用Mathematica演示波的衍射、干涉现象

1 引言 目前,Mathematica系统已广泛应用于从高中到研究生的教学或研究.波的衍射、干涉现象一般是从实验上观察得到的,在物理教学中很少根据理论公式绘制出有关的图形或动画,来解释实验现象.本文利用物理理论公式借助Mathematica演示波的衍射和干涉现象.     

用衍射屏平移相因子计算夫琅禾费衍射场强分布

用Fresnel-Kirchhoff衍射积分求解夫琅禾费衍射场分布时引入衍射屏平移相因子,可简化对较复杂衍射屏夫琅禾费衍射的讨论,加深对衍射、干涉现象的理解．     

散射光干涉图样的一种计算方法

本文从波动光学出发,利用菲涅耳-基尔霍夫衍射公式研究了文献[1]中所描述的干涉现象,并导出了干涉图样的强度分布,得到了条纹极大值的位置,对干涉现象的物理图象作了说明。 关键词：     

劈尖干涉现象的计算机仿真

在《光的干涉》课堂教学中,由于其原理比较抽象,学生难以理解和掌握该部分知识。本文以劈尖干涉为例,借助计算机仿真手段再现劈尖干涉现象,并讨论了入射光波长、劈尖中介质的折射率、劈尖倾角等因素对干涉现象的影响,通过形象直观的图形演示加深学生对劈尖干涉现象的理解。     

双缝衍射现象的实验研究

双缝衍射是指被单缝衍射调制的双缝干涉现象. 以定性分析双缝衍射光强分布为基础,对双缝衍射实验过程中出现的各级明条纹中心的光强并不相等,且包络内中间光强并不是最大的现象作了深入分析和研究,并指出这些现象出现的原因.     

谱衍射干涉的计算模拟

本文提出谱衍射干涉的计算模拟方法.着重讨论了谱为几何图案时的干涉现象,得到干涉场强正比于物体沿图案路径的线积分.根据实验观察用二次位相函数来近似模拟酒精灯火焰的位相延迟,相应计算了几种特殊谱分布的衍射干涉强度分布,得到与实验相一致的结果.本文还讨论了几种特殊谱衍射干涉的特点,得到了一些结论.     

含时微扰系统中跃迁概率的衍射、干涉及共振现象

主要应用Mathematica等计算软件讨论量子力学教学中重要的量子跃迁问题.借助解析分析和计算绘图的方法,给出了量子跃迁过程中概率波所表现出的衍射和干涉现象,通过与光波的类比让学生理解概率波的波动性以及相干叠加所导致的量子共振现象.以含时微扰理论为基础,计算了恒定微扰和谐振微扰概率跃迁的叠加问题,从量子概率干涉的角度解释了概率波共振跃迁的物理机制.     

偏振光干涉的课外探讨

光学教学中偏振光干涉现象很吸引学生,我们在课外经常与学生进行有关方面的探讨。     

双光束干涉中偏振态分布的演示实验

光的干涉现象是波动过程的基本特征之一,是波动光学研究的主要内容.相干条件说明光波的偏振态对光的干涉效应有影响.为了让学生更好地理解光的干涉过程中偏振态的影响,本文设计了一种全息记录光路,利用一种对激发光偏振态敏感的偶氮染料样品,演示了样品经过不同偏振的两束特定波长写入激光作用后,可以观察到写入光和探测光的衍射现象.这些衍射现象说明样品中可以形成的不同类型的折射率光栅,而这些折射率光栅来源于样品表面不同偏振态的周期分布导致的染料分子的周期取向分布,从而形象地说明了光的干涉过程中相位差的重要性,有助于学生对光的干涉的深入理解.     

牛顿环实验的拓展

牛顿环实验的拓展单慧波（华东理工大学上海２００２３７）牛顿环实验是我国工科物理实验中的一个基本实验，设计和安排这个实验的主要目的是：（１）使学生对干涉现象增加感性认识，更好的理解光的波动性．（２）让学生初步了解干涉现象在生产、科研等领域的应用．当前学...     

Reflection of Rayleigh waves from a mechanical resonator grating

The problem of Rayleigh wave scattering from a set of N chains of closely spaced identical mechanical resonators is considered. The distance between the chains is identical to the half-wavelength of Rayleigh waves at the frequency ω taken to be identical or close to the natural frequency of the chain of resonators with allowance for the associated elasticity. The coefficient of reflection of Rayleigh waves from the diffraction grating specified above is calculated.     

Diffraction of evanescent waves and nanomechanical displacement detection

Sensitive displacement detection has emerged as a significant technological challenge in mechanical resonators with nanometer-scale dimensions. A novel nanomechanical displacement detection scheme based upon the scattering of focused evanescent fields is proposed. The sensitivity of the proposed approach is studied using diffraction theory of evanescent waves. Diffraction theory results are compared with numerical simulations.     

