Space-time analogy for partially coherent plane-wave-type pulses

In this Letter we extend the well-known space-time duality to partially coherent wave fields and, as a limit case, to incoherent sources. We show that there is a general analogy between the paraxial diffraction of quasi-monochromatic beams of limited spatial coherence and the temporal distortion of partially coherent plane-wave pulses in parabolic dispersive media. Next, coherence-dependent effects in the propagation of Gaussian Schell-model pulses are retrieved from that of their spatial counterpart, the Gaussian Schell-model beam. Finally, the last result allows us to present a source linewidth analysis in an optical fiber communication system operating around the 1.55 microm wavelength window.     

时空非相干光孤子的传播和相干特性

研究了时空非相干椭圆形高斯光束在饱和对数型非线性介质中的自陷行为,得到了孤子的形成条件并分析了其相干特性,讨论了光束自陷的变化形式,发现光束的初态和材料非线性对其有决定性的影响, 并进一步获得了光束半径和光束相干半径的解析表达式,发现光束的相干特性不但会随传播距离产生周期性的变化,且随组份频率的增大而减弱.     

Phase-contrast imaging of nanostructures by soft x rays from a femtosecond-laser plasma

The possibility of phase-contrast imaging of nanostructures has been analyzed with the use of a femtosecond-laser plasma as a spatially coherent soft x-ray source and a LiF crystal as an x-ray detector having both the submicron spatial resolution in a wide field of view and a high contrast. It is demonstrated that the spatial coherence length of radiation in the wavelength range 1–13 nm at a distance of 30 cm from the femtosecond-laser plasma source is ?1.5 μm. The achieved spatial coherence of the source is sufficient to obtain high-quality phase-contrast x-ray images of foils with various chemical compositions and a thickness of ?100 nm.     

Correlation between intensity fluctuations of light scattered from a quasi-homogeneous random media

The correlation between intensity fluctuations of light scattered from a quasi-homogeneous random media was analytically derived. We showed the correlation depends on spatial Fourier transforms of both the intensity and degree of spatial correlation of scattering potentials of the media, while the normalized correlation equals the squared modulus of the degree of spatial coherence of the scattered fields.     

First- and second-order statistics of optical near fields

The statistical properties of the intensity in close proximity to highly scattering, randomly inhomogeneous media are investigated. Whereas the intensity probability density function obeys the same law irrespective of the distance z from the interface, the second-order intensity correlation length changes for distances smaller than the wavelength. Contrary to predictions of the conventional coherence theory, the corresponding field correlation length can be smaller than the wavelength of light.     

Surface plasmons modulate the spatial coherence of light in Young's interference experiment

It is shown how surface plasmons that travel between the slits in Young's interference experiment can change the state of spatial coherence of the field that is radiated by the two apertures. Surprisingly, the coherence can both be increased and decreased, depending on the slit separation distance. This results in a modulation of the visibility of the interference fringes. Since many properties of a light field-such as its spectrum, polarization, and directionality - may change on propagation and are dependent on the spatial coherence of the source, our results suggest that the use of surface plasmons provides a new way to alter or even tailor the statistical properties of a light field.     

非均匀部分相干光束在自由空间中的传输

本文介绍了非均匀部分相干光束的概念, 并用数值模拟的方法详细研究了其在自由空间传输后的变化. 研究结果表明, 经过自由空间传输后非均匀部分相干光束会发生不同于传统相干模型光束的显著变化. 这种变化和光束传输距离、光源空间相干度分布、光源光强分布密切相关. 经过传输后, 源平面自相干附近点的空间相干度发生突变, 在短距离传输过程中源平面高相干区域的空间相干度会降低, 接收面各点的空间相干曲线不再相同, 随着传输距离增加, 非均匀空间相干度会逐渐趋于均匀.     

Study on the spatial coherence of vortex Gaussian beams passed atmospheric turbulence

In this paper, the spectral degree of coherence formula was derived by using the generalized Huygens–Fresnel principle and the method of Rytov phase structure function quadratic approximation. The spatial coherence of vortex Gaussian beams passed atmospheric turbulence was studied. It showed that the spatial coherence was mainly affected by the coherence of light source, the number of topological charges and the transmission distance. The distance of transmission was farther, the spatial coherence of beam was better. The number of topological charges were more, the spatial coherence of beam was better. In a certain transmission distance, the coherence of light source was better, the spatial coherence of beam was worse. In addition, there were coherent vortexes which spectral degree of coherence was zero after the partially coherent vortex beams getting through atmospheric turbulence transmission.     

