Structure of boundary diffraction wave revisited

The physically appealing boundary diffraction wave theory which suggests that diffraction patterns arise due to interference of an undisturbed (geometrical) wave and the boundary diffraction wave generated by edge of the diffracting aperture, simplifies the solution of diffraction problems by reducing the Fresnel–Kirchhoff surface integral into a line integral over the illuminated boundary of the diffracting aperture. The present work reports experimental investigations carried out on the structure of the boundary diffraction wave. It has been shown that the boundary diffraction wave is continuous behind the diffracting aperture and apparently there does not exist any discontinuity at the geometrically light to shadow transition boundary, as is required by the theory. PACS 42.25.-p; 42.25.Fx; 42.25.Hz     

Cornu's spiral in the Fresnel regime studied using ultrasound: a phase study

A simple experimental technique for measuring the phase and amplitude of diffracting ultrasound wave [A. Hitachi and M. Takata, Am. J. Phys. 78, 678 (2010)] has been applied to diffracting objects with straight edges as a demonstration of the Cornu spiral. Babinet's principle is studied observing the ultrasound field behind a slit and a complementary strip obstacle and is verified directly by comparing vectors (phasors) in the complex plane. The phase of the diffracted wave observed in the geometrical shadow of the straight screen has the form of a cylindrical wave originating at the edge of the straight screen as the boundary diffraction wave proposed by Young. In addition, the incident wave has a phase delay of π/4 behind the wave passing through on the center line of the slit, the plane of symmetry, has been observed as predicted by Huygens-Fresnel diffraction theory.     

Detection of a cylindrical boundary diffraction wave emanating from a straight edge by light interaction

The paper shows that the boundary diffraction wave originating at an edge is an omnidirectional cylindrical wave. The experimental set-up used to demonstrate this property employs a He-Ne laser beam. The beam is split into three beams using a glass plate. One of the beams passes straight through, the second beam passes through the glass plate and the third beam is the reflected beam. It is shown that the interference patterns are observed in all three beams. Analysis of these patterns shows that the boundary diffraction wave originating from the edge is an omnidirectional cylindrical wave. This analysis also provides strong evidence that the boundary diffraction wave travels not only within the beam where it originates but also to the neighboring coherent beam. The energy re-distribution was also shown to be dependent on the wavelength of the incident light beam and hence provides further evidence as to why longer wave lengths disperse more compared to shorter wavelengths in white light diffraction by an edge.     

Knife-edge diffraction pattern as an interference phenomenon: An experimental reality

This paper demonstrates that a knife-edge diffraction pattern is, indeed, due to the interference of two superimposing waves: the geometrical wave and the boundary diffraction wave. Within the framework of boundary diffraction wave theory it is shown that this diffraction pattern can easily be broadened in such a manner that a single fringe covers the whole field of view. At this point the system converges to a schlieren diffraction interferometer and could be used for the study of phase objects using diffraction-limited optics. Experimental observations show that the method bears a similarity to that of any known two-beam interferometer, e.g. Mach-Zehnder interferometer. The experimental details have been presented and the results are compared with a two-beam holographic interferometer and a point diffraction interferometer.     

Boundary diffraction waves at multiple Fresnel-Kirchhoff diffraction

The theory of boundary diffraction wave is generalized to the case of multiple Fresnel-Kirchhoff diffraction on several sequentially situated holes (screens). The generalized boundary wave is the sum of boundary diffraction waves with different multiplicities described by integrals whose maximal multiplicity is equal to the number of obstacles. It is shown that the proposed generalized boundary wave method provides a multiple time gain in calculations, as compared to the aperture integration method. Results of numerical calculations agree with experimental dependences.     

Wide-angle diffraction of the laser beam by a sharp edge

Using a rigorous theory of diffraction, we explain the origin and analyze the structure of a wide-angle illuminated area observed when a limited beam is diffracted by the sharp edge of an opaque screen. It is shown that the formed plume has the structure of a cylindrical wave traveling from the screen edge and its amplitude is proportional to the beam amplitude at this edge. The observed structure is Young’s boundary wave produced by diffraction of the limited beam.     

圆孔“衍射波”的相位特性

在标量衍射理论的基础上,导出了圆孔衍射的“边界衍射波”的级数表达式,提出圆孔衍射产生的“衍射波”概念,对“边界波”和“衍射波”的相位特性作了讨论和比较.     

Diffraction of spherical waves at an annular aperture in the use of the boundary diffraction wave theory: A comparison of different diffraction integral approaches

The integral expression for divergent spherical waves diffracted at an annular aperture is derived based on the theory of the boundary diffraction wave. The expressions for divergent spherical waves diffracted at a circular aperture and a disk, and the axial field are treated as the special cases of our general one. Numerical calculation results for axial and transversal intensity distributions are given to compare our results with the Kirchhoff diffraction integral, first and second Rayleigh diffraction integrals. As expected, our results are in agreement with those in the use of the Kirchhoff diffraction integral, but the computer time is reduced greatly by using the boundary diffraction wave theory. The four diffraction formulae are shown to be consistent for axial and transversal intensity distributions, if the source and observation points are positioned equally from the aperture, or the observation point is located enough far from the aperture. Otherwise, the mean value of the first and second Rayleigh diffraction integrals is equal to the result of the boundary diffraction wave theory.     

