Scattering of a pulsed wave by a sphere with an eccentric spherical inclusion

A dielectric sphere with an eccentric spherical dielectric inclusion and an incident amplitude-modulated plane electromagnetic wave constitute an exterior radiation problem, which is solved in this paper. A solution is obtained by combined use of the Fourier transform and the indirect-mode-matching method. The analysis yields a set of linear equations for the wave amplitudes of the frequency-domain expansion of the electric-field intensity within and outside the externally spherical inhomogeneous body; that set is solved by truncation and matrix inversion. The shape of the backscattered pulse in the time domain is determined by application of the inverse fast Fourier transform. Numerical results are shown for a pulse backscattered by an acrylic sphere that contains an eccentric spherical cavity. The effects of cavity position and size on pulse spreading and delay are discussed.     

Investigating the enhancement of three-dimensional diffraction tomography by using multiple illumination planes

The three dimensional (3-D) extension of the two well-known diffraction tomography algorithms, namely, direct Fourier interpolation (DFI) and filtered backpropagation (FBP), are presented and the problem of the data needed for a full 3-D reconstruction is investigated. These algorithms can be used efficiently to solve the inverse scattering problem for weak scatterers in the frequency domain under the first-order Born and Rytov approximations. Previous attempts of 3-D reconstruction with plane-wave illumination have used data obtained with the incident direction restricted at the xy plane. However, we show that this restriction results in the omission of the contribution of certain spatial frequencies near the omegaz axis for the final reconstruction. The effect of this omission is studied by comparing the results of reconstruction with and without data obtained from other incident directions that fill the spatial frequency domain. We conclude that the use of data obtained for incident direction in only the xy plane is sufficient to achieve a satisfactory quality of reconstruction for a class of objects presenting smooth variation along the z axis, while abrupt variations along the z axis cannot be imaged. This result should be taken into account in the process of designing the acquisition geometry of a tomography scanner.     

Inverse scattering of buried inhomogeneous biaxial dielectric cylinders coated on a conductor

The inverse scattering of buried inhomogeneous biaxial dielectric cylinders coated on a conductor with known cross section is investigated. Dielectric cylinders with known cross section coated on a conductor of unknown permittivities are buried in one half space and scatter a group of unrelated waves incident from another half space where the scattered field is recorded. By proper arrangement of the various unrelated incident fields, the difficulties of ill‐posedness and nonlinearity are circumvented, and the permittivity distribution can be reconstructed through simple matrix operations. The algorithm is based on the moment method and the unrelated illumination method. Numerical results are given to demonstrate the capability of the inverse algorithm. Good reconstruction is obtained both with and without Gaussian noise in measured data. In addition, the effect of noise on the reconstruction result is also investigated. © 2008 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 18, 228–236, 2008; Published online in Wiley InterScience (www.interscience.wiley.com).     

Inversion of reflection data in an isotropic multilayered medium

Summary In the time domain, the inverse problem using reflection data is investigated for a number of homogeneous (isotropic) layers which are sandwiched betweeen two homogeneous half spaces. The present approach is applicable to elastic as well as electromagnetic waves. The main feature of the approach is that the reflected wave is determined through the incident pulse in a simple explicit way by applying properly the consequences of the continuity conditions at interfaces separating the layers. The time record of the reflected wave provides then the travel time across the single layer and hence its impedance, by means of simple recursive algebraic operations.     

Electromagnetic transverse electric-wave inverse scattering of a conductor by the genetic algorithm

The genetic algorithm is used to reconstruct the shape of a perfectly conducting cylinder illuminated by transverse electric (TE) waves. A cylinder of unknown shape scatters the incident TE wave in a free space and the scattered field is recorded outside. Based on the boundary condition and the measured scattered field, a set of nonlinear integral equations is derived and the imaging problem is reformulated into an optimization problem. The genetic algorithm is then employed to find out the global extreme solution of the cost function. Numerical results demonstrated that the genetic algorithm can tackle the inverse problem of a larger scatterer. Even when the electrical dimension of the scatterer exceeds one wavelength and the initial guess is far from the exact one, good reconstruction was obtained. In such a case, gradient-based methods often get stuck in a local extreme. In addition, the effect of Gaussian noise on the reconstruction results is investigated. © 1998 John Wiley & Sons, Inc. Int J Imaging Syst Technol, 9, 388–394, 1998     

Robust topology optimization of optical cloaks under uncertainties in wave number and angle of incident wave

This article presents a robust topology optimization method for optical cloaks under uncertainties in the wave number and angle in the incident wave. We first discuss the governing equation derived from Maxwell's equation, and extend it to the entire domain including the dielectric material and air, based on the level set-based topology optimization method. Next, a robust optimization problem is formulated as a minimization problem of the weighted sum of the scattered wave norm and its standard deviation with respect to the wave number and angle of the incident wave. The standard deviation is mathematically expressed by the Taylor series approximation and the use of the adjoint variable method. The design sensitivity of the objective functional is also derived by the adjoint variable method. An optimization algorithm is then constructed, based on the proposed formulation for robust designs of optical cloaks. Several numerical examples are finally provided to demonstrate the validity and utility of the proposed method.     

