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.     

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.     

圆孔的菲涅耳衍射

得到了圆孔菲涅耳衍射光强分布的表达式,此式由贝塞尔函数的数列(或Lommel函数)给出,因此很容易利用普及的数学软件算出结果.并且利用CCD照相机量度了衍射光强分布,与运算的结果作了比较,也与Burch在1985报导的结果作了比较.     

Analytic expression of the diffraction of a circular aperture

Recurring to the characteristic of Bessel function, we give the analytic expression of the Fresnel diffraction by a circular aperture, thus the diffractions on the propagation axis and along the boundary of the geometrical shadow are discussed conveniently. Since it is difficult to embody intuitively the physical meaning from this series expression of the Fresnel diffraction, after weighing the diffractions on the axis and along the boundary of the geometrical shadow, we propose a simple approximate expression of the circular diffraction, which is equivalent to the rigorous solution in the further propagation distance. It is important for the measurement of the parameter of the beam, such as the quantitative analysis of the relationship of the wave error and the divergence of the beam. In this paper, the relationship of the fluctuation of the transverse diffraction profile and the position of the axial point is discussed too.     

Near-field properties of diffraction through a circular subwavelength-size aperture

Analytical nonparaxial vectorial electric field expressions for both Gaussian beams and plane waves diffracted through a circular aperture are derived by using the vector plane angular spectrum method for the first time,which is suitable for the subwavelength aperture and the near-field region.The transverse properties of intensity distributions and their evolutions with the propagating distance,and the power transmission functions for diffracted fields containing the whole field,the evanescent field and the propagating field are investigated in detail,which is helpful for understanding the relationship between evanescent and propagating components in the near-field region and can be applied to apertured near-field scanning optical microscopy.     

Spectrum apodization of a time-dependent Gaussian pulse incident on the apodized circular aperture in far-field

The diffraction spectral intensity characteristics of a time-dependent Gaussian pulse from an apodized circular aperture in the far field are studied both theoretically and numerically. It is shown that the apodization of the diffracted Gaussian pulse spectrum can be found. Also the red or blue shift of the spectral intensity maximum of the incident pulse is presented.     

Propagation analysis of flattened circular Gaussian beams with a circular aperture in turbulent atmosphere

The propagation properties of flattened Gaussian beam with aperture in turbulent atmosphere have been studied by using the extended Huygens-Fresnel principle. From the study and numerical calculation, the effects of aperture on the propagation of flattened Gaussian beams in turbulent atmosphere have been illuminated. It shows that when the value of the truncation parameter δ is bigger, for example δ?2, the effects of aperture on the propagation properties are too small to be neglected. But when the truncation parameter δ is smaller, for example δ<2, the effects of aperture are complex. The peak value of the average intensity descends more rapidly and the beam spot spreads quicker with aperture than that without aperture when the propagation distance increases. Meanwhile, with the propagation distance increasing, the average intensity profiles of flattened Gaussian beams gradually convert into Gaussian average intensity profiles. In addition, some limiting cases are also discussed. It agrees with the existing results.     

大孔径会聚光束的圆孔和圆屏衍射及其反演变换

实验中发现,经常使用的大孔径会聚光束的圆孔和圆屏衍射图样不同于一般的菲涅耳圆孔和圆屏衍射图样.通过对这种光束进行的实验性研究发现,这是一种由球差引起的畸变了的会聚球面波光束.解释了衍射图样的形成,证明了这种光束的衍射图样中存在反演变换关系.利用这种光束可以对微小的衍射物体进行反演放大.     

Focusing and diffraction by an optical lens and a small circular aperture

Based on the vectorial Rayleigh–Sommerfeld diffraction integrals, analytical expressions for the transversal and axial field distribution of plane waves propagating through a thin lens followed by a small circular aperture are derived and used to study the focusing and diffraction properties of plane waves. Some special cases of our general result are discussed, and illustrative numerical calculation results are given. It is found that the vectorial nonparaxial approach should be applied if the aperture dimension is comparable with the wavelength or the focusing is strong.     

Propagation analysis of flattened circular Gaussian beams with a misaligned circular aperture in turbulent atmosphere

The propagation properties of flattened Gaussian beam with a misaligned circular aperture in turbulent atmosphere have been studied by using the extended Huygens-Fresnel formula. From the study and numerical calculation, the effects of aperture parameters on the propagation properties of flattened Gaussian beams in turbulent atmosphere have been illuminated. The results show that angle misalignments and lateral displacements of aperture create unsymmetrical average intensity distribution at any cross section. The intensity distributions are much more sensitive to the lateral displacement than to the angle misalignments. And the propagation properties of different flattened Gaussian beams in turbulent atmosphere are also compared.     

