Integral equation method in near-field optical microscopy of scattering

Based on the integral equation method, the boundary problem of classical optics of finding the strength of the electromagnetic field scattered by a probe positioned in the near zone of a plane surface is solved in the context of application in near-field optical microscopy of scattering. Only the dipole component of the scattered field was taken into account in the calculations. The obtained theoretical expressions were compared to the known experimental data on scanning the surface of SiC. Good agreement between the experimental and the theoretical results was obtained outside the region of the resonant interaction of the probe of a near-field microscope and the surface under study.     

Analysis of stress field in a single anisotropic diamond/square shaped inclusion using the volume integral equation method and the numerical equivalent inclusion method

A volume integral equation method (VIEM) is used to study elastostatic problems in an unbounded elastic solid containing a single diamond/square shaped inclusion subject to uniform tensile stress at infinity. The inclusion is assumed to be a long parallel diamond/square cylinder composed of isotropic or anisotropic elastic materials and perfectly bonded to the isotropic matrix. The solid is assumed to be under plane strain on the plane normal to the cylinder. A detailed analysis of the stress field at the interface between the isotropic matrix and the single isotropic/orthotropic diamond/square shaped inclusion is carried out. The effects of a single isotropic/orthotropic diamond/square shaped inclusion on the stress field at the interface between the matrix and the inclusion are investigated in detail. The accuracy of the volume integral equation method for the interfacial stress field is validated and compared by the numerical equivalent inclusion method (NEIM) and the finite element method (FEM) using ADINA. Through detailed analysis of plane elastostatic problems using the parallel volume integral equation method (PVIEM) in an unbounded isotropic matrix with multiple isotropic diamond shaped inclusions under uniform remote tensile loading, it is demonstrated that the volume integral equation method can also be applied to solve general two- and three-dimensional elastostatic problems involving multiple isotropic/anisotropic inclusions whose shape and number are arbitrary.     

Role of the probe quadrupole moment in apertureless near-field optical microscopy

A theory of an apertureless scanning near-field optical microscope is developed that takes into account the quadrupole moment of the probe in forming the near field and the scattered wave in the far-field zone. It is shown that the quadrupole moment can lead to a change in the conditions for the resonant coupling of the probe tip with the sample surface, as well as to the appearance of additional resonances in the frequency dependence of the response of a near-field microscope. The theory developed is found to be in good agreement with known experimental data in the region of resonant tip—sample coupling.     

雪层覆盖地面电磁散射的矩量法

为实现分层介质粗糙面电磁散射的矩量法研究,给出一种分层介质粗糙面电磁积分方程的区域分解方法.将格林定理应用于粗糙面所分的各子空间,结合波动方程和格林函数推导分层粗糙面的电磁积分方程,利用矩量法对其进行离散,数值计算得到雪层覆盖地面散射系数的角分布曲线,其中,粗糙表面由一维带限Weierstrass分形谱和Monte Carlo方法模拟.通过与时域有限差分法数值结果的比对,验证该方法的准确性,并分析散射系数随雪和地面参数、介质参数以及入射波参数的变化,获得了较完整的散射特征.     

非探针近场光学显微镜的成像实现

介绍一种非探针近场光学显微镜，并对它的图像实现过程及处理方法进行了讨论。该装置以阿达玛变换成像理论为基础，用纳米多孔编码板代替光纤探针获得了较高的光学信噪比。成像研究表明，该装置可对近场衰逝波分量进行有效探测并能实现超衍射极限成像，为近场光学探测研究提供了一种新的思路。     

Wave propagation in a random medium: The solution of the m-nth moment equation with different wavenumbers

The moment equation with different wavenumbers and different transverse coordinates for wave propagation in a random medium is a linear differential equation. It often appears in the study of problems related to wave propagation in a random medium. The differential equation can be converted into an integral equation by using Green's functions and the integral equation can be solved by iteration. The moment equation is solved by the method of successive scatters, too. The solution of the moment equation is a Dyson expansion. The physical implication of the successive solution of the moment equation with different wavenumbers is explained.     

The role of propagating and evanescent waves in scanning near-field optical microscopy

Theoretical study on the image formation in scanning near-field optical microscopy is carried out in the framework of the direct moment method. Information brought, respectively, by the propagating and evanescent components in the optical near field that is collected by a scanning fiber tip with a sub-wavelength aperture is numerically and systematically analyzed in the light of the resolution achieved by the microscope. The analyses reveal that resolutions beyond the diffraction limit can be achieved even in the absence of the evanescent waves. That is, it is incorrect or at least incomplete to believe that a microscope that collects only the propagating waves is limited by the diffraction. Our studies show that a scanning near-field optical microscope can achieve resolutions beyond the diffraction limit by collecting only the propagating waves.     

