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。     

伪部分相干高斯-谢尔模型光束在湍流大气中传播的闪烁孔径平滑效应

采用光传播的数值模拟方法, 对伪部分相干高斯-谢尔模型光束大气传播过程进行数值模拟, 统计分析不同接收口径内的光强起伏特性,计算闪烁的孔径平滑因子, 讨论了表征伪部分相干光的调制相位屏的相对变化频率对闪烁指数的影响, 并将其与充分发展的部分相干高斯-谢尔模型光束及完全相干光的闪烁指数对比. 结果表明: 降低光源相干性可大幅度降低闪烁指数, 但同时其闪烁指数的孔径平滑效应减弱, 在相同接收孔径下, 伪部分相干光闪烁指数的孔径平滑效果要比完全相干光差; 增大调制相位屏的相对变化频率可在一定程度上降低闪烁指数, 随着其相对频率的增大, 伪部分相干光的闪烁指数与部分相干光的结果趋于一致. 关键词： 伪部分相干高斯-谢尔模型光束 湍流大气 孔径平滑闪烁指数 数值模拟     

湍流中漫射目标偏振部分相干激光的闪烁特性

采用广义惠更斯-菲涅耳原理和矩阵光学理论,研究了湍流大气中偏振部分相干激光波束从发射机到目标和从目标到接收机双程路径的闪烁特性。将产生任意偏振光束的琼斯矩阵和ABCD传输矩阵进行结合,围绕接收机处波场四阶矩展开推导,得出双程路径下偏振部分相干激光波束在接收机处的闪烁指数表达式,数值分析了大气折射率结构常数、激光波束的波长、束宽、相干长度对接收机处光强闪烁指数的影响。结果表明:偏振部分相干激光波束的闪烁指数随着目标与发射机之间距离呈现先增大、到达峰值后逐渐减小的变化趋势;相干性差的光束产生的闪烁指数小,相干长度微小的变化将会产生较大的闪烁指数变化,相干性好的光束产生较大的闪烁指数,但是相干长度的变化对闪烁指数的影响很小。     

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.     

Propagation factor of a truncated partially coherent flat-topped beam in turbulent atmosphere

Analytical expression for the propagation factor of a truncated partially coherent flat-topped (FT) beam in turbulent atmosphere is derived based on the extended Huygens-Fresnel integral and the second-order moments of the Wigner distribution function. Numerical results show that the radius of the aperture (i.e., truncation parameter) has strong influence on the evolution properties of the propagation factor of a truncated partially coherent FT beam, and the advantage of a truncated partially coherent FT beam over a truncated Gaussian Schell-model (GSM) beam or a truncated coherent FT beam for overcoming the turbulence-induced degradation disappears gradually with the decrease of the radius of the aperture.     

Partially coherent Lorentz Gaussian beam and its scintillations

We study the scintillation aspects of partially coherent Lorentz Gaussian (LG) beams via numerically integrating the average and average squared intensity expressions. Within the examined range of input and propagation medium parameters, the LG beams are generally found to offer less and less scintillations against the pure Gaussian beam, particularly when the Lorentzian feature of the beam is emphasized more. This lower scintillation property is exhibited for collimated coherent beams with different Lorentz widths and at on-axis and off-axis positions of the receiver plane. When focusing is introduced, at shorter propagation distances the ordering of the beams remains as described above, but at longer propagations distances a complete reversing of the beam order is observed. Raising the turbulence levels by increasing the structure constant inevitably causes rises in scintillations, while preserving the advantage of LG beams over the pure Gaussian beam. Partial coherence reduces scintillations as expected, at the same time nearly eliminating the scintillation differences between the beam types.     

