广义双曲正弦-高斯光束的Gyrator变换性质和暗空心光束产生

基于Gyrator变换,推导了广义双曲正弦-高斯光束场分布的解析表达式,研究了广义双曲正弦-高斯光束在Gyrator变换平面上的光强分布和相位特性.结果表明,在Gyrator变换过程中,具有边缘位错相位特性的双曲正弦-高斯光束能转换为具有涡旋的暗空心光束,并确定产生的暗空心光束的拓扑荷指数为一,而不具有边缘位错相位特性的双曲余弦-高斯光束则不可能出现空心结构.对影响变换场强度和相位分布的束结构参数及系统参数进行了分析讨论.     

径向洛伦兹阵列光束在自由空间的传输特性

推导出有初始相位分布的径向洛伦兹阵列光束在自由空间传输的解析公式,用以研究相干合成光束在自由空间的传输特性。结果表明:在远场,具有不同相位分布的光束光强剖面成为空心形状,具有相同相位分布的光束光强剖面中心为亮斑。合成光束束宽和桶中功率与子光束束腰宽度、径向阵列的初始相位分布和半径有关。对所得结果用数值计算例做了说明。当阵列半径较大和束腰宽度较小时,具有不同相位分布和相同相位的光束束宽随传输距离的变化曲线和桶中功率都趋于一致。     

空心高斯涡旋光束的远场特性

基于角谱法和稳相法,推导出了空心高斯涡旋光束的TE波和TM波在自由空间远场传输和能流密度的解析表达式,研究了其相位奇点和能流密度分布。结果表明,空心高斯涡旋光束的远场特性主要跟控制参数有关。改变光束中的涡旋离轴量,光涡旋和能流密度黑核会发生移动。圆刃型位错线的半径和能流密度暗环位置跟束腰宽度有关,而能流密度的对称性主要受涡旋离轴量的影响。     

等束腰宽度超短脉冲光束传输的脉冲修正方法

利用角谱分析和傅里叶变换的方法,得到一种描述几个周期的等束腰宽度脉冲光束传输的脉冲修正方法。以准单色光束传输的结果为出发点,通过对准单色光束的解进行泰勒级数展开,得到了一种相对简单的修正方法,可以精确的描述具有任意时间波形和横向光束分布的不短于一个周期的超短脉冲光束的传输行为。给出等束腰宽度超短脉冲的近似解,具体研究高斯脉冲光束的传输特性,分析几种不同的频谱对脉冲光束传输行为的影响。     

超衍射极限相干反斯托克斯拉曼散射显微成像技术中空心光束的形成

空心光束的质量是超衍射极限相干反斯托克斯拉曼散射显微成像技术中决定成像质量的一个至关重要的因素. 本文基于菲涅耳衍射理论,分析了螺旋相位片法产生空心光束的物理机理,并且模拟了不同的入射条件对产生的空心光束的影响. 模拟结果表明:波长与相位片中心波长匹配且光强呈圆对称分布的高斯光垂直入射到相位片上,当高斯光束中心与相位片中心完全对准时,可获得较理想的空心光束;入射光光强分布的圆对称性以及入射光中心与相位片中心的对准程度都会影响产生的空心光束的强度分布;同时,高斯光束小角度倾斜入射时,空心光的强度分布仍呈圆对称,却在观察面发生一定的位移;此外,入射光中心波长偏离相位片中心波长不大时,对产生的空心光束的强度分布几乎没有影响. 上述分析结果对用于超衍射相干反斯托克斯拉曼散射显微成像技术中理想空心光束的获取具有重要的指导意义. 关键词： 空心光束 超衍射极限 相干反斯托克斯拉曼散射 螺旋相位片     

