Digital holographic reconstruction of a local object field using an adjustable magnification

In the research of digital holography, this paper presents a numerical method using an adjustable magnification for local object field reconstruction together with experiment verification. The method first designs a spherical wave according to the given magnification to illuminate the digital hologram, then through a Fourier transform of diffraction, it calculates the reconstructed image plane. Afterward, a filtering window is set in the image plane to extract the image of the local object field, and then the object field reached hologram plane is formed using diffraction's inverse operation. Finally, the object field is reconstructed through diffraction's angular spectrum theory.     

Closed-form approximations for the angle-of-arrival variance of plane and spherical waves propagating through homogeneous and isotropic turbulence

The calculation of the aperture-averaged angle-of-arrival variance, observed with a telescope with a circular aperture, of a plane or spherical wave propagating through homogeneous and isotropic turbulence is one of the classical problems in the theory of wave propagation through random media. We present and discuss approximate closed-form solutions on the basis of the Rytov approximation. For both plane and spherical waves, the accuracy of the approximations is better than 0.25% for all ratios of aperture diameter and Fresnel length.     

Electromagnetic applications of a new finite-difference calculus

The accuracy of finite-difference analysis in electromagnetics can be qualitatively improved by employing arbitrary local approximating functions, not limited to Taylor expansion polynomials. In the proposed new class of flexible local approximation methods (FLAME), desirable local analytical approximations (such as harmonic polynomials, plane waves, and cylindrical or spherical harmonics) are directly incorporated into the finite-difference scheme. Although the method usually (but not necessarily) operates on regular Cartesian grids, it is in some cases much more accurate than the finite-element method with its complex meshes. This paper reviews the theory of FLAME and gives a tutorial-style explanation of its usage. While one motivation for the new approach is to minimize the notorious "staircase" effect at curved and slanted interface boundaries, it has much broader applications and implications. As illustrative examples, the paper examines the simulation of: 1) electrostatic fields of finite-size dielectric particles in free space or in a solvent with or without salt; 2) scattering of electromagnetic waves; 3) plasmon resonances; and 4) wave propagation in a photonic crystal.     

Optical response of a single spherical particle in a tightly focused light beam: application to the spatial modulation spectroscopy technique

We develop a new and numerically efficient formalism to describe the general problem of the scattering and absorption of light by a spherical metal or dielectric particle illuminated by a tightly focused beam. The theory is based on (i) the generalized Mie theory equations, (ii) the plane-wave decomposition of the converging light beam, and (iii) the expansion of a plane wave in terms of vector spherical harmonics. The predictions of the model are illustrated in the case of silver nanoparticles. The results are compared with the Mie theory in the local approximation. Finally, some effects related to the convergence of the beam are analyzed in the context of experiments based on the spatial modulation spectroscopy technique.     

Extension of geometrical-optics approximation to on-axis Gaussian beam scattering. I. By a spherical particle

The geometrical-optics approximation of light scattering by a transparent or absorbing spherical particle is extended from plane wave to Gaussian beam incidence. The formulas for the calculation of the phase of each ray and the divergence factor are revised, and the interference of all the emerging rays is taken into account. The extended geometrical-optics approximation (EGOA) permits one to calculate the scattering diagram in all directions from 0 degrees to 180 degrees. The intensities of the scattered field calculated by the EGOA are compared with those calculated by the generalized Lorenz-Mie theory, and good agreement is found. The surface wave effect in Gaussian beam scattering is also qualitatively analyzed by introducing a flux ratio factor. The approach proposed is particularly important to the further extension of the geometrical-optics approximation to the scattering of large spheroidal particles.     

