An Efficient Rescaled Formulation for Tensor Green’s Function Computation in Cylindrical Multilayered Media

A robust formulation is presented to eliminate overflow, underflow, and convergence problems that arise the computation of tensor Green's functions in cylindrical multilayered media under finite-precision arithmetic. This is done by first introducing a set of rescaled functions associated to the (canonical) cylindrical Bessel and Hankel functions representing standing waves and outgoing waves along the radial direction. The rescaled cylindrical functions are designed to avoid the poor scaling inherent to the canonical cylindrical functions for very small or very large arguments. In addition, a parabolic Sommerfeld integration path is constructed in the spectral complex plane to yield a numerical integration with good convergence properties for a wide range of parameter values.