The effects of longitudinal spatial coherence of light in interference experiments

The physical conditions needed to observe the effects of longitudinal spatial coherence of emission of an extended thermal source are considered. Results of experiments on observation of interference pulses of longitudinal spatial coherence, performed using a scanning longitudinal shearing Michelson interferometer, are presented. Distinctions between the effects of temporal and longitudinal spatial coherence of light are established. It is shown that the presence of a noncompensated optical layer in one of the arms of the interferometer makes the interference pulses of the temporal and spatial coherence of light shift relative to each other (“recession”).     

用于制作光纤光栅的Talbot干涉仪的分析与建模

对用于制作光纤光栅的Talbot干涉仪进行了分析.当考虑准分子激光器的空间相干性和时间相干性时,几何光学中的光线法并不能给出Talbot干涉仪干涉场的真实强度分布情况,而通过光的电磁理论,则可以提供对干涉场的详细描述.基于电磁理论,建立了一个Talbot干涉仪干涉场计算模型,并首次将Talbot干涉仪的反射镜转角作为模型计算参数加以考虑,随后进行了一系列的计算.计算结果显示了干涉场的分布,同时表明空间相干性对Talbot干涉仪的近场干涉和远场干涉影响都很大,其中远场干涉对空间相干性的要求更严格,且对于远场干涉,反射镜转角的影响不可忽视.     

Longitudinal pure spatial coherence of a light field with wide frequency and angular spectra

We have observed the longitudinal pure spatial coherence of a light field in an interference experiment when the length of the temporal coherence is significantly smaller than the length of the longitudinal spatial coherence of the light field. We introduce into consideration new spatial and temporal scales of a light field: the length of the coherent (free) run and the coherent time (the time of life) of a wave train.     

Optical interference and pulse propagation in multimode fibers

The role played by optical interference in determining the propagation of pulses in multimode fibers is examined under conditions of mode independence and mode coupling. Single pulses and pulse-pairs generated by a source that has arbitrary temporal and spatial coherence are considered, and the role played by the spatial integration at the detector, which effectively is a form of spatial incoherence, is investigated. It is shown that three forms of optical interference may result under different conditions of source spatiotemporal coherence—intramodal, intermodal, and interpulse interference. These effects change the profile of received pulses in a, in general, nonlinear way.     

深远海线性内波条件下声场时间相关性的空间分布

深海声场特定的干涉结构导致其时间相关性的空间起伏,研究这种空间特性可以为水声信号的探测与处理提供重要参考。利用抛物方程声场仿真模型,联合Monte-Carlo数值方法计算分析了深远海线性内波条件下声场时间相关性的空间分布特性。与现有的研究相比,给出了时间相关性的距离和深度起伏特征。结果表明,当接收达到一定距离,声场时间相关性的空间分布具有与声场干涉条纹类似的结构,声场干涉越强,时间相关性越好。此外,声源频率和声速标准差的变化会引起时间相关性空间分布规律的改变,且会聚区传播模式下的改变强于深海声道传播模式。      

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.     

Optical interference and pulse propagation in multimode fibers

The role played by optical interference in determining the propagation of pulses in multimode fibers is examined under conditions of mode independence and mode coupling. Single pulses and pulse-pairs generated by a source that has arbitrary temporal and spatial coherence are considered, and the role played by the spatial integration at the detector, which effectively is a form of spatial incoherence, is investigated. It is shown that three forms of optical interference may result under different conditions of source spatiotemporal coherence—intramodal, intermodal, and interpulse interference. These effects change the profile of received pulses in a, in general, nonlinear way.     

Coherent fluorescence emission by using hybrid photonic–plasmonic crystals

The spatial and temporal coherence of the fluorescence emission controlled by a quasi‐two‐dimensional hybrid photonic–plasmonic crystal structure covered with a thin fluorescent‐molecular‐doped dielectric film is investigated experimentally. A simple theoretical model to describe how a confined quasi‐two‐dimensional optical mode may induce coherent fluorescence emission is also presented. Concerning the spatial coherence, it is experimentally observed that the coherence area in the plane of the light source is in excess of 49 μm², which results in enhanced directional fluorescence emission. Concerning temporal coherence, the obtained coherence time is 4 times longer than that of the normal fluorescence emission in vacuum. Moreover, a Young's double‐slit interference experiment is performed to directly confirm the spatially coherent emission. This smoking gun proof of spatial coherence is reported here for the first time for the optical‐mode‐modified emission.     

