余弦高斯光束在梯度折射率介质中的传输特性

 为了研究光束在梯度折射率介质中的传输规律,利用广义惠更斯-菲涅耳衍射积分法,推导出余弦高斯光束在梯度折射率介质中传输的解析表达式,对余弦高斯光束在梯度折射率介质中的传输特性进行了分析,并进一步讨论了介质梯度折射率系数和调制参数对传输特性的影响。结果表明,余弦高斯光束在梯度折射率介质中传输时,轴上光强分布呈现周期性变化,横向光强分布受梯度折射率系数和调制参数影响较大。余弦高斯光束传输时具有不稳定性,通过适当调节参数,可在空间某位置实现余弦高斯光束的整形。     

高斯光束在对数型非线性介质中自诱导效应

从标量Helmholtz方程出发,推导了对数饱和非线性介质中光场满足的非线性Schr dinger方程(NLSE)。通过与梯度折射率下的光场满足的方程比较,发现高斯光束在对数型饱和非线性介质中可自诱导梯度折射率。利用数值计算,详细地讨论了自诱导梯度折射率对高斯光束传输特性的影响。发现高斯光束在其自诱导的梯度折射率的影响下,呈振荡形式的准稳定的传输。光束注入介质中的初始状态,直接影响着光束的振荡形式(先发散还是先聚焦)、振荡深度(幅度)、振荡周期。得到高斯光束形成孤子的条件,以及若使高斯光束在对数饱和非线性介质中保持小损耗、高稳定的传输,应该使光束在阈值(孤子条件)附近注入介质的结论。     

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。     

梯度折射率介质中高斯光束的非线性传输特性

 利用无像差自聚焦理论研究了梯度折射率非线性Kerr介质中高斯光束的传输特性,得到了高斯光束光斑半径和波面曲率半径的表达式。解析结果清楚地表明了衍射、自聚焦以及梯度折射率效应之间的竞争对高斯光束传输行为的影响。梯度折射率效应使光束自聚焦的距离缩短。     

平顶高斯光束在梯度折射率介质中的传输特性

 利用广义惠更斯-菲涅耳衍射积分法,推导出平顶高斯光束在梯度折射率介质中传输时的解析表达式,对平顶高斯光束在梯度折射率介质中的传输特性进行了分析,讨论了介质梯度折射率系数和光束阶数对传输特性的影响。研究表明,平顶高斯光束在梯度折射率介质中传输时轴上光强分布呈现周期性变化,其周期决定于介质梯度折射率系数,而与光束的阶数无关;轴上峰值处的横向光强分布受梯度折射率系数和光束阶数的影响较大,横向光强的最大值随着梯度折射率系数的增大而增大。     

负折射率平板透镜系统中的光束聚焦及相位补偿特性

利用平面角谱理论,建立厄米-高斯光束和拉盖尔-高斯光束在负折射率平板透镜系统中的傍轴传输模型,研究负折射率平板透镜中厄米-高斯光束和拉盖尔-高斯光束强度聚焦及相位补偿特性。结果发现:负折射率平板透镜产生的反向Gouy相移可以补偿空气中Gouy相移导致的相差,因而在满足相位匹配条件下,光束在物平面和像平面之间的相差为零;当强度聚焦和相位匹配条件同时满足的条件下,光束在物平面强度和相位分布可在像平面实现完全重构。     

部分相干平顶光束在梯度折射率介质中的传输特性

利用广义惠更斯-菲涅尔衍射积分方法,推导出部分相干平顶光束在梯度折射率介质中传输的交叉谱密度函数解析表达式,对部分相干平顶光束在梯度折射率介质中的传输特性进行了分析,并进一步讨论了介质梯度折射率系数、光束阶数以及光束相干性对传输特性的影响.结果表明,部分相干平顶光束在梯度折射率介质中传输时的轴上光强分布呈现周期性变化了,且周期由梯度折射率系数决定,而与光束相干性无关.光束阶数越高、相干性越好、介质梯度折射率系数越大,则在介质中的轴上峰值光强越大.并且,在光强峰值位置附近的光强分布随传输距离的变化非常剧烈.     

