This paper studies the difference between retro-directive beamforming technique and retroreflective beamforming technique in the context of wireless power transmission applications. In all of our studies, a wireless power receiver broadcasts continuous-wave pilot signal; the wireless power transmitter receives and analyzes the pilot signal; finally, the wireless power transmitter transmits continuous-wave power with phase profile conjugate to that of the received pilot signal. Our study demonstrates that a linear equi-spaced antenna array configuration employed by the wireless power transmitter behaves as a retro-directive beamformer when the wireless power receiver resides in the far-zone of the wireless power transmitter, whereas it behaves as a retro-reflective beamformer when the wireless power receiver is not in the far-zone. This paper further investigates two types of array configurations other than linear equi-spaced array when the wireless power transmitter behaves as a retro-reflective beamformer. One is a V-shaped array, which is obtained by deforming the linear equi-spaced array to a "V" shape. The other is termed "perturbed array:" on the basis of linear equi-spaced array, all the elements' locations are perturbed randomly. It is particularly interesting to compare the equi-spaced array and perturbed array. When the wireless power receiver resides 5 or 6 wavelengths away, a 6-element equi-spaced array and a 6-element perturbed array produce the same power level at the near-zone focal point, but the maximum far-zone gain associated with the perturbed array is 1 dB lower than the equi-spaced array. All the conclusions drawn in this paper are supported by numerical results as well as experimental results.

The development of time domain integral equation solvers with robust late-time stability properties has been a long-standing quest. Among the many methods that have been investigated, those leveraging quasi-exact integration techniques appear to be the most successful. This paper presents stable and accurate marching-on-in-time (MOT) solvers for time domain electric, magnetic, and combined field integral equations (EFIE, MFIE, and CFIE) based on quasi-exact integration technique. The novel MOT solvers exhibit excellent stability while yielding highly accurate results, as demonstrated by various numerical examples. In addition, the solvers’ excellent stability and accuracy properties are used to examine spurious modes encountered when time domain integral equations are applied to closed surfaces. It is demonstrated that MOT solutions to the time domain EFIE and MFIE often are polluted by spurious modes at the cavity’s resonant frequencies whereas those of the CFIE solver are devoid of such contamination.