高斯光束自由电子激光小信号增益分析

由增益的三维公式出发,对高斯光束时的小信号增益进行了分析。对电子束截面远大于光束截面情况给出了解析的增益渐近公式;对电子束截面远小于光束截面的情况。给出了解析的增益近似公式,结果与用计算机模拟所得相符。     

漂移对聚焦高斯光束闪烁影响的数值模拟

 采用非自适应坐标变换对聚焦高斯光束在湍流大气中的传输进行了数值模拟,结果显示轴闪烁指数并没有出现如Rytov理论所预言的随初始光束半径的增大而明显减小的现象,其原因在于Rytov近似理论未考虑大尺度湍涡产生的漂移效应对闪烁的贡献。对比数值模拟结果与漂移理论结果以及相关实验结果,三者相吻合,表明未考虑漂移效应的Rytov近似理论不能完全准确地描述聚焦光束的闪烁特征,在研究聚焦光束的闪烁时,应当考虑漂移的影响。     

Scintillation index of astigmatic annular beams in a turbulent atmosphere

The scintillation properties of astigmatic annular beams in a weak turbulent atmosphere are investigated. Expression for the on-axis scintillation index of an astigmatic annular beam is derived. It is found that the scintillation index of an astigmatic annular beam can be smaller than that of a Gaussian beam, an elliptical Gaussian beam and a stigmatic annular beam in a weak turbulent atmosphere under certain conditions. The scintillation properties of astigmatic annular beams are closely controlled by its beam parameters.     

Design and Analysis of Diffractive Axicons for Gaussian Beam Illumination

The diffractive axicon for the illumination with Gaussian beams is designed. The stationary phase method and the numerical calculation are used to analyze the diffraction integral describing the diffraction field. It is shown that with the Gaussian beam illumination of a smaller beam radius, the axicon can produces the uniform-axial-intensity with the lower oscillation frequency and the smaller oscillation amplitude. In addition, with the Gaussian beam illumination of a suitable beam radius, we can achieve the more uniform central-core width.     

Creation of a sharper focus by using a rectified TEMp0 beam

The superresolution technique is usually used in optical imaging for its ability to make the central diffractive spot smaller than the Airy spot. In this paper, we apply the superresolution technique for transforming a symmetrical TEM_p0 Laguerre-Gauss beam into a Gaussian intensity distribution in the plane of a converging lens. The beam shaping is achieved by an annular binary Diffractive Optical Element having a transmittance, alternatively equal to −1 or + 1, modelled on the p light rings of the incident beam. It is observed that the rectified TEM₃₀ beam at focus has a focal volume 170 times smaller than that of a Gaussian beam.     

Scintillation index of elliptical Gaussian beam in turbulent atmosphere

A tensor method is used to formulate the on-axis scintillation index for an elliptical Gaussian beam (EGB; astigmatic Gaussian beam) propagating in a weak turbulent atmosphere. Variations of the on-axis scintillation of an EGB are studied. It is interesting to find that the scintillation index of an EGB can be smaller than that of a circular Gaussian beam in a weakly turbulent atmosphere under certain conditions and is closely related to the ratio of the beam waist size along the long axis to that along the short axis of the EGB, the wavelength, and the structure constant of the turbulent atmosphere.     

Design and Analysis of Diffractive Axicons for Gaussian Beam Illumination

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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.     

Investigation in the far field characteristics of TM polarized Gaussian beam from the vectorial structure

Based on the vectorial structure of electromagnetic beam and the method of stationary phase, the analytical TE and TM terms of TM polarized Gaussian beam, the rigorous solution of Maxwell's equations for a confocal resonator, have been presented in the far field. Then in terms of the vectorial structure, TM polarized Gaussian beam is compared with Gaussian TEM₀₀ mode. The TE term is located at the y-axis, and the TM term the x-axis. At the non-paraxial case, the whole beam spot is elliptical, and the long axis is located at the y-axis. Moreover, the whole beam spot of TM polarized Gaussian beam is smaller than that of Gaussian TEM₀₀ mode. At the paraxial case, the whole beam spot is circular, and TM polarized Gaussian beam reduces to be Gaussian TEM₀₀ mode.     

Scintillation properties of dark hollow beams in a weak turbulent atmosphere

The on-axis scintillation index for a circular dark hollow beam (DHB) propagating in a weak turbulent atmosphere is formulated, and the scintillation properties of a DHB are investigated in detail. The scintillation index for a DHB reduces to the scintillation index for a Gaussian beam, an annular beam and a flat-topped beam under certain conditions. It is found that the scintillation index of a DHB is closely related to the beam parameters and can be lower than that of a Gaussian beam, an annular beam and a flat-topped beam in a weak turbulent atmosphere at smaller waist sizes and longer propagation lengths. PACS 42.25.Bs; 42.68.Ay     

大气湍流对径向分布高斯列阵光束扩展和方向性的影响

采用积分变换的技巧,推导出了径向分布高斯列阵光束通过湍流大气传输的二阶矩束宽和远场发散角的解析公式,并详细研究了大气湍流对光束扩展和方向性的影响.研究表明,相干合成情况下,子光束数N越小、径向分布半径r₀越大,列阵光束扩展受湍流影响越小.相干较非相干合成时列阵光束的扩展小,但非相干合成时列阵光束扩展受湍流的影响比相干合成时的小.特别地,N足够小或r₀足够大时,相干与非相干合成列阵光束的远场束宽相等.另一方面,还给出了相干和非相干合成径向分布高斯列阵 关键词： 径向分布高斯列阵光束 大气湍流 相干和非相干合成 二阶矩束宽     

Roughness and gradient parameters for characterising shape uniformity of laser beams

We define six parameters, the roughness parameter, the local gradient parameter, the directionless gradient parameter, the integral gradient parameter, the directionless integral gradient parameter and the absolute gradient parameter for characterising the uniformity of a laser beam in its transversal section. For shape-invariant beams the roughness parameter is propagation invariant. The absolute gradient parameter is propagation invariant for symmetric shape invariant beams. As an example, five of the defined parameters are calculated for a dummy irradiance. The values of the roughness parameter and the absolute parameter are calculated and tabulated for symmetric Hermite–Gaussian, Laguerre–Gaussian, spherical Gaussian, flattened Gaussian (at the waist plane) and super Gaussian beams (at the waist plane). The results are discussed.     