多层介质中的光自旋霍尔效应研究

本文研究了光束通过多层介质分界面的光自旋霍尔效应. 以三层介质为例,建立了光束通过棱镜-空气-棱镜结构的传输模型,揭示了横移与空气介质的厚度、折射率梯度以及入射角等因素的定性关系. 发现对某一特定的圆偏振光束,改变两棱镜之间的折射率梯度可以调控横移,反射场与传输场的横移方向取决于折射率梯度. 相对于两层介质来说,高斯光束通过三层介质能明显地增强光自旋霍尔效应. 研究多层介质中光自旋霍尔效应横移的影响因素可为调控和增强光自旋霍尔效应提供理论依据. 关键词： 光自旋霍尔效应 横移 折射率梯度     

任意光束形状和介质厚度的Z扫描技术

利用分步傅里叶算法结合坐标变换理论,建立了在光致折射率改变介质中任意形状光束的传输、聚焦模拟方法,能够用于计算任意光束形状、任意介质厚度的Z扫描开孔和闭孔拟合曲线。在薄介质和高斯光束条件下,该方法的拟合曲线与经典算法相吻合。在平顶光束情况下,该方法的拟合结果与实验数据基本一致。利用此方法测量了LiTaO3晶体的非线性吸收和非线性折射率系数,并对高斯光束和涡旋光束在厚介质中的Z扫描过程进行了分析。     

高斯光束在任意分布的径向梯度折射率介质中传输的计算方法

根据弱波导近似,本文建立了处理高斯光束在任意分布的径向梯度折射率介质中传输的计算方法,并具体计算和讨论了高斯光束腰斑在沿径向呈抛物型分布的介质中随传输距离的变化情况,其数值结果与解析近似符合。     

Mutual-focusing of two co-propagating beams and formation of trapped spatial breather pair in saturable nonlinear media

In this paper, using parabolic equation approach, coupled propagation of two coaxially co-propagating and mutually incoherent bright cylindrical beams in saturable nonlinear medium has been investigated. Considering the coupling coefficient equal to unity (κ=1), a detailed account of formation of spatial soliton pair (i.e. both beams are stationary trapped) and spatial breather pair (i.e. width of each beam oscillates with the propagation distance) has been provided and existence of spatially trapped breather pair (i.e. average width of each breather of the pair does not change with the propagation distance) has been shown. Conditions of formation of trapped spatial breather pair and their existence line has also been revealed for arbitrary beam width ratio of the beams. It is revealed that spatial soliton pairs are just a special case of trapped breather pair. The regions (conditions) of mutual-focusing and mutual-defocusing of spatial soliton pair/breather pair have also been identified. Lastly, the law of trapped breather pair formation is proposed.     

A closed form of a kurtosis parameter of a hypergeometric-Gaussian type-Ⅱ beam

Based on the irradiance moment definition and the analytical expression of waveform propagation for hypergeometricGaussian type-Ⅱ beams passing through an ABCD system, the kurtosis parameter is derived analytically and illustrated numerically. The kurtosis parameters of the Gaussian beam, modified Bessel modulated Gaussian beam with quadrature radial and elegant Laguerre–Gaussian beams are obtained by treating them as special cases of the present treatment. The obtained results show that the kurtosis parameter depends on the change of the beam order m and the hollowness parameter p, such as its decrease with increasing m and increase with increasing p.     

复宗量Laguerre-Gauss光束在强非局域非线性介质中的传输

研究得到了偏离束腰入射的复宗量Laguerre-Gauss光束在强非局域非线性介质中传输的解析表达式,并且得到了其二阶矩束宽的解析解.通过例子研究了偏离束腰入射的复宗量Laguerre-Gauss光束在强非局域非线性介质中传输性质.结果表明：非(0, m)模的复宗量Laguerre-Gauss光束的光束形状随着传输而发生改变,并以Δz=πz_c为周期做周期性演化.而(0,m)模复宗量Laguerre-Gauss光束在演化过程中则形状保持不变,仅改变光束宽度;不论功率多大,在偏离束腰入射条件下总是表现为呼吸子;只有当其为束腰入射,并且入射功率等于临界功率时才能形成孤子. 关键词： 强非局域非线性 复宗量Laguerre-Gauss光束 二阶矩束宽 空间光孤子     

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.     

