John G. Fikioris

Radiation properties of microstrip dipoles

The fundamental problem of printed antennas is addressed. The printed or microstrip dipole is considered, and its radiation characteristics are investigated. The Greens function to the problem is obtained in dyadic form by solving the problem of a Hertzian dipole printed on a grounded substrate. Input impedance computations are presented, and the numerical solution for the Sommerfeld integrals is discussed.

Scattering from an eccentrically stratified dielectric sphere

In this paper the scattering from eccentrically stratified spheres is considered. For the case of a spherical inhomogeneity embedded inside a dielectric sphere, the method of separation of variables is used in conjunction with translational addition theorems for spherical vector waves. Analytical results are obtained when the difference in the dielectric constants of the two spheres is small by employing a special perturbation technique. Scattering properties such as distortion of the scattering patterns, variation of total and backscattering cross sections, and depolarization for randomly oriented scatterers are investigated. Methods of detection and identification of inhomogeneities are discussed.

Electromagnetic scattering from an eccentrically coated infinite metallic cylinder

In this work the scattering from an eccentrically coated infinite metallic cylinder is considered. The problem is solved using classical separation of variables techniques combined with translational addition theorems. For small eccentricities κd, where d is the distance between the two axes and κ the wave number of the dielectric coating, exact closed‐form expressions of the form S(d)=S(0)[1+g′(κd)+g″(κd)2+O(κd)3] are obtained for the scattered field and the various scattering cross sections of the problem. Both polarizations are considered for normal incidence. Numerical and graphical results for various values of the parameters are also discussed.

Scattering from an inhomogeneity inside a dielectric-slab waveguide

Scattering from cylindrical inhomogeneities immersed inside a dielectric-slab waveguide is investigated analytically. A volume integral equation technique based on Green’s function theory in regions with planar boundaries is used to formulate the problem. For the case of circularly inhomogeneous shapes, an analytical solution is developed when |b(k1 − k2) < 1, where k1 − k2 is the difference between the wave numbers of the slab and the circular inhomogeneity whose radius is b. Analytical expressions for the reflection and transmission coefficients in the slab, when a guided surface mode is incident upon the inhomogeneity from the left, are derived up to order [b(k1 − k2)]3. Numerical results are computed and plotted for several cases.

Scattering of plane waves from an eccentrically coated metallic sphere

Abstract In this paper the scattering of plane electromagnetic waves from eccentrically coated metallic spheres is considered. Inhomogeneous, surface, singular integral equations are used to formulate the problem. Their solution is obtained in terms of spherical vector wave functions in conjunction with related addition theorems. Analytical, closed-form results are obtained in the case of small eccentricities kd , where d is the distance between the two centers and k the wave number of the dielectric coating. Thus the scattered field and the various scattering cross-sections of the problem are given by expressions of the form: S(d) = S(0)[1+g’(kd)+g”(kd) 2 +0(kd) 3 ] . Numerical and graphical results for various values of the parameters are also discussed.

Scattering from thin and finite dielectric fibers

The electromagnetic scattering from finite-length dielectric fibers with a diameter much smaller than the wavelength and for a perpendicular incidence case is considered. The induced fields are assumed to be uniform on the cross section of the fiber. This yields a one-dimensional integral equation for the inner field which is solved by employing Galerkin’s method. Numerical results for the scattering amplitude are obtained for specific cases. In addition, it is shown that the energy finiteness criterion is satisfied.

Cutoff wavenumbers and the field of surface wave modes of an eccentric circular Goubau waveguide

Abstract The cutoff wavenumbers knm and the field of surface wave modes of a circular cylindrical conductor eccentrically coated by a dielectric are determined analytically. The electromagnetic field is expressed in terms of circular cylindrical wave functions referred to both axes, in combination with related addition theorems. When the solutions are specialized to small eccentricities kd, where d is the distance between the two axes, exact closed-form expressions are obtained for the coefficients gnm in the resulting relation knm(d)=knm(0)[1+gnm(knmd)2+...] for the cutoff wavenumbers of the waveguide. Similar expressions are obtained for the field. Numerical results for all types of modes are given. For certain values of the parameters, it is possible to enhance the operating bandwidth of the basic hybrid mode HE11 over the conventional concentric guide.

Field induced in inhomogeneous spheres by external sources. I. The scalar case

The evaluation of acoustic or electromagnetic fields induced in the interior of inhomogeneous penetrable bodies by external sources is based on well-known volume integral equations; this is particularly true for bodies of arbitrary shape and/or composition, for which separation of variables fails. In this paper the investigation focuses on acoustic (scalar fields) in inhomogeneous spheres of arbitrary composition, i.e., with r-, θ- or even φ-dependent medium parameters. The volume integral equation is solved by a hybrid (analytical–numerical) method, which takes advantage of the orthogonal properties of spherical harmonics, and, in particular, of the so-called Dini’s expansions of the radial functions, whose convergence is optimized. The numerical part comes at the end; it involves the evaluation of certain definite integrals and the matrix inversion for the expansion coefficients of the solution. The scalar case treated here serves as a steppingstone for the solution of the more difficult electromagnetic problem.

Direct and efficient solutions of integral equations for scattering from strips and slots

Singular integral or integro‐differential equations (SIE or SIDE) are often used for the analytical formulation of two‐dimensional boundary‐value problems. The methods for solving them depend primarily on the complexity of their kernel and on the kind (first or second) of the SIE itself. First‐kind SIEs with a Laplacian kernel are characteristic in electrostatics. A successful method for solving them is a regularization approach based on the transformation of the SIE to an equivalent Fredholm regular integral equation of the second kind. Well‐known inversion formulas are essential to this approach. In electromagnetics, a Hankel‐type kernel complicates matters considerably; inversion formulas and regularization techniques end up as cumbersome indirect procedures making necessary the recourse to a more direct method. Such a method is developed in this paper in combination with a very suitable expansion of the Bessel function, that multiplies the logarithmic singularity of the Hankel kernel, into a series of...

Acoustic resonant frequencies in an eccentric spherical cavity

The interior boundary‐value scalar (acoustic) problem in the region between two spheres of radii R1, R2 and distance d between their centers is considered for both Dirichlet and Neumann boundary conditions. Surface singular integral equations are used to formulate the problem. Their solution is obtained in terms of spherical wave functions in combination with related addition theorems. It is then specialized to the case of small values for kd=2πd/λ to yield exact, closed‐form expressions for the coefficients gns in the resulting relations ωns(kd) =ωns(0) [1+gns(kd)2+⋅⋅⋅] for the resonant (natural) frequencies of the cavity. Numerical results, comparisons, and possible generalizations are also included.