经光阑衍射的平顶涡旋光束位相奇点的演化特性

推导出了平顶涡旋光束通过有光阑ABCD光学系统的传输解析式,并以光阑透镜和矩形光阑系统为例,与平顶光束比较研究了截断参量、相对离轴距离和光束阶数对衍射场中位相奇点演化特性的影响.数值计算表明,平顶涡旋光束通过上述光学系统均存在位相奇点,即使源处涡旋被光阑阻拦时,衍射场中也会出现位相奇点;而平顶光束通过光阑透镜系统存在刃型位错,随着截断参量增大,会发生刃型位错的演化和湮灭现象,且平顶光束通过矩形光阑系统没有发现位相奇点.     

经光阑衍射的平顶涡旋光束位相奇点的演化特性

推导出了平顶涡旋光束通过有光阑ABCD光学系统的传输解析式,并以光阑透镜和矩形光阑系统为例,与平顶光束比较研究了截断参量、相对离轴距离和光束阶数对衍射场中位相奇点演化特性的影响.数值计算表明,平顶涡旋光束通过上述光学系统均存在位相奇点,即使源处涡旋被光阑阻拦时,衍射场中也会出现位相奇点;而平顶光束通过光阑透镜系统存在刃型位错,随着截断参量增大,会发生刃型位错的演化和湮灭现象,且平顶光束通过矩形光阑系统没有发现位相奇点.     

Cross-spectral density matrix of a random electromagnetic beam propagating through an apertured axially nonsymmetrical optical system

Using the fact that a hard-edged rectangular aperture function can be approximated by a two-dimensional multi-Gaussian series, analytic formulas for the elements of the cross-spectral density matrix of a random electromagnetic beam truncated by a rectangular aperture and passing through an axially nonsymmetrical optical system is derived. The analysis is illustrated by numerical examples relating to changes in the spectral degree of polarization of electromagnetic Gaussian Schell-model beams propagating through free space, focal system and dual-focus system. In particular, the effect of the size of the hard aperture on the spectral degree of polarization of the beam along its optical axis is discussed.     

Theoretical Demonstration of a Newly Designed Micro-Rotator Driven by Optical Pressure on a Light Incident Surface

A newly designed cylindrical optical micro-rotator which has slopes for trapping and rotation on its upper surface is proposed. The cylindrical shape is effective in decreasing viscous drag force (damping factor) in the medium. A ray-tracing method considering the beam waist is employed to analyze the radiation pressure exerted on the upper surface of the rotator. We have demonstrated optical trapping and high speed rotation for various optical beam parameters such as the lens numerical aperture and the Gaussian mode profile as well as rotator shape parameters including oblique angle, height and diameter.     

Effects of a rectangular aperture on the vectorial structure of a Gaussian beam in the far-field regime

With the help of the angular spectrum representation and the Gaussian function expansions of the hard-edge aperture function, the vectorial structure of a linearly polarized Gaussian beam (GB) diffracted by a rectangular aperture is analyzed in detail. It is found that the sizes of the energy flux density spots and the energy fluxes of the TE and TM terms depend on the aperture configuration and the polarization direction of the incident GB. The far fields may have smaller spots and larger energy fluxes for a GB diffracted by a rectangular aperture compared to that by a square aperture with the same beam intensity. And another potential application in information encoding and transmission for free-space communications is also proposed in addition to re-focusing to enhance the optical storage density. This encoding scheme has the benefit of easy implementation without modulating any properties of the light source.     

Propagation characteristics of the two-dimensional off-axial Hermite-cosh-Gaussian beams through rectangular apertured and misaligned optical systems

By introducing a hard aperture function into a finite sum of complex Gaussian functions, an approximate analytical expression for the two-dimensional off-axial Hermite-cosh-Gaussian beams passing through a rectangular apertured and misaligned paraxially ABCD optical system has been derived. The results provide more convenience for studying their propagation and transformation than the usual way by using diffraction integral directly. Some numerical simulations are also illustrated for the propagation characteristics of a two-dimensional off-axial Hermite-cosh-Gaussian beam through a rectangular apertured ABCD optical system.     

