Physical Optics Solution Research Articles

Comparison of Improved Slope Uniform Theory of Diffraction with Some Geometrical Optic and Physical Optic Methods for Multiple Building Diffractions

This article presents a review of diffraction algorithms based on the uniform theory of diffraction for multiple building transition zone diffractions and proposes an improved uniform theory of diffraction model for fast and more accurate field prediction for multiple diffractions. The proposed method is based on the improved version of the slope uniform theory of diffraction and Fresnel zone concept, called the slope uniform theory of diffraction with convex hull. This article also provides a comparison for uniform theory of diffraction based algorithms and discusses the results for computation time and accuracy. Furthermore, the slope uniform theory of diffraction and the slope uniform theory of diffraction with convex hull methods are compared with a physical optics solution based on numerical computation of the Kirchhoff-Huygens integrals. Results of extensive simulations are presented and discussed for the development of fast and accurate radio network planning tools.

A UAPO-BASED MODEL FOR PROPAGATION PREDICTION IN MICROCELLULAR ENVIRONMENTS

A propagation model is presented in this paper for predicting the fleld strength in microcellular environments. According to the Geometrical Theory of Difiraction, the total fleld at a given observation point is calculated by summing the Geometrical Optics contributions and the fleld difiracted by the edges of each structure. The difiraction contributions are here evaluated by means of a Uniform Asymptotic Physical Optics solution to the corresponding canonical problem. Such a solution, expressed in terms of the standard transition function of the Uniform Theory of Difiraction, has resulted to be able to compensate the Geometrical Optics discontinuities at the shadow boundaries. In this framework, the structures are treated as constituted by lossy dielectric materials assumed to be non penetrable. The efiectiveness of the here proposed model has been tested in some typical scenarios by means of comparisons with the Finite Difierence Time Domain method.

Scattering from a cylindrical reflector: modified theory of physical optics solution

The problem of scattering from a perfectly conducting cylindrical reflector is examined with the method of the modified theory of physical optics. In this technique the physical optics currents are modified by using a variable unit vector on the scatterer's surface. These current components are obtained for the reflector, which is fed by an offset electric line source. The scattering integral is expressed by using these currents and evaluated asymptotically with the stationary phase method. The results are compared numerically by using physical optics theory, geometrical optics diffraction theory, and the exact solution of the Helmholtz equation. It is found that the modified theory of physical optics scattering field equations agrees with the geometrical optics diffraction theory and the exact solution of the Helmholtz equation.

TD-UAPO Solution for the Field Diffracted by a Junction of Two Highly Conducting Dielectric Slabs

The aim of this paper is to propose the time domain version of the Uniform Asymptotic Physical Optics solution for the field diffracted by a junction formed by two thin layers consisting of highly conducting nonmagnetic dielectrics. The incidence direction is assumed to be orthogonal to the junction. The time domain diffracted field is obtained from the knowledge of the corresponding frequency domain expression, which contains the transition function of the Uniform Geometrical Theory of Diffraction, in the hypothesis of resistive sheet having resistivity not depending on the frequency. The Veruttipong's approach is applied by taking advantage from the fact that the corresponding high-frequency solution is given as superposition of the contributions due to each half-plane. The response to an incident unit step function plane wave is considered.

A UAPO Diffraction Contribution to Take into Account the Edge Effects in Microstrip Reflectarrays

This paper describes a proposed solution for the diffraction problem related to a plane wave incident on a semi-infinite periodic structure, representative of a given distribution of equal microstrip patches. It belongs to the set of the uniform asymptotic Physical Optics solutions and allows one to account for the edge effects in the design of microstrip reflectarrays. The non-diagonal matrix related to the specular direction of reflection is considered in the Physical Optics approximation of the equivalent electric and magnetic surface currents induced on the illuminated face of the truncated structure. Such current densities are inserted in the expression of the radiation integral and the diffracted field is evaluated by performing a uniform asymptotic evaluation of the resulting integral.

