Comparative study on the propagation performance of coherently combined and incoherently combined beams

Taking phase error, turbulent atmosphere, jitter, vacancy factor and tilt error into consideration, we propose a general propagation formula for both coherent and incoherent combined beams with different kinds of aberrations. Comparative study on the propagation performance of coherent and incoherent combined beams is presented. Beam propagation factor (BPF) defined as laser output power in a specified far-field bucket divided by the total output power radiating from the effective near-field exit aperture of the laser beam is introduced as the beam quality factor to give a quantitative study. It is revealed that the coherent combined beam has great advantage when propagating in free-space compared with the incoherent combined beams. However, the coherent combined beam is more sensitive to the environmental aberrations, and the beam quality degrades faster with an increase in the aberrations’ intensity. Scintillation index as the high moments of the combined intensity field is also studied. It is revealed that both coherent and incoherent combined beams exhibit less scintillations compared with a single-aperture beam, and the incoherent combined beam demonstrates better scintillations reducing the performance. Our methodology offers an all-round performance evaluation on the two kinds of laser systems.     

高斯光束的合成特性分析

 建立了矩形阵列高斯光束合成模型,采用数值模拟方法计算了光束间距、单元光束特性以及阵列结构等参数对非相干合成和同相位相干合成的远场峰值强度及光束质量的影响,描述了非同相位相干合成可能产生的结果,讨论了同轴与非同轴合成,相干与非相干合成的特点。结果表明：非相干和同相位相干合成时的光束质量随着单元光束的增多而变差,并且随着光束间距与单元光束束腰之比的增大而下降;而非同相位相干合成的结果较为复杂,可能产生完全相消干涉,合成光束“重心”离轴及束腰位置偏移等现象。分析认为：同轴合成可以获得最佳的光束质量,是值得采用的合成方式。此外,同轴相干合成优于非相干合成的充分条件是将单元光束之间的相位差控制在(-π/4,π/4)以内。     

高功率光纤激光部分相干合成的可行性及效果分析

提出部分相干合成的概念,论证了谱线宽度和偏振特性并不是影响高功率光纤激光部分相干合成的瓶颈.与完全相干合成的理想情形相比,随着光束线宽的增大,部分相干合成光束的远场光斑图样基本保持不变,但峰值强度和斯特尔(Strehl)比随之减小,光斑能量越来越分散.利用数值计算的方法对部分相干合成与非相干合成光束的远场效果进行了比较分析.计算结果表明,尽管线宽的存在降低了部分相干合成的效果,但与非相干合成相比,部分相干合成的光束仍具有较大优势.     

Photorefractive two-wave mixing in the presence of an incoherent beam

We present the numerical results of the photorefractive two-wave mixing in the presence of an incoherent beam by considering the influence of the ratios of the intensities and the light-excitation cross sections of the incoherent beam to the coherent beams on the space-charge field and the effective coupling coefficient. The results show that the incoherent beam can control the intensity of the coherent beams effectively. The experimental results agree with the theory well. One application is demonstrated to obtain the positive and negative coherent replicas of an incoherent image. The coherent images have a resolution of 80.6 line pairs/mm. Received: 2 March 1999 / Revised version: 26 July 1999 / Published online: 20 October 1999     

湍流对离轴列阵高斯光束相干与非相干合成的影响

研究了湍流对离轴列阵高斯光束相干与非相干合成的影响.推导出了相干合成光束的传输方程.采用二阶矩束宽、桶中功率和参数β作为光束质量评价参数比较了离轴列阵高斯光束通过湍流大气的相干与非相干合成,并对主要结果给予了合理的物理解释.研究表明：一方面,不论是相干合成还是非相干合成,湍流都使得合成光束扩展、峰值光强下降,并且子光束数越多,合成光束受湍流影响就越小.另一方面,非相干合成光束较相干合成光束受到湍流的影响要小. 关键词： 相干与非相干合成 湍流大气 离轴列阵高斯光束     

非傍轴径向阵列高斯激光束的传输特性

推导出相干和非相干非傍轴径向阵列高斯激光束的传输公式,并用以研究了径向阵列光束在自由空间的传输特性,重点分析了阵列光束参量对合成光束光强分布的影响。结果表明:阵列半径与束腰宽度之比是一个关键参量,当它固定时,相干和非相干合成光束的光强分布都保持不变,但合成光束的光强分布和远场轴上光强最大值都与合成方式有关。     

