关,而且与初始束腰宽度和波长之比有关;当截断参数趋近于0时,远场发散角趋于渐近值63.435°;对于光束阶数为1和截断参数趋于无穷大的特例,计算结果分别退化为非傍轴截断高斯光束和非傍轴无截断平顶光束的结果;功率密度的二阶矩方法可用于截断光束,并克服了光束质量因子的发散困难。