表面声道对深海风成噪声垂直空间特性的影响规律

水下风成噪声的垂直空间特性包括噪声垂直方向性和垂直相关性,研究海洋环境对其影响规律对提升声呐性能、增加海洋环境参数反演的准确性具有重要意义.本文利用Pekeris割线下的简正波理论描述噪声的传播过程,研究了深海环境下存在表面声道时,表面声道以下噪声垂直空间特性的变化规律及其原因.研究表明,在临界深度以上,表面声道的存在导致噪声垂直方向性在水平凹槽边缘靠近海底方向上的峰值升高,噪声垂直相关性随垂直距离增加先后周期地向正相干和负相干方向偏移;在临界深度以下,表面声道的存在导致水平方向上的噪声能量增强,噪声垂直相关性整体向正相干方向偏移.当表面声道的参数变化时,表面声道的厚度变化对噪声垂直空间特性影响较大,而表面声道内的声速梯度变化对噪声垂直空间特性几乎没有影响.结合各类简正波的变化分析表明,存在表面声道时,噪声源激发的折射简正波阶数增加,强度增强,是表面声道引起噪声垂直空间特性变化的主要原因.     

Consistency of the Surface Roughness Determined from Soft-X-Ray Reflectance and Surface Profiles Measured Using a Scanning Tunnelling Microscope: Coherence Length of the Soft X-Rays

There exists serious inconsistency between the rms surface roughness determined from the Debye-Waller factor for the soft-x-ray reflectance analysis and that measured with an optical surface profiler. We have measured the surface profile of evaporated films using a scanning tunnelling microscope, and reproduce the profile with the Fourier components whose spatial wavelength is shorter than the coherence length of the incident soft x-rays in the reflectance measurement. The rms surface roughness derived from the high-pass filtered profile agrees well with that determined using the reflectance measurement. This result explains straightforwardly the photon-energy dependence of the surface roughness estimated by the soft-x-ray reflectance method.     

Doppler展宽准Λ型四能级系统中传播效应的位相相关性

利用数值计算详细研究具有真空诱导相干的准Λ型四能级原子系统中探测场和驱动场之间的相对位相(Φ)对传播效应的影响。结果表明:通过选择Φ的取值可以获得更大的GWI和更长的存在无反转增益的传播距离,从而获得更高的LWI强度;Doppler展宽存在时,Doppler展宽宽度及探测场和驱动场传播方向对位相相关的GWI和LWI强度的空间演化有明显的调制作用。     

部分相干光光束的振荡自陷特性

用互相干函数法研究了圆形横截面的部分相干光光束在光折变晶体中的自陷行为.光束的初态及材料的非线性决定了光束自陷的变化形式,导出空间周期表达式,获得了光束相干半径的解析表达式,发现部分相干光光束的相干特性会随传播距离发生周期性的演化,并将圆形光束的讨论结果扩展到椭圆形光束中. 关键词： 空间孤子 部分相干光光束 相干半径     

同材质颗粒不同填充密度的随机介质中光场的空间分布

用时域有限差分法研究了同一材质的颗粒在不同填充密度下的随机介质中光局域化问题. 依据随机介质激光的实验参数,模拟了颗粒填充密度不同的随机介质中光场的空间分布. 结果表明：当散射颗粒的散射平均自由程与波长相当时,随机介质中的光场分布呈现局域化的特征,而且随着颗粒填充密度增大,光场的局域化程度增强. 因此,在同样的抽运激励下,颗粒填充密度越大的随机增益介质越容易产生激光辐射. 数值模拟结果与实验定性符合. 关键词： 随机激光 时域有限差分法 颗粒填充密度 局域化     

Radiative transfer limit of two-frequency Wigner distribution for random parabolic waves: An exact solution

The present Note establishes the self-averaging, radiative transfer limit for the two-frequency Wigner distribution for classical waves in random media. Depending on the ratio of the wavelength to the correlation length the limiting equation is either a Boltzmann-like integral equation or a Fokker–Planck-like differential equation in the phase space. The limiting equation is used to estimate three physical parameters: the spatial spread, the coherence length and the coherence bandwidth. In the longitudinal case, the Fokker–Planck-like equation can be solved exactly. To cite this article: A.C. Fannjiang, C. R. Physique 8 (2007).     