Analytic Analysis of Transient Scattering From a Finite Second-Order Surface Illuminated by an Incident Plane Wave

A closed-form analytic solution based on a time-domain (TD) physical optics (PO) approximation is developed for the scattering from a finite second-order surface when illuminated by a transient impulsive plane wave. This TD-PO solution can be applied via a convolution to derive the early time transient fields scattered from the same scatterer that is illuminated by a realistic astigmatic finite-energy pulse. The closed form TD-PO solution is obtained by inverting the corresponding frequency-domain PO solution into TD. This solution can be expressed in terms of reflection and diffraction components of the scattering mechanisms as in other conventional high-frequency asymptotic solutions. Numerical examples are presented to demonstrate its physical phenomenon of the scattering mechanisms

Modified theory of physical optics solution of impedance half plane problem

The scattering of electric polarized plane waves from an impedance half plane problem is examined by the method of modified theory of physical optics (MTPO). Two integrals, consisting of incident and reflected scattered fields, are obtained. These integrals are evaluated asymptotically by the methods of stationary phase and edge point. The obtained scattered fields are compared with the exact solution numerically.

Equivalent functions for the Fresnel integral

Fresnel integral is modeled with three equivalent functions. The first function is derived by considering the sum of the first term of the Fresnel integral's asymptotic expansion {F(x)} and an exponential function which approaches to infinity at the zero of the Fresnel function's argument and has the properties of a unit step function. The second one is the sum of a unit step function and the transition function defined for the simplified uniform theory of diffraction. The third function considers directly eliminating the infinity coming from F(x). The amplitude and the phase of Fresnel integral and its equivalent functions are compared numerically. The result is applied to the modified theory of physical optics solution of the diffraction of edge waves from a half plane problem.

Scattering of a Gaussian Laser Beam by a Large Perfectly Conducting Cylinder: Physical Optics and Exact Solutions

Two particularly accurate solutions representing the scatter of a Gaussian laser beam from a perfectly conducting cylinder, one a physical optics solution using a series Green's function and the other an exact solution, are developed. A comparison of their resulting numerical data follows in order to validate the two solutions. The practicality of these solutions is then demonstrated by using the exact solution to plot the power distribution of the scattered beam on a sensor, and to confirm that the strategic placement of a cylinder in the path of a laser beam enables amplification of the laser beam deflection angle.

Time Domain Version of the Uapo Solution for the Field Diffracted by an Anisotropic Impedance Half-Plane

This work deals with the time domain version of the Uniform Asymptotic Physical Optics solution for the field diffracted by the edge of a nonpenetrable half-plane characterized by an anisotropic impedance boundary condition. A transient plane wave is assumed obliquely incident on the scatterer in the more general case of principal axes of anisotropy not coincident with the edge. The time domain solution is obtained from the knowledge of the corresponding frequency domain expression in the hypothesis that the impedance tensor components along the principal axes of anisotropy do not depend on the frequency. An inverse Laplace's transform is used to this end. The response to an incident unit step function plane wave is explicitly considered.

Efficient integral equation formulation of diffraction at the edge of a truncated dielectric structure based on PO solutions: Application to the case of arbitrarily polarized line sources

The radiation patterns of electric and magnetic line sources placed near the truncation of a semi‐infinite grounded dielectric layer structure have been investigated. Two polarizations (parallel and normal to the edge) have been considered for both sources. In order to perform the analysis a new formulation is proposed for the aperture integral equations derived from the principle of equivalence. The novelty of this formulation is that it involves only the fringe components of the magnetic current. The total magnetic current flowing on the aperture is expressed in terms of the physical optics (PO) current and the fringe current. Although the PO current is not known analytically, we can calculate the field excited by this current using the relationship between the surface magnetic PO current on the aperture and the electric polarization PO current in the grounded dielectric slab. The latter PO current is approximated analytically by the expansion wave concept. This step opens a simple and effective way to calculate the right part of the integral equations and as a consequence the radiation pattern of the line sources. For comparison reasons the problem is solved also by using the method of Physical Optics and the Uniform Theory of Diffraction.

