Realization of a spherical boundary by a layer of wave-guiding medium

In this paper the concept of wave-guiding medium, previously introduced for planar structures, is defined for the spherically symmetric case. It is shown that a quarter-wavelength layer of such a medium serves as a transformer of boundary conditions between two spherical interfaces. As an application, the D'B'-boundary condition, requiring vanishing of normal derivatives of the normal components of D and B field vectors, is realized by transforming the DB-boundary conditions. To test the theory, scattering from a spherical DB object covered by a layer of wave-guiding material is compared to the corresponding scattering from an ideal D'B' sphere, for varying medium parameters of the layer

Deriving Spin within a discrete-time theory

We prove that the classical theory with a discrete time (chronon) is a particular case of a more general theory in which spinning particles are associated with generalized Lagrangians containing time-derivatives of any order (a theory that has been called "Non-Newtonian Mechanics"). As a consequence, we get, for instance, a classical kinematical derivation of Hamiltonian and spin vector for the mentioned chronon theory (e.g., in Caldirola et al.'s formulation).Comment: 10 pages; LaTeX fil

Electromagnetic Force and Momentum in Classical Macroscopic Dipolar Media

Using realistic classical models of microscopic electric-charge electric dipoles and electric-current (Amperian) magnetic dipoles, it is proven that the Einstein-Laub macroscopic electromagnetic force on a macroscopic-continuum volume of these classical dipoles equals the sum of the microscopic electromagnetic forces on the discrete classical dipoles in that volume. The internal (hidden) momentum of the discrete Amperian magnetic dipoles is rigorously derived and properly included in the determination of the macroscopic force from the spatial averaging of the microscopic forces. Consequently, the Abraham/Einstein-Laub rather than the Minkowski macroscopic electromagnetic-field momentum density gives the total microscopic electromagnetic-field momentum in that volume. The kinetic momentum is found for the volume of the macroscopic continuum from Newton's relativistic equation of motion. It is shown that the difference between the kinetic and canonical momenta in a volume of the macroscopic continuum is equal to the sum of the "hidden electromagnetic momenta" within the electric-current magnetic dipoles and within hypothetical magnetic-current electric dipoles replacing the electric-charge electric dipoles in the classical macroscopic continuum. To obtain the correct unambiguous value of the force on a volume inside the continuum from the force-momentum expression, it is mandatory that the surface of that volume be hypothetically separated from the rest of the continuum by a thin free-space shell. Two definitive experiments performed in the past with time varying fields and forces are shown to conclusively confirm the Einstein-Laub/Abraham formulation over the Minkowski formulation.Comment: 16 pages, 1 figur

Absence of a consistent classical equation of motion for a mass-renormalized point charge

The restrictions of analyticity, relativistic (Born) rigidity, and negligible O(a) terms involved in the evaluation of the self electromagnetic force on an extended charged sphere of radius "a" are explicitly revealed and taken into account in order to obtain a classical equation of motion of the extended charge that is both causal and conserves momentum-energy. Because the power-series expansion used in the evaluation of the self force becomes invalid during transition time intervals immediately following the application and termination of an otherwise analytic externally applied force, transition forces must be included during these transition time intervals to remove the noncausal pre-acceleration and pre-deceleration from the solutions to the equation of motion without the transition forces. For the extended charged sphere, the transition forces can be chosen to maintain conservation of momentum-energy in the causal solutions to the equation of motion within the restrictions of relativistic rigidity and negligible O(a) terms under which the equation of motion is derived. However, it is shown that renormalization of the electrostatic mass to a finite value as the radius of the charge approaches zero introduces a violation of momentum-energy conservation into the causal solutions to the equation of motion of the point charge if the magnitude of the external force becomes too large. That is, the causal classical equation of motion of a point charge with renormalized mass experiences a high acceleration catastrophe.Comment: 13 pages, No figure

Electrically Small Supergain Arrays

The theory, computer simulations, and experimental measurements are presented for electrically small two-element supergain arrays with near optimal endfire gains of 7 dB. We show how the difficulties of narrow tolerances, large mismatches, low radiation efficiencies, and reduced scattering of electrically small parasitic elements are overcome by using electrically small resonant antennas as the elements in both separately driven and singly driven (parasitic) two-element electrically small supergain endfire arrays. Although rapidly increasing narrow tolerances prevent the practical realization of the maximum theoretically possible endfire gain of electrically small arrays with many elements, the theory and preliminary numerical simulations indicate that near maximum supergains are also achievable in practice for electrically small arrays with three (and possibly more) resonant elements if the decreasing bandwidth with increasing number of elements can be tolerated.Comment: 10 pages, 11 figures, submitted to IEEE Transactions on Antennas and Propagation (December 2006