Radiation of complex sources in reflecting environments: A Wigner function approach

The radiation of complex sources in either free-space or reflecting environments is described through a statistical approach involving the field-field correlation function. A representation in phase-space, the Wigner distribution function, is used to unveil the wave mechanics of waves propagated in the near-and far-fields. An evolution operator for these Wigner functions is derived and approximation schemes are presented using densities of ray families. This provides efficiency gains by reducing the dimension of the calculation. Numerical results are presented and discussed for near-homogeneous sources radiating in front of planar metallic reflectors. The approximated correlation is found to reproduce the interference pattern of the intensity accurately near the reflector. These results are fundamental for understanding and predicting emissions from sources in more complicated environments.