贝塞尔高斯涡旋光束在大气湍流中的传输特性

基于广义惠更斯-菲涅耳原理,推导了贝塞尔高斯涡旋光束在湍流大气中传输时系统平均光强的解析表达式,研究了贝塞尔高斯空心涡旋光束在湍流大气中的光强传输特性,同时分析了大气湍流的强弱、涡旋光束的拓扑荷等对光束质量的影响.结果表明:贝塞尔高斯涡旋光束在大气湍流中传输时,光强分布经历几个连续的变化,相位奇异性也会在传输过程中消失,该过程与涡旋光束拓扑荷的数目、光束的束腰宽度以及大气湍流的强弱等因素密切相关.拓扑荷数目高的涡旋光束在湍流大气中传输时,其奇异性的保持较拓扑荷数目低的涡旋光束要好.另外,基于桶中功率理论,分析研究了涡旋光束的拓扑荷数目、大气湍流强弱和束腰宽度对贝塞尔高斯涡旋光束在大气湍流中传输时的光束质量的影响.     

正弦高斯涡旋光束的远场传输特性

根据角谱法和稳相法,推导了正弦高斯涡旋光束TE波和TM波在远场传输和能流密度的解析表达式,研究了正弦高斯涡旋光束在远场中的相位奇点和能流密度分布.结果表明:正弦高斯涡旋光束的远场特性与高斯光束的束腰宽度、涡旋离轴量、坐标位置以及与正弦项相关的参量有关.在一定条件下,远场中会出现相位奇点和能流密度黑核;当控制参量改变时,相位奇点和黑核的位置会发生移动,但原点处不受影响.相位奇点和能流密度的对称性主要受涡旋离轴量影响,当涡旋离轴量为0时,相位奇点和能流密度分布关于原点对称;当涡旋离轴量改变时,相位奇点和能流密度分布呈现出非对称性.     

线偏振高斯光束通过复合型衍射光栅的传输特性

提出一种集合浮雕和折射率周期分布调制的复合型衍射光栅,并利用角谱表示和严格的模式理论研究了线偏振高斯光束通过这种复合型衍射光栅的传输特性.数值计算结果表明,在光栅的同一透射深度处复合型衍射光栅光强的起伏频率要比浮雕型光栅光强的起伏频率小.最后使用复合型衍射光栅模型,研究了亚波长体积相位全息光栅的表面起伏和入射光束的束腰宽度对衍射效率的影响. 关键词： 复合型衍射光栅 亚波长体积相位全息光栅 高斯光束 严格模式理论     

利用纯相位型液晶空间光调制器实现空心光束

为了提高激光系统的整体效率,需要将出射光强整形为空心分布。采用纯相位型液晶空间光调制器整形近高斯分布光强到空心分布。基于能量守恒定律和等光程原理,分析了纯相位型液晶空间光调制器光束整形系统,得出了整形系统所需的相位分布。采用衍射光学方法,数值模拟了整形效果,讨论了入射光束束腰半径和强度分布等因素对整形效果的影响。利用纯相位型液晶空间光调制器实验实现了空心光束,实验测得的转换效率大于99%。     

截断非傍轴标量高斯光束的传输特性

基于精确光强定义下非傍轴标量光束的二阶矩理论,计算了不同束腰及光阑孔径条件下截断非傍轴标量高斯光束的束腰半径、远场发散角以及质量因子等光束传输特性,并将截断非傍轴标量高斯光束与自由高斯光束和平面波圆孔衍射光束进行了比较.数值计算表明截断参量的不同对截断高斯光束的传输特性影响很大.当R2ω0时,截断高斯光束与高斯光束在自由空间传输特性趋于一致,因此在精确光强定义下,对于非傍轴标量光束来说,当光阑孔径大于2倍束腰时,可以不考虑光阑对高斯光束的衍射作用.当R0.3ω0时,截断高斯光束传输特性趋于平面波通过圆孔的衍射曲线.因此,在这种情况下,可以将高斯光束作为平面波处理.只有当光阑孔径介于0.3倍束腰和2倍束腰之间时,需要同时考虑光阑孔径和高斯束腰对衍射的影响.     

