Electromagnetic wave propagation through a dielectric-chiral interface and through a chiral slab

The reflection from and transmission through a semi-infinite chiral medium are analyzed by obtaining the Fresnel equations in terms of parallel- and perpendicular-polarized modes, and a comparison is made with results reported previously. The chiral medium is described electromagnetically by the constitutive relations D = εE + iγB and H = iγE + (1/μ)B. The constants ε, μ, and γ are real and have values that are fixed by the size, the shape, and the spatial distribution of the elements that collectively compose the medium. The conditions are obtained for the total internal reflection of the incident wave from the interface and for the existence of the Brewster angle. The effects of the chirality on the polarization and the intensity of the reflected wave from the chiral half-space are discussed and illustrated by using the Stokes parameters. The propagation of electromagnetic waves through an infinite slab of chiral medium is formulated for oblique incidence and solved analytically for the case of normal incidence

On Perturbation Theory of Electromagnetic Cavity Resonators

In this note the Lagrangian function for the electromagnetic field of a cavity resonator is found. And from this Lagrangian is deduced a perturbation formula which includes Müller's celebrated result as a special case. The same perturbation formula is derived also from the Boltzmann-Ehrenfest adiabatic theorem in a most simple manner

An Application of Sommerfeld's Complex Order Wave Functions to Antenna Theory

In the past wave functions of integral order have been used quite advantageously in the solution of certain antenna and boundary-value problems. However, in some instances these wave functions are completely alien to the problem and introduce difficulties which, indeed, can be resolved but only at the expense of logical simplicity. To place in evidence the usefulness and "naturalness" of complex order wave functions for the solution of certain problems, we examine theoretically the input admittance of a boss antenna with the aid of these functions

On the Index of Refraction of Spatially Periodic Plasma

A knowledge of the change produced in the index of refraction of a uniform plasma by the spontaneous generation of coagula or inhomogeneities is essential to the use of electromagnetic waves as a diagnostic tool. The general problem is a difficult one to handle, but certain non-trivial cases are mathematically tractable. One of these, which is also of some practical import, occurs when the inhomogeneities are periodically distributed throughout the plasma. Here this special case is analyzed within the framework of the theory of periodic structures. The problem is reduced by virtue of Floquet's theorem to an equivalent problem for the domain of a unit cell with periodic boundary conditions. An approximate solution is obtained by a simplified theory. As a specific application the calculation for a plasma with periodically spaced spherical inhomogeneities is worked out in detail

Surface Currents on a Conducting Sphere Excited by a Dipole

This paper treats the problem of determining the current distribution on the surface of a perfectly conducting sphere when driven by a dipole antenna erected on its surface. Curves of the real and imaginary parts of the surface currents are given for the case of a half‐wave dipole and various radii of the sphere

Diffraction by a Strip

The problem of diffraction by an infinite strip or slit has been the subject of several investigations. There are at least two "exact" methods for attacking this problem. One of these is the integral equation method, the other the Fourier-Lamé method. The integral equation obtained for this problem cannot be solved in closed form; expansion of the solution in powers of the ratio (strip width/wavelength) leads to useful formulas for low frequencies. In the Fourier-Lamé method the wave equation is separated in coordinates of the elliptic cylinder, the solution appears as an infinite series of Mathieu functions, and the usefulness of the result is limited by the convergence of these infinite series, and by the available tabulation of Mathieu functions. The variational technique developed by Levine and Schwinger avoids some of the difficulties of the above-mentioned methods and, at least in principle, is capable of furnishing good approximations for all frequency-ranges. The scattered field may be represented as the effect of the current induced in the strip, and it has been proved by Levine and Schwinger that it is possible to represent the amplitude of the far-zone scattered field in terms of the induced current in a form which is stationary with respect to small variations of the current about the true current. Substitution, in this representation, of a rough approximation for the current may give a remarkably good approximation of the far-zone scattered field amplitude. In this note we assume a normally incident field polarized parallel to the generators of the strip. As a rough approximation, we take a uniform density of the current induced in the strip. Since the incident magnetic field is constant over the strip, Fock's theory may be cited in support of the uniformity of the current distribution, except near the edges where the behaviour of the field indicates an infinite current density. A more detailed analysis of the current, by Moullin and Phillips, is available but was not used here. Once the (approximate) amplitude of the far-zone field has been obtained, the scattering cross-section may be found by the application of the scattering theorem which relates this cross-section to the imaginary part of the amplitude of the far-zone scattered field along the central line of the umbral region. In spite of the crude approximation adopted for the induced current, the scattering cross-section shows a fair agreement with other available results

Electromagnetic Radiation in the Presence of Moving Simple Media

The radiation pattern of an arbitrary source immersed in a moving simple medium is calculated by deducing the differential equation for the potential 4‐vector in the rest frame of the source and then solving the equation in terms of a Green's function. As an illustrative example, the case where the source is an oscillating dipole is worked out in detail