孪生光束干涉法测量光源的空间相干性

定量测定光源空间相干性在部分相干光成像, 非相干全息术及光信息处理领域具有重要的研究价值. 本文基于三角全息干涉光路提出了一种测量光源空间相干性的新方法. 利用三角干涉全息光路系统中分束镜产生的孪生光束进行干涉获得干涉图, 通过调整光源中心位置在写入平面内偏离光轴的量, 改变两孪生光束空间分离量的大小, 采集对应的一系列干涉图, 计算干涉图样的对比度, 从而对光源照明空间的波前上一系列不同距离的点对之间的空间复相干度进行测量. 实验系统光路配置较为简单且不需要使用特殊加工的光学元件. 针对一个准单色的扩展光源设计并进行实验, 结果表明利用文中提出的方法可以准确的测量光源的空间相干性, 实验结果相对于理论计算值的误差仅为3.8%. 关键词： 相干性 全息干涉 干涉仪 光学应用     

An Operator Method of the Theory of Optical Coherence and Radiometry

This paper presents a quantum mechanical formalism of the classical coherence theory, within which the generalized radiance function defined in the time domain is regarded as a phase space representative of a time-dependent correlation operator of a polychromatic field. The theory deals with both stationary and nonstationary fields and, for a stationary field, provides a new operator formalism of the usual theory of optical coherence developed in the space-frequency domain. New results include an operator representation of the mutual coherence function, an operator version of the Wiener-Khintchine theorem, and an operator theorem that projects the correlation operator of a polychromatic field onto a particular spectral component. As illustrative examples, the previous formulas regarding the relationship between temporal coherence and spatial coherence, and the relationship between spectral properties and coherence properties are derived from the new operator formulas. The correspondence of the present formalism to the usual formalism using Dirac notation to describe the propagation of a stationary, partially coherent, quasi-monochromatic field is also considered.     

Spatial and temporal coherence effects in interference microscopy and full‐field optical coherence tomography

Low‐coherence optical microscopy or optical coherence microscopy uses light with short coherence length. The well‐known case is: “white‐light interferometry”, which became recently more known as: “optical coherence tomography”. However, when lenses and microscope objectives are used to create interferometric images, in what is known classically as “interference microscopy” or today as “full‐field optical coherence tomography” the spatial coherence starts to play a critical role. In this article the coherence effects in low‐coherence optical microscopy are reviewed. As this technology is becoming increasingly publicized due to its importance in three‐dimensional imaging, particularly of scattering biological media and optical metrology, the understanding of the fundamental physics behind it is essential. The interplay between longitudinal spatial coherence and temporal coherence and the effects associated with them are discussed in detail particularly when high numerical apertures are used. An important conclusion of this study is that a high‐contrast, high‐resolution system for imaging of multilayered samples is the one that uses narrowband illumination and high‐NA objectives with an index‐matching fluid. Such a system, when combined with frequency‐domain operation, can reveal nearly real‐time three‐dimensional images, and is thus competitive with confocal microscopy.     

扩展光源的时间和空间相干性效应分析

在干涉仪不同支路臂中分别加入透明光学层,将扩展光源入射到迈克尔逊干涉仪,观察光场的时间和空间相干现象,发现2种情况下出射光的时间和空间相干包络极值位置发生错位现象。论证了不同支路臂中的光学层可破坏干涉场中的光波相干特性,从而导致时间和空间相干性出现超前或滞后的空间位置互易效应。利用该效应,在2个入射光源条件下,可以得到一种测量光学样品的几何厚度和折射率的实验途径,并给出了相关的计算公式。     

Influence of Partially Spatially Coherent Illumination on the Measurement of Two-dimensional Correlation Function

A coherent optical filtering is often applied to the measurement of correlation function of two-dimensional patterns. The present report treats the influence of spatial coherence on such an optical filtering. A general formula for optical filtering with partially spatially coherent illumination is obtained. The intensity distribution of correlation in the output image plane for several special cases is calculated, where different kinds of coherence conditions of illumination in the process of holographic recording of a filter, or of filtering are assumed. An experiment is performed to verify the theory.     