余弦-高斯光束

提出一种新的可以较好地描写带有相位台阶光学谐振腔的模式的光束模型-余弦-高斯光束。这种光束是由两束高斯球面波的相干叠加形成的,其光束质量因子可以小于1。     

Tailored TEMp0 beams for large size 3-D laser prototyping

The Laser-Lithography technique allows the fabrication of complex objects having microsizes by selectively solidifying polymeric materials layer by layer upon exposure to a focused Gaussian laser beam having a beam propagation factor M²=1. We can expect that extension of this technique to large sizes 3-D prototyping comes up against a large increase in the design time. A possible solution is the increase in the focused spot size, but unfortunately at the price of a great reduction in the longitudinal resolution due to the resulting increase in the depth of focus. To overcome these difficulties, we propose the use of a rectified TEM_p0 beam allowing the obtaining of a Gaussian beam intensity profile in the focus plane of a lens. The reshaped TEM_p0 beam has a beam propagation factor M²≈(2p+1), and this yields to a relative improvement of the longitudinal resolution although the spot size is increased for reducing the processing time.     

Laser range finder using Gaussian beam range equation

A new range equation for laser range finder using Gaussian beam profile is proposed. Unlike conventional range equations, the proposed equation can be applied to any ranging conditions, regardless of a beam size of incident light upon targets. We also show an operational coefficient for estimating the returned power using the proposed Gaussian beam range equation as an empirical correction factor.     

Polychromatic Gaussian beams emitted by dispersive laser resonators

In-vacuum propagation of a polychromatic Gaussian beam emitted by a dispersive laser resonator and its passage through thin plates are studied under following assumptions: optical fields are stationary and plane-polarized, the paraxial wave equation is valid for each monochromatic component of the beam, the waist position and the Rayleigh range depend on wavelength and diffraction edge effects are negligible. Mathematical expressions for beam radius, divergence, beam parameter product and beam propagation factor are obtained. The use of thin plates for waist position achromatization is analyzed.     

Field correlations of flat-topped Gaussian and annular beams in turbulence

Starting from the second order moment formulation for multi-beam incidence, field correlations at the receiver plane of flat-topped Gaussian and annular beams are found in turbulence. Reflecting the information on both the randomness due to turbulence and the field profile of the incident field, field correlations of the flat-topped Gaussian beams are found to become larger at larger source size, smaller flatness parameters and smaller turbulence strengths. For the annular beam structures, field correlations are larger for thicker beams. Field correlations of larger primary beam sized annular incidences are smaller at smaller diagonal distances and larger at larger diagonal distances. As expected, annular beam field correlations are found to be larger at smaller structure constants and at smaller wavelengths. However, at large link lengths, field correlations could be larger than at smaller link lengths due to fact that for annular beams, the field at the centre of the receiver attains very small value at smaller link lengths, however, on propagation in turbulence, receiver field distribution changes to a Gaussian profile.     

平顶飞秒激光经圆锥透镜在熔融石英中成丝及超连续辐射

实验研究了平顶飞秒激光经圆锥透镜后在熔融石英中的成丝及超连续辐射.与高斯飞秒激光的成丝对比发现,平顶飞秒激光可以获得在圆锥透镜焦深区域内强度分布更为均匀的等离子体细丝,这一特征更有利于飞秒激光在固体介质中进行微纳加工等领域的应用.并且,在不损伤熔融石英的条件下,平顶飞秒激光成丝可以获得更高能量、更高转换效率的超连续辐射,这是因为若产生光强相近的细丝,平顶飞秒激光所需的初始激光能量更高,此激光能量下产生的细丝长度更长、均匀性更好.     

高斯光束照射下的Vander Lugt相关器的特性研究

针对特定目标图像,定量分析了在Vander Lugt相关器中照明光束为高斯光束时输出相关峰值随高斯光束特性参量的变化情况。结果表明,输出相关峰值随高斯光束腰斑半径的减小和输入场景中目标位置偏离高斯光束中心距离的增加而减小。为了得到高的输出相关峰值,由扩束准直光学系统输出的高斯光束腰斑半径应满足一定的要求。     

Generalised ABCD matrix treatment for laser resonators and beam propagation

A generalised ABCD matrix treatment for laser resonators and beam propagation is developed for computer programming. In this treatment, imaginary parts are introduced into the matrixes for all optical elements, and the beam quality factor M² and the index of the medium are also taken into account. When the imaginary parts of the complex matrix are zero and the beam quality factor M² and medium index are unity, the stated method is transformed back into the more classic ABCD matrix format in which the fundamental-mode Gaussian beam transmits through real elements in the vacuum. Based on this method, laser resonator software is realised by the VB programme language. The software can be used to analyse and design stable/unstable standing/travelling cavities, phase-conjugate cavities and beam transformations.