涡旋光束轨道角动量在大气湍流传输下的特性分析

从拉盖尔-高斯涡旋光束表达式出发,基于瑞利衍射理论,通过研究涡旋光束在大气湍流中传输时的旋转相干函数的变化规律,总结了涡旋光束在大气湍流中传输时各轨道角动量之间的串扰情况,使用了拓扑荷数探测概率描述串扰规律,并推导了拓扑荷数探测概率的解析表达式。研究了涡旋光束通过湍流后的拓扑荷数的分布情况,并将结果与涡旋光束通过大气随机相位屏的数值仿真结果进行了对比,给出了理论与仿真的拓扑荷数的探测概率随湍流强度以及初始涡旋光束拓扑荷数大小的关系图对比,验证了推导的拓扑荷数探测概率解析表达式的正确性。通过该表达式可进一步研究大气湍流与涡旋光束相互作用从而影响涡旋光束轨道角动量散射的本质,为涡旋光束的空间光通信中选择合适的拓扑荷数间隔,以及在不同湍流强度下选择合适束腰大小以减少串扰带来的误码率提供了理论依据。     

Spiral spectrum of anomalous vortex beams propagating in a weakly turbulent atmosphere

ABSTRACT

We study the spiral spectrum of anomalous vortex beams propagating through a turbulent atmosphere. Based on the Huygens–Fresnel integral and the Rytov approximation, the integral expression and then the analytical expression for the spiral spectrum of anomalous vortex beams in the weakly turbulent atmosphere are derived. The capacity of wireless optical links using the anomalous vortex beam is obtained. It is found that the spiral spectrum of the anomalous vortex beam is less affected by turbulence than that of the Laguerre-Gaussian beam. And thus, the information capacity of wireless optical links using the anomalous vortex beam is larger than that using the Laguerre-Gaussian beam. The influence of beam order, wavelength, topological charge, propagation distance, refractive index structure constant and the radius of receiver aperture on spiral spectrum is investigated. These results contribute to reduce the disturbing effects of atmospheric turbulence on the orbital angular momentum of the vortex beam.     

Propagation based on second-order moments for partially coherent Laguerre–Gaussian beams through atmospheric turbulence

Abstract

The Wigner distribution function (WDF) has been used to study the propagation properties of partially coherent Laguerre Gaussian (PCLG) beams through atmospheric turbulence. Based on the extended Huygens–Fresnel principle, an analytical formula of the propagation matrixes in terms of the second-order moments of the WDF for PCLG Beams in the receiving plane is derived. And then the analytical formulae for the curvature radii of PCLG Beams propagating in turbulence are given by the second-order moments of the WDF. The numerical results indicate that the curvature radius of PCLG Beams changes more rapidly in turbulence than that in the free space. The influence of the transverse coherence width and the beam waist width on the curvature radius of PCLG Beams is obvious, while the laser wavelength and the inner scale of turbulence have a slight effect. The study results may be useful for remote sensing and free space optical communications.     

Comparative study of the beam-width spreading of partially coherent Hermite-sinh-Gaussian beams in atmospheric turbulence

Taking the partially coherent Hermite-sinh-Gaussian (H-ShG) beam as a more general type of partially coherent beams, a comparative study of the beam-width spreading of partially coherent H-ShG beams in atmospheric turbulence is performed by using the relative width, normalized beam width, and turbulence length. It is shown that the relative width versus the beam parameters, such as the spatial correlation length sigma(0), beam orders m, n, Sh-part parameter Omega(0), and waist width w(0), provides a simple and intuitive insight into the beam-width spreading of partially coherent H-ShG beams in turbulence, and the results are consistent with those using the turbulence length. The validity of our results is interpreted physically.     

Vortex beam propagation through atmospheric turbulence and topological charge conservation

The propagation of vortex beams through weak-to-strong atmospheric turbulence is simulated and analyzed. It is demonstrated that the topological charge of such a beam is a robust quantity that could be used as an information carrier in optical communications. The advantages and limitations of such an approach are discussed.     

