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 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).     

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.     

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.     

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.     

Characteristics of paraxial propagation of a super Lorentz—Gauss SLG01 mode in uniaxial crystal orthogonal to the optical axis

Analytical propagation expression of a super Lorentz-Gauss（SLG） 01 mode in uniaxial crystal orthogonal to the optical axis is derived.The SLG 01 mode propagating in uniaxial crystal orthogonal to the optical axis mainly depends on the ratio of the extraordinary refractive index to the ordinary refractive index.The SLG 01 mode propagating in uniaxial crystals becomes an astigmatic beam.The beam spot of the SLG 01 mode in the uniaxial crystal is elongated in the x-or y-direction,which is determined by the ratio of the extraordinary refractive index to the ordinary refractive index.With the increase of the deviation of the ratio of the extraordinary refractive index to the ordinary refractive index from unity,the elongation of the beam spot also augments.In different observation planes,the phase distribution of an SLG 01 mode in the uniaxial crystal takes on different shapes.With the variation of the ratio of the extraordinary refractive index to the ordinary refractive index,the phase distribution is elongated in one transversal direction and is contracted in the other perpendicular direction.This research is beneficial to the practical applications of an SLG mode.     

Wigner distribution function of Lorentz and Lorentz–Gauss beams through a paraxial ABCD optical system

Based on the Collins integral formula and the Hermite–Gaussian expansion of a Lorentz function, an analytical expression for the Wigner distribution function (WDF) of Lorentz and Lorentz–Gauss beams through a paraxial ABCD optical system is derived. The properties of the WDF of Lorentz and Lorentz–Gauss beams propagating in free space are demonstrated. The normalized WDFs of Lorentz and Lorentz–Gauss beams at the different spatial points are depicted in the several observation planes. The influences of the beam parameters on the WDF of Lorentz and Lorentz–Gauss beams in free space are also analyzed at different propagation distances. The special WDF of a Lorentz beam results in its higher angular spreading than the Gaussian beam.     

Spectral switches of partially coherent nonparaxial beams diffracted at an aperture

Based on the generalized Rayleigh diffraction integral, the spectral shifts and spectral switches of nonparaxial partially coherent beams diffracted at an aperture are studied. Our main attention is paid to the effect of beam nonparaxiality on the spectral switches of partially coherent beams. It is shown that the spatial coherent parameter β, trunction parameter δ and waist width-to-central wavelength ratio w₀/λ₀ affect the behavior of spectral switches. Only when β, δ and w₀/λ₀ satisfy certain conditions, can the difference between the nonparaxial and paraxial results be negligible. The discrepancy arises physically from the change of the spectral modifier by using the paraxial approximation.     

大气湍流中光束束宽扩展和角扩展的比较研究

以厄米-双曲余弦-高斯（H-ChG）光束为例,对H-ChG光束通过大气湍流传输时的束宽扩展和角扩展做了详细研究.用相对束宽和相对角扩展代替束宽和角扩展来研究湍流对光束影响的灵敏程度.研究表明,折射率结构常数C²_n越小,光束束宽扩展和角扩展越小.有较大阶数m,n,较小参数Ω₀和束腰宽度w₀ H-ChG光束的角扩展受湍流影响较小.当传输距离足够远时,这一结论对H-ChG光束的束宽扩展也成立.当传输距离不长时,对H-ChG光束相对束宽随Ω₀和w₀的变化规律做了分析.用数值计算例做了说明,并对结果的正确性做了物理解释.厄米-高斯,双曲余弦高斯和高斯光束在大气湍流中的扩展可作为H-ChG光束的特例来处理. 关键词： 束宽扩展和角扩展 大气湍流 厄米-双曲余弦-高斯光束     

Intensity fluctuations in J-Bessel–Gaussian beams of all orders propagating in turbulent atmosphere

The scintillation index of a J _n -Bessel–Gaussian beam of any order propagating in turbulent atmosphere is derived and numerically evaluated at transverse cross-sections with the aid of a specially designed triple integral routine. The graphical outputs indicate that, just like the previously investigated J ₀-Bessel–Gaussian beam, higher-order members of the family also offer favorable scintillation characteristics at large source sizes. This advantage is maintained against rising beam orders. Viewed along the propagation axis, beams with lower orders and smaller widths exhibit smaller values of the scintillation index at shorter propagation distances and large values at longer propagation distances. Further, it is shown that the scintillation index of the J _n -Bessel–Gaussian beams (n>0) is larger than that of the fundamental Gaussian and the J ₀-Bessel–Gaussian beams only near the on-axis points, while remaining smaller towards the edges of the beam.     

Polarization fluctuations of Gaussian Schell-model type photon beams in a slant channel with non-Kolmogorov turbulence

Polarization properties of Gaussian Schell-mode type photon beams propagating through the non-Kolmogorov turbulence in a slant channel are studied which are based on the model of quantum field and the effective photon annihilation/creation operator. Our numerical results show that the degree of polarization increases with the increasing of the transverse coherent width of source ρ_s0, the source's transverse size ω₀ and the power law of the turbulent spectrum, but the degree of polarization P decreases as the zenith angle θ increases. The effect of the wavelength of light beam on the degree of polarization of Gaussian Schell-model beams is small.     