Expansion of an arbitrarily oriented, located, and shaped beam in spheroidal coordinates

Within the framework of the generalized Lorenz-Mie theory (GLMT), the incident shaped beam of an arbitrary orientation and location is expanded in terms of the spheroidal vector wave functions in given spheroidal coordinates. The beam shape coefficients (BSCs) in spheroidal coordinates are computed by the quadrature method. The classical localization approximation method for BSC evaluation is found to be inapplicable when the Cartesian coordinates of the beam and the particle are not parallel to each other. Once they are parallel, all the symmetry relationships existing for the BSCs in spherical coordinates (spherical BSCs) [J. Opt. Soc. Am. A11, 1812 (1994)] still pertain to the BSCs in spheroidal coordinates (spheroidal BSCs). In addition, the spheroidal BSCs computed by our method are verified by comparing them with those evaluated by Asano and Yamamoto for plane wave incidence [Appl. Opt.14, 29 (1975)]. Furthermore, formulas are given for field reconstruction from the spheroidal BSCs, and consistency is found between the original incident fields and the reconstructed ones.     

Potential and limits of holographic reconstruction algorithms

For the purpose of ultrasonic nondestructive testing of materials, holography in connection with digital reconstruction algorithms has been proposed as a modern tool to extract crack sizes from ultrasonic scattering data. Defining the typical holographic reconstruction algorithm as the application of the scalar Kirchhoff diffraction theory to backward wave propagation, we demonstrate its general incapability of reconstructing equivalent sources, and hence, geometries of scattering bodies. Only the special case of a planar measurement recording surface, that is to say, a hologram plane, and a planar crack with perfectly rigid boundary conditions parallel to the hologram plane and perpendicular to the incident field yields a nearly perfect correlation between crack size and reconstructed image; the reconstruction algorithm is then referred to as the Rayleigh-Sommerfeld formula; it therefore represents the optimal case matched to that special geometrical situation and, hence, may be interpreted as a quasi-matched spatial filter. Using integral equation theory and physical optics, we compute synthetic holographic data for a linear cracklike scatterer for both plane and spherical wave incidence, the latter case simulating a synthetic aperture impulse echo situation, thus illustrating how the Rayleigh-Sommerfeld algorithm or its Fresnel approximation increasingly fail for cracks inclined to the hologram plane and excited nonperpendicularly. Furthermore, we point out how the physical data recording process may additionally influence the reconstruction accuracy, and, finally, guidelines for a careful and serious application of these holographic reconstruction algorithms are given. The theoretical results are supported by measurements.     

Single-scattering theory of light diffraction by a circular subwavelength aperture in a finitely conducting screen

A perturbation theory based on a single-scattering approximation is developed from the rigorous differential theory of diffraction in cylindrical coordinates. It results in analytical formulas in the inverse space for the field amplitudes providing results that are in quantitative agreement with the results of the rigorous method, in both the near- and far-field regions, when a proper correction to the incident field inside the aperture is made by using the renormalized Born approximation. When working in reflection by a screen having permittivity high in modulus, the method proposes an equivalence with the simple model consisting of the emission by a single magnetic dipole excited inside the pierced layer, emission that is then transferred back into the cladding following the Fresnel's coefficients of transmission from the layer into the cladding. The theory predicts a directivity of the radiation pattern that increases for smaller values of modulus of permittivity, both for dielectrics and metals, thus independently of the possibility of plasmon surface wave excitation along the interface. The theory can take into account such surface wave resonances, as well as the waveguide supported by a dielectric slab, but cannot implicitly recognize the modes carried out by the cylindrical waveguide corresponding to the aperture. This fact limits its domain of validity when used in transmission, although the far- and near-field maps can be reconstructed sufficiently well within a multiplicative factor corresponding to the enhanced transmission due to the excitation of these modes.     

Irradiance-variance behavior by numerical simulation for plane-wave and spherical-wave optical propagation through strong turbulence

