A generalized Debye source approach to electromagnetic scattering in layered media

The standard solution to time-harmonic electromagnetic scattering problems in homogeneous layered media relies on the use of the electric field dyadic Green's function. However, for small values of the governing angular frequency $\omega$, evaluation of the electric field using this Green's function exhibits numerical instability. In this short note, we provide an alternative approach which is immune from this low-frequency breakdown as $\omega \to 0$. Our approach is based on the generalized Debye source representation of Maxwell fields. Using this formulation, the electric and magnetic fields gracefully decouple in the static limit, a behavior similar to that of the classical Lorenz-Debye-Mie representation of Maxwell fields in spherical geometries. We derive extensions of both the generalized Deybe source and Lorenz-Debye-Mie representations to planar geometries, as well as provide equations for the solution of scattering from a perfectly conducting half-space and in layered media using a Sommerfeld-like approach. These formulas are stable as $\omega$ tends to zero, and offer alternatives to the electric field dyadic Green's function.