Dispersion relations for extinction of acoustic and electromagnetic waves

Abstract: This thesis deals with physical limitations on scattering and absorption of acoustic and electromagnetic waves. A general dispersion relation for the extinction cross section of such waves is derived from the holomorphic properties of the scattering amplitude in the forward direction. The result states that for a given volume, there is only a limited amount of scattering and absorption available in the entire frequency range. The dispersion relation is shown to be valuable for a broad range of problems in theoretical physics involving wave interaction with matter over a frequency interval. The theory of broadband extinction of electromagnetic waves is also applied to a large class of causal and reciprocal antennas to establish physical realizability and upper bounds on bandwidth and directive properties. The results are compared with classical limitations based on eigenfunction expansions, and shown to provide sharper inequalities and, more importantly, a new fundamental understanding of antenna dynamics solely based on static properties. In modeling of metamaterials, the theory implies that for a narrow frequency band, engineered composite materials may possess extraordinary characteristics, but tradeoffs are necessary to increase its bandwidth.