Propagation properties of beams generated by Gaussian mirror resonator in uniaxial crystals

Based on the paraxial vectorial theory of beams propagating in uniaxially anisotropic media, we have derived the analytical propagation equations of beams generated by Gaussian mirror resonator (GMR) in uniaxial crystals, and given the typical numerical example to illustrate our analytical results. Due to the anisotropy crystals, the ordinary and extraordinary beams originated by incident beams generated by GMR propagate with different diffraction lengths, thus the linear polarization state and axial symmetry of the incident beams generated by GMR do not remain during propagating in crystals.     

Propagation properties of three-dimensional flattened Gaussian beams in uniaxially anisotropic crystals

Starting from the paraxial vectorial theory of beams propagating in uniaxially anisotropic media, the analytical propagation equations of three-dimensional flattened Gaussian beams (FGBs) in uniaxial crystals are derived and illustrated numerically. It is shown that, due to the anisotropy of crystals, the ordinary and extraordinary beams originated by incident FGBs propagate with different Rayleigh lengths, thus the linear polarization state and axial symmetry of incident FGBs do not remain during propagation in crystals.     

一种新空心光束的理论及实验研究

提出了一种用来描述空心光束的新理论模型——空心高斯光束模型，通过控制光束参数可以方便地调制空心光束黑斑的大小.导出了空心高斯光束经傍轴光学系统的解析传输变换公式.利用导出的公式计算分析了空心高斯光束在自由空间的传输特性.在实验上利用矩阵本征值方法设计了能输出空心高斯光束的光学谐振腔，对实验上得到的空心高斯光束进行了传输特性的研究.结果表明，理论和实验相吻合.该空心高斯光束产生的光势阱为控制冷原子提供了一条新途径. 关键词： 空心高斯光束 光学谐振腔 传输特性     

Wigner distribution function matrix of electromagnetic beams propagating through uniaxial crystals orthogonal to the optical axis

The Wigner distribution function matrix of electromagnetic beams propagating in uniaxial crystals is introduced, and its analytical propagation expressions through uniaxial crystals orthogonal to the optical axis are derived. The application of the Wigner distribution function matrix of the electromagnetic beams propagating through uniaxial crystals orthogonal to the optical axis is illustrated with the stochastic electromagnetic beams.     

Hollow Gaussian beams and their propagation properties

A new mathematical model, described as hollow Gaussian beams (HGBs), is proposed to describe a dark hollow laser beam (DHB). The area of the dark region across the HGBs can easily be controlled by proper choice of the beam parameters. Based on the Collins integral, an analytical propagation formula for the HGBs through a paraxial optical system is derived. The HGBs also can be expressed as a superposition of a series of Lagurerre-Gaussian modes by use of a polynomial expansion. As a numerical example, the propagation properties of a DHB in free space are illustrated graphically. The HGBs provide a convenient and powerful way to describe and treat the propagation of DHBs and can be used conveniently to analyze atoms manipulated with a DHB.     

Propagation and the kurtosis parameter of Gaussian flat-topped beams in uniaxial crystals orthogonal to the optical axis

The analytical formulae for the Gaussian flat-topped beams propagating in uniaxial crystals orthogonal to the optical axis are derived. The numerical results show that the Gaussian flat-topped beams spread at different rates in the directions parallel and orthogonal to the optical axis due to anisotropic crystals. An analytical expression for the kurtosis parameter of the Gaussian flat-topped beams propagating in uniaxial crystals is derived and illustrated with numerical examples. It is shown that the evolution of the kurtosis parameters K_x and K_y depend on the ratio of extraordinary to ordinary refractive indices.     

Propagation of the Hermite–Gaussian beams through misaligned optical system with a circular aperture

By means of expanding a hard-edged aperture into a finite sum of complex Gaussian functions, the approximate analytical formula of one kind of higher-order Gaussian beams called the Hermite–Gaussian beams (HGBs) passing through circular apertured and misaligned optical system is obtained in this paper. The result provides more convenience for studying its propagation than the usual way by using diffraction integral directly. Some numerical simulations are also given for illustrating the propagation properties of the HGBs through the circular apertured optical systems.     

