Finite Dielectric Slab Research Articles

Interior Green's Function Solution for a Thick and Finite Dielectric Slab

An interior Green's function solution is presented for a two-dimensional thick and finite dielectric slab. In the present development, the source and the field points are assumed to be inside the dielectric slab. The result is composed of two parts. The first part which has a discrete spectrum of eigenfunctions includes the surface wave multiple interactions, and is obtained by using the generalized scattering matrix and method of moments. The second part, which is a closed-form integral, is obtained for a separable dielectric slab that is closely related to the finite slab. The closed form integral is evaluated numerically and added to the surface wave solution. The solution accounts for the mode conversions at the end caps which occur when surface waves are reflected and diffracted. Test cases show very good agreement with a finite-element solver, even when the source is near the end caps.

Optical extinction by closely spaced parallel cylinders inside a finite dielectric slab

The formulation for the extinction and scattering cross sections of closely spaced parallel infinite cylinders in a dielectric medium of finite thickness is presented. We consider the general case of dissimilar refractive indices for the half-spaces on both sides of the slab, and the diameter and refractive index of each cylinder can be different. The formulation accounts for the coherent scattering between the cylinders and scattering of the multiply reflected internal waves inside the slab. Discontinuity in the refractive index across the dielectric slab interfaces results in boundary reflections that modify the angular distribution of the scattered intensity in both forward and backward directions. The extinction cross section, which is derived by a formal application of the optical theorem, is shown to consist of both a forward and a backward component. The general solution is applied to obtain the formulas for the cases of cylinders in front of a reflecting plane, cylinders inside a semi-infinite dielectric medium, and cylinders in free space.

Quasi-TEM modes in parallel-line transmission structures with conductors embedded in dielectrics

A transmission structure of many parallel conductors is capable of propagating many distinct quasi-TEM modes. A field theory of such modes was developed for a theoretically infinite number of very thin conductors placed on a dielectric substrate. The current paper extends this work to include a large number of thin parallel conductors embedded within finite dielectric slabs. The theory is illustrated by the following three structures: a large number of parallel wires embedded in dielectric slabs with substrates of infinite width, both with and without a ground plane; and a large number of thin wires embedded in a finite dielectric slab without a ground plane. This extension to a finite dielectric structure is obtained using a superposition method where both vertical and horizontal surfaces are considered infinite in turn. A major application of the derived formulation is the investigation of velocity distributions and crosstalk within these structures. Comparison of these structures with ones where the conductors are on the substrate (as opposed to embedded) indicates how the placement and structure of the conducting channel affects the modal velocities and crosstalk.

Light scattering by closely spaced parallel cylinders embedded in a finite dielectric slab

A theory of light scattering by closely spaced parallel radially stratified cylinders embedded in a finite dielectric slab is presented. The refractive indices of the slab and the half-spaces on both sides of the slab are assumed to be real but arbitrary. No restriction is placed on the polarization and the propagation direction of the incident wave, the diameter of the cylinders, the intercylinder spacing, and the wavelength of the incident radiation. Each cylinder can have any number of concentric layers of stratification, and the complex refractive index of each layer can be different. A rigorous solution of Maxwell’s equations is developed by accounting for depolarization effects that are due to oblique incidence on the cylinders, refraction of scattered waves at the slab boundaries, and coherent scattering between the cylinders. The scattering characteristics of a slab containing a specific configuration of cylinders are examined by numerical data for several combinations of refractive indices of the slab and the half-spaces. In addition, the present scattering theory is applied to obtain the solutions for the cases of cylinders embedded in a semi-infinite medium, cylinders located in front of a reflecting–transmitting plane, and cylinders in an infinite homogeneous medium.

Directivity enhancement by layered radomes

Single and layered radomes are often used to protect radiating elements. A two-dimensional analysis is used to investigate their influence on the antenna directivity and radiation patterns. Image-theory and integral-equation methods are used to formulate the problem for a line source and layered dielectrics of finite length over a ground plane, and solved numerically using the moment method. It is shown that, for a sufficiently long single-layer slab, the directivity enhancement is approximately equal to the square root of its relative permittivity. Properly truncating the slab can even improve the directivity. The optimum length of a finite dielectric slab is determined to maximize the directivity. For multilayer slabs, the directivity enhancement is much greater and they can be used with low-permittivity dielectrics to simulate a single-layer one of higher permittivity. Frequency dependency of the enhanced gain is also studied. Useful information for how to incorporate the radome parameters into the antenna design and use it for gain or directivity enhancement is provided.