Experimental and theoretical investigation of loss of coherence on scattering of a beam with helical wavefront

Theoretical and experimental investigations of the second order intensity coherence for a beam with helical wavefront i.e. an optical vortex scattered through a rotating ground glass have been reported. The results have been compared with scattering of the Gaussian beam of a He-Ne laser. It shows that the second order intensity coherence or intensity correlation curve for the vortex decreases much faster than that of the Gaussian beam of the He-Ne laser. We attribute this behaviour to the helicity of the wavefront.     

激光空间相干性对照明均匀性的影响

 研究了激光相干性对照明均匀性的影响，为照明激光器的选择提供了理论参考。其中，部分相干高斯光束分解为模式间相互独立的厄米-高斯光束的迭加。采用相位屏的近似处理方法对激光通过大气湍流的传输进行计算模拟。数值模拟的结果表明：当照明光束的空间相干性降低时，其照明均匀度逐步提高。因此对于照明激光器而言，选择空间相干性较差的激光器对其照明均匀度更加有益。     

真空中线性啁啾时空高斯脉冲传输特性的分析

利用稳态相位点的方法研究了线性啁啾时空高斯脉冲传输过程中的相位特性，并在二阶近似的情况下讨论了其传输过程中的时空特性，两种方法从不同侧面得出了相同的结论，即：时空高斯脉冲在传输的过程中，在无穷远处交退化为球面波，或者在旁轴近似的情况下退化为平面波。     

湍流大气传输高斯谢尔光束的到达角起伏

研究了在弱大气湍流起伏环境下以窄带宽高斯谢尔光束为激光光源的大气通信问题,分析了大气湍流强度和光源空间相干度对通信光束到达角起伏的影响.采用窄带宽光场的交叉谱密度函数代替光场互相干函数的近似方法和采用包含大气湍流内外尺度的简化折射率谱密度函数,得出了湍流大气中传输高斯谢尔光束的波结构函数(WSF) 和到达角起伏方差解析近似关系.分析表明,光源的空间相干度和传输光束的湍流扩展是影响高斯谢尔光束的相位起伏结构函数和传输光束到达角起伏的重要因素.     

Spatial coherence properties and directionality of partially coherent cosh-Gaussian beams

Based on the theory of optical coherence, the spatial coherence properties and directionality of partially coherent cosh-Gaussian (ChG) beams are studied. It is shown that unlike Gaussian Schell-model (GSM) beams, in the strict sense there do not exist partially coherent ChG beams which may produce the same far-field radiant intensity distribution as a fully coherent laser beam. However, under certain conditions it is possible to find partially coherent ChG beams with the same far-field radiant intensity distribution as a fully coherent laser beam.     

Influence of transverse effects on coherence length measurements using two-beam interferences

It has been demonstrated in a previous work (Opt. Commun. 233 (2004) 39-43), for a monochromatic laser beam, that imperfect collimation leads to systematic errors in the determination of the spectral bandwidth of a Gaussian beam. In this work, we demonstrate that such transverse effects could also make wrong the measurement of the coherence length of a non-monochromatic Gaussian beam. In addition, we have demonstrated that this systematic error is increased when the laser beam under study is made up of a mixing of spatial modes.     

Coherence properties of an amplified spontaneous emission laser: experiments on a 10 Hz vacuum–ultraviolet H2-laser

Spatial coherence properties of a mirrorless laser, namely a 10 Hz Lyman-band molecular hydrogen laser pumped by femtosecond pulses of only 200 mJ, are studied. Assuming a Gaussian Schell-model source and using the generalized van Cittert–Zernike theorem we are able to measure both the coherence length arising from free-space propagation and the coherence length at the source plane. This analysis is particularly suitable to the study of the coherence properties of lasers operating in the amplified spontaneous emission regime and is particularly indicated for x-ray lasers. Measurements at various target lengths show a monotonic increase in the degree of spatial coherence and decrease in the source size versus length of the gain column. As a consequence, a monotonic decrease in the number of sustained transverse modes with length of the gain medium is observed, demonstrating the effects of gain guiding and refractive antiguiding.     

Transient calorimetric diagnostics for plasma processing

We present a detailed study of the Gaussian laser propagation through a dielectric system composed by two right angle prisms. We investigate the transition between the spatial coherence limit, which exhibits wave-like properties and for which the resonance phenomenon can be seen, and the decoherence limit, which exhibits particle-like properties and for which the multiple diffusion occurs. We also analyze the tunneling at critical angles. In our numerical analysis, we shall use BK7 and Fused Silica prisms and a Gaussian He-Ne laser with a wavelength of 632.8 nm and beam waists of 2 mm and 200 μm.     

The characteristics analysis of a new-style four-mirror axisymmetric-fold-combination cavity adapting to cylindrical discharge region

An axisymmetric-fold-combination (ASFC) cavity composed of two planar mirrors and spherical mirrors was designed. It is a stable-unstable resonator cavity. The light field of radial direction is Gaussian distribution. And in angular orientation, the distribution keeps invariant. It could generate annular CO₂ laser beam with excellent spatial coherence. And the spatial coherence is commendably realized with its stable-unstable cavity structure. The output light intensity distribution of this special model was discussed and simulated. With exterior lenses group, the output beams can be adjusted and controlled better to meet the manufactural requirements. Some references were provided for further research of the cavity with cylindrical discharge region.     