径向阵列非傍轴椭圆高斯光束的相干和非相干合成

 从瑞利-索末菲衍射积分公式出发,推导出径向阵列非傍轴离轴椭圆高斯光束相干合成和非相干合成在自由空间中的解析传输公式,给出其远场分布和傍轴表示式。研究表明:合成光束的光强分布与f参数、径向阵列半径、光束数、传输距离和合成方式有关;N束光相干合成和非相干合成在远场的光强最大值分别为单光束在远场最大值的N₂和N倍。     

Coherence enhancement of spatially incoherent light beams through soliton interactions

We show that the spatial coherence of a partially incoherent light beam can be greatly enhanced through an energy-conserving interaction with an incoherent or a coherent dark spatial soliton. Computer simulations show that during this process a portion of the incoherent beam is trapped within the dark notch of the dark soliton, thus forming a sharp intensity spike. In this region the correlation length dramatically increases by at least 2 orders of magnitude.     

非傍轴部分相干厄米-高斯光束的相干和非相干合成

推导出二维非傍轴部分相干厄米-高斯（H-G）光束相干合成和非相干合成的交叉谱密度和光强的解析公式,并分析了一些特例. 合成光束的光强不仅决定于f参数,f_σ参数,离轴参数,合成光束的束数和阶数以及传输距离z,而且还决定于合成方式. 对部分相干光的相干合成和非相干合成概念做了物理诠释,其正确性为数值计算例证实. 关键词： 部分相干光的相干和非相干合成 非傍轴部分相干厄米-高斯（H-G）光束 自由空间中的传输方程     

Beam couplings and phase conjugate effects in reflection and transmission in BaTiO3

The details of experiments showing the effects of self-pumped phase conjugation on reflection and on transmission in barium titanate crystal are given. The specular reflection and the second-surface reflection of an extraordinary polarized beam, incident on the face of the crystal parallel to itsc-axis, get reduced in intensity as the phase conjugation develops. It has been found that parts of the self-pumped phase conjugate beam emerge out of the crystal as additional transmission beams. They grow in intensity as the phase conjugation develops. Other measurements which combine coherent or incoherent coupling beams are presented and used to explain the observations.     

Dark incoherent soliton splitting in biased photorefractive-photovoltaic crystals

Using the coherent density approach, we study the dark incoherent soliton splitting in biased photorefractive-photovoltaic crystals. We show that when the full width half maximum (FWHM) of the optical beam’s intensity is increased, the odd incoherent dark beam splits into an odd-number sequence of multiple dark stripes, whereas the even incoherent dark beam splits into an even-number sequence of multiple dark stripes. We find that when more incoherent solitons are generated, the separations between adjacent dark stripes become smaller and the stripes far away from the center become less visible and that for a given physical system and for a given splitting, the separations between adjacent dark stripes decrease with an increase in the intensity FWHM of the optical beam. On the other hand, the dark incoherent soliton splitting in biased photorefractive-photovoltaic crystals is the dark incoherent screening soliton splitting when the bulk photovoltaic effect is neglectable and the dark incoherent closed- and open-circuit photovoltaic soliton splitting when the external bias field is absent.     

Propagation of a partially coherent beam through Selfoc fibers

Propagation of a partially coherent beam through a Selfoc fiber is considered. The inhomogeneous Helmholtz equations satisfied by the mutual coherence function are solved using the modal expansion. The result is applied to the cases when the incident beam is either incoherent or coherent. An expression for the intensity distribution is also obtained.     

Propagation properties of off-axis Hermite--cosh--Gaussian beam combinations through a first-order optical system

Based on the Collins integral formula, the analytic expressions of propagation of the coherent and the incoherent off-axis Hermite--cosh--Gaussian (HChG) beam combinations with rectangular symmetry passing through a paraxial first-order optical system are derived, and corresponding numerical examples are given and analysed. The resulting beam quality is discussed in terms of power in the bucket (PIB). The study suggests that the resulting beam cannot keep the initial intensity shape during the propagation and the beam quality for coherent mode is not always better than that for incoherent mode. Reviewing the numerical simulations of Gaussian, Hermite--Gaussian (HG) and cosh--Gaussian (ChG) beam combinations indicates that the Hermite polynomial exerts a chief influence on the irradiance profile of composite beam and far field power concentration.     

