A surface wave interpretation for the resonances of a dielectric sphere

The calculated radar and bistatic cross sections of dielectric spheres exhibit numerous resonances when plotted versus frequency. These resonances may be related to the excitation of electromagnetic eigenvibrations of the sphere, with resonance frequencies calculable from a characteristic equation. It is shown that the resonances may be viewed as originating from families of circumferential (surface, or creeping) waves that are generated during the scattering process; at each eigenfrequency of the sphere, one of these surface waves matches phases after its repeated circumnavigations around the sphere, with the ensuing resonant reinforcement leading to the given scattering resonance. This mechanism explains the existence of electromagnetic eigenvibrations of a general smooth dielectric object; for the case of a sphere, it is shown that the surface waves suffer a phase jump ofpi/2at each of their two convergence points. We calculated numerical values of the eigenfrequencies of dielectric spheres, and obtain dispersion curves for the phase velocities of the surface waves.     

Electromagnetic resonances of immersed dielectric spheres

The complex natural resonances (CNR) for lossless dielectric spheres in a lossless dielectric medium are investigated. Significant differences between the external and internal resonances are presented. The external resonances are related to the external creeping waves and the internal resonances to the internally reflected waves. The internal resonances are more important in practice because of their smaller damping factors. A simple physical interpretation for predicting the resonance behavior of a general dielectric sphere is obtained     

Resonant attenuation in electromagnetic wave scattering fromconducting elongated objects

The authors study the resonant attenuation as determined by the imaginary parts of the complex eigenfrequencies of perfectly conducting elongated objects: spheroids, cylinders with flat ends, and cylinders with hemispherical endcaps. Complex resonance frequencies are obtained from the principle of phase matching of surface waves. For the case in which these surface waves are generated by plane waves at broadside incidence, the simultaneous presence of cylindrical circumferential-wave resonances and of the resonances of meridionally propagating surface waves is discussed     

Complex frequency poles of radar scattering from coated conducting spheres

The radar scattering amplitude, as a function of frequency, possesses poles whose importance was recognized in the framework of the singularity expansion method (SEM); they are located at the scatterer's complex eigenfrequencies and are characteristic for its shape and composition. For perfectly conducting targets, these poles lead to little pronounced, broad frequency resonances in the radar echoes while for dielectrically coated objects, such resonances can be very prominent. We here present pole patterns in the complex-frequency plane for dielectrically-coated spheres, and obtain the movement of the poles under changes of the thickness and dielectric constant of the coating. The results explain the appearance and disappearance of resonance peaks in previously calculated radar cross sections.     

Solution of the inverse electromagnetic scattering problem in the resonance case

In the scattering process of electromagnetic waves from dielectric or conducting targets, one often encounters resonances in frequency in the returned echo signals. In previous studies on the scattering of acoustic and elastic waves, analogous resonant echoes were shown to contain a wealth of information on the properties of the scattering target, permitting, in fact, the complete solution of the corresponding inverse problem. The same is recognized to be the case for the electromagnetic scattering problem considered here. For the case of dielectric or coated conducting spherical targets, the spacing and the widths of the resonances are shown to determine the dielectric constant and the coating thickness of the target in a direct fashion.     

Scattering of electromagnetic waves from dielectric coated conducting spheres

Several series of rigorous numerical calculations of the backscatter cross section of a conducting sphere with a thin lossless dielectric coating were carried out. The ratio of the radius to wavelength was varied from about 0.02 to 10.0; the dielectric constant of the coating was taken to be 2.56, 4.0, or 6.0; and the thickness of the coating was 0.1 or 0.05 times the outer radius of the coated sphere. Curves of the results are presented which indicate that the backscatter cross section of a coated sphere may be increased by as much as a factor of ten over that of an uncoated sphere of the same size, and, due to interference effects, an even greater decrease may be obtained. Further, small changes (less than one per cent) in the thickness or dielectric constant of the coating, or in the wavelength, may bring about large changes in the cross section. The numerical results are also compared with some experimental measurements, and with predictions of a "creeping-wave" type of analysis carried out by Helstrom.     

