会聚厄米-双曲余弦高斯光束的光强分布和焦移

 基于厄米-双曲余弦高斯光束通过无光阑限制薄透镜聚焦的解析传输公式，研究了厄米-双曲余弦高斯光束聚焦区域的光强分布，并对光束的焦移进行了分析，讨论了偏心参数对光强主极大位置的影响。结果表明：TEM₁₁模厄米-双曲余弦高斯光束的相对焦移（绝对值）随偏心参数和菲涅尔数的减小而增大，菲涅尔数较大时相对焦移趋于零。TEM₂₂模光束在偏心参数小于0.54时，轴外与轴上光强极大值的比值大于1，此时光强主极大在轴外，偏心参数大于0.54时则相反；在偏心参数等于0.54时比值为1，此时光束有两个主极大，偏心参数愈大光强愈集中于轴上。使用LW法和GH法得到的TEM₂₂模光束的相对焦移（绝对值）随偏心参数和菲涅尔数的变化规律与TEM₁₁模光束一致，但相同参数下使用这两种方法得出的具体结果不同。     

多色矢量高斯-谢尔模型光束的焦移和焦开关

从交叉谱密度矩阵的传输公式出发,对多色矢量高斯-谢尔模型（GSM）光束的焦移和焦开关作了详细的研究.插入偏振片之前,多色矢量高斯-谢尔模型（GSM）光束通过硬边光阑透镜分离光学系统后,有焦移,但无焦开关;而插入偏振片之后,会出现焦开关.改变偏振片的旋转角度可以控制焦开关的特性.     

部分相干光被环形透镜聚焦而产生的焦移

 从理论上研究部分相干光被一环形透镜聚焦,在焦点附近的轴上点的光强分布。研究结果表明,当部分相干光被一环形透镜聚焦时,最大聚焦光强不在几何焦点,而是位于透镜与几何焦点之间,出现焦移现象。并且,焦移量不仅依赖于透镜外半径的菲涅耳数,还依赖于部分相干光的空间相干度和中心拦截比。透镜的菲涅耳数越小,焦移越大;部分相干光的空间相干度越低,焦移越大。当菲涅耳数一定时,环形透镜的中心拦截比越大,焦移越大;当空间相干度很小时,情况就变得比较复杂。     

部分相干光通过光阑-透镜分离系统的光谱特性

通过部分相干光的传输理论,研究了部分相干光通过光阑-透镜分离系统的光谱位移和光谱开关.理论分析和数值计算结果表明,部分相干光的光谱相移和光谱开关主要决定于光束的相干性、光阑的菲涅耳数以及光阑和透镜之间的距离.所取系统参量不同,光谱开关的数量和位置会随之发生变化.     

部分相干光经柱面球差透镜聚焦所产生的焦移

利用Collins公式得出光强均匀部分相干光经柱面球差透镜聚焦后的轴上光强分布,并通过数值模拟的方法研究了入射光的菲涅耳数、相干度和透镜的球差对轴上点光强分布的影响.结果显示,当菲涅耳数较小、空间相干度较小的部分相干光经无球差透镜聚焦时,轴上点光强分布会产生焦移现象,而当部分相干光被球差透镜聚焦时,也会有焦移现象产生.     

拉盖尔-高斯截断级数展开法的应用

 用拉盖尔-高斯截断级数模拟了任意半径的圆孔硬边光阑窗口函数,并应用于研究高斯光束和零阶贝塞尔-高斯光束通过硬边光阑的衍射。对高斯光束和零阶贝塞尔-高斯光束的轴向和横向光强分布的计算结果表明：当积分面不是很靠近光阑时，用参数最佳化选取的拉盖尔-高斯截断级数法与用直接数值积分所得结果符合很好。     

自旋-轨道相互作用下X型涡旋光束的传播特性

研究了 X型涡旋光束在左旋/右旋圆偏振状态下在紧聚焦系统中的传播特性,讨论了 自旋-轨道相互作用下焦平面光强的横向焦移和传播方向旋转现象的特点及其调控方法.研究发现:相位分布因子c是X型涡旋光束产生横向焦移和光强旋转的主要原因,而半孔径角α、偏振态和拓扑荷数对光强分布均有调控作用;由于自旋-轨道相互作用,入射光为左旋圆...     