Nanostructures with small- and large-scale periodic and random rough surfaces and lateral fluctuations in the permittivity and permeability-scattered near fields

The scattered electromagnetic near fields due to fluctuations in the surface height and/or lateral variations in the electromagnetic me- dium parameters are evaluated using a full-wave approach. Since the scales of the height and medium fluctuations considered could be sig- nificantly smaller or larger than the electromagnetic wavelengths, the familiar perturbation and physical/geometrical optics solutions cannot be used nor is it possible to investigate subwavelength features based on far-field measurements. The full-wave approach employs complete field expansion that includes propagating and evanescent waves as well as lateral waves and surface waves, which are not accounted for in the perturbation and physical optics solutions. Exact boundary conditions for the electric and magnetic fields are imposed at the rough interfaces. The complete modal expansions do not uniformly converge at the irregular boundaries, therefore the interchange of orders of differentiation and summation/integration of the field expansions is avoided. Large-scale and small-scale (relative to electromagnetic wavelength) approximations for the full-wave near-field solutions are expressed as integrals over the complete scattered wave number variables. Random rough surfaces as well as periodic and quasiperiodic structures are also considered. © 2002 Society of Photo-Optical Instrumentation Engineers. (DOI: 10.1117/1.1489050) Subject terms: near fields; electromagnetic wave scattering; lateral waves; sur- face waves; irregular stratified media; nanostructures.

High-frequency diffraction by a rectangular impedance cylinder on an impedance plane

The scattering of a line source field by a rectangular impedance cylinder on an infinite impedance plane is studied. The diffraction problem is formulated into a modified Wiener–Hopf equation of the third kind and then solved approximately. The solution contains two infinite sets of constants satisfying two infinite systems of linear algebraic equations. Numerical solutions of these systems are obtained for various values of the surface reactance, width and height of the rectangular cylinder, whereby the effects of these parameters on the diffraction phenomenon is studied. The results are compared with the corresponding physical optics solution and the agreement is very satisfactory.

Errata to "A UAPO solution for the field diffracted by building corners in wireless radio environments"

A uniform asymptotic physical optics (UAPO) solution is proposed to determine the field diffracted by building edges in mobile radio environments. A Gaussian rough lossy surface model is applied to describe the wedge surfaces. The diffraction coefficients are obtained by using a physical optics (PO) approximation of the surface current densities induced by an incident electromagnetic field on the illuminated face and by performing a uniform asymptotic evaluation of the resulting radiation integral. The resulting analytical expression is given in terms of the transition function of the uniform theory of diffraction (UTD) and is easy to handle and to implement in a computer code.

Multi-aspect detection of surface and shallow-buried unexploded ordnance via ultra-wideband synthetic aperture radar

An ultra-wideband (UWB) synthetic aperture radar (SAR) system is investigated for the detection of former bombing ranges, littered by unexploded ordnance (UXO). The objective is detection of a high enough percentage of surface and shallow-buried UXO, with a low enough false-alarm rate, such that a former range can be detected. The physics of UWB SAR scattering is exploited in the context of a hidden Markov model (HMM), which explicitly accounts for the multiple aspects at which a SAR system views a given target. The HMM is trained on computed data, using SAR imagery synthesized via a validated physical-optics solution. The performance of the HMM is demonstrated by performing testing on measured UWB SAR data for many surface and shallow UXO buried in soil in the vicinity of naturally occurring clutter.