Complex eigenfrequencies of axisymmetric objects: Physical interpretation in terms of resonances

We calculate and compile complex eigenfrequencies of spheroids and finite-length cylinders for electromagnetic and acoustic vibrations. This includes eigenvibrations of nonlongitudinal type, studied by us earlier for the first time. We provide a physical explanation for these in terms of the resonances caused by the phase matching of helical surface waves on the object.     

Scattering from coated targets using a frequency-dependent, surfaceimpedance boundary condition in FDTD

One method for reducing the radar cross section of objects such as aircraft and missiles is the application of a lossy coating. Computing scattering from targets coated with dielectric/magnetic materials is challenging due to the reduced wavelengths of an incident field inside the coating. These smaller wavelengths require finer sampling of the fields. A technique for implementing this calculation without greatly increased memory requirements or computation times has previously been developed using a finite-difference time-domain (FDTD) code which has been tested in one, two, and three dimensions. The method requires knowledge of the frequency behaviour of the complex permittivity and permeability, and the thickness of the dielectric coating and is applicable to thin coatings when one or more reflections from the conducting surface are significant. The impedance at the surface of the coating is computed based on the given information and then approximated using a summation of causal functions. The approximated impedance is Z-transformed and added to the FDTD code in special update equations for the fields at the surface of the coating. No computations are required inside the coatings so the FDTD grid can be sized based on the free-space wavelength. The result obtained is valid over the entire frequency range of interest, assuming that the approximated surface impedance is a good match over the entire range. Comparisons with measurements of a scale model coated missile show good agreement and almost no increase in resource requirements over a standard FDTD calculation for an uncoated metal target     

Resonance frequencies of conducting spheroids and the phase matching of surface waves

The complex resonance frequencies of conducting spheroids have been obtained by us for both transverse electric (TE) and transverse magnetic (TM) modes, using theT-matrix approach. The resonances originate from a phase matching of repeatedly circumnavigating surface waves, and we develop a quantitative model of this phenomenon. The propagation constants vary continuously during the passage of the waves over the curved surface along a geodesic, depending to first order on the local curvature along the path. This curvature dependence was obtained in a calculation of Franz and Galle in terms of a power series expansion ink^{-2/3}, comprising five terms of the series. Using this, we formulate the phase matching as an integral condition over the closed path, in the sense of Fermat's principle, and verify that the complex eigenfrequencies as obtained by us earlier indeed satisfy the phase matching condition. This indicates the correctness of both our physical phase-matching model, and of theT-matrix results for the eigenfrequencies.     

Scattering of electromagnetic pulses by simple-shaped targets withradar cross section modified by a dielectric coating

We study the scattering interaction of electromagnetic pulses with a spherical target. The target is a perfectly conducting sphere coated with a thin dielectric layer. Two different hypothetical materials are specified: a lossy dielectric and a dielectric that also has magnetic losses. The monostatic radar cross section (RCS) is computed in each case and we examine the influence of the coating on the RCS. In particular, we compare the RCS of the coated sphere with the (normalized) backscattered power when a large perfectly conducting flat plate coated with the same dielectric layer is illuminated at normal incidence by the same waveform. In particular, we find that except for frequencies below those within the efficiency band of the absorbent material, the normalized RCS of the coated sphere agrees well with the power reflection coefficient of the plate covered with the same kind of coating. For low-frequency incidences, the peaks and dips in the RCS are more prominent for the coated target than they are for the bare one. Analyzing the response of the spherical targets in the combined time-frequency domain we demonstrate that the coating itself, although reducing the RCS could introduce additional resonance features in the target's signature at low frequencies that could be used for target recognition purposes. This observation is also confirmed by a study of the bistatic RCS of these coated objects, which we have displayed in various color graphs     