Propagation properties of Lorentz beam in uniaxial crystals orthogonal to the optical axis

The properties of Lorentz beams propagating in uniaxial crystals orthogonal to the optical axis are studied. The diffraction field components and effective beam sizes of the Lorentz beams are derived in analytical forms. Numerical results show that, upon propagating in uniaxial crystals, a Lorentz beam loses its initial Lorentz type distribution. Also, after propagating for sufficient distances, the transverse components would finally convert into a specific four-petal profile with an axial shadow, which may find applications in the optical trapping of particles. It also shows that the Lorentz beam parameters w_0x, w_0y and the ratios of refractive indices have strong influences on the diffraction field components and on the effective beam sizes when propagating in uniaxial crystals.     

Propagation of partially polarized, partially coherent beams in uniaxial crystals orthogonal to the optical axis

The propagation of partially polarized and partially coherent beams in uniaxial crystals orthogonal to the optical axis is investigated. The analytical formulae for the elements of the cross-spectral density matrix of partially polarized and partially coherent beams propagating through uniaxial crystals orthogonal to the optical are derived. The numerical results show that the degree of polarization decreases with the increase of the ratio of extraordinary to ordinary refractive indices at a certain propagation distance, and the influence of uniaxial crystals on the degree of coherent is not so evident. And the beams spread more rapidly in the direction parallel to the optical axis than orthogonal to the optical axis in positive crystal with the propagation distance increasing.     

Ultrasonic diffraction of Bessel light beams in uniaxial gyrotropic crystals

Specific features of the acousto-optic diffraction of Bessel light beams propagating in the vicinity of the optical axis of a uniaxial gyrotropic crystal have been investigated. The dependences of the diffraction efficiency on the acousto-optic interaction length, ultrasound power, and polarization state of the incident Bessel light beam have been analyzed using the coupled-wave equations and the overlap-integral method. It is shown that polarization-independent diffraction of Bessel light beams is observed in paratellurite crystals, when the Bragg diffraction efficiency is independent of the polarization state of the incident beam. The physical reason for this diffraction has been established (both theoretically and experimentally) to be simultaneous implementation of two processes of anisotropic scattering, at which the Bragg synchronism conditions are satisfied for orthogonal polarized Bessel beams with elliptical polarization.     

Propagation of nonparaxial vector hollow Gaussian beams through a circular aperture

Based on the vectorial Rayleith-Sommerfeld formulae, the nonparaxial propagation properties of the vector hollow Gaussian beams (HGBs) through a circular aperture are studied in detail. We describe the derivation of the integral expressions of the propagation of nonparaxial vector HGBs through a circular aperture. The derived expression is independent the approximation of paraxial and far field, which are valid for either far and near field and for the systems in which aperture radius is comparable to or even smaller than wavelength. And it is also strict integral formula for the light field on the axis. Numerical calculation results indicate that there is no difference between derived formulae and the Collins formulae in the situation of paraxial approximation. Using the formula deduced, we calculate the propagation properties of HGBs. The calculated results indicate that the propagation field of vector hollow Gaussian beams is asymmetric in near field, while the propagation field is symmetric in far field. These research results could well shed light on the further understanding of the vectorial property of HGBs through a circular aperture, and would play a guiding role in the practical application of HGBs.     

依据强非局域介质中光孤子相互作用实现全光互联

根据强非局域介质构成的平面介质波导中同频率和同极化的多光束共同传输模型方程,求得了任意斜入射多光束相互作用的精确解析解。基于强非局域介质空间双光孤子的相互作用原理,提出了利用全同孤子作为信号光来实现全光互联,但实现的逻辑也仅仅局限于短距离作用,还对全光开关抑或反相器作了详细叙述,通过实例给出了这类设计的优化方案。     

Hollow elliptical Gaussian beams generated by a triangular prism

Based on the tensor method, an analytical formula for hollow Gaussian beams (HGBs) generated by a triangular prism has been derived, and the propagation properties have been studied. It is shown that hollow elliptical Gaussian beams (HEGBs) can be obtained in the near field after the prism, and that the eccentricity of the output beam is affected by parameters such as the incidence angle, refractive index of the prism and the order of the HGB. It shows that by using a triangular prism one can conveniently obtain HEGBs.     