We have simulated optical propagation through atmospheric turbulence in which the spectrum near the inner scale follows that of Hill and Clifford [J. Opt. Soc. Am. 68, 892 (1978)] and the turbulence strength puts the propagation into the asymptotic strong-fluctuation regime. Analytic predictions for this regime have the form of power laws as a function of beta0(2), the irradiance variance predicted by weak-fluctuation (Rytov) theory, and l0, the inner scale. The simulations indeed show power laws for both spherical-wave and plane-wave initial conditions, but the power-law indices are dramatically different from the analytic predictions. Let sigmaI(2) - 1 = a(beta0(2)/betac(2))-b(l0/Rf)c, where we take the reference value of beta0(2) to be betac(2) = 60.6, because this is the center of our simulation region. For zero inner scale (for which c = 0), the analytic prediction is b = 0.4 and a = 0.17 (0.37) for a plane (spherical) wave. Our simulations for a plane wave give a = 0.234 +/- 0.007 and b = 0.50 +/- 0.07, and for a spherical wave they give a = 0.58 + /- 0.01 and b = 0.65 +/- 0.05. For finite inner scale the analytic prediction is b = 1/6, c = 7/18 and a = 0.76 (2.07) for a plane (spherical) wave. We find that to a reasonable approximation the behavior with beta0(2) and l0 indeed factorizes as predicted, and each part behaves like a power law. However, our simulations for a plane wave give a = 0.57 +/- 0.03, b = 0.33 +/- 0.03, and c = 0.45 +/- 0.06. For spherical waves we find a = 3.3 +/- 0.3, b = 0.45 +/- 0.05, and c = 0.8 +/- 0.1.     

焦区附近球形粒子对高斯光束的弹性散射

本文应用复源球面波理论,将高斯光束场按矢量球波函数展开,对高斯光束入射到单个球形粒子上时的弹性散射问题进行了理论分折。并对球形粒子在波束传播轴上时的远场散射光强角分布进行了数值计算,同时还与平面波散射的结果进行了比较。     

Caustics in a meridional plane produced by plano-convex conic lenses

We study the formation of caustic surfaces formed in both convex-plano and plano-convex conic lenses by considering a plane wave incident on the lens along the optical axis. By using the caustic formulas and a paraxial approximation, we derive analytic expressions to evaluate the spherical aberration to the third order, and a formula to reduce this aberration is provided. Furthermore, we apply the formulas to evaluate the circle of least confusion for a positive lens as a function of all parameters involved in the process of refraction through the conic lenses.     

Generalized Investigations into the Brewster Angle

The standard elementary theory of the Brewster angle generated by a plane interface separating two homogeneous isotropic media, through which incident and transmitted electromagnetic waves are propagating, is well known. We introduce here a more general inhomogeneous medium for which a Brewster wave and a Brewster angle can be defined. The properties of this wave are investigated, together with a model whose field can be expressed in terms of a special degenerate hypergeometric function. Other angles of incidence also yield zero reflectivity, but these are carefully distinguished from the Brewster angle.     

First-principles calculations of ground-state and high-pressure phase of magnesium telluride

We study the ground-state properties of MgTe and the behavior under pressure using the new full potential augmented plane wave plus local orbital method (FP-LAPW + lo) within the local spin density approximation (LSDA) to density functional theory. The calculations were performed in the rocksalt (B1), cesium chloride (B2), zincblende (B3), wurtzite (B4) and nickel arsenide (B8₁) type structures. Our calculations clearly indicate that there is a structural transition from the B8 to B2, confirming recent experimental suggestions and also show that the ground-state phase of MgTe is the nickel arsenide (B8₁) structure.     

Wave-optical structure design with the local plane-interface approximation

Abstract

The design of an optical element profile with specified transmission function for a given incident wave is of fundamental concern in optical design. A well-known example is the design of an aspherical surface in order to realize a spherical phase-only transmission. Various wave-optical system design methods lead to transmission functions as a first step. Then, often the thin-element approximation is applied in a second step to obtain an element structure with the desired transmission. However, if the refraction at the optical interface cannot be neglected, the thin-element approximation is not valid. In this case, a higher version of the local plane-interface approximation can be used for the element structure design. An algorithm for this model is introduced and its characteristics are discussed for the example of a non-paraxial Gaussian-to-tophat beam shaping element.     

