A New Propagator Matrix Algorithm to Compute Electromagnetic Fields in Multilayered Formations With Full Anisotropy

A new and succinct semi-analytical algorithm has been developed to compute the electromagnetic (EM) fields radiated by a magnetic or electrical dipole source in planar-stratified formations with full anisotropy. The new algorithm is based on a modified propagator matrix (MPM) approach to elaborate the propagations of spectral EM waves. First, the original boundary condition equation is modified, so that each linear equation only consists of three unknown amplitude vectors. These amplitudes are then connected by artificially assembling all boundary conditions, giving rise to a global linear system with a tridiagonal matrix. Using the diagonal matrix algorithm, the spectral EM fields are readily obtained via a set of
$2\times2$
matrix operations. A hybrid integral approach is then developed in order to accurately convert the spectral EM fields into the spatial domain. Taking advantages of the Gauss–Legendre quadrature (GLQ) approach in conjunction with the sine/cosine digital filtering method, the high oscillating problem of the inverse Fourier transform (IFT) has been addressed. Considering the attenuation changes of the EM waves under different wavenumbers, a self-adaptive model reduction scheme is also proposed to effectively cut off the unnecessary and remote formations. This model simplification can significantly speed up the computation in favorable conditions. Numerical experiments show that the proposed semi-analytical method is efficient, robust, and stable, and it has provided a fast simulator for the EM radiation problems in the presence of multilayered formations with full anisotropy.