二维光纤干涉理论

分析了由三根单模保偏光纤纤端出射光场的干涉特性,建立了二维光纤干涉的理论模型.在一级近似下,推导了二维光纤干涉光场场强分布的理论表达式.讨论了实现二维光纤干涉的相关条件,并用二维傅里叶变换方法,分析了干涉图的空间频谱特性.给出了相关实验结果.     

合肥国家同步辐射光源软X射线束空间相干性实验研究

本文从实验角度对合肥国家同步辐射实验室软X射线束的空间相干性进行了研究.利用放置在物面上的高分辨正性光刻胶,记录了中心波长为3.2nm的波带片和针孔直径为30μm组合的光场分布(光斑),获得相应条件下的爱里斑及空间相干直径实验数据;完成了一个双缝干涉实验.所得的这些结果与理论计算相一致.     

INTERFERENCE EFFECTS IN DIFFERENT FIFTH-ORDER POLARIZATIONS WITH BROADBAND NOISY LIGHT

Based on the second-order coherence function, we have studied a phase-conjugate ultrafast modulation spectroscopy due to the interference between the fifth- and fifth-order optical polarizations in cascade three-level Doppler-broadened system. It is found that the temporal behaviour of the beat signal depends on the stochastic properties of the lasers and the transverse relaxation rate of the transition. The beat signal depends on the second-order coherence function, which is determined by the laser line shape. Since different stochastic models of the laser field only affect higher than second-order coherence functions, they have little influence on the general temporal modulation behaviour of the beat signal. The cases that pump beams have either narrow band or broadband linewidth are considered and it has been found that for both cases the overall accuracy for the energy-level difference measurement is determined by the homogeneous linewidths of the optical transitions. Finally, the spatial modulation behaviour of the beat signal has also been discussed.     

The interference component of low-coherent radiation backscattering

An interference component of backscattering of low-coherent radiation is calculated for the first time based on the previously developed approach consisting of direct simulation of the Bethe-Salpeter equation in terms of the Monte Carlo method. It is shown that, upon an increase in the spatial coherence length, it plays the role of the characteristic scale of the backscattering instead of the transport length. The effect of localization of backscattering of an ultrashort pulse in relation to the penetration depth is revealed. Both the theory and the numerical simulation predict, in accordance with experiment, a considerable broadening of the peak of coherent backscattering with decreasing coherence length, which significantly extends the application field of the effect, especially in biomedical diagnostics.     

热光的高阶双缝干涉

干涉效应反映了光场的相干性,非相干光源中无序性会破坏干涉.然而对于高阶干涉来说这一看法并不成立.文章作者最近的理论和实验研究表明,横向传播方向无序的热光源可以实现高阶双缝干涉.尽管单个探测器的强度分布是均匀的,处于不同位置的两个探测器的联合强度关联却出现了干涉条纹.当两个探测器同步反向移动时,条纹间距减小为一阶干涉条纹的一半.实验结果同不久前报道的在自发参量下转换过程中产生的纠缠双光子对的双缝实验中所观察到的亚波长干涉效应十分类似.实验结果可以用多模热光场的二阶空间关联性质来解释.热光的高阶双缝干涉是著名的Hanbury-Brown和Twiss实验的空间干涉版本,因此也可称其为Hanbury-Brown和Twiss型双缝干涉。     

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.     

Numerical correction of coherence gate in full-field swept-source interference microscopy

A big problem in low-coherence interference microscopy is the degradation of the coherence signal caused by shift of the angular and temporal spectrum gates. It limits the depth of field in confocal optical coherence microscopy and degrades images of sample inner structure in most interference microscopy techniques. To overcome this problem we propose numerical correction of the coherence gate in application to full-field swept-source interference microscopy. The proposed technique allows three-dimensional sample imaging without mechanical movement of the microscope components and is also capable of determining separately the geometrical thickness and the refractive index of the sample layers, when the sample contains a transversal pattern. The applicability of the proposed technique is verified with numerical simulation.