Nonintegrability of the energy density of “complex sources” wavefields

As is well known, time-harmonic “complex sources” wavefields that show a Gaussian-type localization, are solutions of inhomogeneous Helmholtz equation where source functions are supported by certain antennas with a circular edge. We address energy density of a “complex source” wavefield in a neighborhood of the edge of the antenna and show that it is nonintegrable.