Radiated spectrum from two partially correlated dipoles

Abstract
We examine the spatial directivity and the temporal spectrum of the field radiated by two partially correlated linear dipoles. The two dipoles are parallel and have identical spectra in their source excitation. Expressions are derived for the radiated spectrum, for the total emitted power, and for the directivity. We illustrate these results by calculating the radiated spectrum for a particular choice of the frequency-dependent correlation function. Results for the limiting cases of fully correlated dipoles and for uncorrelated dipoles are also derived.