Synthesis of spatial coherence

The mutual intensity function plays a major role in characterizing quasi-monochromatic, partially coherent optical signals. We propose to use the mutual intensity as a carrier of information to avoid speckle noise in coherent illumination systems and to permit the use of complex functions that are prohibited spatially incoherent sources. To do this we require methods for encoding the information as a coherence function. An optical system for synthesizing a beam with a given mutual intensity function is proposed. The optical system permits the synthesis of any desired mutual intensity function. The illumination is supplied by a quasi-monochromatic, spatially incoherent source. Experimental results demonstrate the performance of this system for several cases.     

基于并行梯度下降算法模拟高功率固体激光装置的相干合成

 多路光的相干合成是高功率固体激光装置的关键技术之一。基于合成模型,对4组tilt/tip-piston镜采用并行梯度算法,通过模拟计算实现了光束间的位相锁定和相干合成。结果表明有限次算法迭代次数内,相干合成时远场焦斑10 μm半径范围内的强度比约为非相干合成时的4倍。基于高频响应驱动器和对应的高速控制算法将有可能实现高功率固体激光装置多路输出光束间的相干合成。     

多束超高斯激光相干合成的数值模拟

 建立了超高斯光束的相干叠加的数学模型,对比了光束间距为1 cm、超高斯阶数为12条件下25束高斯光束相干叠加与非相干叠加时的光强分布,发现相干合成的峰值光强为非相干叠加的峰值光强的近10倍,且光束质量也得到大大提高,有利于提高能量的利用率。分析了多种条件下相干合成的光强分布特性,结果表明：随机相位差小于十分之一波长时,相位差的变化对相干合成效果影响不大;当超高斯阶数大于10时对相干合成的峰值光强影响较小;随着相干发射阵列光束间距的增大,相干合成光强迅速减小,光束质量变差。得到了传输距离分别为10 m,100 m,1 km和5 km下的光强分布,表明合成的峰值光强随着传输距离的增加而由小变大,最后随着传输距离的进一步增大而衰减。最后得到了不同传输距离处的环围功率比。     

暗光伏孤子的实验研究

在LiNbO3∶Fe晶体中,采用相位掩模对部分空间非相干和相干暗光伏孤子进行了实验研究.实验观察到了部分空间非相干和相干的一维和二维暗光伏孤子,它们的形成来源于光伏效应,是自散焦效应和衍射效应平衡的结果.实验和理论分析表明,暗光伏孤子的形成与光的传输方向,强度梯度与晶体c轴夹角有关;只有在一定的条件下,才能得到稳态的部分空间非相干暗光伏孤子.     

The polarization property and irradiance distribution of incoherent and coherent Gaussian beam combinations

Based on the beam coherence-polarization (BCP) matrix, the polarization property of coherent and incoherent Gaussian beam combinations is studied in detail. The general expressions for the degree of polarization P of the resulting beam in case of incoherent and coherent combinations are derived. It is shown that P is dependent on the incoherent or coherent combination, propagation distance, separation, azimuth of the polarization plane and numbers of beamlets in general. The irradiance distribution of the resulting beam for the coherent cases depends on the azimuth of the polarization plane of beamlets. However, for the incoherent case it does not.     

Light-induced scattering in SBN：Cr crystal under external electric fields and its suppression

In this paper, the enhancement of light-induced scattering in congruent SBN:Cr (Sr_{0.61}Ba_{0.39}Nb_2O_6:Cr) crystals in the presence of an externally applied electric field and its suppression are studied. If a coherent image is focalized in SBN:Cr crystal without applying external electric field, the output image will remain clear, because of the weak photorefractive effect in the crystal. When a field is applied properly along the crystal axis, markedly enhanced scattering from the signal beam and the output image dispersion can be observed due to the increase of the photorefractive two-beam coupling gain and the light-induced index change in SBN:Cr crystals. By introducing a coherent or incoherent beam with higher intensity the light-induced scattering can be suppressed through the erasure of scattering gratings. The difference between coherent and incoherent beam is that the former can also amplify the signal beam as the scattered light is removed, whereas the latter can only make the signal beam revert to its initial state. The results obtained under different experimental conditions are consistent with theoretical analysis.     

Fidelities of output coherent images produced by photorefractive two-wave mixing

We study theoretically the fidelities of output coherent images in incoherent-to-coherent conversion based on photorefractive two-wave mixing in the presence of an incoherent image-bearing beam. A vector version of the whole beam split step method is developed. The dependencies of the fidelities of output coherent images on geometric and physical parameters such as the incident direction of the beams, the intensity ratios between the beams, and coupling coefficients are investigated in detail. PACS 42.65.Hw