Interaction between a vortex and an edge dislocation nested in a cos‐Gaussian beam passing through a tilted lens

The interaction between a vortex and an edge dislocation nested in a cos‐Gaussian beam passing through a tilted lens was studied analytically and numerically. It is shown that in the presence of the tilted lens, by varying the cos‐part parameter of the beam, the slope of the edge dislocation, or the tilt coefficient of the lens, the topological charge is conserved for the case of the off‐axis edge dislocation, while charge conservation does not hold true for the case of an on‐axis edge dislocation, irrespective of the on‐axis or off‐axis vortex. The relation between the transverse positions (x, y) of vortices and the tilt coefficient is linear, and is interpreted.     

Scintillation of astigmatic dark hollow beams in weak atmospheric turbulence

The scintillation properties of astigmatic dark hollow beams (DHBs) in weak atmospheric turbulence were investigated in detail. An explicit expression for the on-axis scintillation index of an astigmatic DHB propagating in weak atmospheric turbulence was derived. It was found that the scintillation index value of an astigmatic DHB with suitable astigmatism (i.e., ratio of the beam waist size in the x direction to that in the y direction), dark size, beam waist size, and wavelength can be smaller than that of a stigmatic DHB and that of stigmatic and astigmatic flat-topped, annular, and Gaussian beams in weak atmospheric turbulence particularly at long propagation ranges. Our results will be useful in long-distance free-space optical communications.     

Coupling characteristics and kurtosis parameter of partially coherent beams in turbulent atmosphere

Coupling properties and kurtosis parameter (K parameter) of arbitrary beams propagating through atmospheric turbulence are investigated. A correlation factor (C⁴-factor) is introduced to describe the influence of turbulence on coupling characteristics. The general analytical expression for C⁴-factor of arbitrary beams in atmospheric turbulence is derived. It is shown that C⁴-factor of arbitrary beams in the turbulent atmosphere depends on the initial second-order moments and fourth-order moments and turbulence quantities. Taking the partially coherent anomalous elliptical hollow Gaussian (PCAEHG) beam as an example, we can obtain that C⁴-factor decreases as structure constant of the refractive index fluctuations and inner scale increase, and waist width and transverse coherence length decrease when z?>?5?km. Moreover, K parameter of PCAEHG beam in turbulent atmosphere converges to 2 when propagation distance is large enough. It indicates that the profile of PCAEHG beams in turbulent atmosphere finally evolves into fundamental Gaussian distribution.     

Rotation of the wavefront of an optical vortex in free space

It is shown experimentally and theoretically that when an optical vortex propagates in free space, its wavefront rotates through an angle numerically equal to the Gouy phase. It is found that both the energy maximum of the optical vortex light flux and the amplitude zero of the perturbed optical vortex field propagate along the ray surface. It is shown that the ray surface, which is a consequence of the relativistic constraints on the beam group velocity, forms an unparted hyperboloid of revolution and has various properties: 1) the circulation of the Poynting vector on the surface does not depend on the longitudinal coordinate z; 2) the evolution of the light flux and a pure screw dislocation takes place along straight lines of this surface; 3) the Poynting vector on the ray surface is always perpendicular to the wavefront surface. Pis’ma Zh. Tekh. Fiz. 25, 87–94 (March 12, 1999)     

复宗量双曲正弦高斯光束的传输特性

对复宗量双曲正弦高斯(EshG)光束的一些基本特性进行了研究。由Collins公式出发推导出了光束通过近轴ABCD光学系统传输的场分布函数,根据二阶矩的定义和光束在近轴ABCD光学系统中的传输公式推导出了光束通过近轴ABCD光学系统光斑尺寸的解析表达式。得到了复宗量双曲正弦高斯光束在自由空间传输时束腰宽度和位置的解析表达式以及M2因子的表达式。对光强分布、光斑尺寸、束腰宽度及其位置和M2因子进行了数值计算,并对计算结果作了分析。本文所得结果具有广泛的意义,因为正弦高斯光束、双曲正弦高斯光束和复宗量正弦高斯光束均可视为其特例。     