偏离束腰入射对非局域非线性介质中高斯光束演化的影响

从1+1维强非局域模型出发，讨论了偏离束腰入射的高斯光束在非局域非线性介质中的传输 特性，得到了精确的解析解.结果表明，在聚焦介质中偏离束腰入射时，不论入射功率多大 ，光束束宽将发生周期性波动，光孤子不复存在，这与从高斯光束束腰入射的情况有本质的 不同；入射功率决定了光束平均束宽的大小，入射位置决定了光束初始的演化趋势.比较了在入射位置相同的条件下，聚焦介质、散焦介质和线性均匀介质中光束的演化.给出了“空 间啁啾”的定义，偏离束腰入射的物理本质是光束的不同入射位置对应不同的初始空间啁啾 .空间啁啾的概念， 关键词： 非局域非线性介质 空间光孤子 高斯光束     

Roughness and gradient parameters for characterising shape uniformity of laser beams

We define six parameters, the roughness parameter, the local gradient parameter, the directionless gradient parameter, the integral gradient parameter, the directionless integral gradient parameter and the absolute gradient parameter for characterising the uniformity of a laser beam in its transversal section. For shape-invariant beams the roughness parameter is propagation invariant. The absolute gradient parameter is propagation invariant for symmetric shape invariant beams. As an example, five of the defined parameters are calculated for a dummy irradiance. The values of the roughness parameter and the absolute parameter are calculated and tabulated for symmetric Hermite–Gaussian, Laguerre–Gaussian, spherical Gaussian, flattened Gaussian (at the waist plane) and super Gaussian beams (at the waist plane). The results are discussed.     

ABCD matrix formalism for propagation of Gaussian beam through left-handed material slab system

We apply a simple ABCD matrix formalism to investigate beam propagation in left-handed material (LHM) slab systems. Firstly, we derive the expressions for the matrix elements for a single LHM slab. Based on the ABCD matrix, we obtain the field distributions both inside and outside the LHM slab, and the conditions for focusing and phase compensation of the Gaussian beam. Secondly, the derived ABCD law is applied to analyze the propagation properties of Gaussian beams through various cascaded LHM slab systems. The corresponding focusing and phase compensation conditions of the Gaussian beam are also obtained. Our theoretic formalism may be applied as a compact and effective tool for the research of light beam propagation in complex LHM slab systems, since it avoids the complicated integral operation.     

强非局域非线性介质中光束传输的Ince-Gauss解

利用强非局域非线性介质中傍轴光束传输的线性模型（Snyder-Mitchell模型）讨论了椭圆坐标系下光束传输过程,通过设立Ince多项式对Gauss函数的调制解得到了强非局域非线性介质中光束稳定传输的Ince-Gauss解.当Ince-Gauss光束的入射功率为临界功率时,光束保持孤子形式传输,否则传输光束的束宽呈现周期性波动,即为呼吸子形式.同时还数值模拟了呼吸子的传输过程.Ince-Gauss光在一定条件下可以连续转换为Hermite-Gauss光或Laguerre-Gauss光,图示展现了几个低阶Ince型光孤子及其转换情况. 关键词： 强非局域非线性介质 Ince-Gauss光 Laguerre-Gauss光 Hermite-Gauss光     

Propagation of elegant Laguerre–Gaussian beams through an annular apertured paraxial ABCD optical system

Based on the generalized Huygens–Fresnel diffraction integral and the expansion of the hard aperture function into a finite sum of complex Gaussian functions, the approximate analytical expression of elegant Laguerre–Gaussian beams passing through a paraxial ABCD optical system with an annular aperture is derived. Meanwhile, the corresponding closed-forms for the unapertured, circular apertured or circular black screen cases are also given. The obtained results provide more convenience for studying their propagation and transformation than the usual way by using diffraction integral formula directly. Some numerical examples are given to illustrate the propagation properties of elegant Laguerre–Gaussian beams.     

Range of turbulence-negligible propagation of Gaussian Schell-model array beams

For linear Gaussian Schell-model (GSM) array beams, the range of turbulence-negligible propagation, in which all of the spatial and angular spreading and the beam propagation factor increasing due to turbulence can be neglected, has been investigated in detail. It is shown that this range of GSM array beams increases with decreasing turbulent parameter and coherent parameter, and depends on the beam number, the waist width, and the relative beam separation distance. This range of a GSM array beam is larger than that of a coherent Gaussian array beam, and this range of a GSM array beam with a large relative beam separation distance is larger than that of a single GSM beam, implying that a GSM array beam may be more appropriate to be used in atmospheric optical communication links than a coherent Gaussian array beam or a GSM beam.