Development, Study and Applications of Causal Directed Electromagnetic Wavelets

摘要

Substantial progress was made in analyzing the physical sources needed to realize pulsed-beam wavelets in practice. This was accomplished by extending classical potential theory to complex space-time, where point sources become distributions supported on disk-like dishes emitting pulsed beams. A careful and rigorous regularization method had to be devised for these distributions to be well defined. This also led to an explicit computation of the Fourier transform of pulsed-beam wavelets, which is expected to play an important role in computational methods based on the previously proposed generalized radar analysis. The viability of modeling reception, as well as emission, on pulsed-beam wavelets was proved by showing that the Green function, when extended analytically to complex observation points as well as complex emission points, can be sensibly interpreted as a coupling between transmitting and receiving dishes, both having pulsed-beam transmission and reception patterns. A start was made toward understanding the current densities needed to produce electromagnetic pulsed-beam wavelets by computing the rotating current density necessary to produce holomorphic Coulomb fields.