Effect of turbulence on the beam quality of apertured partially coherent beams

The effects of turbulence on the beam quality of apertured partially coherent beams have been studied both analytically and numerically. Taking the Gaussian Schell-model (GSM) beam as a typical example of partially coherent beams, closed-form expressions for the average intensity, mean-squared beam width, power in the bucket, beta parameter, and Strehl ratio of apertured partially coherent beams propagating through atmospheric turbulence are derived. It is shown that the smaller the beam truncation parameter is, the less affected by turbulence the apertured partially coherent beams are. Furthermore, the apertured partially coherent beams are less sensitive to the effects of turbulence than unapertured ones. The main results are interpreted physically.     

Effective radius of curvature of partially coherent Hermite–Gaussian beams propagating through non-Kolmogorov turbulence

Based on the extended Huygens–Fresnel principle and non-Kolmogorov spectrum, the analytical expression for the effective radius of curvature of partially coherent Hermite–Gaussian (PCHG) beams propagating through non-Kolmogorov turbulence is derived, and the relative effective radius of curvature is used to describe the effect of turbulence on the effective radius of curvature. It is shown that the effective radius of curvature of PCHG beams depends on the beam and non-Kolmogorov turbulence parameters and on the propagation distance. The variation of relative effective radius of curvature with increasing generalized exponent parameter α of non-Kolmogorov turbulence is non-monotonic. The longer the propagation distance is, the larger the effect of turbulence on the effective radius of curvature of PCHG beams is. The effective radius of curvature of PCHG beams with shorter wavelength, smaller beam order, larger beam waist width or better spatial coherence is more affected by the non-Kolmogorov turbulence. The results are interpreted physically.     

Evolution of decentred laser beams propagating through atmospheric turbulence

The changes of the average intensity, the centre of beam gravity and the position of intensity maximum of decentred laser beams propagating through atmospheric turbulence are examined in detail. It is shown that the decentred intensity distribution is amended gradually with increasing the propagation distance and the strength of turbulence, and it becomes an off-axis Gaussian-like beam when the propagation distance and the strength of turbulence become large enough. The centre of beam gravity is independent of both the propagation distance and the strength of turbulence. On the other hand, there are two intensity maxima, and their positions are symmetrical around the propagation z-axis when the propagation distance z is small. With increasing z, there is only one intensity maximum. As z further increases, position of the intensity maximum is further shifted towards the z-axis. When z is large enough, the position of the intensity maximum is unchanged. The unchanged position of the intensity maximum moves further away from the z-axis with an increase in the refraction index structure constant, the decentred parameter and the waist width.     

Spreading and directionality of partially coherent Hermite-Gaussian beams propagating through atmospheric turbulence

The closed-form expression for the mean-squared beam width of partially coherent Hermite-Gaussian (H-G) beams propagating through atmospheric turbulence is derived. The influence of turbulence on the spreading of partially coherent H-G beams is studied quantitatively by examining the mean-squared beam width. It is found that the smaller the coherence length sigma(0) of the source is, and the larger the beam order m and the wavelength lambda are, the less partially coherent H-G beams are affected by the turbulence, although the beams with smaller sigma(0), larger m, and larger lambda have greater spreading in free space. In addition, it is shown that two partially coherent H-G beams may generate the same angular spread and that there exist equivalent partially coherent H-G beams that may have the same directionality as a fully coherent Gaussian beam in free space and also in turbulence. The results are illustrated by examples, and a comparison with previous work is also made.     

Reciprocal path-scattering effects for a ground-based, monostatic laser radar tracking a space target through turbulence

A phenomenological model is developed for the strength and spatial width of the coherent intensity peak of backscatter produced by reciprocal path scattering through atmospheric turbulence. The model is applied to a ground-based, monostatic laser radar tracking a space target under the condition of optical atmospheric turbulence saturation.     