空间相干光通信外差效率及天线像差的影响

空间相干光通信中接收天线像差会使光外差效率下降.对本振光为高斯分布,信号光为爱里斑分布的光外差效率进行了研究,给出了无像差时外差效率的解析表达式.当焦平面上爱里斑半径与本振高斯光束光腰半径之比为1.71时,有最大外差效率81.45%.然后以本振光为理想的高斯光束,信号光受像差的影响,研究了倾斜、离焦、球差、彗差、像散等像差引起的光外差效率损失,给出了存在像差时外差效率的一维积分表达式.研究表明即使在采用离焦校正后,一个波长的球差引起的附加外差效率损失仍可达0.9 dB.因此对于爱里斑位于光轴上的接收天线,在设计时需仔细处理球差的影响.     

The disturbance of a plane dyadic wave by a small spherical cavity

Dyadic scattering offers a general setting for solving wave-obstacle interaction problems in Continuum Mechanics, because it eliminates the direction of polarization from the scattering formulation. Once the dyadic problem has been solved, any classical scattering problem for the displacement field is recoverable through a contraction with the given polarization. In the present work we solve the scattering problem of a plane dyadic incident field which is disturbed by a spherical cavity in the medium of propagation. The cavity is considered to be small in the sense that its characteristic dimension is much less than the wave length of the incident field. The zeroth and the first order low-frequency approximations of the near field as well as the leading approximation of the far-field (which is of the third order) are obtained explicitly via an appropriate generalization of the Papkovich representation for dyadic fields. The leading approximation of the scattering cross-section is also provided. The results are then used to check the credibility of related vector results obtained from the Boundary Element Method and an amazing coincidence is observed, at least for small enough frequencies.     

Uniform rational approximation of functions of several variables

We present a program which has given excellent results for uniform approximation of functions by polynomials, rational functions, generalized polynomials, and generalized rational functions. The algorithm is described in detail and several examples are discussed. The approximation is done over a finite point set, which is commonly a set of real numbers or points in the plane (in the latter case we are doing what is often known as surface fitting). Input to and output from the program is in tabular form. The method used is a linear programming approach known as the differential correction algorithm, which has been shown by several authors to always converge in theory (quadratically in some situations). In practice, we have obtained convergence in nearly every case, and quadratic convergence in most cases. The program can also be used for simultaneous approximation of several functions.     

圆柱壳辐射声场重构的波叠加方法

将声全息技术应用到水下结构的声场重建问题中。通过理论推导和数值仿真,分析一两端带半球帽的圆柱壳模型在不同激励作用下声场的重建效果及影响重建精度的因素。考虑到实际应用,全息面分别采用柱形全息面和平行的双平面全息面。仿真结果表明,该方法是一种稳健的全波数空间声场重构技术;其重建精度受到等效源面参数、全息面参数及测量环境信噪比等多因素的影响;在含有测量噪声的条件下,应用Tikhonov结合L曲线的正则化方法仍可以较精确地重构声场;相比于其它方法,波叠加方法具有测点少,计算速度快等优点,有很好的应用前景。     

Properties of caustics produced by a positive lens: meridional rays

We study the formation of the caustic surfaces formed in both convex-plane and plano-convex spherical lenses by considering a plane wave incident on the lens along the optical axis. Using the caustic formulas and a paraxial approximation we derive analytical expressions to evaluate the spherical aberration to third order. Furthermore, we apply the formulas to evaluate the circle of least confusion for a positive lens.     

Reflection and refraction of plane waves at interface between two piezoelectric media

This paper analyses reflection and refraction of plane waves at a perfect interface between two anisotropic piezoelectric media. The equations of elastic waves, quasi-static electric field, and constitutive relationships for the piezoelectric media are derived. A solution based on the inhomogeneous wave theory is developed to address the inconsistency between the numbers of independent wave modes in the media and the numbers of interfacial boundary conditions to obtain accurate reflection and refraction coefficients in case of strong piezoelectric media, where all the elastic and electric continuity conditions across the interface are satisfied simultaneously. The study shows that there exist independent and zero energy wave modes satisfying the general Snell’s law and propagating along the interface for any incident wave angle. These waves can be treated as pseudo surface waves. It is further found that all the reflection/refraction waves including the pseudo surface waves obey the energy conservation law at the interface boundary. In addition, the analysis also reveals that the reflection and refraction elastic waves can turn into pseudo surface waves at some critical incident angles.