Coherent backscattering spectroscopy

Coherent backscattering (CBS) of light in random media has been previously investigated by use of coherent light sources. Here we report a novel method of CBS measurement that combines low spatial coherence, broadband illumination, and spectrally resolved detection. We show that low spatial coherence illumination leads to an anomalously broad CBS peak and a dramatic speckle reduction; the latter is further facilitated by low temporal coherence detection. Thus CBS can be observed in biological tissue and other media that previously were beyond the reach of conventional CBS measurements. We also demonstrate, for the first time to our knowledge, spectroscopic analysis of CBS. CBS spectroscopy may find important applications in probing random media such as biological tissue in which depth-selective measurements are crucial.     

Spatial coherence and coherent interactions of broadband dispersed laser beams

Analytical expressions are obtained that describe the changes in the degree of coherence and in the thickness of the coherence layers occurring upon propagation of a dispersed broadband laser beam. It is found that the greater the tilting of the coherence layers with respect to the phase fronts, the more rapidly the spatial coherence is violated with increasing distance. A comparison with the case of an undispersed beam is performed. It is shown that, as the beam propagates, the decrease in the degree of coherence is accompanied by the appearance of spatial fluctuations of this parameter. The degree of mutual coherence of intersecting dispersed beams with parallel correlated coherence layers, which determines the efficiency of their coherent interaction, is investigated. The existence of spatial fluctuations of the degree of mutual coherence is established.     

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。     

Enhancement of spatial coherence during light propagation in bounded media

The spatial coherence of thermal light propagated through passive bounded media is measured. It is found that specular reflection at the boundaries enhances the degree of coherence. This result has considerable implications for the spatial coherence of light from laser and amplified spontaneous emission (A.S.E.) systems.     

Propagation Characteristics of a Partially Coherent Gaussian Schell-model Array Vortex Beam in the Joint Turbulence Effect of a Jet Engine and Atmosphere

This work investigates the joint effects of jet engine exhaust-induced turbulence and atmospheric turbulence on the propagation of a partially coherent Gaussian Schell-model Array (GSMA) vortex beam. Using the two-process propagation method, analytical formulae are derived for the cross-spectral density, spectral density, degree of coherence, and beam width of the considered beam. The results show that the considered beam takes different shapes; when the spatial coherence is large, the spectral density of the GSMA vortex beam takes an elliptical shape, whereas when the spatial coherence is smaller, the spectral density remains a Gaussian shape. The evolution profile of the degree of coherence weakens gradually when the propagation distance, topological charge, and turbulence strength increase. Moreover, the profile of the degree of coherence takes the Gaussian profile when the propagation distance is longer or turbulence atmospheric is stronger. Furthermore, the results reveal that the corresponding beam spreads faster with a larger propagation distance, lower spatial coherence, and high-strength turbulence. This study also concludes from the results that the beam is affected more when its propagation is near the jet engine exhaust, which means that this latter has a significant impact.     

Changes in the coherence of quasi-monochromatic electromagnetic Gaussian Schell-model beams propagating through turbulent atmosphere

Based on the extended Huygens-Fresnel principle, the mutual coherence function of quasi-monochromatic electromagnetic Gaussian Schell-model (EGSM) beams propagating through turbulent atmosphere is derived analytically. By employing the lateral and the longitudinal coherence length of EGSM beams to characterize the spatial and the temporal coherence of the beams, the behavior of changes in the spatial and the temporal coherence of those beams is studied. The results show that with a fixed set of beam parameters and under particular atmospheric turbulence model, the lateral coherence of an EGSM beam reaches its maximum value as the beam propagates a certain distance in the turbulent atmosphere, then it begins degrading and keeps decreasing along with the further distance. However, the longitudinal coherence length of an EGSM beam keeps unchanging in this propagation. Lastly, a qualitative explanation is given to these results.