ABSTRACT
Impedance matching is one of the most important practices in wave engineering as it enables one to maximize the power transfer from the signal source to the load in the wave system. Unfortunately, it is bounded by the Bode-Fano criterion which states that, for any passive, linear, and time-invariant matching network, there is a stringent trade-off between the matching bandwidth and efficiency, implying severe constraints on various electromagnetic and acoustic wave systems. Here, we propose a matching paradigm that overcomes this issue by using a temporal switching of the parameters of a metamaterial-based transmission line, thus revoking the time-invariance assumption underlying the Bode-Fano criterion. Using this scheme we show theoretically that an efficient wideband matching, beyond the Bode-Fano bound, can be achieved for short-time pulses in challenging cases of very high contrast between the load and the generator impedances, and with significant load dispersion, situations common in, e.g., small antenna matching, cloaking, and with applications for ultrawideband communication, high resolution imaging, and more.
ABSTRACT
We present a practical algorithm for designing an aperture field (source) that propagates along a predefined generic beam trajectory that consists of both convex and concave sections. We employ here the mechanism that forms the well-known Airy beam in which the beam trajectory follows a smooth convex caustic of the geometric optics rays and generalize it for a class of beams that are referred to as "caustic beams" (CBs). The implementation is based on "back-tracing" rays from the predefined beam trajectory to the source's aperture to form its phase distribution. The amplitude is set in order to form a uniform smooth amplitude of the CBs along their trajectories. Several numerical examples are included.
ABSTRACT
An efficient method for computing the problem of an electromagnetic beam transmission through deep periodic dielectric gratings is presented. In this method the beam is decomposed into a spectrum of plane waves, transmission coefficients corresponding to each such plane wave are found via Rigorous Coupled Wave Analysis, and the transmitted beam is calculated via inverse Fourier integral. To make the approach efficient for deep gratings the fast variations of the transmission coefficients versus spatial frequency are accounted for analytically by casting the summations and integrals in a form that has explicit rapidly varying exponential terms. The resulting formulation allows computing the transmitted beam with a small number of samples independent of the grating depth.
ABSTRACT
Presented here is an ultra-wideband-correlation-based scheme for imaging and inversion of an unknown weak and lossless scatterer embedded in a known background medium. The scheme uses an excitation and reception of ultra wideband/short-pulsed fields by an array of transducers located outside the imaging domain. The scatterer image is formed by cross correlating (in the short-pulsed domain or via spectral integration in the ultra wideband domain) the numerically/analytically back-propagated, measured, and scattered data set with the forward-propagation excitations. It is shown that in the ultra wideband domain, the forward-backward propagation functions form a frame set in a finite Hilbert space. Within the weak scattering assumption (Born approximation) the scatterer's image and object function (velocity profile) are related via the corresponding frame operator. Therefore, an exact inversion scheme of the frame operator is readily available to yield the object function via an iterative scheme or using the dual frame set. Numerical examples that demonstrate the performance of the imaging and inversion schemes for scatterers with various velocity profiles are presented. It is shown that the scatterer image is generally of poor resolution. However, on inversion, a high-quality velocity profile is obtained that captures the scatterer fine details.