Image reconstruction for a partially immersed imperfectly conducting cylinder by genetic algorithm

This article presents a computational approach to the imaging of a partially immersed imperfectly conducting cylinder. An imperfectly conducting cylinder of unknown shape and conductivity scatters the incident transverse magnetic (TM) wave in free space while the scattered field is recorded outside. Based on the boundary condition and the measured scattered field, a set of nonlinear integral equations, and the inverse scattering problem are reformulated into an optimization problem. We use genetic algorithm (GA) to reconstruct the shape and the conductivity of a partially immersed imperfectly conducting cylinder. The genetic algorithm is then used to find out the global extreme solution of the cost function. Numerical results demonstrated that, even when the initial guess is far away from the exact one, good reconstruction can be obtained. In such a case, the gradient‐based methods often get trapped in a local extreme. In addition, the effect of random noise on the reconstruction is investigated. © 2009 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 19, 299–305, 2009     

A marching-on-in-time method for 2-D transient electromagnetic scattering from homogeneous, lossy dielectric cylinders using boundary elements

A method for determining the fields scattered by arbitrarily shaped cylindrical, lossy dielectric structures with a transient incident wave is described. The transient scattering problem is reduced to the solution of a time-domain integral equation which is solved directly in the time domain by a time-stepping method. As the scatterer is homogeneous, the solution can be obtained by means of a boundary integral formulation and the problem-independent free-space Green's function. The approximate electromagnetic impulse response for a number of cylindrical targets is calculated using this method.<>     

A computational inverse diffraction grating problem

Consider the diffraction of a time-harmonic plane wave incident on a perfectly reflecting periodic surface. A continuation method on the wavenumber is developed for the inverse diffraction grating problem, which reconstructs the grating profile from measured reflected waves a constant distance away from the structure. Numerical examples are presented to show the validity and efficiency of the proposed method.     

频域测量中的慢极化效应

对同一钛酸锶钡陶瓷样品作了频域和时域介电测量.在10^-3Hz至10⁴Hz范围可以测出复介电常数.但时域测量表明样品的慢介电常数甚大于快介电常数.实验观察到在正弦外电压作用下通过样品的电流主要是不遵从RLC电路方程的慢极化效应所提供.这时的复介电常数的意义成为存在争议的复杂问题.     

Multistatic-multiview resolution from Born fields for strips in Fresnel zone

We address the inverse scattering problem of estimating the resolution limits achievable in the reconstruction of a dielectric strip object within a two-dimensional and scalar geometry. The scattered field is observed over a bounded rectilinear domain located in the Fresnel zone, and a single-frequency multistatic-multiview configuration is considered. The analysis is performed by casting the problem as the inversion of the linearized scattering operator arising from the Born approximation and by means of its singular-value decomposition. Finally, the role of the geometrical parameters of the measurement configuration is highlighted.     

An Efficient Inverse Scattering Algorithm for a Complex Cylinder Buried in a Three Layer Structure

In this paper, we present a computational approach to the imaging of a complex cylinder object buried in three layers by the unrelated illumination method. The electromagnetic imaging for a complex cylinder object buried in three layers by transverse electric (TE) wave illumination is investigated. A dielectric cylinder of unknown permittivities coated on a conductor with known cross section are buried in the second layer and scatter a group of unrelated TE waves incident from the first layer where the scattered field is recorded. By proper arrangement of the various unrelated incident fields, the difficulties of ill-posedness and nonlinearity are circumvented, and the permittivity distribution can be reconstructed through simple matrix operations. The algorithm is based on the moment method and the unrelated illumination method. Numerical results show that good reconstruction has been obtained both with and without Gaussian noise in measured data. In addition, the effects of noise are also investigated.     

Image reconstruction of buried inhomogeneous dielectric cylinders coated on a conductor

The image reconstruction of buried inhomogeneous dielectric cylinders coated on a conductor with known cross‐section is investigated. Inhomogeneous dielectric cylinders coated on a conductor is buried in one half space and scatter a group of unrelated waves incident from another half space, where the scattered field is recorded. By proper arrangement of the various unrelated incident fields, the difficulties of ill‐posedness and nonlinearity are circumvented, and the permittivity distribution can be reconstructed through simple matrix operations. The algorithm is based on the moment method and the unrelated illumination method. Numerical results show that good reconstruction has been obtained both with and without Gaussian noise in measured data. © 2005 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 15, 172–177, 2005     

Application of the sinc basis moment method to the reconstruction of infinite circular cylinders

A solution of the ultrasonic scattering and inverse scattering problem has been obtained by solving the inhomogeneous Helmholtz wave equation by the sinc basis moment method. In this numerical study, the algorithm of S.A. Johnson and M.L. Tracy (1983) has been applied to the reconstruction of an infinite circular cylinder that is subject to an incident cylindrical wave of ultrasound and is surrounded by a homogeneous coupling medium. For weak scattering cylinders, successful reconstructions have been obtained using the known exact solution for the scattered field as the input data for the algorithm. A detailed discussion of sampling requirements for this algorithm is presented, and the threshold derived correlates well with results of a numerical study of variation of the sampling density. Effects of varying object contrast, object size, grid size, sampling density, and method of iteration are investigated. Because the algorithm is slow, optimization of computation is described.     

