Spectral properties of stochastic electromagnetic twist anisotropic Gaussian-Schell model beam truncated by a slit aperture propagating in turbulent atmosphere

With the help of the tensor method, the cross-spectral density matrix for the stochastic electromagnetic twist anisotropic Gaussian-Schell model (ETAGSM) beam truncated by a slit aperture propagating in turbulent atmosphere are derived. The spectral properties of this kind of beam are investigated in detail. It is shown by numerical results and analysis that the affection of the slit aperture on the spectral properties of the stochastic ETAGSM beam is obvious in the near field; while in the far field, the atmospheric turbulence plays an important role; the source beam's coherence can weaken the affection of the slit aperture and the atmospheric turbulence on the spectral properties of the stochastic ETAGSM beam truncated by a slit aperture propagating in turbulent atmosphere, while the twist properties of the source beam can strong the affection of the slit aperture on the spectral properties in the near field. Also, the spectral degree of polarization and normalized spectral density distributions and corresponding contour graphs of the stochastic ETAGSM beam truncated by a slit aperture propagating in turbulent atmosphere and free space at different propagation distances are investigated in detail.     

Spectral properties of apertured stochastic electromagnetic twist anisotropic Gaussian Schell-model beam propagating in turbulent atmosphere

Based on the extended Huygens-Fresnel principle, analytical formulas are derived for the cross-spectral density matrix of an apertured stochastic electromagnetic twist anisotropic Gaussian Schell-model (ETAGSM) beam propagating in a turbulent atmosphere by use of a tensor method. Spectral properties of apertured ETAGSM beam are closely related with the strength of atmospheric turbulence, the aperture widths and the beam's parameters, etc. Our main attention was focused on the influence of the aperture widths, atmospheric turbulence, twist parameters and partial coherence on the spectral properties (including spectral degree of polarization, the spectral degree of coherence and the spectral density) of apertured ETAGSM beam propagating in turbulent atmosphere. Numerical calculation results and analysis are given.     

Focal shift of focused truncated random electromagnetic beams

The focal shifts of focused truncated random electromagnetic beams are investigated. Based on the complex Gaussian expansion method for a hard-edged aperture function, the analytical propagation formula of cross-spectral density matrix for a random electromagnetic beam focused by an optical system with a thin lens and a circular aperture is derived. The Fresnel numbers related with the beam and system parameters are defined and used to examine focal shifts. The dependence of the focal shifts on the different Fresnel numbers and polarization distribution are discussed in detail with numerical examples.     

随机电磁涡旋光束的深聚焦特性

基于德拜矢量积分理论,研究了随机电磁涡旋光束经过大数值孔径透镜之后的聚焦特性及透镜的数值孔径、入射光束的偏振度、拓扑荷以及横向相干长度对焦平面附近聚焦光束的光强分布和相干度的影响.结果表明:适当地选择相关参量,可在焦平面上得到椭圆形光斑的光强分布以及平顶光强分布.随机电磁涡旋光束在焦平面上同一点处两个相互垂直分量之间的相干度,不同两点处两个相同分量之间的相干度以及不同两点处两个相互垂直分量之间的相干度研究表明,入射光束的拓扑荷和横向相干长度对聚焦光束的相干性有着十分明显的影响.     

Effects of different correlations of partially coherent electromagnetic beam on three-dimensional spectral intensity distribution in the focal region

The effects of position-dependent correlations between the x- and y-components of the partially coherent incident electromagnetic beam on the spectral intensity distribution in the focal plane and along the z-axis of an optical imaging system with a high-numerical aperture are studied. The electromagnetic Gaussian Schell-model (GSM) beam is employed as an example to illustrate the analysis.     

Changes in the state of polarization of apertured stochastic electromagnetic modified Bessel–Gauss beams in free-space propagation

By using the generalized Huygens–Fresnel diffraction integral, the analytical expressions for the cross-spectral density matrix, spectral degree of polarization, orientation angle and degree of ellipticity of polarization ellipse of apertured stochastic electromagnetic modified Bessel–Gauss beams (MBGBs) through a paraxial optical ABCD system are derived, and used to study the changes in the state of polarization of apertured stochastic electromagnetic MBGBs propagating in free space. The invariance of the on-axis state of polarization of unapertured stochastic electromagnetic MBGBs propagating through paraxial optical ABCD systems is illustrated analytically and numerically. For apertured stochastic electromagnetic MBGBs, the on-axis spectral degree of polarization, orientation angle and degree of ellipticity of polarization ellipse increase with increasing propagation distance, and approach asymptotic values when the propagation distance is large enough. There is a uniform distribution region of the state of polarization around the center of the beams whose range decreases with increasing truncation parameter. In addition, the state of polarization of apertured stochastic electromagnetic MBGBs upon propagation can be modulated by controlling the truncation parameter.     