Average intensity and spreading of an astigmatic sinh-Gaussian beam with small beam width propagating in atmospheric turbulence

Propagation properties of astigmatic sinh-Gaussian beams (ShGBs) with small beam width in turbulent atmosphere are investigated. Based on the extended Huygens–Fresnel integral, analytical formulae for the average intensity and the effective beam size of an astigmatic ShGB are derived in turbulent atmosphere. The average intensity distribution and the spreading properties of an astigmatic ShGB propagating in turbulent atmosphere are numerically demonstrated. The influences of the beam parameters and the structure constant of atmospheric turbulence on the propagation properties of astigmatic ShGBs are also discussed in detail. In particular, for sufficiently small beam width and sinh-part parameter as well as suitable astigmatism, we show that the average intensity pattern converts into a perfect dark-hollow profile from initial two-petal pattern when ShGBs with astigmatic aberration propagate through atmospheric turbulence.     

Sensitivity of optical sensors based on laser-excited surface-plasmon waves.

We investigate the effect of the divergence of a Gaussian laser beam on the resonance curve and the sensitivity of optical sensors based on surface-plasmon resonance (SPR). For He-Ne laser beams it is found that, for beams with a waist radius of less than 300 mum, the SPR-curve characteristics differ appreciably from the case in which a plane wave is considered. Simple expressions for the sensitivity of (bio)chemical sensors are given. A simple Lorentzian model is used to estimate the maximum possible sensitivity when a multilayer system is used to enhance the resonance peak. It was found that the sensitivity can reach its highest value when the width of the SPR curve is equal to the laser-beam divergence. The results could be particularly important when a SPR curve is used to measure the absolute value of the refractive index of a sample or the dielectric constant and the thickness of a metal layer.     

Influence of atmospheric turbulence on the spatial correlation properties of partially coherent flat-topped beams

The analytical expression for the spectral degree of coherence of partially coherent flat-topped beams propagating through the turbulent atmosphere is derived, and the spatial correlation properties are studied in detail. In particular, we find that the oscillatory behavior and phase singularities of the spectral degree of coherence may appear when partially coherent flat-topped beams propagate through the turbulent atmosphere; this behavior is very different from the behavior of Gaussian Schell-model beams. But the oscillatory behavior becomes weaker with increasing turbulence and even disappears when the turbulence is strong enough. The width of the spectral degree of coherence is always smaller than that of the spectral density in the far field when the turbulence is strong enough, whereas the width of the spectral degree of coherence in free space can be either larger or smaller than that of the spectral density in the far field.     

Beam spreading of vortex beams propagating in turbulent atmosphere

We present some results obtained by numerical modeling of the propagation of vortex beams LG(0l) through a randomly inhomogeneous medium. The vortex beams are the lower order Laguerre-Gaussian modes. Such beams, if propagated under conditions of weak turbulence, also experience distortions, like a Gaussian beam. However, the statistically averaged vortex beams (LG(0l)) conserve the central intensity dip with a nonzero intensity on the beam axis. The beam broadening of vortex beams is analyzed. The average vortex beams are found to be broadened less than the Gaussian beam while propagated through a randomly inhomogeneous medium. The higher the topological charge l is, the smaller the beam broadening is.     

Mode analysis of spreading of partially coherent beams propagating through atmospheric turbulence

The spreading of partially coherent beams propagating through atmospheric turbulence is studied by use of the coherent-mode representation of the beams. Specifically, we consider partially coherent Gaussian Schell-model beams entering the atmosphere, and we examine the spreading of each coherent mode, represented by a Hermite-Gaussian function, on propagation. We find that in atmospheric turbulence the relative spreading of higher-order modes is smaller than that of lower-order modes, whereas the relative spreading of all order modes is the same as in free space. This modal behavior successfully explains why under certain circumstances partially coherent beams are less affected by atmospheric turbulence than are fully spatially coherent laser beams.