Radar backscatter from mechanically generated transient breaking waves. II. Azimuthal and grazing angle dependence

For Pt. I see ibid. vol. 26, pp. 181-200 (2001). This paper describes the results of experimental investigations into the microwave backscatter from mechanically generated transient breaking waves. The investigations were carried out in a 110 m/spl times/7.6 m/spl times/4 m deep model basin, utilizing chirped wave packets spanning 0.75-1.75 Hz. Backscatter measurements were taken by a K-band continuous wave radar (24.125 GHz) at 40/spl deg/ angle of incidence, and at azimuth angles of 0/spl deg/, 45/spl deg/, 90/spl deg/, 135/spl deg/ and 180/spl deg/ relative to the direction of wave propagation. Grazing measurements were conducted using an X-band (10.525 GHz) FMCW radar at 85/spl deg/ angle of incidence, and azimuth angles of 0/spl deg/ and 180/spl deg/. Results show that the maximum radar backscatter was obtained in the upwave direction prior to wave breaking and was caused by the specular or near specular presentation of the wave to the radar. After breaking, the backscatter transitioned from a specular or near-specular dominated scattering, primarily seen in the upwave direction, to a small scale roughness dominated scattering, observed at all azimuths. Physical optics solutions were found to correctly predict the backscatter for the specular or near-specular dominated scattering and the small perturbation method was found to accurately model the VV polarization post-break radar backscatter.

Approximate Diffraction Coefficients for an Anisotropic Impedance Wedge

Two approaches are proposed to determine the diffraction coefficients for a nonpenetrable wedge with the faces characterized by anisotropic impedance boundary conditions when it is illuminated at oblique incidence by an electromagnetic plane wave. In the more general case the anisotropic impedance tensors associated with the faces have their principal axes not coincident with the edge of the wedge. The first solution is obtained by using a physical optics approximation for the surface current densities on the wedge and by performing a uniform asymptotic evaluation of the radiation integral (uniform asymptotic physical optics solution). The second solution is derived by following a heuristic approach. The effectiveness of both solutions is demonstrated by comparing them with analytical solutions available for particular cases.

Scattering by a groove in a conducting plane-a PO-MoM hybrid formulation and wavelet analysis

A novel method is presented to solve the two-dimensional (2-D) problem of scattering of an electromagnetic plane wave by a groove in a perfectly conducting infinite plane. In this method, the unknown induced current is expressed in terms of the known physical optics solution of the unperturbed problem of scattering by an infinite conducting plane plus a yet to be determined localized correction current placed in the vicinity of the groove. It is then shown that a good approximation of the induced current can be obtained using only a few dominant functions in the wavelet expansion of the correction current. Moreover, the same set of dominant wavelet functions serves the purpose of approximating the induced current at different angles of incidence. A numerical example demonstrates these various features of the proposed method of solution.

Diffraction by an anisotropic dielectric half-plane: a uniform asymptotic PO solution

A uniform solution is proposed to, describe the diffraction by a penetrable anisotropic dielectric halfplane illuminated at normal incidence by an electromagnetic plane wave. Resorting to second-order boundary conditions on a sheet simulating a special type of anisotropic dielectric thin layer, a physical optics (PO) approximation for the induced electric and magnetic surface currents is derived. Then, a uniform asymptotic evaluation of the corresponding radiation integral provides the diffracted field in terms of the standard transition function relevant to the uniform theory of diffraction. The effectiveness of the solution is proved by many numerical tests.

A Corrected Physical-Optics Solution to 3-D Wedge Diffraction

A physical-optics (PO) solution to the three-dimensional problem of dipole radiation over an arbitrary-angled wedge is presented. The medium beneath each face of the wedge is nonmagnetic, lossy, and not necessarily the same for both faces. Excitation is provided by an electric dipole that is parallel to the edge of the wedge. The analytical formulation is based on the Stratton-Chu formula. The electromagnetic (EM) field due to a horizontal electric dipole over a lossy half-space is used on the faces and a charge distribution along the edge is introduced to account for the discontinuity of the EM field across the edge. The integral expression for the electric-field intensity far from the edge is evaluated asymptotically, thus resulting in a formula that is uniformly valid. The validity of this edge-corrected PO solution is established through a reciprocity check and comparisons with other solutions.