Hybrid matrix method for stable analysis of wave propagation in multilayered complex media - Ning, Jing (2009)
This thesis presents the analysis of electromagnetic and acoustic wave propagation in multilayered complex media. First of all, a new hybrid matrix method is proposed for stable analysis of electromagnetic wave propagation in multilayered bianisotropic media. The method overcomes the numerical instability of transfer and impedance matrix methods known for the entire thickness and frequency range. To determine the hybrid matrix of each layer, a new and simple self-recursive asymptotic method along with thin-layer asymptotic approximation is introduced. It only requires elementary matrix operations and bypasses the intricacies of eigenvalue-eigenvector approach. The stack hybrid matrix for multilayered bianisotropic media is also obtained by employing matrix recursions. The method is then applied to the study of the dispersion relation of layered bianisotropic waveguides, and to calculating the reflection coefficient and shielding effectiveness of multilayered anisotropic materials for the design of radar absorbers and laminated shields. Then, the propagation, reflection and transmission of light in one-dimensional photonic crystals are investigated. The Bloch-Floquet waves are determined by a new generalized eigenproblem of hybrid matrix method. It overcomes the numerical instability in the standard eigenproblem of transfer matrix method. Using the imaginary part of the Bloch-Floquet wavenumbers, we demonstrate that it is convenient to determine (if any) the frequency range of omnidirectional reflection. The effects of chirality, loss and tunable anisotropy are also discussed along with the numerical results. Finally, the hybrid matrix method is extended for the analysis of acoustic wave propagation in multilayered solids and fluids. The method can still provide robust results even when the thickness tends to infinity or zero. The matrix recursions for multilayered media with different solid and fluid phases are presented.