光子扫描隧道显微镜球形样品二维近场强度分析

采用时域有限差分方法计算全内反射和光子扫描隧道显微镜系统。光子扫描隧道显微镜的基本工作原理是隐失波的产生和探测，当入射光在两种介质的分界面上发生全内反射，并在界面处产生非辐射的电磁波——隐失波时，采取对两界面入射光进行分别设置的方法即“三波法”设置入射激励元。分别计算一个球和两个球形样品的近场分布，并计算散射小球为探针，一个球为样品的扫描图像。结果表明：采用二维时域有限差分方法计算能较直观地显示样品表面的近场分布。表明时域有限差分方法在光子扫描隧道显微镜理论研究中具有很大潜力。     

Simulated Output Images of Near-Field Optics by Volume Integral Equation: Object Placed on the Dielectric Substrate

We investigated near-field optical (NFO) imaging characteristics of a small object placed on a dielectric slab by a computer-code using a three-dimensional volume integral equation with an effective iteration technique called the generalized minimal residual method. A simplified three-dimensional NFO microscope that consists of a small dielectric object placed on the dielectric substrate and a small dielectric sphere as a scanning probe-tip was considered. Calculating two-dimensional output images obtained from scattered far fields, we studied the effect of the substrate on NFO output images, the comparison of NFO output images with electrostatic field around the small object, the dependence of output image characteristics on the wavelength and the difference of imaging characteristics between incident plane waves and incident evanescent waves.     

Stress analysis of multiple anisotropic elliptical inclusions in composites

A volume integral equation method is introduced for the solution of elastostatic problems in an unbounded isotropic elastic solid containing interacting multiple anisotropic elliptical inclusions subject to uniform remote tension or remote in-plane shear. This method is applied to two-dimensional problems involving long parallel elliptical cylindrical inclusions. A detailed analysis of the stress field at the interface between the matrix and the central elliptical inclusion is carried out for square and hexagonal packing of anisotropic inclusions. The effects of the number of anisotropic inclusions and various inclusion volume fractions on the stress field at the interface between the isotropic matrix and the central elliptical cylindrical inclusion are investigated in detail. The stress field at the interface between the isotropic matrix and the central elliptical inclusion is also compared with that between the isotropic matrix and the central circular inclusion.     

Studies on Fast Algorithm for the Scattering of a Large Array of Waveguide-Fed Wide-Slot Antennas in Millimeter Wave Region

We present an effective numerical technique to characterize the scattering of wide-slot antennas fed by waveguides with arbitrary terminations in terms of the method of moment (MoM) and the mixed potential integral equation (MPIE). In particular, the precorrected-fast Fourier transform (P-FFT) eliminates the need to generate and store the usual square impedance matrix andthus leads to speed up the matrix-vector multiplication in the resultant system. This property makes the Rao-Wilton-Glisson (RWG) functions to be useful in simulating electrically large-scale problems. In addition, the scattering from the finite ground surfaces is accounted for in the total scattered field by using the method of equivalent edge currents. The numerical results are presented and compared with both the traditional method of moment results obtained using the entire-domain basis functions and the experimental results, to demonstrate the proposed method to be a good candidate for study on the scattering of arbitrary wide-slot large array.     

基于迈克耳孙干涉仪的近场光学实验

介绍了一种以迈克耳孙干涉仪作为操作平台的近场光学实验系统.该系统可以测量棱镜内表面全内反射产生的隐失场,观察两维光栅样品的近场光学结构,还可以用于光子扫描隧穿显微镜(PSTM)的原理性实验,有助于学生深入了解隐失场的结构和近场光学显微镜的基本工作原理.该装置具有结构简单可靠,操作简便等特点,十分适用于物理实验教学.     

Apertureless near-field laser nanotechnology

We consider apertureless near-field optics that provides subwavelength resolution. We study the enhancement of the electromagnetic field near nanospheres and under the tip of a scanning probe microscope using the finite difference time-domain (FDTD) method. We discuss the mechanisms of field enhancement connected with the system geometry (“lightning rod effect”) and resonance excitation of local plasmon eigenmodes for different materials of the tip and various geometrical parameters of the system. We describe the possible applications in nano-optics and nanotechnology. We present the experimental achievements in apertureless near-field nanolithography.     

