Intensity and spatial correlation properties of tightly focused partially coherent radially polarized vortex beams

By expanding the Debye theory into the tight focusing of partially coherent field, the intensity and spatial correlation properties of partially coherent radially polarized vortex beams are studied. Expressions are derived for the intensity distribution and the spectral degree of coherence in the focal region. It is found that the intensity and the transverse and longitudinal coherence degrees in the focal region change with the variation of the topological charge and coherence length of the vortex beam. In addition, the degree of coherence is shown to exhibit phase singularities.     

Speckle polarization diagnostics of scattering media using partially coherent radiation

The paper discusses a method for probing a randomly inhomogeneous medium using partially coherent radiation and polarization filtering of the radiation scattered by the medium. The method is based on the analysis of the contrast of speckle-modulated images of the object under study as a function of the coherence length of the probe radiation. A theoretical justification of the method is given as applied to systems of discrete scatterers with the subsequent modification of the results obtained for continuously distributed scattering systems. The results of experimental testing of the developed method for scattering media characterized by nondiffusion conditions of propagation of the probe radiation are presented and compared with the results of the theoretical analysis.     

Formation of speckle interferograms characterizing transverse and longitudinal displacements of a light-scattering surface

The speckle-interferometer sensitivity to transverse or longitudinal displacements of a flat diffusively scattering surface is analyzed for the case of double-exposure recording of a speckle photography. It is shown that the interference pattern characterizing the transverse displacement of a scatterer is localized in the far-field diffraction region, and the interferometer sensitivity depends both on the value and sign of curvature of the spherical wavefront of coherent radiation used in the speckle-photography recording stage. The interference pattern charactering the longitudinal displacement of the scatterer is localized in the near-field diffraction region and in order to record it, spatial filtering of the diffraction field should be performed. The experimental data obtained agree with theory. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 47–54, April, 2007.     

部分相干光被环形透镜聚焦而产生的焦移

 从理论上研究部分相干光被一环形透镜聚焦,在焦点附近的轴上点的光强分布。研究结果表明,当部分相干光被一环形透镜聚焦时,最大聚焦光强不在几何焦点,而是位于透镜与几何焦点之间,出现焦移现象。并且,焦移量不仅依赖于透镜外半径的菲涅耳数,还依赖于部分相干光的空间相干度和中心拦截比。透镜的菲涅耳数越小,焦移越大;部分相干光的空间相干度越低,焦移越大。当菲涅耳数一定时,环形透镜的中心拦截比越大,焦移越大;当空间相干度很小时,情况就变得比较复杂。     

Coherent inelastic light scattering from a microwave-excited array of magnetic particles

Inelastic light scattering from an array of Permalloy particles driven by a microwave magnetic field is shown to be a coherent phenomenon in which the scattered radiation is observed only at diffraction angles corresponding to the reciprocal lattice of the array. The results are explained in terms of the phase coherence of the inelastically scattered light by each of the particles.     

Filtration of partially coherent optical radiation by means of multiphonon Bragg diffraction

The filtering properties of three-phonon acousto-optical Bragg diffraction for increasing the degree of coherence of a partially coherent optical field are investigated by the example of multiphonon acousto-optical interaction in a TeO₂ single crystal. Two possible mechanisms of coherent scattering upon the formation of the highest orders are taken into account. It is shown that the three-phonon interaction is more efficient by at least a factor of two than any mode of one-phonon diffraction realized at the same frequency and the same acousto-optical interaction length. The experimental investigation, using partially coherent radiation of a He-Ne laser (λ = 0.63 μm) diffracted from a transverse acoustic wave propagating in a TeO₂ single crystal, on the whole confirmed the basic theoretical foundations.     

Longitudinal purely spatial coherence of a light field

The effects of longitudinal purely spatial coherence of light and the results of observation of these effects in an interference experiment are considered under the condition that the length of temporal coherence l _c is considerably smaller than the length of longitudinal spatial coherence ρ_‖ of the field. It is shown that, for l _c ? ρ_‖, the longitudinal purely spatial coherence of the light field in fact governs the coherence of the wave train in the process of its propagation. The length and the time of coherent (“free”) path of the wave train are considered as new spatial and temporal scales of a partially coherent light field.     

Propagation of phase-locked partially coherent flattened beam array in turbulent atmosphere

Analytical formulae for phase-locked partially coherent flattened beam array propagating in a turbulent atmosphere are derived based on the extended Huygens–Fresnel principle. Beam propagation factor (BPF) is introduced to evaluate the beam quality at the receiving plane. The influence of beam order, transverse coherence width length and the intensity of turbulence is discussed in detail.     

