Time-dependent scalar Beltrami-Hertz potentials in free space

We have solved the Beltrami-Maxwell equations for free space in terms of time-dependent scalar functions, the so-called scalar Beltrami-Hertz potentials. The two Beltrami fields have been represented in terms of scalar Beltrami-Hertz potentials. While the method is formulated for general sources, it is at its most powerful when the impressed source current densities are unidirectional: each Beltrami field, a complex-valued vector, can then be derived from a single scalar Beltrami-Hertz potential. We have calculated the corresponding scalar Green function explicity and given closed-form solutions for dipolar sources. Finally, the connection between the Beltrami-Maxwell formalism and conventional electromagnetic theory has been re-affirmed.