Solution of convergence problem in ultrasound inverse scattering tomography

When the product of contrast and size of an object, which is to be reconstructed by using the ultrasound inverse scattering tomography algorithm, is large, it is well known that those algorithms fail to converge to a unique global minimum. In order to solve this well known and difficult convergence problem, in this paper we present a new method, which converges to the true solution, for obtaining the scattering potential without using the Born or Rytov approximation. This method converts the nonlinear nature of the problem into a linear one. Through computer simulations we will show the validity of the new approach for high contrast two-dimensional scattering objects which are insonified by an incident ultrasound plane wave. Numerical results show that the reconstruction error is very small for circularly symmetric two-dimensional cylindrical objects whose refractive indices range from small to even sufficiently large values for which the previous inverse scattering algorithms fail to converge.     

A hybrid experimental/numerical approach to characterize interfacial adhesion in multilayer low-κ thin film specimens

The strength of multilayer low dielectric (low-κ) constant organo-silicate glass (OSG) and silicon-carbon-nitride (SiCN) thin film interfaces is characterized by a laser spallation technique. Two specimen sets with different OSG/SiCN stacking sequences are evaluated. The effect of helium (He) pretreatment is also investigated. The stress at the low-κ interface is enhanced through the use of a fused silica backing layer to shape the incident pulse and the addition of a thin gold (Au) top layer to increase inertial force during the dynamic failure event. The weakest interface in the multilayer stack (first to fail) is identified through optical images, profilometry and scanning electron microscope images of the spallation zone. The strength of the failed interface is inferred from the incident stress history in combination with a one dimensional dynamic wave propagation analysis. The adhesion strength of the OSG/SiCN interface (372 MPa) is 32% larger than that of Si/OSG (282 MPa) for specimens with no He pretreatement. The interfacial strength of both interfaces is significantly increased by a He pretreatment, making failure by spallation difficult.     

Reflection and transmission of strongly focused light beams at a dielectric interface

The reflection and transmission of tightly focused azimuthally, radially and linearly polarized electromagnetic wave beams with subwavelength spot size and wavefront curvature at a dielectric interface are investigated. For a given wavefront radius, the existence of the optimal radius of beam spot corresponding to a minimal reflectance and maximal transmittance is shown. Significant lateral shift in the transmitted intensity peak is revealed for strongly focused azimuthally and radially polarized beams that are normally incident to an interface. The reflection and transmission of transverse-electric- and transverse-magnetic- polarized extremely narrow wave beams which are obliquely incident on the dielectric interface is analysed. Disappearance of the Brewster angle and total internal reflection effects for the strongly focused beams are predicted. The change in beam profile after reflection and transmission for different polarizations, incident beam spots and incidence angles are analysed.     

A microwave inverse scattering technique for image reconstructionbased on a genetic algorithm

The problem of reconstructing locations, shapes, and dielectric permittivity distributions of two-dimensional dielectric objects from measurements of the scattered electric field is addressed. A numerical approach is proposed which is based on a multi-illumination multiview processing. In particular, the inverse problem is recast as a global nonlinear optimization problem, which is solved by a genetic algorithm. The final objective of the approach is the image reconstruction of highly contrasted bodies     

The electromagnetic envelope soliton propagating in a dielectric

The interaction of electromagnetic radiation with a dielectric medium is described in terms of the Schrödinger equation with a logarithmic nonlinearity, and a single-soliton solution to this equation is found. It is shown that an envelope of the electromagnetic wave momentum varies according to the Gauss law. The wave momentum is calculated for certain values of the dielectric medium and the incident wave parameters.     

Near-field optical properties and surface plasmon effects generated by a dielectric hole in a silver-shell nanocylinder pair

Near-field optical properties and surface plasmon effects in a silver-shell nanocylinder pair with five different dielectric holes (DHs) that interact with a transverse magnetic mode incident plane wave are simulated by use of the finite-element method, which includes the investigation of particle-particle interaction. The proposed structure exhibits a redshifted localized surface plasmon that can be tuned over an extended wavelength range by varying the dielectric constant in DHs and the thickness of the nanocylinder silver shell. The increase in the near-field intensity is attributed to a larger effective size of DH that is filled with a higher refractive medium.