Spreading of apertured partially coherent beams in turbulent media

The closed-form expression for the mean-squared width of apertured partially coherent beams propagating through turbulent media is derived by using the integral transform technique. The influence of turbulence on the spreading of apertured partially coherent beams is studied quantitatively by examining the relative mean-squared width, which is defined as the ratio of the mean-squared width of an apertured partially coherent beam in turbulence to the mean-squared width of the same beam in free space. On the other hand, the range of turbulence-independent propagation, also a reasonable measure of the resistance of a beam to turbulence, is obtained by examining the mean-squared width. It is shown that the spreading of apertured partially coherent beams is less affected by turbulence with smaller truncation parameter δ and coherence parameter α than with larger δ and α. In addition, the influence of turbulence on the spreading of apertured partially coherent beams increases first and then decreases due to increasing waist width w₀. The results obtained are explained physically.     

湍流对环状光束扩展的影响

采用积分变换技巧,推导出了环状光束通过湍流大气传输二阶矩束宽的解析表达式,并研究了湍流对环状光束扩展的影响.另一方面,通过分析二阶矩束宽给出了环状光束不受湍流影响的传输范围,指出环状光束将不受到湍流大气影响的条件.研究表明,光束遮拦比ε、阶数M（N）、波长λ越大,束宽w₀越小,则环状光束受湍流大气的影响就越小.并对所得到的主要结果给出了合理的物理解释. 关键词： 环状光束 大气湍流 二阶矩束宽     

Anomalous spectral behavior of vectorial apertured ultrashort pulsed beams beyond the paraxial approximation

Based on the vectorial Rayleigh diffraction integrals, the analytical expression for the spectral intensity of a vectorial nonparaxial ultrashort pulsed Gaussian beam diffracted at a circular hard-aperture is derived. The effect of f-parameter (f = 1/k₀w₀) on the spectral anomalies near phase singularities of the vectorial nonparaxial ultrashort pulsed beams is studied. It is shown that the spectral switch near the phase singularity of diffracted vectorial nonparaxial ultrashort pulsed beam still exists beyond paraxial regime, but disappears when the f-parameter is larger than a certain value.     

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.     

Aperture averaging beam-wander of multi-Schell quantization beam in a turbulent atmosphere

We study the effects of the mode number of the multi-Schell Gaussian model beams on aperture averaging wander of quantization Gaussian beams propagating through weak turbulence fluctuation channel. The results demonstrate that there is an optimal sub-Schell beam number M_opt, in here the beam wander is minimum. Because of the beam spreading of turbulence and vacuum diffraction, and aperture smoothing effect of the multi-beam jitter, the impact of zenith angle of channel and turbulent outer scale on the beam wander is tiny. The beam wander of the multi-Schell Gaussian model beams is increased as the increasing of the wavelength λ.     

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.     

Current neutralization and plasma polarization for intense ion beams propagating through magnetized background plasmas in a two-dimensional slab approximation

A two-dimensional electromagnetic Particle-in-Cell （PIC） simulation model is proposed to study the propagation of intense, ion beams with beaIn width wb small compared to the electron skin depth c/wpe through background plaslnas in tile presence of external applied magnetic fields. The effcctive eleetron gyrora,dius wge is found to be an important parameter for ion beam transport in the presence of magnetic fields,In the bealn regions, the background plasmas respond differently to the ion beanl of width wb〈wge and wb 〉 wge for the given magnetic field and beaan encrgy, For the case of beam width wb 〈 wge with relative weak external magnetic fiehts, the rotalion effects of plasma electrons a,re found to be signifieant and contributes to the signitica,nt enilaneeinent of the self electric and seif-magnetic fields. While for the ease of beam width wb 〉 wge with relative strong external magnetic fields, the rotation effects of plasma cleetrons are strongly inhibited and a, well neutraliza, tion of ion beam current can be found. Finally, the influences of diftiuent beam widths. beam energies and magnetic fields on the neutralization of ion bc, anl eurrellt are summarized for the eases of wb 〈 wge〈 c/wpe,wge 〈wb〈c/wbp and wb〈c/wpe〈wge.     

Mechanism of the quasi-zero axial acoustic radiation force experienced by elastic and viscoelastic spheres in the field of a quasi-Gaussian beam and particle tweezing

The present analysis investigates the (axial) acoustic radiation force induced by a quasi-Gaussian beam centered on an elastic and a viscoelastic (polymer-type) sphere in a nonviscous fluid. The quasi-Gaussian beam is an exact solution of the source free Helmholtz wave equation and is characterized by an arbitrary waist w₀ and a diffraction convergence length known as the Rayleigh range z_R. Examples are found where the radiation force unexpectedly approaches closely to zero at some of the elastic sphere’s resonance frequencies for kw₀ ? 1 (where this range is of particular interest in describing strongly focused or divergent beams), which may produce particle immobilization along the axial direction. Moreover, the (quasi)vanishing behavior of the radiation force is found to be correlated with conditions giving extinction of the backscattering by the quasi-Gaussian beam. Furthermore, the mechanism for the quasi-zero force is studied theoretically by analyzing the contributions of the kinetic, potential and momentum flux energy densities and their density functions. It is found that all the components vanish simultaneously at the selected ka values for the nulls. However, for a viscoelastic sphere, acoustic absorption degrades the quasi-zero radiation force.