Andrey Semichaevsky

Phase-space interpretation of deterministic phase retrieval.

Deterministic phase retrieval is reinterpreted in terms of phase-space optics. A novel derivation of the transport-of-intensity equation is presented based on the Wigner distribution function and the ambiguity function. The phase retrieval problem is formulated as estimating the local first-order moment of the Wigner function from intensity information. A comparison with phase-space tomography suggests a generalization of deterministic phase retrieval that provides larger flexibility for signal recovery. In addition, one particular numerical implementation of generalized deterministic phase retrieval is presented. Simulated intensity data are used to validate the method.

HOMOGENIZATION OF METAMATERIAL-LOADED SUBSTRATES AND SUPERSTRATES FOR ANTENNAS

This article deals with an approach to the design of planar antennas that use metamaterial-loaded substrates based on the effective medium approximations. Metamaterials are structured composite materials with unique electromagnetic properties due to the interaction of electromagnetic waves with the finer scale periodicity of conventional materials. They may be used to modify the effective electromagnetic parameters of planar antenna substrates and to design antennas with the improved coupling to the feed, increased impedance matching bandwidths, miniaturized dimensions, and narrower beamwidths compared to those that use conventional dielectric materials for the same purposes. The electromagnetic analysis and optimization based on the effective medium approximations of metamaterials is very convenient since it deals with only a few bulk medium parameters instead of a large number of parameters describing a discrete structure. At the same time, the most common way of obtaining these effective medium parameters is transmission/reflection simulations or measurements in free space or in a homogeneous background medium. For a host medium which is not homogeneous, as for a grounded substrate, the effective medium parameters are different from the free space ones. The scattering losses in a metamaterial medium need to be accurately taken into account and included as parameters in full-wave bulk medium models. For this reason, in the effective medium approach for antenna substrates, one needs to use the appropriate effective medium approximations that take the coupling between inclusions into account and also to evaluate the effects of the scattering losses. In practice, this is done by finding the effective medium parameters inside an arbitrary substrate medium, and not in a homogeneous host medium or in free space. This paper presents the methodology and the results of FDTD analysis of planar antennas that have substrates

Novel BI-FDTD approach for the analysis of chiral cylinders and spheres

A versatile time-domain technique, known as bi-isotropic finite difference time domain (BI-FDTD), has recently been introduced for the numerical analysis of electromagnetic wave interactions with complex bi-isotropic media. However, to date only one-dimensional BI-FDTD schemes have been successfully implemented. This paper presents novel two-dimensional (2-D) and three-dimensional (3-D) dispersive BI-FDTD formulations for the first time. The update equations for these new 2-D and 3-D BI-FDTD approaches are developed and applied to the analysis of electromagnetic wave scattering by chiral cylinders and spheres in free space. The distinctive feature of this technique is the use of two independent sets of wavefields representing the left- and right-polarized waves in the chiral medium. This wavefield decomposition approach allows dispersive models for the chirality parameter as well as the permittivity and permeability of the medium to be readily incorporated into an FDTD scheme. The 2-D and 3-D BI-FDTD simulation results are compared with available analytical solutions for the scattering from a circular chiral cylinder and a chiral sphere respectively

A new uniaxial perfectly matched layer absorbing boundary condition for chiral metamaterials

This paper presents a new implementation of the uniaxial perfectly matched layer absorbing boundary condition (UPML-ABC) to terminate the finite difference time domain formulation for electromagnetic wave interaction with a chiral medium. Magnetoelectric coupling in the medium is modeled via the bi-isotropic finite difference time domain (BI-FDTD) approach. The proposed perfectly matched layer uses the same wavefield decomposition approach as the BI-FDTD technique and implements the dispersion relations through finite difference equations. The new UPML formulation is illustrated with an example in which the permittivity and permeability are both represented as Lorentzian functions of frequency, and the magnetoelectric coupling, or chirality, follows the Condon model. The proposed dispersive ABC can be used to represent double-negative materials (/spl epsiv/<0 and /spl mu/<0) with magnetoelectric coupling.