矢量空心高斯光束横纵向光场传输特性

基于矢量瑞利-索末菲衍射积分,研究了矢量空心高斯光束横向光场和纵向光场在自由空间中的传输特性.研究结果表明,空心高斯光束的横向光场与纵向光场在传输过程中光强分布情况并不相同,横向光场的光强分布具有旋转对称性,并且保持空心特性的距离受光束阶数的影响,而纵向光场不再具有旋转对称性,并且在理想状态下纵向光场可以一直保持空心特...     

Generation of thin and hollow beams by the axicon with a large open angle

We propose a method to produce diffraction-free thin and hollow beams. The method is based on Laguerre-Gaussian (LG) beams incident on a large open-angle axicon. We use the vector diffraction integrals and stationary phase method to deduce a simple and analytical formula of the propagating field of the linearly polarized LG beams through an axicon. The numerical results show that the hollow beams of whose diameter is in the order of the wavelength can be obtained by using the axicon with the refractive index n = 2 and the open angle α = 25°. These diffraction-free thin and hollow beams may be very useful to accurately trap and manipulate atoms. However, when the open angle is over large, the conversion efficiency from the LG beam to the diffraction-free hollow beam will decrease obviously.     

部分相干平顶光束在增益或损耗介质中传输的M2因子

 根据光束在介质中传输强度二阶矩计算公式,推导出部分相干平顶光束在增益或损耗介质中传输的M2因子解析表达式,并将高斯 谢尔模型光束在增益或损耗介质中的传输作为特例统一于一般表达式中。研究结果表明：部分相干平顶光束在增益或损耗介质中传输时的M2因子与光束传输距离、光束相干长度、光束阶数及介质的特性有关。光束在增益或损耗介质中传输的这种特性为应用和控制光束传输提供了理论依据。     

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。     

Spin Hall effect of light in one-dimensional photonic crystal

We established a general propagating model to investigate the spin Hall effect of light in one-dimensional photonic crystal. A polarized (spin dependent) Gaussian beam which was incident obliquely through one-dimensional photonic crystal was demonstrated. Having decomposed a polarized Gaussian beam into different plane wave components charactering individual wave vectors, we revealed the transmission coefficient and reflection coefficient of each plane wave which propagates through the one-dimensional photonic crystal. It enabled us to obtain exact solution to the electric field of transmitted and reflected beams, and the analytical formula of light intensity, accordingly. A method based upon the partial differentials with the intensity distribution of the transmitted and reflected Gaussian beams was presented to determine the transverse and longitude shifts explicitly. Spin dependent shifts in one-dimensional photonic crystal provide alternative evidence for the spin Hall effect of light.     

Excitation of surface wave beams at the interface between linear and nonlinear media

The spatial evolution of quasi-optical electromagnetic-wave beams propagating in the vicinity of an interface between linear and nonlinear media is studied. It is demonstrated that three-dimensional nonlinear surface beams can efficiently be excited by Gaussian beams of optimal shape, incident onto the nonlinear interface at angles exceeding the total internal reflection angle, and that giant nonlinear Goos-Hänchen effect can result from this process.     

Modified hollow Gaussian beam and its paraxial propagation

A model named modified hollow Gaussian beam (HGB) is proposed to describe a dark hollow beam with adjustable beam spot size, central dark size and darkness factor. In this modified model, both the beam spot size and the central dark size will be convergent to finite constants as the beam order approaches infinity, which are much different from that of the previous unmodified model, where the beam spot size and the central dark size will not be convergent as the beam order approaches infinity. The dependences of the propagation factor of modified and unmodified HGBs on the beam order are found to be the same. Based on the Collins integral, analytical formulas for the modified HGB propagating through aligned and misaligned optical system are derived. Some numerical examples are given.