Spatial correlation properties of apertured partially coherent radially polarized beams in turbulent atmosphere

Based on the extended Huygens–Fresnel integral, the analytical formulae for the cross-spectral density matrix of the partially coherent radially polarized beams diffracted at a circular aperture in turbulent atmosphere are derived. The unapertured and free-space cases can be viewed as the special cases of our general result. By using the degree of coherence formula, the spatial correlation properties of the apertured partially coherent radially polarized beams in turbulent atmosphere are studied. The analyses indicate that the spatial correlation of the apertured partially coherent radially polarized beams are more affected by the atmospheric turbulence with the larger structure constant, the smaller truncation parameter, the larger coherence length, and the farther propagation distance.     

Three-dimensional diffuser and three-dimensional speckles

The well-known model of a diffusely scattering surface as a set of randomly distributed point scatterers is generalized to the case of a volume diffuser. Assuming that the coordinates of the coherent radiation source, the observer, and also the diffuser shape are arbitrary, a formula is obtained for the spatial correlation function of the scattered radiation intensity in a free field. Expressions to determine the transverse and longitudinal dimensions of the speckles are obtained for diffusers in the form of a rectangular parallelepiped and a cylinder. Zh. Tekh. Fiz. 68, 59–63 (December 1998)     

部分相干光照明下光栅的塔尔博特效应

首先利用部分相干光理论详细地分析了在部分相干光照明下光栅的菲涅耳衍射,给出了观察面上衍射光强分布的一般公式,并就光源的发光面积对光栅塔尔博特效应的影响进行了讨论,得到了光栅衍射光强的分布随着照明光源的发光尺寸的增加而逐渐变得平滑这一结论．并且,当光源发光尺寸增加到毫米量级时,光栅的塔尔博特效应将完全消失。在实验上埘不同发光尺寸的扩展作相干光源照明光栅时的菲涅耳衍射光强进行了测量,实验结果与理论分析得出的结论相符合。     

Coherence Volume of an Optical Wave Field with Broad Frequency and Angular Spectra

We consider the sizes of a region in a three-dimensional space in which an optical wave field excites mutually coherent perturbations. We discuss the conditions under which the length of this region along the direction of propagation of the wave field and, correspondingly, its volume are determined either by the width of the frequency spectrum of the field or by the width of its angular spectrum, or by the parameters of these spectra simultaneously. We obtain expressions for estimating extremely small values of the coherence volume of the fields with a broad frequency spectrum and an extremely broad angular spectrum. Using the notion of instantaneous speckle-modulation of the wave field, we give a physical interpretation to the occurrence of a limited coherence volume of the field. The length of the spatiotemporal coherence region in which mutually coherent perturbations occur at different times is determined. The coherence volume of a wave field that illuminates an object in high-resolution microscopy with frequency broadband light is considered. The conditions for the dominant influence of the angular or frequency spectra on the longitudinal length of the coherence region are given, and the conditions for the influence of the frequency spectrum width on the transverse coherence of the wave field are examined. We show that, when using fields with broad and ultrabroad spectra in high-resolution microscopy, this influence should be taken into account.     

Intensity fluctuations of partially coherent laser beam arrays in?weak atmospheric turbulence

The intensity fluctuation of a partially coherent laser beam array is examined. For this purpose, the on-axis scintillation index at the receiver plane is analytically formulated via the extended Huygens–Fresnel diffraction integral in conditions of weak atmospheric turbulence. The effects of the propagation length, number of beamlets, radial distance, source size, wavelength of operation and coherence level on the scintillation index are investigated for a horizontal propagation path. It is found that, regardless of the number of beamlets, the scintillation index always rises with an increasing propagation length. If laser beam arrays become less coherent, the scintillation index begins to fall with growing source sizes. Given the same level of partial coherence, slightly less scintillations will occur when the radial distance of the beamlets from the origin is increased. At partial coherence levels, lower scintillations are observed for larger numbers of beamlets. Both for fully and partially coherent laser beam arrays, scintillations will drop on increasing wavelengths.     