Edge diffraction of a Laguerre light beam

The phenomenon of transverse diffusion of ray amplitude along two principal orthogonal directions on the cylindrical surface of a diffracted boundary wave is observed in the diffraction of a Laguerre laser beam by the straight sharp edge of a planar safety-razor blade.     

Direct visualization of Young’s boundary diffraction wave

Experimental investigations on Young’s boundary diffraction wave are presented where a wavefront division interferometric scheme is used on diffracted wavefront to generate two-beam interference fringes in the geometrically shadow region. These fringes have good visibility and are observable in the whole space, strongly advocating the physical existence of Young’s boundary diffraction wave as a separate entity. Analysis of these fringes may provide vital information about the structure and nature of boundary diffraction wave e.g. existence in whole space, dependence of amplitude on obliquity factor etc.     

T-matrix analysis of electromagnetic wave differaction from a Fourier grating

This paper is described for T-matrix analysis of the electromagnetic wave diffraction from a Fourier grating that the boundary value problem is treated by applying the extended boundary condition. The rigorous form of the expression of matrix elements is presented in the term of Bessel functions of the first kind. The error of power conservation versus the truncated number has been examined for mode number. Diffraction efficiencies versus groove depth and wavelength for a second or third harmonic wave of Fourier grating have been discussed. Numerical results are in good agreement with those obtained from other method and experimental values. Reasonable numerical results are presented for a groove depth per period of the Fourier grating less than 0.25.     

1维介质光栅近场及其衍射的FDTD分析

 应用FDTD方法计算了单色平面波斜入射时1维介质光栅的近场，进而求出介质光栅的衍射效率。借助于周期边界条件，整个计算区域为周期结构的一个单元。考虑入射波在两种介质界面上会产生反射和透射，故在总场边界上引入入射波、反射波和透射波。给出了光栅单元截面为矩形和梯形的算例。该方法可用于斜入射情形下具有复杂结构和任意单元截面的介质栅近场及其衍射特性分析。     

边界衍射波理论公式的准确性数值分析

利用数值分析的方法分析了由边界波理论公式所得的圆形光阑衍射场的光强分布.通过对边界波理论公式所得的光强分布曲线,对几何照明区与阴影区的光强分布曲线与面衍射积分公式所得的光强分布曲线进行比较,分析了边界波理论公式对衍射场描述的准确性.     

Boundary diffraction wave theory of junctions between two surfaces with different face impedances

The line integral of the boundary diffraction wave theory is derived for the diffraction process of waves by a junction between two surfaces with different face impedances. The exact solution of Maliuzhinets is used with this aim. The resultant integral is applied to the diffraction of waves by a circular junction between two impedance surfaces. The results are examined numerically.     

体全息光栅透镜的设计和应用

设计了一种新型的体全息光栅透镜, 在一块光学平板（体全息记录材料）内可以将输入光束产生横向传输并聚焦, 或对输入光点产生横传的准直. 它由一束平面波和一束球面波正交入射到光学平板上干涉形成的. 研究了该体全息透镜的光栅间距变化情况, 为设计和制备体全息光栅透镜及相关器件提供了理论依据. 基于两光束耦合波理论, 得到了该光栅透镜的耦合波方程, 近似计算了该透镜的衍射效率及其达到高衍射效率时透镜的最佳尺寸. 最后, 讨论了该透镜在集成光学等领域中的应用.     

The method of the boundary diffraction wave for impedance surfaces

The line integral of the boundary diffraction wave theory is extended for the diffraction process of waves by the impedance surfaces with edge discontinuities. With this aim, the exact diffraction field expression of Maliuzhinets is transformed into a line integral. The method is applied to the scattering problems of waves by a spherical reflector with edge discontinuity and the diffracted fields are evaluated asymptotically. The resultant expressions of the waves are examined numerically.     

Boundary diffraction wave theory of resistive surfaces with edge discontinuities

The line integral of the boundary diffraction wave theory is derived by considering the exact diffracted fields of a resistive half-plane. The line integral is generalized for arbitrary resistive surface with edge discontinuity. The method is applied to the diffraction problem of waves by a convex resistive spherical reflector and the resultant field expressions are investigated numerically.     

Diffraction by an Elongated Body of Revolution with Impedance Boundaries: the Boundary Integral Parabolic Equation Method

Acoustical Physics - The problem of diffraction by an elongated body of revolution with impedance boundary conditions is studied. The case of axial incidence of a high-frequency wave is considered....     

Uniform theory of the boundary diffraction wave

A uniform version of the potential function of the Maggi-Rubinowicz boundary diffraction wave theory is obtained by using the large argument expansion of the Fresnel integral. The derived function is obtained for the problem of diffraction of plane waves by a circular edge. The results are plotted numerically.     

Charge density wave dislocation as revealed by coherent x-ray diffraction

Coherent x-ray diffraction experiments have been performed on high quality crystals of the charge density wave (CDW) system K0.3MoO3. The satellite reflections associated with the CDW have been measured as a function of the 20-microm-diameter beam position. For some positions, regular fringes have been observed. We show that this observation is consistent with the presence of a single CDW dislocation. Beyond charge density wave systems, this experiment shows that coherent x-ray diffraction is a suitable tool to probe topological defects embedded in the bulk.