Dwight L. Jaggard

The fractal random array

A novel method of random array synthesis is presented. This new method relies on the application of the underlying self-similarity inherent in random fractals to the problem of antenna array theory. Several examples demonstrate the synthesis procedure and its usefulness in producing robust, low sidelobe arrays.

Electromagnetic chirality and its applications

Chirality is a geometric notion which refers to the handedness of an object. A chiral object is, by definition, a body that cannot be brought into congruence with its mirror image by translation and rotation. In other words, such a body lacks bilateral symmetry, and cannot be superposed on its mirror image. An object of this sort has the property of handedness and is said to be either right-handed or left-handed. An object that is not chiral is achiral. Some chiral objects occur in two versions relatedto each other as a chiral object and its mirror image. Objects so related are said to be enanriomorphs of each other. If a chiral object is found to be lefthanded, its enantiomorph is right-handed, and vice versa. Two examples of chiral objects, the Mbbius strip and the irregular tetrahedron, and their enantiomorphs are shown in Fig. 1. Note that these objects and their mirror images are incongruent

Scattering from fractally corrugated surfaces

We consider the problem of scattering of optical or electromagnetic waves from a family of irregular rough surfaces characterized by band-limited fractal functions. This method provides a unified and realistic method for examining rough surfaces without the use of random or periodic functions. We relate the angular distribution and the amount of energy in the specularly scattered field to the fractal characteristics of the surfaces by finding their analytical expressions under the Kirchhoff limit and calculating the scattering patterns.

Electromagnetic waves in Faraday chiral media

Plane wave propagation in two kinds of Faraday chiral media, where Faraday rotation is combined with optical activity, is studied to examine methods of controlling chirality. The two types of media studied are magnetically biased chiroplasmas and chiroferrites. For propagation along the biasing magnetic field, four wavenumbers and two wave impedances are found which are dependent on the strength of the biasing field. Dispersion diagrams for the chiroplasma case are plotted. Propagation at the plasma frequency of the chiroplasma is also investigated. >

Canonical sources and duality in chiral media (antenna arrays)

The authors examine the characteristics of antenna arrays embedded in unbounded chiral media using the Greens dyadic for electric sources and the Greens vector for magnetic sources. The purpose is to bring to light the new characteristics of sources, both point and extended, which interact with this medium and to examine general characteristics of sources located in a medium with handedness. Very simple quality relations are presented that are characteristic of chiral media when the results are written in terms of the circular eigenmodes. Appropriate measures of chirality such as the chirality admittance and impedance and a dimensionless chirality factor are introduced as needed. It is shown that, in the far field, both point and extended sources, whether electric or magnetic, radiate two electromagnetic eigenmodes which are of opposing handedness. Sources that access only one of the eigenmodes of the medium are demonstrated. Several applications of the results and array performance in chiral media are noted. >

Fractal surface scattering: A generalized Rayleigh solution

We consider the scattering of electromagnetic waves from perfectly conducting fractal surfaces. The surface is modeled by a multiscaled bandlimited continuous fractal function. We analytically develop a generalized Rayleigh solution for electromagnetic wave scattering from such fractal surfaces. After an examination of the convergence of the Rayleigh systems, we numerically calculate the coupling strengths and relate the angular scattering energy distribution to the fractal descriptors of the surface. We find that the slope of the coupling strengths as a function of their corresponding spatial frequencies on a logarithmic scale depends monotonically on the fractal dimension of the scattering surface.

Wave interactions with generalized Cantor bar fractal multilayers

The reflection and transmission properties of finely divided fractal layers are investigated and characterized. The results for electromagnetic or optical waves normally incident upon generalized Cantor bar fractal multilayers are found for various fractal dimensions and stages of growth. A new exact self‐similar algorithm is described which makes use of the self‐similarity of the structures to clearly display the underlying physics. This fractal computational scheme provides the reflection and transmission coefficients for fractally distributed layers with extreme economy when compared to traditional approaches. Finally, a method for extracting fractal descriptors from scattered data is discussed. High‐ and low‐ frequency regimes are examined.

Periodic chiral structures

The electromagnetic properties of a structure that is both chiral and periodic are investigated using coupled-mode equations. The chirality is characterized by the constitutive relations D= epsilon E+i xi /sub c/B and H=i xi /sub c/E+B/ mu , where xi /sub c/ is the chiral admittance. The periodicity is described by a sinusoidal perturbation of the permittivity, permeability, and chiral admittance. The coupled-mode equations are derived from physical considerations and used to examine bandgap structure and reflected and transmitted fields. Chirality is observed predominantly in transmission, whereas periodicity is present in both reflection and transmission. >

Accurate one-dimensional inverse scattering using a nonlinear renormalization technique

A nonlinear method based on the inversion of the Riccati equation is presented here for the one-dimensional nondispersive inverse-scattering problem. This method avoids the significant errors in both amplitude and phase that plague most linearized (e.g., Born or its varients) inversion schemes. Instead, a nonlinear approximation to the Riccati equation is used for the accurate determination of the refractive-index amplitude from reflection data. This information is subsequently used to stretch the coordinates so as to remove the phase-accumulation error. The resulting refractive-index reconstructions are therefore accurate both in amplitude and in longitudinal placement as evidenced by the excellent comparison with exact theory. The method is applicable to both continuous and discontinuous refractive profiles and is supported by experimental measurements.

Diffraction by band-limited fractal screens

The concept of band-limited fractals is introduced and used to describe the diffraction of electromagnetic and optical waves by irregular structures. This concept is demonstrated through the example of plane-wave diffraction by a fractal phase screen of finite extent. The effect of the fractal phase screen is noted on the evolution of an incident wave with the fractal dimension and other descriptors used as parameters. Of particular interest is the result that, for random fractal phase screens, the diffraction pattern from a single realization of the model phase screen can be identical to the pattern averaged over an ensemble of screens. In these cases an orderly pattern emerges from a chaotic one. This problem of fractal diffraction is of intrinsic interest because of the variety of problems found to be described by fractal, as opposed to Euclidean, geometry. The results have potential applications to the propagation of waves through random media, the reflection of waves from rough surfaces, and the characterization of these processes through remote means.