Gyrator transform of Gaussian beams with phase difference and generation of hollow beam

The optical expression of Gaussian beams with phase difference, which is caused by gyrator transform (GT), has been obtained. The intensity and phase distribution of transform Gaussian beams are analyzed. It is found that the circular hollow vortex beam can be obtained by overlapping two GT Gaussian beams with π phase difference. The effect of parameters on the intensity and phase distributions of the hollow vortex beam are discussed. The results show that the shape of intensity distribution is significantly influenced by GT angle α and propagation distance z. The size of the hollow vortex beam can be adjusted by waist width ω₀. Compared with previously reported results, the work shows that the hollow vortex beam can be obtained without any model conversion of the light source.     

Propagation of a four-petal Gaussian vortex beam through a paraxial ABCD optical system

Based on the Collins diffraction integral formula, an analytical expression of a general four-petal Gaussian vortex beam passing through a paraxial ABCD optical system is derived by means of the mathematical technique. As a numerical example, the normalized intensity distribution of a four-petal Gaussian vortex beam propagating in free space is graphically demonstrated. The influences of beam order and topological charge on the normalized intensity distribution are discussed in detail. This research is useful to the optical trapping, optical communications, and beam splitting techniques, etc.     

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.     

高斯-谢尔模型列阵光束的远场发散角和远场辐射强度

推导出了高斯-谢尔模型（GSM）列阵光束通过自由空间传输其二阶矩束宽、远场发散角和远场辐射强度的解析表达式,并给出了GSM列阵光束与高斯光束具有相同远场发散角的条件.研究表明,具有相同远场发散角的GSM列阵光束与对应的高斯光束并不具有相同的远场辐射强度分布,这一特性与单束GSM光束的差异很大. 关键词： 高斯-谢尔模型列阵光束 远场发散角 远场辐射强度     

The optical Airy transform and its application in generating and controlling the Airy beam

We propose an optical Airy transform in this paper, and obtain the analytical expressions for the Airy transform of fundamental Gaussian beams and finite energy Airy beams. The setup for performing the optical Airy transform is presented. The Airy transform for Gaussian beams and finite energy Airy beams are theoretically calculated and analyzed. Our results show that the Airy beam can be conveniently generated and controlled through the optical Airy transform of the Gaussian beam. The optical Airy transform also can be used to directly modulate the beam parameters of the incident Airy beam, and it can transform the incident Airy beam into the Gaussian beam.     

Four-petal Gaussian beams and their propagation

A new form of laser beams called four-petal Gaussian beams is introduced. Based on the Collins integral, two kinds of analytical propagation expressions for this new kind of beams through a paraxial ABCD optical system are derived. The propagation properties of the four-petal Gaussian beams are studied and illustrated with numerical examples. At the source plane the beam has four-petals; the space among the petals is determined by the beam order. In the far field the beam evolves into a number of mirror symmetric petals and the petals of higher order beams can be equally spaced.     

The representation of waist-to-waist transformation of Gaussian beams by the scaled fractional Fourier transform

The beam waist-to-waist transformation of Gaussian beams between input and output reference planes described by the scaled fractional Fourier transform is analyzed in this paper. We obtain the transfer matrix of ABCD optical system that corresponds to the scaled fractional Fourier transform. The results show that the beam waist-to-waist transformation of Gaussian beams can be described by the scaled fractional Fourier transform when the ABCD optical system has a suitable transfer matrix. The relationship between the input and output waist planes and some particular cases when a Gaussian beam passes through a thin lens is also discussed.     

Hollow Gaussian Schell-model beam and its propagation

In this paper, we present a new model, hollow Gaussian Schell-model beams (HGSMBs), to describe the practical dark hollow beams. An analytical propagation formula for HGSMBs passing through a paraxial first-order optical system is derived based on the theory of coherence. Based on the derived formula, an application example showing the influence of spatial coherence on the propagation of beams is illustrated. It is found that the beam propagating properties of HGSMBs will be greatly affected by their spatial coherence. Our model provides a very convenient way for analyzing the propagation properties of partially coherent dark hollow beams.