Efficient Calculation of Propagation Coefficients in Anisotropic Media Through Transfer Matrix Method Based on Eigenvalue Analysis

To explore the anisotropic nature and improve computational efficiency, eigenvalue (EV-) analysis is adopted to implement the transfer matrix method (TMM), abbreviated as EV-TMM, enabling the accurate capture of propagation coefficients with different polarizations under the inhomogeneous multi-layer background. When the plane waves carrying electromagnetic information enters an anisotropic medium from air, it will excite four beams with different energies and propagation directions in the medium. Starting from the anisotropic Maxwell’s equations, the governing equation in matrix form is constructed from constitutive relations of the electromagnetic field. When facing different anisotropy, the eigenvalues along the vertical direction are obtained calculating the partial differential equation. Subsequently, given the electric intensity in the co-polarization direction, other relevant components can be easily acquired based on the aforementioned governing equation and Faraday’s law. For characterizing the data connections between different layer media, the tangential conditions of electric and magnetic fields are applied to construct the transfer matrix for the multi-layer media. To verify the reliability of EV-TMM, the commercial software COMSOL, the finite-difference time-domain (FDTD) method, and the conventional TMM (C-TMM) are selected as benchmarks for rigorous validation through two numerical experiments under different plane wave modes. EV-TMM saves at least 51.3% of memory and 57.0% of CPU computation time when analyzing various anisotropic structures. Finally, we utilize the amplitude modulation technology to change the value at the transverse vectors and obtain color images of the propagation coefficient in subsurface multi-layer media by EV-TMM, thus achieving the analysis for geological structure.