Propagation of higher-order cosh-Gaussian beams in uniaxial crystals orthogonal to the optical axis

Propagation properties of higher-order cosh-Gaussian (HOCG) beams in uniaxial crystals orthogonal to the optical axis are studied. Analytical formulae for electric fields and kurtosis parameters are derived. Results show that a HOCG beam with larger acentric parameters or beam orders would better preserve its intensity profile when it propagates in uniaxial crystals. At arbitrary propagation distance flat-topped beams can be shaped by selecting appropriate acentric parameters. It is also indicated that kurtosis parameters τ_x and τ_y both increase when acentric parameters take larger values, however, they show different behaviors due to effects of anisotropic crystals.     

Propagation of Gaussian array beams in uniaxial crystals orthogonal to the optical axis

The propagation of phase-locked and non-phase-locked Gaussian array beams in uniaxial crystals orthogonal to the optical axis is investigated. Analytical formulas are derived and the propagation properties of phase-locked and non-phase-locked Gaussian array beams are illustrated by numerical examples. Our results show that for non-phase-locked combination, the Gaussian array beams involve into an elliptical Gaussian-like distribution when the propagation distance is far enough, while for phase-locked combination, the Gaussian array beams involve into a central peak distribution and some small peaks are around the center peak when the propagation distance is far enough.     

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.     

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 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 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.     

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

The analytical formulae for anomalous hollow beam propagating in uniaxial crystals orthogonal to the optical axis are derived. The numerical results show that the anomalous hollow beam spreads at different rates in the directions along and orthogonal to the optical axis. The beam spreads more rapidly in the direction along the optical axis than orthogonal to the optical axis in positive crystal (n_e/n_o>1), and the beam spreads more rapidly in the direction orthogonal to the optical axis than along the optical axis in negative crystal (n_e/n_o<1).     

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.     

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.     

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.     

平顶高斯光束在单轴晶体中的传输

基于光束在各向异性单轴介质中的近轴矢量传输理论，对平顶高斯光束在单轴晶体中的传输 作了研究，得到了解析的传输公式. 利用该传输公式可用一种简单的方法研究平顶高斯光束 在单轴晶体中的传输. 研究结果表明，由于晶体的各向异性特性使平顶高斯光束初始的圆对 称性在传输过程中不能保持，并且其偏振状态也随传输而变化. 用数值计算例对晶体内源于 入射平顶高斯光束的寻常光和非常光的场分布以及x和y方向的偏振分量在空间中的演化都作 了详细说明. 关键词： 平顶高斯光束 单轴晶体 各向异性 近轴矢量理论 传输公式     

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.     

Propagation of Airy Gaussian vortex beams in uniaxial crystals

The propagation dynamics of the Airy Gaussian vortex beams in uniaxial crystals orthogonal to the optical axis has been investigated analytically and numerically. The propagation expression of the beams has been obtained. The propagation features of the Airy Gaussian vortex beams are shown with changes of the distribution factor and the ratio of the extraordinary refractive index to the ordinary refractive index. The correlations between the ratio and the maximum intensity value during the propagation, and its appearing distance have been investigated.     

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     

Propagation and polarization properties of hollow Gaussian beams in uniaxial crystals

Based on the paraxial vectorial theory of beams propagating in uniaxially anisotropic media, we have derived the analytical propagation equations of hollow Gaussian beams (HGBs) 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 HGBs propagate with different diffraction lengths, thus the linear polarization state and axial symmetry of incident HGBs do not remain during propagating in crystals.     

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 chirped Airy vortex beams with x-polarization through uniaxial crystals

The propagation dynamics of a chirped Airy vortex(CAiV) beam with x-polarization in uniaxial crystals orthogonal to the optical axis is studied analytically and numerically. The effect of the ratio of extraordinary and ordinary refractive indices, the chirp parameter, as well as the propagation distance is analyzed, which shows that the focused position of the CAi V beams can be controlled through changing the ratio of the extraordinary and ordinary refractive indices. In addition,with the propagation distance increasing, the asymmetry of the intensity and the angular momentum of the CAi V beam during propagation becomes much more visible. The variation of the chirp parameters can change the attenuation velocity of the vortex as well.     

Additional beams in optically uniaxial crystals

Reasons for occurrence of additional beams are established for rays reflected from a tilted prism face and transmitted through the interface between two crystal media. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 50–53, July, 2007.     

Generation of singular beams in uniaxial crystals

The process of generation and transformation of the structure of singular beams both coherent and incoherent, in a crystal-polarization compensator-polarizer system is studied. It is shown that this system can transform the topological charge of the initial beam. The value of the transformed charge depends both on the structure of the initial beam and on its polarization. The initial singular beams, transferring topological multipoles, are shown to acquire unique properties after passing through the system. This system, in particular, makes it possible to control the position of bound optical vortices and the magnitudes of their angular momenta, which may find practical application in devices for trapping, transportation, and mutual arrangement of microparticles.