柱面球差透镜聚焦部分相干光束的焦移

通过定义聚焦光束的等效菲涅耳数,研究了部分相干光经柱面球差透镜聚焦后的轴上光强分布,得到了相对焦移的简单公式,即相对焦移反比于等效菲涅耳数的平方.结果表明,这种基于等效菲涅耳数的计算聚焦光学系统的焦移方法是计算部分相干光束经球差透镜聚焦相对焦移简单且有效方法.还讨论了一种特殊等效菲涅耳数为纯虚数情况.结果证明,在这种情况下,该相对焦移简单公式仍然有效.     

部分相干电磁光束的焦移

 基于有效菲涅耳数的概念,给出一种简单的表达式来评估部分相干电磁光束经圆形光阑透镜后所产生的相对焦移,对部分相干电磁光束经透镜聚焦的情况进行了研究。结果表明:当交叉谱密度函数的非对角元素为零时,有效菲涅耳数不仅依赖于真实的菲涅耳数大小,而且依赖于光束的偏振分布和入射部分相干电磁光束两个偏振分量的空间相干长度;相对焦移量仅由等效菲涅耳数决定。将此方法与数值积分法进行的比较表明,等效菲涅耳数可以简单、准确地评估焦移。     

厄米──高斯光束的聚焦场特性

借助广义惠更斯－菲涅尔衍射积分（即Ｃｏｆｆｉｎｓ公式）推导出ＨｅｒｍｉｔｅＧａｕｓｓｉａｎ光束（Ｈ—Ｇ光束）在无光阑限制下的相对焦移和相对光强增量的解析表达式，并作了分析。对有光阑限制下的Ｈ—Ｇ光束的聚焦场特性做了详细的数值计算和讨论。     

Cylindrical vector axisymmetric Bessel-modulated Gaussian beam

Focusing properties of the cylindrical vector axisymmetric Bessel-modulated Gaussian beam with quadratic radial dependence (QBG beam) in high numerical aperture system is investigated theoretically by vector diffraction theory. Results show that intensity distribution in focal region can be altered considerably by beam parameter μ and polarization angle. Polarization angle may adjust transverse intensity distribution, for instance from one focal spot to one ring shape. While μ alters axial intensity distribution remarkably, focal splitting may occur with tunable focal shift, and real value μ also may induce local intensity minimum. For certain case, with increasing imaginary value μ, transverse focal spot shrinks accompanied with higher full width half maximum of axial intensity distribution.     

高斯光束经过负球差透镜的聚焦

本文讨论高斯光束经过负球差透镜的聚焦，得到了聚焦光场轴上点的光强分布的表示式，并对其进行数值计算。数值计算结果表明，在负球差的情况下，得到光强的最大点位置（最佳聚焦点）相对于无球差情况，往透镜方向移动，并且，最佳聚焦点的光强较无球差时大，当Ｎｗ＝１，Ｎａ＝５，ｋＳ１＝－０．２时，得到的最佳聚焦点的光强是无球差时的１．３４倍。本文还讨论了透镜的菲涅尔数对聚焦光场分布的影响。结果表明，当透镜的菲涅尔数小于１时，球差对高斯光束的聚焦的影响可以忽略。     

三环位相型光瞳滤波器的横向超分辨与轴向焦深扩展

用矢量衍射方法分析了线偏振光入射到带有三环位相型光瞳滤波器的高数值孔径物镜时,焦点的轴向和横向光强分布.数值模拟结果表明,高数值孔径物镜聚焦时需同时考虑光强的轴向和横向分布.通过加入三环位相光瞳滤波器,在实现横向超分辨的同时实现了光学系统轴向焦深扩展和轴向光强分布平坦化,并且位相调制深度变化时,会出现轴向焦移现象.对三环位相光瞳滤波器结构进行了优化,得出了优化结果. 关键词： 光学超分辨 扩展焦深 位相型光瞳滤波器 矢量衍射方法     