Eigenvalues of a dielectric-coated conducting cone

The general problem of radiation/scattering from a dielectric coated semi-infinite conical structure excited by an arbitrary surface current distribution on the dielectric layer is formulated. Since the angular eigenfunction expansion is not suitable for this problem, the radial eigenfunction expansion is employed. The boundary value method is applied to obtain the fields in the form of infinite double series over the appropriate eigenfunctions in terms of spherical Hankel and associated Legendre functions. The conical dielectric shell may be lossy or lossless and the series solution generally involves complex eigenvalues which are calculated numerically. Using a small conducting sphere at the tip of the cone, the singularity of the Hankel functions at the origin is overcome, thus permitting the use of the orthogonality relations of Sommerfeld's complex-order wave functions to solve the problem and construct sets of infinite simultaneous linear equations which are presented in matrix form.     

Target identification of coated objects

We consider the three-dimensional electromagnetic inverse scattering problem of determining information about a coated object from a knowledge of the electric far-field patterns corresponding to time harmonic incident plane waves at fixed frequency. We assume that the obstacle is either a perfect conductor coated by a thin dielectric layer or a dielectric coated by a thin layer of a highly conducting material, i.e., the coated portion of the boundary is modeled by either an impedance boundary condition or a conductive boundary condition. No a priori assumption is made on the connectivity of the scattering obstacle nor on the extent of the coating, i.e., the object can be fully coated, partially coated, or not coated at all. We present an algorithm based on the linear sampling method for reconstructing the shape of the scattering obstacle together with an estimate of either the surface impedance or surface conductivity. Numerous numerical examples are given showing the efficaciousness of our method.     

Characteristics of dielectric loaded and covered circular waveguide phased arrays

The use of dielectric materials for the hardening and matching of phased-array antennas in recent years has shown that a more complete understanding of the effects of these materials upon the array performance is necessary. The characteristics of fully loaded, plugged, and sheath covered circular waveguide phase arrays are analyzed and discussed. Numerical solutions of the boundary-value problem are verified by experimental and convergence tests. Particular emphasis is placed on the study of (forced) surface wave resonance effects. Three different cases for surface wave resonances were obtained. These include the case in which surface wave resonances are present in the absence of dielectrics, the case in which they are trapped by the presence of dielectric plugs, as well as the case in which waves are trapped by the presence of a dielectric sheath. The surface wave resonance due to the plug is shown to vanish for certain "bandpass" ranges of plug thickness which repeat periodically for a single trapped waveguide mode. On the other hand, the surface wave trapped in the sheath exhibits no "bandpass" characteristics. Instead, multiple surface wave resonances occur with increasing sheath thickness. Finally, the surface wave resonances observed here appear at isolated points in the scan plane.     

Fields of a curved plasma layer excited by a slot

An analysis of the fields of a plasma coated conducting cylinder of infinite extent, excited by an infinite axial slot, is presented for large radius cylinders. The saddle point evaluation of the radiation fields is discussed for uniform low-loss plasma layers of arbitrary thickness and index of refraction. Patterns are presented and compared with the flat layer case, and the effect of the curvature on the pattern is discussed. The residue series evaluation is considered and a method of determining the poles is discussed. The locus of the first pole for thin lossless dielectric layers is presented and the transition from leaky waves to surface waves is discussed as a function of the dielectric constant and radius of curvature.     

The spectrum of electromagnetic waves guided by a plasma layer

The modal spectrum of a lossless, homogeneous and isotropic planar plasma layer is shown to contain contributions from surface waves and complex modes in addition to the usual continuous spectrum characteristic of open structures. These discrete contributions are only of the E-mode type and occur whenever the plasma dielectric constant εpis negative. The surface waves may be of the forward or the backward type and they carry power in opposite directions in the plasma and air regions. The complex modes are shown to appear always in degenerate pairs and as a consequence they carry no real power but may account for large reactive fields in the neighborhood of sources. For E modes with positive values of εp, and for all H modes, the spectrum is purely continuous; however, nonspectral leaky ways are then present which are significant in radiation considerations.     

