Gauge-Free Whittaker Potentials to Model Wave Propagation in Homogeneous Medium

This article deals with alternative scalar potential formulations where no side effect associated to gauging exists whose purpose is to enhance the variety of accessible methods for efficient calculations of electromagnetic (EM) wave fields. In previous investigations, it was shown that in the process of gauging ordinary electrodynamic potentials, an unintentionally changed phase velocity of certain potentials occurs in specific scenarios. Some workarounds for correction were provided there. This aspect in particular suggests as an overriding goal the desire to circumvent any kind of gauge fixing. To realize that, the unusual Whittaker potentials are utilized, which are closely related to the better known Hertz potentials. Besides reasonable propagation properties, they sometimes allow a promising reduction of equations and simplified boundary conditions. Several specifically defined frameworks based on different coordinate systems facilitate appropriate formulations. Proposed dual gauge transformations enable conversions among the two Whittaker potentials for electrodynamically coupled fields. Many detailed computational demonstrations of realistic radio frequency (RF) scenarios modeled with each Whittaker potential individually enable versatile use for practitioners. Although the idea to combine them already exists, an estimation is given to continue this endeavor. Moreover, broad applicability is emphasized by two static scenarios.