Circular cylindrical lens as a line-source electromagnetic-missile launcher

The energy of an electromagnetic pulse transmitted from an antenna of finite size to a distant receiver can decrease more slowly than the usual 1/r² where r represents the distance from the transmission to reception points. An electromagnetic pulse that is characterized by such a slow decrease in energy is referred to as an electromagnetic missile. The possibility of launching an electromagnetic missile from a circular cylindrical lens is analyzed in terms of optical ray tracing. A more precise series solution for the radiation field and its asymptotic approximation is then given in which the analysis is carried out in the frequency domain with no high-frequency limitation using the Helmholtz equations and the boundary conditions. The frequency-domain representation is of a sequency of pulses, not of a single continuous wave; the energy of the total electromagnetic pulse is then obtained by integration over the frequency. After using the asymptotic expansion for unlimited frequency, the radiation field in the far region is shown to be characterized by electromagnetic-missile effects, i.e. the decay of the energy per unit length is slower than 1/ r