Scattering of electromagnetic waves by a perfectly conductingcylinder with a thin lossy magnetic coating

We study the scattering interaction of electromagnetic (EM) waves with an infinite cylinder coated with a lossy dielectric material with frequency-dependent material properties. These properties are hypothetical, yet representative of a wide class of available materials. The monostatic and bistatic scattered widths (SW) are evaluated for the TM or TE polarization cases. These calculations require the use of algorithms to evaluate Bessel-Hankel functions of complex arguments. These algorithms are based on a continued fraction approach, which ensures stability of the recursion relations. The bistatic plots of the TM and TE scattering widths for the coated body are displayed in a convenient color-graded scale. The reductions in the scattering widths produced by this type of coating are determined in selected frequency bands and angular sectors, in both polarization cases. It is quantitatively shown how curvature and polarization shift the effectiveness band of the coating. The determined regions in which the SW are minimally affected are the most suitable for target identification purposes     

Propagation characteristics of a circular waveguide coated inside with a metamaterial

The problem of guided wave propagation of a circular waveguide that is coated on the inside with a metamaterial coating is studied by a boundary value approach and the propagation features cylindrical waveguide are studied by solving the resultant characteristic equation numerically. The results are compared to those with an inside dielectric coating. The variation of the normalized phase constant is studied as a function of the parameters of the coating including the permittivity and permeability, the coating thickness expressed as a ratio of b/a, and frequency. The behavior of the cylindrical waveguide is shown to be significantly different from that with a dielectric coating.     

Electromagnetic scattering from a dielectric-coated circular cylinder

The normalized backscattering width of an infinitely long, dielectric coated circular cylinder is obtained via a high frequency ray solution. The ray solution provides a physical picture of the scattering process in terms of a geometrical optics ray and two surface waves. It is shown that the surface wave resonance phenomena in the backscattering fields of the coated cylinder can be predicted in terms of the Regge poles of the coated cylinder. The numerical results for the backscattering widths of the cylinder obtained via the high frequency ray solution show excellent agreement with the eigenfunction results. The trajectories of the Regge poles associated with the coated circular cylinder are also presented.     

On Slow and Fast Surface Waves Propagating on Plane Boundaries of Conducting Media with High Conductance. The Zenneck Wave

The regularities of transition of phase and group velocities from slow surface waves (whose velocities are below the light speed) to fast surface waves (whose velocities are above the light speed) on the plane boundaries of highly conducting media are investigated when the parameters of media vary. It is shown that the structure of waves does not change qualitatively in the case of this transition: the waves remain to be surface ones in contrast to surface waves of dielectric waveguides. The latter ones are transformed into leaking waves or their structure changes in a more complicated way in the case of such transition. A result relating, in particular, to the Zenneck wave is obtained.     

Comment on “A rigorous explanation for the resonancesobserved in the scattering from spherical ice particles” [andreply]

In their paper on the “fine scale resonant structure that has been observed both in Mie scattering calculations and in measurements”, Papatsoris and Watson (see ibid., vol.42, p.1350, 1994) state, “various physical explanations have been sought in the past, none of them entirely satisfactory. In this paper, we show that these resonances are directly related to the excitation of the eigenfrequencies of the ice particles, when considered as dielectric resonators.” The most recent prior work in which they mention spheres is a paper written in 1980 regarding surface waves. The authors appear to be unfamiliar with the relevant literature. Papatsoris and Watson reply that qualitative physical explanations for the fine structure of the scattered field form dielectric spheres have been available for many years. They prefer the work of Metz and Dettmar (1963) as being representative as an explanation of the ripple structure. They solved the transcendental equations for ice and presented a comparison between the natural and scattering resonances. They believe that the physical insight offered by their physical explanation is of value