Diffraction characteristics of optical vortex passing through an aperture-iris diaphragm

The diffraction of an optical vortex through an iris diaphragm which is a close approximation to a circular aperture has been investigated. The results are compared with those obtained from the diffraction of a Gaussian beam through the same aperture. In our findings the diffraction of an optical vortex and a Gaussian beam produce ball bearing sort of structure of darkness and brightness. The singularity of the vortex beam is found to be consistent even after the diffraction through the aperture. The presence of singularity at the centre of diffraction pattern of an optical vortex has been confirmed by interferometry. There is a good agreement between the experimental and numerical results. We propose that these results may find various applications in optical trapping experiments.     

Analytical formulas for a circular or non-circular flat-topped beam propagating through an apertured paraxial optical system

Propagation of a flat-topped beam of circular or non-circular (rectangular or elliptical) symmetry through an apertured optical system is investigated. By expanding the hard aperture function as a finite sum of complex Gaussian functions, some approximate analytical propagation formulas are derived for a flat-topped beam of circular or non-circular (rectangular or elliptical) symmetry propagating through an apertured paraxial general astigmatic (GA) optical system or an apertured paraxial misaligned stigmatic (ST) optical system. The derived formulas are very fast to compute. The results obtained by using the approximate analytical expressions are in a good agreement with those obtained by direct numerical integration. The present analytical formulas provide a convenient and effective way for studying the propagation and transformation of a circular or non-circular flat-topped beam through an apertured general optical system.     

Approximate analytical representation of Wigner distribution function for Gaussian beams passing through ABCD optical systems with hard aperture

Based on the treatment that a rectangular function can be expanded as an approximate sum of complex Gaussian functions with finite numbers, the analytical expression of the Wigner distribution function for a Gaussian beam passing through a paraxial ABCD optical system with hard-edged aperture is obtained. By numerical simulation, it is shown that the effect of the aperture on the Wigner distribution function is prominent. By comparing the analytical results with the numerical integral results, it is shown that this method of expanding hard-edged aperture into Gaussian functions with finite numbers is proper and ascendant. This method could be extended to study the Wigner distribution functions of other light beams passing through a paraxial ABCD optical system with hard-edged aperture.     

Multiple optical line traps using a single phase-only rectangular ridge

An optical line trap has the ability to simultaneously trap and align microparticles in line formation due to its intensity profile. In this paper, we demonstrate a straightforward means to generate multiple optical line traps by simply placing a phase-only rectangular ridge in the path of a laser beam. By carefully positioning the rectangular ridge, we were able to control the separation between the optical trapping lines, which were then used to create multiple line formations of trapped particles. The simplicity of the proposed technique lends itself to the realization of a highly efficient optical line trap converter for easy modification of existing optical microscopes.     

高斯光束通过含失调窄缝光阑的失调光学系统的传输特性

 利用硬边窄缝光阑的近似展开式和适用于失调光学系统的广义衍射公式,得出了高斯光束经含失调窄缝光阑的失调光学系统传输的近似解析式。模拟结果表明输出光束场分布与光束参量、光阑尺寸、ABCD矩阵元、光阑失调量和光学系统失调量有关。针对给定的光学系统和高斯光束定量分析了各失调量对输出光束场分布的影响,结果表明:光阑横向位移、光学系统横向位移和角位移均引起垂直于z轴截面内明显的光强非轴对称分布。当光阑半宽度为1 mm时,光阑的衍射作用使腰斑半径为0.5 mm的高斯光束产生-1.586π～1.465π范围的相对相移,且光阑横向位移、光学系统横向位移和角位移均引起焦平面前后相对相移的迅速变化。随光阑宽度变小,各失调量对输出光束特性的影响越明显。     

Propagation characteristics of the rectangular flattened Gaussian beams through circular apertured and misaligned optical systems

Based on the fact that a hard aperture function can be expanded into a finite sum of complex Gaussian functions, the approximate analytical expression for the output field distribution of a rectangular flattened Gaussian beam passing through a circular apertured and misaligned paraxial ABCD system is derived. The result brings more convenient for studying its propagation than the usual way by using diffraction integral directly. Some numerical simulations are also given for illustrating the propagation properties of a rectangular flattened Gaussian beam through a circular apertured and misaligned optical system.     