单模及多模光纤折射率分布测量方法研究

通过对几种单模及多模光纤折射率分布测量方法的分析研究，得到单模光纤与多模光纤折射率分布测量方法的根本区别。由于单模光纤芯径比较小，因而只能用波动理论分析其传输机理，其中的远场法和近场法测量都是基于标量亥姆霍兹波动方程，即以单模光纤的基本传输理论进行测量；而多模光纤由于其芯径比较大，故而用射线理论分析其传输原理较为合理。多模光纤的折射近场法和近场扫描法均是以纤芯半径处数值孔径不同，对应的折射模和传导模不同为依据来进行测量的。     

Parameters Extraction of Millimeter Wave Circuits by Hybrid Vector Finite Element and Moment Method Combined with SOC Technique

This paper presents a hybrid method, which couples the vector finite element method (FEM) and method of moment (MOM) for analyzing the field and current distribution of the millimeter wave circuits. The FEM is applied to handle the interior region of dielectric bodies and MOM is used to solve surface integral equations. Then, These integral expressions are coupled into the FEM equations through the continuity of the tangential fields across the connection boundaries. Simultaneously, the short-open calibration (SOC) technique is used for predicting accurately the scattering parameters of the circuits. Numerical results are well compared with those published in the previous literatures.     

Ultrasonic resonance regulated near-field scanning optical microscope and laser induced near-field optical-force interaction

We have developed a novel sample-tip regulation for a near-field optical microscope: an ultrasonic resonance regulation method. The regulation range is from 0 to 50 nm. It shows not only stability, simplicity in construction, but also versatility in vacuum, magnetic field, and low temperature environments. The main advantage of this technique is that it is a non-optical detecting scheme, which is very important for near-field spectroscopy. Such construction can also be used as a force microscope to study the topography of insulating samples. The laser light induced force interaction in the near-field range has been observed for the first time, showing that aided by laser radiation, the shear force between sample and tip can be changed depending on the type of sample. This can be interpreted as the light induced optical tip-sample interaction of light pressure effect. The van der Waals dispersion energy and the optical binding energy induced by laser beam between dielectric tip and samples play important role. The effect confirms a theoretical prediction. This new technique and phenomenon will add new aspects to near-field optics.     

Use of nonsingular boundary integral formulation for reducing errors due to near-field measurements in the boundary element method based near-field acoustic holography

In the conformal near-field acoustic holography (NAH) using the boundary element method (BEM), the transfer matrix relating the vibro-acoustic properties of source and field depends solely on the geometrical condition of the problem. This kind of NAH is known to be very powerful in dealing with the sources having irregular shaped boundaries. When the vibro-acoustic source field is reconstructed by using this conformal NAH, one tends to position the sensors as close as possible to the source surface in order to get rich information on the nonpropagating wave components. The conventional acoustic BEM based on the Kirchhoff-Helmholtz integral equation has the singularity problem in the close near field of the source surface. This problem stems from the singular kernel of the Green function of the boundary integral equation (BIE) and the singularity can influence the reconstruction accuracy greatly. In this paper, the nonsingular BIE is introduced to the NAH calculation and the holographic BIE is reformulated. The effectiveness of nonsingular BEM has been investigated for the reduction of reconstruction error. Through interior and exterior examples, it is shown that the resolution of predicted field pressure could be improved in the close near field by employing the nonsingular BIE. Because the BEM-based NAH inevitably requires the field pressure measured in the close proximity to the source surface, the present approach is recommended for improving the resolution of the reconstructed source field.     

A uniform asymptotic integral representation for the fourth moment of the field of a wave propagating in a statistically homogeneous medium

In this paper, a uniform integral representation has been obtained for the fourth moment of the field of a wave propagating in a medium with random large-scale irregularities. The solution to the equation was obtained using a method of integral transformations and Maslov's complex WKB method. The representation obtained differs in its form from those reported thus far and in particular from those given by the method of two-scale expansions and the interference integral method. First, the paper considers the case of a plane wave incident on a layer with irregularities, followed by a treatment of the general case of an arbitrary source.     

近场光学显微技术

本文在介绍近场光学显微镜原理的基础上，对近场光学显微技术进行了一定深度的探讨，并着重研究了纳米级探针的制作和纳米级样品与探针间距的控制这两个近场光学显微技术中的关键问题，说明了近场光学显微探针的工作方式，阐述了近场光学成像的衬度类型，介绍了近场光学显微技术在多个领域的应用。在参考大量国内外最新研究成果的基础上，提出了一些个人的见解。     

Theory of Atom Optics: Feynman’s Path Integral Approach

The present theory of atom optics is established mainly on the Schrödinger equations or the matrix mechanics equation. The authors present a new theoretical formulation of atom optics: Feynman’s path integral theory. Its advantage is that one can describe the diffraction and interference of atoms passing through slits (or grating), apertures, and standing wave laser field in Earth’s gravitational field by using a type of wave function and calculation is simple. For this reason, we derive the wave functions of particles in the following configurations: single slit (and slit with the van der Waals interaction), double slit, N slit, rectangular aperture, circular aperture, the Mach-Zehnder-type interferometer, the interferometer with the Raman beams, the Sagnac effect, the Aharonov-Casher effect, the Kapitza-Dirac diffraction effect, and the Aharonov-Bohm effect. The authors give a wave function of the state of particles on the screen in abovementioned configurations. Our formulas show good agreement with present experimental measurements.