Sommerfeld integration for arbitrary, multi-layer dielectric systems: a practical method for seawater antenna modelling

The authors present a formulation of the Sommerfeld integration method to calculate antenna radiation in an arbitrary stack of dielectric slabs. Historically, Sommerfeld integration, in the method of moments, has been used only for two semi-infinite layers (the lower layer often referred to as a ground plane). Here, the authors have returned to Sommerfeld´s original formulation to extend the method for an arbitrary number of layers. The authors show that this algorithm gives accurate results as proved by comparison to other simulations and approximate analytical formulas. The authors motivation is to calculate antenna coupling in a seawater environment at ultra-low frequencies, taking account of seawaves at the seabed and water surface. This is an important problem in marine engineering which cannot be addressed by finite element methods owing to the high aspect ratios and 10⁶-order jumps in complex permittivity across the different layers. As well as validating the algorithm for multiple layers the authors show results from a realistic air/sea/seabed setup. The authors demonstrate that, if the antenna is close to the seabed, surface waves can form on the sea/seabed interface as well as the air/sea interface potentially improving reception.