Timothy J. Garner

Negative refraction through a triangular prism may be explained without assigning a negative refractive index to the prism by using array theory. For the case of a beam incident upon the wedge, the array theory accurately predicts the beam transmission angle through the prism and provides an estimate of the frequency interval at which negative refraction occurs. The hypotenuse of the prism has a staircase shape because it is built of cubic unit cells. The large phase delay imparted by each unit cell, combined with the staircase shape of the hypotenuse, creates the necessary conditions for negative refraction. Full-wave simulations using the finite-difference time-domain method show that array theory accurately predicts the beam transmission angle.

Humans will launch spacecraft that travel at an appreciable fraction of the speed of light. Spacecraft traffic will be tracked by radar. Scattering of pulsed electromagnetic fields by an object in uniform translational motion at relativistic speed may be computed using the frame-hopping technique. Pulse scattering depends strongly on the velocity, shape, orientation, and composition of the object. The peak magnitude of the backscattered signal varies by many orders of magnitude, depending on whether the object is advancing toward or receding from the source of the interrogating signal. The peak magnitude of the backscattered signal goes to zero as the object recedes from the observer at a speed very closely approaching light speed, rendering the object invisible to the observer. The energy scattered by an object in motion may increase or decrease relative to the energy scattered by the same object at rest. Both the magnitude and sign of the change depend on the velocity of the object, as well as on its shape, orientation, and composition. In some cases, the change in total scattered energy is greatest when the object is moving transversely to the propagation direction of the interrogating signal, even though the Doppler effect is strongest when the motion is parallel or antiparallel to the propagation direction.

Scattering by a uniformly translating sphere of a pulse that modulates the amplitude of a linearly polarized plane wave was formulated using the frame-hopping method involving a laboratory inertial reference frame and the sphere’s comoving inertial reference frame. The incident signal was defined in the laboratory frame and transformed to the comoving frame with the Lorentz transformation, thereby altering the incident signal’s spectrum, direction of propagation of the carrier plane wave, and the direction of the incident electric field, depending on the sphere’s velocity. In the comoving frame, the incident signal was Fourier-transformed to the frequency domain, and the scattered field phasors were computed in all directions using the constitutive parameters of the material of the sphere at rest. The scattered signal in the comoving frame was obtained using the inverse Fourier transform. Finally, the scattered signal in the laboratory frame was obtained by inverting the original Lorentz transformation. The backscattered signal was found to depend strongly on the sphere’s velocity, when the sphere’s speed is an appreciable fraction of the speed of light in free space. The change in the backscattered signal compared with the backscattered signal from a stationary sphere is the greatest when the sphere’s velocity is either parallel or antiparallel to the direction of propagation of the incident signal. The backscattered signal is also affected by motion transverse to the incident signal’s direction of propagation; then, the backscattered signal depends on whether or not the motion is aligned with the direction of the incident electric field.

This paper considers slotted ALOHA networks in Weibull fading channels. A simplified signal capture model is used to analyze both capture probability and throughput of the slotted ALOHA protocol.