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。     

Optimized multiemitter beams for free-space optical communications through turbulent atmosphere

Using laser beams with less than perfect spatial coherence is an effective way of reducing scintillations in free-space optical communication links. We report a proof-of-principle experiment that quantifies this concept for a particular type of a partially coherent beam. In our scaled model of a free-space optical communication link, the beam is composed of several partially overlapping fundamental Gaussian beams that are mutually incoherent. The turbulent atmosphere is simulated by a random phase screen imprinted with Kolmogorov turbulence. Our experiments show that for both weak-to-intermediate and strong turbulence an optimum separation between the constituent beams exists such that the scintillation index of the optical signal at the detector is minimized. At the minimum, the scintillation reduction factor compared with the case of a single Gaussian beam is substantial, and it is found to grow with the number of constituent beams. For weak-to-intermediate turbulence, our experimental results are in reasonable agreement with calculations based on the Rytov approximation.     

非均匀关联径向偏振部分相干光的产生

从理论和实验两方面对非均匀关联径向偏振部分相干光的产生进行了研究.理论上,基于相位关联与相干度的联系,推导出了非均匀关联径向偏振部分相干光的2×2阶交叉谱密度矩阵及相干度分布.实验上,利用一个相位型液晶空间光调制器的不同区域,对入射的完全相干的径向偏振光的两个正交偏振分量分别加载随机相位调制,并实验测量了这种光束的相干度分布及其对光强分布的影响.实验结果验证了光束相干度的非均匀关联结构,并且通过改变随机相位的高斯调制半宽可以改变光束的相干性分布.研究表明,随着随机相位的高斯调制半宽的增加,光束中两点间的相干度逐渐减小,其光强分布由圆环状逐渐变化为类平顶的光强分布.这种非均匀关联的径向偏振部分相干光在激光微操纵和材料加工等领域具有一定的潜在应用价值.     

Long-distance propagation of pseudo-partially coherent Gaussian Schell-model beams in atmospheric turbulence

Propagation properties of spatially pseudo-partially coherent Gaussian Schell-model beams through the atmo- spheric turbulence over a long-distance uplink path are studied by numerical simulation. A linear coordination trans-formation is introduced to overcome the window effect and the loss-of-resolution problem. The beam spreading, beam wandering, and intensity scintillation as functions of turbulence strength, source correlation length, and change frequency of random phase that models the partial coherence of the source are analyzed. It is found that the beam spreading and the intensity scintillation of the partially coherent beam are less affected by the turbulence than those of the coherent one, but it suffers from a more severe diffractive effect, and the change frequency of random phase has no evident influence on it. The beam wandering is insensitive to the variation of source correlation length, and decreases firstly then goes to a fixed value as the change frequency increases.     

Numerical Simulation for Coherent and Partially Coherent Beam Propagation through Atmospheric Turbulence

Propagation properties of coherent and partially coherent beams in atmospheric turbulence are investigated respectively by using numerical simulation It is found that a partially coherent beam has a spreading larger than a coherent beam. However, from the point view of relative beam spreading and intensity scintillation, a partially coherent beam is less affected than the corresponding coherent beam, which may be the most important virtue of partially coherent beams that could be utilized to improve the performance of laser engineering. The beam wandering is almost independent of the degree of the source coherence. More aperture averaging occurs when beam becomes more coherent.     

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.     

Experimental generation of a partially coherent flat-topped beam

An efficient optical system is proposed to generate a partially coherent flat-topped (FT) beam theoretically. Furthermore, we report the experimental generation of a partially coherent FT beam based on the proposed optical system. The intensity distribution and the modulus of the square of the spectral degree of coherence of the generated partially coherent FT beam are measured. The experimental results are consistent with the theoretical results.     

Study correlation vortices in the near-field of partially coherent vortex beams diffracted by an aperture

We have derived the analytical expression of the electric cross-spectral density in the near-field of partially coherent vortex beams diffracted by an aperture. Taking the Gaussian Schell-model vortex beam as a typical example of partially coherent vortex beams, the spatial correlation properties and correlation vortices in the near-field of partially coherent vortex beams diffracted by a rectangle aperture are studied. It is shown that the off-axis displacement, spatial degree of coherence parameter, propagation distance, and the opening factor of the aperture affect the spectral degree of coherence and positions of correlation vortices. With the optimization algorithm, we obtain the symmetric distributing coherent vortex.     

