Localization and characterization of simple defects in finite-size photonic crystals

Structured materials like photonic crystals require for optimal use a high precision both on position and optical characteristics of the components which they are made of. Here, we present a simple tomographic algorithm, based on a specific Green's function together with a first-order Born approximation, which enables us to localize and characterize identical defects in finite-size photonic crystals. This algorithm is proposed as a first step to the monitoring of such materials. Illustrative numerical results show in particular some possibility of focalization beyond the Rayleigh criterion.Comment: submitted to Journal of the Optical Society of America

Embedding approach to modeling electromagnetic fields in a complex two-dimensional environment

An approach is presented to combine the response of a two-dimensionally inhomogeneous dielectric object in a homogeneous environment with that of an empty inhomogeneous environment. This allows an efficient computation of the scattering behavior of the dielectric cylinder with the aid of the CGFFT method and a dedicated extrapolation procedure. Since a circular observation contour is adopted, an angular spectral representation can be employed for the embedding. Implementation details are discussed for the case of a closed 434 MHz microwave scanner, and the accuracy and efficiency of all steps in the numerical procedure are investigated. Guidelines are proposed for choosing computational parameters such as truncation limits and tolerances. We show that the embedding approach does not increase the CPU time with respect to the forward problem solution in a homogeneous environment, if only the fields on the observation contour are computed, and that it leads to a relatively small increase when the fields on the mesh are computed as well

Signal processing based method for solving inverse scattering problems

The problem of reconstructing an image of the permittivity distribution inside a penetrable and strongly scattering object from a finite number of noisy scattered field measurements has always been very challenging because it is ill-posed in nature. Several techniques have been developed which are either computationally very expensive or typically require the object to be weakly scattering. I have developed here a non-linear signal processing method, which will recover images for both strong scatterers and weak scatterers. This nonlinear or cepstral filtering method requires that the scattered field data is first preprocessed to generate a minimum phase function in the object domain. In 2-D or higher dimensional problems, I describe the conditions for minimum phase and demonstrate how an artificial reference wave can be numerically combined with measured complex scattering data in order to enforce this condition, by satisfying Rouche‘s theorem. In the cepstral domain one can filter the frequencies associated with an object from those of the scattered field. After filtering, the next step is to inverse Fourier transform these data and exponentiate to recover the image of the object under test. In addition I also investigate the scattered field sampling requirements for the inverse scattering problem. The proposed inversion technique is applied to the measured experimental data to recover both shape and relative permittivity of unknown objects. The obtained results confirm the effectiveness of this algorithm and show that one can identify optimal parameters for the reference wave and an optimal procedure that results in good reconstructions of a penetrable, strongly scattering permittivity distribution

An accurate boundary value problem solver applied to scattering from cylinders with corners

In this paper we consider the classic problems of scattering of waves from perfectly conducting cylinders with piecewise smooth boundaries. The scattering problems are formulated as integral equations and solved using a Nystr\"om scheme where the corners of the cylinders are efficiently handled by a method referred to as Recursively Compressed Inverse Preconditioning (RCIP). This method has been very successful in treating static problems in non-smooth domains and the present paper shows that it works equally well for the Helmholtz equation. In the numerical examples we specialize to scattering of E- and H-waves from a cylinder with one corner. Even at a size kd=1000, where k is the wavenumber and d the diameter, the scheme produces at least 13 digits of accuracy in the electric and magnetic fields everywhere outside the cylinder.Comment: 19 pages, 3 figure

Image reconstruction of inhomogeneous biaxial dielectric cylinders buried in a slab medium

100學年度研究獎補助論文[[abstract]]The image reconstruction of inhomogeneous biaxial dielectric cylinders buried in a slab medium is investigated. A biaxial dielectric cylinder of unknown permittivities buried in a slab scatters a group of unrelated incident waves from outside. The scattered field is recorded outside the slab. 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 reconstructed results are obtained even in the presence of additive Gaussian random noise in measured data. In addition, the effect of noise on the reconstruction result is also investigated.[[incitationindex]]SCI[[incitationindex]]EI[[booktype]]紙

Buried Object Detection by an Inexact Newton Method Applied to Nonlinear Inverse Scattering

An approach to reconstruct buried objects is proposed. It is based on the integral equations of the electromagnetic inverse scattering problem, written in terms of the Green's function for half-space geometries. The full nonlinearity of the problem is exploited in order to inspect strong scatterers. After discretization of the continuous model, the resulting equations are solved in a regularization sense by means of a two-step inexact Newton algorithm. The capabilities and limitations of the method are evaluated by means of some numerical simulations

Location and Shape Reconstruction of 2D Dielectric Objects by Means of a Closed-Form Method: Preliminary Experimental Results

An analytical approach to location and shape reconstruction of dielectric scatterers, that was recently proposed, is tested against experimental data. Since the cross-sections of the scatterers do not depend on the z coordinate, a 2D problem can be formulated. A closed-form singular value decomposition of the scattering integral operator is derived and is used to determine the radiating components of the equivalent source density. This is a preliminary step toward a more complete solution, which will take into account the incident field inside the investigation domain in order to provide the dielectric features of the scatterer and also the nonradiating sources. Reconstructions of the equivalent sources, performed on some scattering data belonging to the Fresnel database, show the capabilities of the method and, thanks to the closed-form solution, results are obtained in a very short computation time