Effects of a rectangular aperture on the vectorial structure of a Gaussian beam in the far-field regime

With the help of the angular spectrum representation and the Gaussian function expansions of the hard-edge aperture function, the vectorial structure of a linearly polarized Gaussian beam (GB) diffracted by a rectangular aperture is analyzed in detail. It is found that the sizes of the energy flux density spots and the energy fluxes of the TE and TM terms depend on the aperture configuration and the polarization direction of the incident GB. The far fields may have smaller spots and larger energy fluxes for a GB diffracted by a rectangular aperture compared to that by a square aperture with the same beam intensity. And another potential application in information encoding and transmission for free-space communications is also proposed in addition to re-focusing to enhance the optical storage density. This encoding scheme has the benefit of easy implementation without modulating any properties of the light source.     

Propagation of a stochastic electromagnetic Gaussian Schell-model beam through an optical system in turbulent atmosphere

A generalized diffraction integral formula for stochastic electromagnetic beams propagating through an optical system in turbulent atmosphere is derived with the help of tensor method. Some analyses are illustrated by a numerical example relating to changes in the average intensity and the degree of polarization of an electromagnetic Gaussian Schell-model beam propagating through a double-lenses system. It is shown that the optical system has strong influence on the propagation properties of the beam. The method used in this paper can be widely applied to the propagation of astigmatic beams through an optical system in turbulent atmosphere.     

光源参数及大气湍流对电磁光束传输偏振特性的影响

根据光束扩展理论,以部分相干的电磁高斯-谢尔光束为研究对象,分析了电磁光束传输时其偏振特性的变化机理.结果表明,光源参数和大气湍流对电磁光束分量扩展的影响是导致传输过程中电磁光束偏振特性变化的原因.在真空中传输时,电磁光束两分量的相干性存在差异,导致传输时电磁光束两分量扩展快慢不同,从而引起传输路径上光束谱偏振度的变化.在大气湍流中,电磁光束两分量扩展的快慢与光源参数和大气湍流强度均有关,当传输路径较短时,电磁光束偏振变化主要与光源参数有关,变化特性与在真空中传输时的情况类似,而传输距离较远时,电磁光束偏振变化受大气湍流的影响明显,变化特性与在真空中传输时的情形存在不同.     

随机电磁高阶Bessel-Gaussian光束在海洋湍流中的传输特性

利用广义惠更斯-菲涅耳衍射积分公式得到了随机电磁高阶Bessel-Gaussian光束在海洋湍流中传输的交叉谱密度矩阵的一般表达式,通过数值计算主要研究了随机电磁高阶Bessel-Gaussian光束在海洋湍流中传输时其在远场输出面的统计特性的变化,包括归一化光谱强度、光谱偏振度、两点的光谱相干度等.数值模拟结果显示海洋湍流能够对随机电磁高阶Bessel-Gaussian光束的归一化光谱强度分布产生影响,随着传输距离的增加,零阶Bessel-Gaussian光束中心出现凹陷,高阶Bessel-Gaussian光束中心会变平坦继而又凹陷下去,不管零阶还是高阶,当传输距离增加到足够远,光强分布都会演变成最终的类高斯分布.x轴上各点的偏振度改变与相干长度δ_(xx),δ_(yy)以及海洋湍流参数有关.x轴上任意一点和原点这两点的光谱相干度也随x的增加而呈振荡变化,并且海洋的均方温度耗散率χT对光谱相干度有影响.     

Spectral shift of a stochastic electromagnetic Gaussian Schell-model beam in a Gaussian cavity

Spectral changes of a stochastic electromagnetic Gaussian Schell-model (EGSM) beam interacting with a Gaussian cavity are investigated. It is shown that the spectral shift is mainly determined by the degree of polarization of the initial beam and by the parameters of the cavity. Generically the blue shift occurs at on-axis points, while the red shift can occur at off-axis points. The condition under which the relative spectral shift is independent of the degree of polarization of the initial beam is analyzed.     

部分空间相干部分光谱相干厄米-高斯脉冲电磁光束的偏振特性

基于非稳态场的相干理论,对部分空间相干部分光谱相干二维厄米-高斯脉冲电磁光束在自由空间传输时的偏振特性做了详细的数值研究.结果表明,脉冲电磁光束的偏振度分布由光束阶数、光束的空间相关长度、时间相干长度和场点位置等因素共同决定.研究表明,当空间相关长度趋于零或无穷大时,轴上点偏振度趋于一固定值,与光束阶数和场点位置无关....     

Polarization and coherence properties of a beam formed by superposition of a pair of stochastic electromagnetic beams

General expressions are derived for the spectral degree of polarization and for the spectral degree of coherence of a beam generated by the superposition of two stochastic electromagnetic beams. A method to calculate the mutual cross-spectral density matrix of the superposed beam is discussed, as well as experiments to determine it.     