Intensity distribution and focal depth of axicon illuminated by Gaussian Schell-model beam

In view of second-order coherence theory, the generalized diffractive axicon illuminated by partially coherent Gaussian Schell-model (GSM) beams is analyzed. An analytical equation for focal depth of axicon without aperture illuminated by spatial partially coherent GSM beam is derived. We showed that the off-axis images can be evaluated by using the method of stationary phase at any correlation state, hence we demonstrated that the intensity distribution of diffracted beam is a superposition of Bessel Beams of various orders. We also showed that the diffracted beam is nondiffractive only on the boundaries of the focal depth.     

Partially coherent elegant Hermite–Gaussian beams

Elegant Hermite–Gaussian beams (EHGBs) are extended to the partially coherent case. An explicit and analytical formula is derived for the cross-spectral density of a partially coherent EHGB propagating through an aligned or misaligned paraxial ABCD optical system. The propagation properties of a partially coherent EHGB in free space and its focusing properties through a thin lens are studied numerically, and are compared to those of a partially coherent standard Hermite–Gaussian beam (SHGB). It is found that the propagation and focusing properties of a partially coherent EHGB are closely related to its initial coherence. A partially coherent EHGB spreads slower than a partially coherent SHGB in free-space propagation. A partially coherent EHGB can be focused more tightly than a partially coherent SHGB.     

新型部分相干光束的产生及其相干特性

利用相干理论,研究了新型部分相干光束的相干特性.用激光光束透过旋转的特殊毛玻璃,产生一种相干性分布特殊的新型部分相干光束.实验上经双孔干涉,记录了该光束经不同小孔间距双孔产生的干涉条纹,计算得出所对应的相干度,并获得了该光束在不同传输距离下的相干度分布情况,发现该光束的相干度分布与高斯-谢尔模型光束的相干度分布不相同,其相干度随着传输距离的增大而变强.     

被光阑衍射部分偏振高斯-谢尔模型光束的远场特性

从部分相干光的传输理论出发,采用光束相干-偏振矩阵方法研究了被光阑衍射部分偏振高斯-谢尔模型光束的远场特性,对远场偏振和光强特性作了详细的数值计算和物理分析。研究结果表明,光阑衍射部分偏振高斯-谢尔模型光束的远场特性与光阑截断参量、光的空间相干性和衍射角有关。并与自由空间的传输特性和以前的工作作了比较分析。     

部分相干余弦-高斯光束

引入部分相干余弦-高斯光束,推导出部分相干余弦-高斯光束通过近轴ABCD光学系统的传输公式和M2因子,研究了部分相干余弦-高斯光束通过像散透镜的传输特性.结果表明,部分相干余弦-高斯光束的M2因子与部分相干余弦-高斯光束的空间相干参量和离心参量有关,但与透镜的像散系数无关.适当选取空间相干参量,离心参量或像散系数,在几何焦面处可得到类高斯、平顶和空心等不同的光强剖面,实现部分相干余弦-高斯光束的空间整形.     

Partially coherent elegant Hermite–Gaussian beam in turbulent atmosphere

Based on the extended Huygens–Fresnel integral, analytical formulas for the cross-spectral density, mean-squared beam width and angular spread of a partially coherent elegant Hermite–Gaussian (HG) beam in turbulent atmosphere are derived. The evolution properties of the average intensity, spreading and directionality of a partially coherent elegant HG beam in turbulent atmosphere are studied numerically. It is found that the partially coherent elegant HG beam with smaller initial coherence width, larger beam order and longer wavelength is less affected by the atmospheric turbulence. Compared to the partially coherent standard HG beam, the partially coherent elegant HG beam is less affected by turbulence under the same condition. Furthermore, it is found that there exist equivalent partially coherent standard and elegant HG beams, equivalent fully coherent standard and elegant HG beams, and an equivalent Gaussian–Schell-model beam may have the same directionality as a fully coherent Gaussian beam whether in free space or in turbulent atmosphere. Our results can be utilized in short and long atmospheric optical communication systems.