菲涅耳衍射区和夫琅和费衍射区的动态部分相干光散斑场特性

研究了菲涅耳衍射区和夫琅和费衍射区动态部分相干光散斑的特性.利用部分相干光互强度传播的理论，得出了在部分相干光照明时，由运动散射体产生的动态散斑光强时空交叉的自相关函数的一般形式，并由此得出了散斑沸腾和平移的一般规律.通过适当选择光源和调整光路参数，在实验上得到了菲涅耳和夫琅和费衍射区的部分相干光散斑，对夫琅和费面上的动态部分相干光散斑的平移和沸腾现象进行了定性研究；采用光子计数及数据自动采集的方法，对部分相干光散斑随时间的演化及动态部分相干光散斑的沸腾进行了定量测量.这些实验结果与理论结果相符合. 关键词： 部分相干光动态散斑 时空交叉相关函数 沸腾     

Threshold fields for stimulated Brillouin scattering in spatially limited plasma

Brillouin scattering in an infinite medium is anisotropic, in this case the threshold of absolute instability is caused by attenuation of scattered waves. If the collision attenuation mechanism prevails, the minimum threshold value is observed during backward scattering. For a scattering region limited in the longitudinal direction (parallel to the direction of pumping wave propagation), the backward scattering threshold will be greater than for an infinite medium due to convective loss associated with energy removal by scattered waves. In this paper, the scattering of a wide wave beam in plasma is considered, whose dimension in the transverse direction to the pumping wave propagation substantially exceeds the dimension in the longitudinal direction. It was revealed that in this case, during angle scattering the instability threshold can be less than the threshold for backward scattering due to the increased time of radiation removal from the interaction region. This effect was not taken into account previously. In turn, the decrease of the threshold leads to increasing the radiation loss, which is important in plasma heating problems. The results can also be used for plasma diagnostics.     

Effects of energy spread on brightness and coherence of undulator sources

The (spectral) brightness for partially transverse coherent sources such as synchrotron radiation and free‐electron laser sources can be defined as the maximum of the Wigner distribution. Then, the brightness includes information on both coherence and wavefront characteristics of the radiation field. For undulator sources, it is customary to approximate the single‐electron electric field at resonance with a Gaussian beam, leading to great simplifications. Attempts to account for the modified spatial and angular profile of the undulator radiation in the presence of detuning due to energy spread, currently build on the simplified brightness expression derived under the assumption of Gaussian beams. The influence of energy spread on undulator radiation properties is becoming important in view of diffraction‐limited rings with ultralow emittance coming on‐line. Here the effects of energy spread on the brightness of undulator radiation at resonance are discussed, as well as relevant relations with coherence properties.     

菲涅耳深区散斑强度统计特性及演化

利用直透光波和高斯散斑场的叠加理论和基尔霍夫近似研究了菲涅耳深区散斑的构成,给出了菲涅耳深区散斑场及其强度概率密度和对比度的表达式.利用原子力显微镜测量的随机散射表面高度分布数据模拟菲涅耳深区不同散射距离处散斑,并计算绘出其强度概率密度和对比度曲线.理论与模拟相结合研究这两个统计函数的特征和直透光强所占比例的影响,以及它们随散射距离的演化规律.     

Diffractive optical elements with a double identical microstructure for determination of statistical parameters of random phase objects

Physical processes of interference pattern formation in partially coherent and coherent optical systems containing special diffractive optical elements with a double identical microstructure are studied in the case when a thin scattering object is present in the optical system. Methods for determining the spatial coherence function of the light field, the autocorrelation function of transmission of random phase screens, and the statistical parameters of the screens are considered.     

部分相干双曲余弦-高斯光束的传输特性和空间整形

 通过加入高斯项的空间相干度，引入部分相干双曲余弦-高斯（ChG）光束，推导出部分相干ChG光束通过近轴ABCD光学系统传输的解析表达式，并用以研究其传输特性和空间整形。结果表明，部分相干ChG光束的光强分布不能保持传输不变性，其光强分布不仅与传输距离和离心参数有关，而且还与空间相干参数有关。在传输距离固定时，适当改变部分相干ChG 光束的离心参数和空间相干参数，可实现光束的空间整形。光束质量因子随空间相干性的增大和离心参数的减小而减小。高斯-谢尔模型光束和完全相干ChG光束可作为部分相干ChG光束的特例处理。     

Partially coherent Fresnel diffraction by a slit aperture. III. Fresnel diffraction patterns

The intensity distribution in the Fresnel diffraction pattern of a slit aperture illuminated with partially coherent light is obtained, as a function of the coherence condition across the aperture, by evaluating the formula developed in a previous paper. It is shown that the Fresnel diffraction pattern is affected by the coherence condition of illumination across the aperture and its form.