现代数字物理教学连载③——关于机械波的数字化教学

以机械波的教学为例,介绍了数字教学技术在波动教学改革中的作用:数字教学大大丰富了波动教学的内容,使传统的波动知识结构更加完整;提高了学生对波动研究的实际能力,扩大了学生对波的研究范围和空间.     

Interactions of ion acoustic multi-soliton and rogue wave with Bohm quantum potential in degenerate plasma

This work investigates the interactions among solitons and their consequences in the production of rogue waves in an unmagnetized plasmas composing non-relativistic as well as relativistic degenerate electrons and positrons, and inertial non-relativistic helium ions. The extended Poincare′–Lighthill–Kuo(PLK) method is employed to derive the two-sided Korteweg–de Vries(Kd V) equations with their corresponding phase shifts. The nonlinear Schr o¨dinger equation(NLSE) is obtained from the modified Kd V(m Kd V) equation, which allows one to study the properties of the rogue waves. It is found that the Fermi temperature and quantum mechanical effects become pronounced due to the quantum diffraction of electrons and positrons in the plasmas. The densities and temperatures of the helium ions, degenerate electrons and positrons, and quantum parameters strongly modify the electrostatic ion acoustic resonances and their corresponding phase shifts due to the interactions among solitons and produce rogue waves in the plasma.     

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.     

Method of Coupled Waves in the Theory of Diffraction of Light by Elastic Waves in Crystals

Diffraction of light by elastic waves in crystals is described by the method of coupled waves in a form different from that used by other researchers. The difference is determined by the treatment of two pairs of orthogonal coordinate systems whose principal axes are oriented along the directions of phase and energy transfer of two optical waves interacting on a sound wave. Due to this, the equations of coupled waves assume the most compact form, which was previously unknown for crystals. These equations are easily solved by the conventional methods in terms of quasi-plane waves and also admit of a wider class of solutions for bounded interaction regions. Two different diffraction regimes are compared in the present work, namely, the transmission and reflection diffraction. It is indicated that the suggested approach allows one to refine the parameters that define the efficiency of diffraction of light by elastic waves in crystals.     

Numerical and experimental studies on the effects of stage risers

The acoustic effects of stage risers, especially on the sound of lower string instruments, are numerically and experimentally analyzed. To discuss the effects of the vibration of riser’s boards due to the mechanical force from an instrument, a structural-acoustical coupling approach is applied based on the mode expansion and the boundary element technique. Measurement results of the mechanical force from real instruments are used in the numerical study. The vibration of the top board of a riser affects the sound field only around the natural frequencies of the board and the cavity of the riser. In contrast, the acoustic diffraction due to the riser affects the sound field in a wide frequency range. The riser’s sideboard that faces to receiving points increases the sound pressure levels because it reflects waves diffracted at the riser’s edge to the front. To verify the numerical results, the effects of acoustic diffraction due to risers are especially investigated in detail through a scale model experiment.     

Diffraction-biased shear wave fields generated with longitudinal magnetic resonance elastography drivers

Magnetic resonance elastography (MRE) is a technique for quantifying the acoustic response of biological tissues to propagating waves applied at low frequencies in order to evaluate mechanical properties. Application-specific MRE drivers are typically required to effectively deliver shear waves within the tissue of interest. Surface MRE drivers with transversely oriented vibrations have often been used to directly generate shear waves. These drivers may have disadvantages in certain applications, such as poor penetration depth and inflexible orientation. Therefore, surface MRE drivers with longitudinally oriented vibrations are used in some situations. The purpose of this work was to investigate and optimize a longitudinal driver system for MRE applications. A cone-like hemispherical distribution of shear waves being generated by these drivers and the wave propagation being governed by diffraction in the near field are shown. Using MRE visualization of the vector displacement field, we studied the properties of the shear wave field created by longitudinal MRE drivers of various sizes to identify optimum shear wave imaging planes. The results offer insights and improvements in both experimental design and imaging plane selection for 2-D MRE data acquisition.     

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.     

记录结构对体光栅各向异性衍射选择特性研究

以静态体光栅各向异性衍射理论分析模型为基础,将与体光栅厚度有关的记录光强调制度引入到各向异性耦合波方程中.利用耦合波理论分析了光折变晶体中体光栅的各向异性衍射性能,研究了在不同初始记录光强比的条件下,记录光入射角的改变对光折变体光栅各向异性布喇格衍射性能的影响.结果表明：记录光入射角和记录光初始光强比均对体光栅的各向异性衍射具有选择性;与此相比,记录光入射角和记录光初始光强比对于体光栅各向同性衍射不具备选择性.