Changes in the spectrum, polarization, and coherence of stochastic spatially and spectrally partially coherent electromagnetic J0-correlated Schell-model pulsed beams propagating in free space

Taking the stochastic electromagnetic J ₀-correlated Schell-model pulsed (JSMP) beam as a typical example of stochastic spatially and spectrally partially coherent electromagnetic pulsed beams, the analytical expressions for the cross-spectral density matrix, spectral density, spectral degree of polarization and spectral degree of coherence of stochastic electromagnetic JSMP beams propagating in free space are derived, and used to study the changes in the spectrum, polarization, and coherence of stochastic spatially and spectrally partially coherent electromagnetic JSMP beams. It is shown that the on-axis spectrum is blue-shifted in free-space propagation and is dependent on the pulse temporal coherence length and spatial correlation parameter. The distribution of the on-axis spectral degree of polarization depends on the frequency and spatial correlation parameter. The spectral degree of coherence increases with increasing pulse temporal coherence length. The results derived are interpreted physically.     

Modulation in the statistical properties of stochastic electromagnetic beams through an electromagnetic induced transparency atomic vapor

We report analytical expressions for the elements of the 2 × 2 cross-spectral density matrix of a stochastic electromagnetic beam passing through an electromagnetic induced transparency (EIT) atomic vapor. By use of the derived formulas the changes in the spectral density, the spectral degree of coherence, and the spectral degree of polarization of such a beam on propagation can be studied in detail. Numerical examples show that the statistical properties of the stochastic electromagnetic beam can be modulated by the Rabi frequency of the control light when the beam propagates through the EIT atomic vapor.     

部分相干平顶光束经光阑衍射的偏振特性

根据光束的相干-偏振矩阵和传输理论,对部分相干平顶光束经正多边形光阑衍射的偏振特性进行了系统的研究.给出了部分相干平顶光束偏振度传输公式,并将高斯-谢尔模型光束以及部分相干平顶光束在自由空间传输的偏振度作为特例统一于一般表达式中.研究表明：部分相干平顶光束经光阑衍射的偏振特性与光阑截断参数、光束的空间相干性、衍射角、传输距离、平顶光束的阶数有关. 关键词： 部分相干平顶光束 偏振特性 相干-偏振矩阵 正多边形光阑 光阑衍射     

经光阑衍射的平顶涡旋光束位相奇点的演化特性

推导出了平顶涡旋光束通过有光阑ABCD光学系统的传输解析式,并以光阑透镜和矩形光阑系统为例,与平顶光束比较研究了截断参量、相对离轴距离和光束阶数对衍射场中位相奇点演化特性的影响.数值计算表明,平顶涡旋光束通过上述光学系统均存在位相奇点,即使源处涡旋被光阑阻拦时,衍射场中也会出现位相奇点;而平顶光束通过光阑透镜系统存在刃型位错,随着截断参量增大,会发生刃型位错的演化和湮灭现象,且平顶光束通过矩形光阑系统没有发现位相奇点.     

经光阑衍射的平顶涡旋光束位相奇点的演化特性

推导出了平顶涡旋光束通过有光阑ABCD光学系统的传输解析式,并以光阑透镜和矩形光阑系统为例,与平顶光束比较研究了截断参量、相对离轴距离和光束阶数对衍射场中位相奇点演化特性的影响.数值计算表明,平顶涡旋光束通过上述光学系统均存在位相奇点,即使源处涡旋被光阑阻拦时,衍射场中也会出现位相奇点;而平顶光束通过光阑透镜系统存在刃型位错,随着截断参量增大,会发生刃型位错的演化和湮灭现象,且平顶光束通过矩形光阑系统没有发现位相奇点.     

部分相干平顶光束经光阑衍射的偏振特性

根据光束的相干-偏振矩阵和传输理论，对部分相干平顶光束经正多边形光阑衍射的偏振特性进行了系统的研究.给出了部分相干平顶光束偏振度传输公式，并将高斯-谢尔模型光束以及部分相干平顶光束在自由空间传输的偏振度作为特例统一于一般表达式中.研究表明：部分相干平顶光束经光阑衍射的偏振特性与光阑截断参数、光束的空间相干性、衍射角、传输距离、平顶光束的阶数有关.     

Changes of polarization of light beams on propagation through tissue

The values of the degree of polarization and the coherence of the light beam are of great importance in many areas. In this paper, we study the effects of tissue turbulence on the degree of polarization of a partially coherent electromagnetic beam. Based on the unified theory of coherence and polarization for random electromagnetic beams and the spectral density of the index of refraction fluctuations of tissue, we have established the detailed formula for calculating the change of the degree of polarization of the beam when propagating through tissue. Compared with the light propagation through atmosphere, the result shows that although the propagation distance in tissue imaging is very short, the degree of polarization of the beam may change greatly. An example was given which clearly shows the effect of the correction properties and the tissue turbulence on the degree of polarization of the light beam propagating within the tissue.