Hermite hyperbolic/sinusoidal Gaussian beams in ABCD systems

For a Hermite hyperbolic/sinusoidal Gaussian beam with focusing properties, passing through an arbitrarily shaped rectangular aperture on the source plane and an on-axis x–y asymmetric ABCD system, the receiver plane expression is derived using the Collins integral. The specific example of a single thin lens placed on the propagation path is examined at selected source, propagation and optical element parameters. Viewing the progress of the beam in propagation, we find that subjecting the source beam to an aperture will give rise to excessive spreading during propagation. The lens setup will act to concentrate the energy of the beam around its focal point as expected, while in some circumstances it will also execute beam profile changes. By adjusting the aperture opening in the shape of a narrow slit, the beam will become aligned in the opposite direction after propagating after having traveled sufficiently. The results are presented as intensity graphs in the form of contour plots and 3D illustrations.     

迈克尔逊干涉光谱仪动镜倾斜误差容限分析

系统分析了迈克尔逊干涉光谱仪中平面动镜在运动过程中发生倾斜致使反射光束偏转时对干涉图的影响.结果表明,光束偏转带来的误差分为三部分：光束偏转导致整体增加的恒定光程差,垂直光轴方向因不同光线而引入的偏移光程差以及偏转光束中心相对于光轴的偏移量.从调制度和相位误差角度给出了平面动镜倾斜误差容限,并讨论了减小干涉图受光束偏转影响的方法.     

光阑对平面光波傍轴性的影响

 根据单色光傍轴度的定义,分别研究了圆形光阑和方形光阑对平面光波傍轴性的影响。推导出平面光波经圆形光阑和方形光阑衍射后其傍轴度的解析表达式。平面光波经圆形光阑或方形光阑衍射后,其傍轴性下降,傍轴度小于1,傍轴度下降量取决于光阑尺寸与入射平面光波波长的比值。数值计算结果表明：随光阑尺寸与入射平面光波波长的比值从零开始增大,平面衍射光波的傍轴度从零开始快速增大而后趋于一饱和值,但光阑的形状不影响平面衍射光波的傍轴性。     

Spin-to-orbital angular momentum conversion in a strongly focused optical beam

As a fundamental property of light, the angular momentum of photons has been of great interest. Here, we demonstrate that optical spin-to-orbital angular momentum conversion can occur in a homogeneous and isotropic medium. This Letter presents both theoretical and experimental studies of this conversion in a tightly focused beam and shows that the orbital rotation speeds of trapped particles are altered because of this conversion as predicted by theory.     

基于LabVIEW的光学现象模拟

以牛顿环干涉和夫琅禾费矩孔衍射实验为例介绍了在LabVIEW环境下实现光学现象模拟的具体方法和过程.表明基于LabVIEW软件可以方便的实现牛顿环干涉和矩孔衍射等光学现象的计算机模拟.     

厄米-高斯光束在内含硬边光阑光学系统中的传输

把硬边光阑从复杂光学系统中“移”出来,即把任意一个含有硬边光阑的复杂光学系统体现到含有入射光瞳和出射光瞳的光学系统中，使硬边光阑的作用转化为出射光瞳的作用，以便求出观察面上的解析解。对入射面上的二维厄米 高斯光束，利用柯林斯公式和入射光瞳与出射光瞳的物像关系，可得到所要求观察面的场分布和解析结果，通过数值模拟验证了其正确性。通过分析计算得到如下结论：对于任意一个含有硬边光阑的复杂光学系统，都可以把光阑的作用从系统中“移”出来，把其看作是出射光瞳的作用，从而可以较为简便地求出观察面上的场分布。     

Bessel光束经椭圆环形孔径后的衍射光场

基于菲涅耳衍射积分理论及硬边孔径的复高斯函数展开法导出了Bessel光束经椭圆环形孔径后的光场表达式, 数值模拟了其光场的强度分布. 研究了Bessel光束经椭圆环形孔径后的光场变化及其传播过程; 在实验上利用轴棱锥输出的近似无衍射Bessel光, 通过椭圆环形孔径, 使用电荷耦合器件拍摄得到不同传播距离处的光强分布. 理论结果和实验结果均表明无衍射光束经椭圆环形孔径后会产生空心光束.     

Observation of discrete solitons and soliton rotation in optically induced periodic ring lattices

We report the first experimental demonstration of ring-shaped photonic lattices by optical induction and the formation of discrete solitons in such radially symmetric lattices. The transition from discrete diffraction to single-channel guidance or nonlinear self-trapping of a probe beam is achieved by fine-tuning the lattice potential or the focusing nonlinearity. In addition to solitons trapped in the lattice center and in different lattice rings, we demonstrate controlled soliton rotation in the Bessel-like ring lattices.