准直圆孔衍射高斯光束远场发散度

将夫琅和费衍射积分中的贝塞尔函数用高斯函数近似,得到经圆孔径准直光学系统衍射后高斯光束远场发散角的近似解析式.在不同衍射情况下,将其与严格夫琅禾费衍射积分进行比较,发现二者求解出的远场发散度接近.衍射孔径大小相同情况下,近似解析式与真实值的误差随准直前光束初始束腰的增大而减小;初始束腰不变的情况下,随着衍射孔径的增大,误差值略有上升,但最终趋于平稳.在初始束腰半径不小于2μm的前提下,误差值最大不超过3.4%.该近似解析式在各种衍射情况下都能较为准确地表征准直圆孔衍射高斯光束远场发散度,且形式简单.对比不同衍射孔径和光束初始束腰条件下的光束发散度仿真结果可知,光束发散度随衍射孔径的增大而减小,随初始束腰的增大而增加.     

圆孔限制下有相位变化的高斯光束远场发散度的理论分析

依据夫琅和费衍射理论,通过引入高斯变换,即把夫琅和费衍射积分中的贝赛尔函数用一高斯函数来近似,详细分析并推导出圆孔限制下具有相位变化的高斯光束远场发散度的近似计算公式.与传统数值积分求光束发散度相比,它避免了繁琐数值积分,其误差不超过3％.     

高斯光束通过非线性介质后的远场衍射图样的研究

 利用菲涅尔－基尔霍夫衍射积分公式，对发散和会聚高斯光束通过薄非线性介质时形成的远场衍射图样进行了研究。模拟计算结果表明：当发散高斯光束通过自散焦介质或会聚高斯光束通过自聚焦介质时，远场均会出现中央较暗、向外围逐渐增强、分布尺度较大的粗衍射环；当发散高斯光束通过自聚焦介质或会聚高斯光束通过自散焦介质时，远场均会出现中心强度最大、向外围逐渐减弱、分布尺度较小的细衍射环。不同远场衍射图样归根结底是入射高斯光束因介质折射率变化造成的空间自相位调制及其波前曲率共同作用的结果。     

高斯光束经圆形光阑衍射的远场发散特性

线偏振高斯光束经圆形光阑衍射后,其远场可表示成互相正交的横电(TE)项和横磁(TM)项之和。利用TE项和TM项的远场能流分布,导出了高斯衍射光束的TE项和TM项远场功率的解析表达式,由此可度量TE项和TM项在远场占总功率的比例。基于能流二阶矩的定义,给出了高斯衍射光束、TE项和TM项远场发散角的解析式以及三者远场发散角间的关系通式,重点分析了f参数和截取参数对远场发散角的影响。结果表明:随着f参数的增大,远场发散角先增大后趋向于各自的饱和值。截取参数对远场发散角的影响与f参数相关,当f参数较大时,截取参数对远场发散角的影响不明显;当f参数适中时,随着截取参数的增大,远场发散角先减小后趋向于各自的最小值;但当f参数较小时,高斯衍射光束和TM项二者的远场发散角出现一定的波动性。     

高斯光束经圆形光阑衍射的远场发散特性

线偏振高斯光束经圆形光阑衍射后,其远场可表示成互相正交的横电(TE)项和横磁(TM)项之和。利用TE项和TM项的远场能流分布,导出了高斯衍射光束的TE项和TM项远场功率的解析表达式,由此可度量TE项和TM项在远场占总功率的比例。基于能流二阶矩的定义,给出了高斯衍射光束、TE项和TM项远场发散角的解析式以及三者远场发散角间的关系通式,重点分析了f参数和截取参数对远场发散角的影响。结果表明:随着f参数的增大,远场发散角先增大后趋向于各自的饱和值。截取参数对远场发散角的影响与f参数相关,当f参数较大时,截取参数对远场发散角的影响不明显;当f参数适中时,随着截取参数的增大,远场发散角先减小后趋向于各自的最小值;但当f参数较小时,高斯衍射光束和TM项二者的远场发散角出现一定的波动性。     

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.     

介质平面波导TE0模衍射场的光束参量

对于傍轴光束，提出了介质平面波导衍射场的近场模场半宽度、远场发散角半宽度和光束传输因子M^2等光束参量之间满足简单的关系式，三个光束参量均可直接由波导模式场分布精确计算，或由可实际精确测量的远场衍射频谱分布精确计算。M^2因子的计算公式可表述为以二阶矩和微分算子定义的近场模场半宽度的比值，或以二阶矩和微分算子定义的远场发散角半宽度的比值。最后推导出介质平面波导TE0模衍射场光束参量的解析函数和光束参量的范围。     

高斯光束通过非线性折射和吸收介质的光强分布

以衍射理论为基础,推导并模拟了高斯光束通过非线性折射和吸收效应介质后的远场光强分布。结果表明:入射高斯光束引起的介质折射率变化和光束波前曲率影响介质出射面光束的径向调制相位,安装在焦点前的有自聚焦效应的介质和安装在焦点后的有自散焦效应的介质具有闪耀光栅的能力,使远场出现中心为暗斑外侧为亮环的衍射图样。非线性折射效应为主的介质,其非线性吸收效应的变化同时改变远场衍射图样的数目和光强值,但对于非线性吸收效应为主的介质,衍射图样的数目随吸收效应的变化不明显,吸收效应只影响光强值。     