Influence of viscosity on the diffraction of sound by a circular aperture in a plane screen

The linearized equations of viscous fluid flow are used to analyze the diffraction of a time-harmonic acoustic plane wave by a circular aperture in a rigid plane screen. Arbitrary aperture size and arbitrary angle of incidence are considered. Sets of dual integral equations are derived for the diffracted velocity and pressure fields, and are solved by analytic reduction to sets of linear algebraic equations. In the case of normal incidence, numerical results are presented for the fluid velocity in the aperture and the power absorption due to viscous dissipation. The theoretical results for power absorption are compared to previously obtained results from high amplitude acoustic experiments in air. The conditions under which the dissipation predicted by linear theory becomes significantare quantified in terms of the fluid viscosity and sound speed, the acoustic frequency, and the aperture radius.     

Side-lobeless far-field spectrum of a short pulse from a circular aperture with Gaussian form of transmittance

The spectrum change of a Gaussian pulse in the far field is studied with the Fresnel diffraction integral when it is incident on an aperture with Gaussian form transmittance. It is found that the side-lobes of the diffracted spectral intensity, which exist in a normal circular aperture with unit transmittance, can be eliminated completely under such a condition. Also, the red shift and blue shift of the spectral intensity maximum of the incident pulse are presented.     

圆孔衍射光强分布的数值计算

利用数值积分的方法,计算了由点光源经圆孔衍射形成的光强分布,分别得到夫琅禾费及菲涅耳衍射图样,宽定量分析了满足夫琅禾费衍射的条件。     

Propagation of cosh-Gaussian beams diffracted by a circular aperture in turbulent atmosphere

An analytical formula for the average intensity of cosh-Gaussian (ChG) beams diffracted by an aperture in turbulent atmosphere is derived and some limiting cases are discussed. By using the average intensity formula, some numerical simulation comparisons are made and some special cases are studied, especially the influences of the ChG beam parameter (Ω₀), the propagation distance, the aperture and its size on the average normalized intensity distribution. It is determined that the evolution properties of the average normalized intensity profile in turbulent atmosphere with aperture are different not only from those of free space with aperture but also from those in turbulent atmosphere without aperture. PACS 42.68.Bz; 42.79.Ag; 42.25.Fx     

高斯型激光圆孔衍射中的光束畸变调控研究北大核心CSCD

从光波衍射的基本理论出发,利用高斯型分布的激光束,研究开普勒望远镜系统在衍射过程中光束畸变调控方法。利用中阶Zernike多项式构建像差函数法来模拟望远镜系统中的四叶畸变现象,并将该Zernike因子引入光学系统中弥补畸变效果。研究发现,波长和孔径会对奇异光强的分布产生明显的影响,波长增大的时候会改变光斑的形状,孔径会影响光斑强度和尺寸,11阶的Zernike四叶形变因子可以抵消望远镜系统的畸变现象。     

The rigorous electromagnetic theory of the diffraction of vector beams by a circular aperture

The rigorous electromagnetic theory of the diffraction of vector beams by an aperture is proposed and numerically evaluated by the diffraction of vector Gaussian beams by a circular aperture. The results are compared with those, by using the vector Rayleigh–Sommerfeld diffraction integrals and angular-spectrum expression theory, showing a good consistency. The numerical calculation shows that the result calculated by the rigorous theory is much more precise than those calculated by the integral method in diffraction near field, and a highly consistency reaches by the three methods in diffraction far field. A further extension of the theory is discussed.     

Two-photon near- and far-field fluorescence microscopy with continuous-wave excitation

We report on scanning far- and near-field two-photon microscopy of cell nuclei stained with DAPI and bisbenzimidazole Hoechst 33342 (BBI-342) with the 647-nm laser line of a cw ArKr mixed-gas laser. Two-photon-excited fluorescence images are obtained for 50-200 mW of average power at the sample. A nearly quadratic dependence of fluorescence intensity on laser power confirmed the two-photon effect. The nonlinearity was further supported by evidence of three-dimensional sectioning in a scanning far-field microscope. We find that the cw two-photon irradiation sufficient for imaging within typically 5 s does not significantly impair cell cycling of BBI-342-labeled live cells. Finally, high-resolution imaging in scanning near-field microscopy with good contrast is demonstrated.     

3种圆孔衍射的两种计算方法研究

根据菲涅耳-基尔霍夫衍射积分公式,给出点源、平面光以及高斯光束照射圆孔衍射的一种数值计算方法,借鉴相关方法推导了这3种圆孔衍射的菲涅耳衍射及其特殊情况下夫琅禾费衍射的解析计算式,并利用Matlab软件模拟了它们傍轴区的衍射场。模拟实验表明:这两种计算方法对这3种常见且重要的圆孔衍射都是有效可行的。     

菲涅耳圆孔衍射计算机模拟演示的实现

为了克服菲涅耳衍射积分计算的复杂性和因光波频率高而导致的采样点数目巨大两大难题,利用Hankel变换算法,将二维计算变换为一维计算,并利用球面波因子处理,在普通PC上实现了菲涅耳圆孔衍射的计算机模拟演示．