Temporal Modal Analysis of Small Radiators

Abstract

Resonance is a common physical phenomenon in real world, and the modal analysis is a useful tool. Within the regime of electromagnetics, characteristic mode theory is established in frequency domain (FD), and it is doubtful that whether we can find similar modes in time domain (TD). In this paper, resonating modes of a vibrating string are briefly reviewed. Special attentions are paid to the time-domain behaviors of the resonating modes, by following which a temporal modal analysis is proposed. Additionally, a narrow plate is selected as an example since it has a similar structure as the vibrating string. Temporal modal behaviors of the plate are presented and discussed. To further demonstrate this concept, a rigorous analysis of a sphere is provided. A frequency-independent condition is discussed and verified for small objects, and it results in a band-limited constraint. In addition, the temporal modal analysis with excitations is presented, and its potential applications are discussed with emphasis on the analyzing and optimizing transient behaviors of antennas. This work expands largely the field of characteristic mode and may find applications for scattering and antennas.