厄米-高斯光束通过圆孔衍射的两种计算方法比较

应用Collins公式和硬边圆孔函数拓展为有限复高斯函数和的方法,推导出厄米-高斯（Hermite—Gaussian）光束通过圆孔的衍射场分布的近似解析公式．模拟结果表明使用该解析公式所得结果和直接对Collins公式进行数值计算的结果符合较好,并讨论两种方法的差异性以及各自的优缺点．     

非傍轴矢量高斯光束的圆屏衍射

利用矢量瑞利衍射积分公式，推导出非傍轴矢量高斯光束圆屏衍射的解析表示式.非傍轴矢量高斯光束圆屏衍射的轴上场分布、远场表示式、自由空间中的传输公式，以及傍轴近似下高斯光束圆屏衍射的菲涅耳和夫琅禾费衍射公式可以作为一般公式的特例统一处理.数 值计算和比较实例说明了非傍轴矢量高斯光束的光强分布和远场特性.分析表明，在圆屏衍 射中，f参数和截断参数决定光束的非傍轴行为. 关键词： 传输光学 非傍轴矢量高斯光束 圆屏衍射 矢量瑞利衍射积分公式     

Study on the approximative formula for the far-field of a Gaussian beam under circular aperture diffraction and its divergence

The approximative formula for the far-field diffraction of a Gaussian beam through a circular aperture is obtained by using the superposition of Gaussian beams instead of the aperture function, and the explicit expression for calculating the beam divergence is also gained. Using the formula, the influences of the aberrations on the far-field wavefront and the beam's divergence are researched, and the results show that the large aberrations badly affect the far-field wavefront and the divergence. It is suggested that the aberrations and the diffractions should be avoided when designing the transmitter.     

Series representation of the Gaussian beam far-field diffracted by annular aperture

Accurate, analytical series expressions for the far-field diffraction of a Gaussian beam normally incident on a circular and central obscured aperture are derived with the help of the integration of parts method. With this expression, the far-field intensity distribution pattern can be obtained and the divergence angle is deduced too. Using the first five items of the series, the accuracy can satisfy most laser application fields. Compared with the conventional numerical integral method, the series representation is very convenient for understanding the physical meanings.     

Fresnel diffraction of truncated Gaussian beam

We study the Fresnel diffraction of Gaussian beam truncated by one circular aperture, and give the general analytic expression of the Fresnel diffraction of truncated Gaussian beam denoted by Bessel functions. Then the characteristic of the axial diffraction fluctuation and the influence of the caliber of the circular aperture and the wave waist of Gaussian beam on the diffraction distributions are discussed, respectively. Through the numerical calculations, the characteristics of the transverse diffraction are presented and the relationship of the fluctuation of the transverse diffraction profile and the position of the axial point is shown. The physical origin of the fluctuation of Fresnel diffraction intensities of truncated Gaussian beam is expressed in terms of Fresnel half-zone theory. These phenomena and the conclusions are important for the measurement of the parameters of the beam and its applications.     

Spectral shifts and spectral switches of a pulsed Bessel–Gauss beam from a circular aperture in the far field

The far-field spectral characteristics of a broadband-pulsed Bessel–Gauss beam passing through a circular aperture are studied. Based on the expansion of a hard aperture function into a finite sum of complex Gaussian functions and starting from the Fresnel diffraction integral, the approximate analytical expression for the spectral distribution of the diffraction field is derived. The “aperture dispersion”, that is, the red and blue shifts of the spectral intensity maximum and the spectral intensity shape distortion and distribution under different conditions are studied and illustrated with numerical calculations. It is shown that the far-field, on-axis maximum spectral intensity always shifts to the right (blue shift) and the amount of the spectral shift is dependent on the source bandwidth only. However, for the cases of off-axis, when the observation angle θ approaches a critical value, a rapid spectral switch occurs.     

超短脉冲经线性小孔阵列衍射时的光谱开关特性

研究了超短高斯脉冲光束经线性排列的矩形光阑阵列衍射后的远场光谱奇变现象。基于菲涅耳积分公式,通过将光阑函数展开为有限项复高斯函数的叠加,得到了超短脉冲光束经线性排列的小孔光阑阵列衍射后的谱强度解析表达式,并对衍射场的光谱红移和蓝移现象进行了数值计算和分析,分析了小孔间距和光阑半径对光谱强度的影响。研究表明:在衍射场的某些观测点,即在调制函数为零的位置附近,存在光谱开关现象。     

超短脉冲经线性小孔阵列衍射时的光谱开关特性

研究了超短高斯脉冲光束经线性排列的矩形光阑阵列衍射后的远场光谱奇变现象。基于菲涅耳积分公式,通过将光阑函数展开为有限项复高斯函数的叠加,得到了超短脉冲光束经线性排列的小孔光阑阵列衍射后的谱强度解析表达式,并对衍射场的光谱红移和蓝移现象进行了数值计算和分析,分析了小孔间距和光阑半径对光谱强度的影响。研究表明：在衍射场的某些观测点,即在调制函数为零的位置附近,存在光谱开关现象。     

Effect of a turbulent medium on the near- and far-field diffraction of a circular aperture

The near- and far-field diffraction due to a circular aperture illuminated with partially coherent light produced by a turbulent medium has been theoretically studied. Formulations are developed for investigating the near- and far-field diffraction patterns. The phase structure function, which is generated by the turbulent medium and determines the partially coherent condition of a light beam passing through it, is assumed to take both the Gaussian form and the 5/3-power law. Numerical results concerning the far-field intensity distribution and the axial intensity distribution in the near-field region are presented in diagrams and discussed.