Propagation of partially coherent controllable dark hollow beams with various symmetries in turbulent atmosphere

Normalized intensity distribution, the complex degree of coherence and power in the bucket for partially coherent controllable dark hollow beams (DHBs) with various symmetries propagating in atmospheric turbulence are derived using tensor method and investigated in detail. Analytical results show that, after sufficient propagation distance, partially coherent DHBs with various symmetries eventually become circular Gaussian beam (without dark hollow) in turbulent atmosphere, which is different from its propagation properties in free space. The partially coherent DHBs return to a circular Gaussian beam rapidly for stronger turbulence, higher coherence, lower beam order, smaller p or smaller beam waist width. Another interesting observation is that the profile of the complex degree of coherence attains a similar profile to that of the average intensity of the related beam propagating in a turbulent atmosphere. Besides the laser power focusablity of DHBs are better than that of Gaussian beam propagating in turbulent atmosphere.     

Coherence and intensity moments of laser light

Taking the modal behaviours of the laser field into account, the coherence properties of laser light can be characterized by mode coherence functions (MCFs) and mode coherence coefficients (MCCs). Changes in laser light properties due to optical operations can be described by transformation laws for the MCFs and the MCCs. The transformation laws as well as transformation matrices for propagation in free space, phase transformations, spatial amplitude modulations and aperturizing are given. Furthermore, intensity distributions and intensity moments in the spatial and in the spatial frequency domains are expressed in terms of the MCCs. General expressions for the beam quality factors,M ²s, obtained using the intensity moments and some useful expressions for intensity moments of higher order are discussed.     

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。     

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.     

Correlation properties of random electromagnetic beams in laser resonators

With the help of the generalized Huygens–Fresnel principle and the tensor approach for electromagnetic stochastic beams we investigate the behavior of their two-point spatial correlation properties on interaction with a laser resonator. In particular, the evolution of the degree of coherence, of the degree of cross-polarization and of the intensity correlations (at one and two points in space) is analyzed for typical beams and cavities. The theory is illustrated by numerical curves pertaining to various correlation properties of typical electromagnetic Gaussian Schell-model beams.     

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.     

Spatial coherence resonance induced by coloured noise and parameter diversity in a neuronal network

Spatial coherence resonance in a two-dimensional neuronal network induced by additive Gaussian coloured noise and parameter diversity is studied. We focus on the ability of additive Gaussian coloured noise and parameter diversity to extract a particular spatial frequency (wave number) of excitatory waves in the excitable medium of this network. We show that there exists an intermediate noise level of the coloured noise and a particular value of diversity, where a characteristic spatial frequency of the system comes forth. Hereby, it is verified that spatial coherence resonance occurs in the studied model. Furthermore, we show that the optimal noise intensity for spatial coherence resonance decays exponentially with respect to the noise correlation time. Some explanations of the observed nonlinear phenomena are also presented.     

Development of a full spatial coherent X-ray laser at 13.9 nm

We have succeeded in developing a laser-pumped X-ray laser with full spatial coherence at 13.9 nm. The X-ray laser beam with a very small divergence of 0.2 mrad was generated from double target experiments, where a seeding light from the first laser medium was amplified in the second laser medium. The observed divergence was close to the diffraction limit value within a factor of two. The seeding light was amplified in the second medium without refraction influence and the gain coefficient was 7.9 cm^-1. From the measurement of visibility, it was found that the spatial coherent length was longer than the beam diameter. PACS 41.50+h; 42.55.Vc     

Spatial partial coherence in Young''s interferograms

Young's interferograms with high visibility reveals a high degree of spatial coherence of first order. But, spatially partial coherence of second order can be observed when it interferes itself through a compensated Michelson's interferometer attached at the exit of the Young's slit pair. We show that the patterns at the exit of the Michelson's interferometer are Young's interferograms with modulation fringes, which allow an estimation of the degree of the high order spatial coherence.     

Spatial coherence of random laser emission

We experimentally studied the spatial coherence of random laser emission from dye solutions containing nanoparticles. The spatial coherence, measured in a double slit experiment, varied significantly with the density of scatterers and the size and shape of the excitation volume. A qualitative explanation is provided, illustrating the dramatic difference from the spatial coherence of a conventional laser. This work demonstrates that random lasers can be controlled to provide intense, spatially incoherent emission for applications in which spatial cross talk or speckle limit performance.     

Effect of spatial coherence on the scintillation properties of a dark hollow beam in turbulent atmosphere

With the help of a tensor method, we derive an explicit expression for the on-axis scintillation index of a circular partially coherent dark hollow (DH) beam in weakly turbulent atmosphere. The derived formula can be applied to study the scintillation properties of a partially coherent Gaussian beam and a partially coherent flat-topped (FT) beam. The effect of spatial coherence on the scintillation properties of DH beam, FT beam and Gaussian beam is studied numerically and comparatively. Our results show that the advantage of a DH beam over a FT beam and a Gaussian beam for reducing turbulence-induced scintillation increases particularly at long propagation distances with the decrease of spatial coherence or the increase of the atmospheric turbulence, which will be useful for long-distance free-space optical communications.