Focal shift and focal switch of flat-topped Mathieu-Gaussian beams passing through an apertured lens system

By introducing a hard aperture function into a finite sum of complex Gaussian functions, an approximate analytical expression predominating the distribution of axial intensity for the flat-topped Mathieu-Gauss (FTMG) beams passing through a system with the aperture and lens separated has been derived. The focal shift and the focal switch effect of FTMG beams passing through the system is studied in detail. Numerical calculations have shown that the position of real focal plane is not coincident with the geometrical focus but is somewhat shifted toward the lens. The focal shift and focal switch of FTMG beams take place when the relative separation s/f = 1 by a suitable choice of beam parameter and truncation parameter, for example, the beam parameter is smaller than its corresponding critical value or the truncation parameter is between its two corresponding critical values.     

Improved expressions for performance parameters for complex filters

Improved expressions are given for the performance parameters for transverse and axial gains for complex pupil filters. These expressions can be used to predict the behavior of filters that give a small axial shift in the focal intensity maximum and also predict the changes in gain for different observation planes.     

Optimization of Axial Intensity Point Spread Function

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Optimization of Axial Intensity Point Spread Function

It is known that for the converged laser beam, the axial intensity distribution corresponds to a Gaussian curve, that is, the intensity on the focal plane is the peak intensity. When it defocuses, the intensity would decrease rapidly. In optical data storage, for instance, we expect the intensity within a certain distance to be almost equal. In this paper, we propose to use a pure phase superresolution apodizer to optimize the axial intensity distribution of the converged laser beam and at the same time improve the resolution. The intensity point spread function remains almost identical in a wide range within the focal depth.     

Axial intensity distribution and focal shifts of focused partially coherent conical Bessel–Gauss beams

Based on the generalized Huygens–Fresnel diffraction integral and the theory of partially coherent light, the axial intensity distribution and the focal shifts of focused partially coherent conical Bessel–Gauss beams are investigated. The dependence of the maximum on-axis intensity and the associated focal shift on the Fresnel number and the coherence parameter are examined and illustrated numerically. The results related to the J ₀-correlated beams and the fully coherent Bessel–Gauss beams are obtained as particular cases of this study.     

Focal shift and focusing properties generation by radial cosine phase masks

Focal shift and focusing properties of Gaussian beams induced by radial cosine phase masks are investigated. Results show that focal shift and the energy distribution among intensity peaks are controlled by two different parameters of the radial cosine phase mask. Increasing the value of frequency parameter in the cosine part of the phase mask, focal shift and focal switch may occur, simultaneously, the focal shift direction may change. Moreover, by altering frequency parameter or phase variation parameter of the phase mask will change the energy distributions of maximum intensity peak and other small intensity peaks. And novel focal patterns also evolve considerably, such as from only one peak to six of multiple peaks. The tunable focal shift can be used to construct controllable optical tweezers. In practice, the tunable phase mask can be implemented through liquid crystal spatial light modulator, which can conveniently alter the wavefront phase distribution of the incident laser beam in the control of computer.     

部分相干平顶高斯光束通过球差透镜的聚焦特性

 基于部分相干光的传输理论，研究了部分相干平顶高斯光束通过球差透镜聚焦后轴上点的光强分布。数值计算表明:轴上最佳聚焦点随着球差从负到正的变化而向几何焦点方向移动；光束阶数越大，实现最佳聚焦点越过几何焦点所需的正球差值越小；正负球差对应的最佳聚焦点始终分居于无球差时最佳聚焦点的两侧;轴上最佳聚焦点的光强随着球差从负到正的变化而变小；当正负球差绝对值较大时，光强随球差的变化较为缓慢，而在球差值为0附近，光强随球差的变化比较剧烈。