Phase retrieval and phase-space tomography from incomplete data sets

The problem of signal recovery from incomplete data is investigated in the context of phase-space tomography. Particular emphasis is given to the case where only a limited number intensity measurements can be performed, which corresponds to partial coverage of the ambiguity function of the signal. Based on numerical simulations the impact of incomplete knowledge of the ambiguity function on the performance of phase-space tomography is illustrated. Several schemes to address the limited data problem are evaluated. This includes the use of prior information about the phase retrieval problem. In addition, the redundancy of phase-space representations is investigated as the means to recover the signal from partial knowledge of phase space. A generalization of deterministic phase retrieval is introduced which allows one to obtain a model based phase estimate for bandlimited functions. This allows one to use prior information for improving the phase estimate in the presence of noise.

Automated target morphing applied to objects in cluttered backgrounds

We describe an automated target tracking algorithm which is based on a linear spectral estimation technique, termed the PDFT algorithm. Typically, the PDFT algorithm is applied to obtain high resolution images from scattered field data by incorporating prior information about the target shape into the reconstruction process. In this investigation, the algorithm is used iteratively for determining the target location and a target signature which can be used as the input to an automated target recognition systems. The implementation and the evaluation of the algorithm is discussed in the context of low resolution imaging systems with special reference to foliage penetration radar and ground penetrating radar.

Novel FDTD approach for the analysis of chiral cylinders

This article deals with the analysis of electromagnetic wave scattering by a chiral cylinder in free space. Techniques for the numerical electromagnetic analysis of biisotropic media based on the finite difference time domain method have been previously proposed and investigated. One of these techniques, called BI-FDTD, is used in this paper to compute the scattered field. The distinctive feature of the technique is the use of two independent sets of wavefields representing the left- and right-polarized waves in the chiral medium. The simulation results are compared with the analytical solutions for the circular cylinder derived using the plane wave decomposition into spherical harmonics.

Unsupervised constrained radar imaging of low resolution targets

Abstract A linear spectral estimation technique, the PDFT algorithm, is used as part of a nonlinear iterative reconstruction scheme to obtain improved radar images. The iterative PDFT algorithm is used to address the limited resolution problem inherent to imaging objects buried in soil and hidden under foliage. This is achieved by subsequent application of two properties of the PDFT algorithm: the energy parameter of the PDFT algorithm is used to determine the target shape, while the shape information in turn is used to obtain super-resolved images. We describe algorithms able to exploit both properties automatically and without manual intervention. Two methods are investigated in particular, one iteratively optimizing the constraints by monitoring the energy parameter, the other method computing energy values for all points, from which a weighted prior function is determined. In addition, we discuss variants of both algorithm which provide an optimized trade-off between computation time and performance. Additional attention is given to situations, where a known target is embedded in an unknown background. Imaging results are presented for both synthetic and measured data.

Inverse scattering of strongly scattering targets using redundant data sets

For weakly scattering permittivities, each measurement of the scattered far field can be interpreted as a sampling point of the Fourier transformation of the object. Furthermore, each sampling point can be accessed by more than one combination of wavelength, propagation direction, and polarization of the incident field. This means, a set of measurements which access the same sampling point can be regarded as being redundant. For strongly scattering objects the Fourier diffraction slice theorem does not apply. We show that measurements which are redundant in the weakly scattering case can be exploited to resolve difficulties associated with imaging of the strongly scattering objects. One dimensional geometries are investigated to estimate the potential redundant data sets offer for addressing the inverse scattering problem of strongly and multiply scattering objects. In addition, we discuss preliminary results for solving 2D imaging problems.

Anything optical rays cannot do

The limits of ray optical methods to provide a valid model for describing the propagation of electromagnetic radiation are explored. We briefly review fundamentals of ray optics as well as various extensions. This review is partially intended to emphasize that existing ray based methods are able to address most, if not all, wave phenomena. In addition, we propose an extension of ray optics which interprets rays as generalized trajectories in an abstract configuration state. This allows us to propose the use of rays and ray optics as fundamental and practical concept to compute any wave phenomenon, including rigorous diffraction problems. Wave optics, in this context, becomes a convenient and efficient method to calculate the ray transfer properties. In addition, our concept facilitates interfacing conventional ray-tracing methods with wave optical methods to predict diffraction.