Reflection and Transmission Coefficients in Multilayered Fully Anisotropic Media Solved by Transfer Matrix Method With Plane Waves for Predicting Energy Transmission Course

In this article, we rapidly and accurately solve out reflection and transmission coefficients in the multilayered fully anisotropic media (MFAM) based on the transfer-matrix method (TMM) so that we could find out the energy transmission course (ETC) of plane waves that transmit through MFAM in the air background. Beginning with Maxwell's equations, MFAM's Helmholtz equation could be obtained by the known transverse- k vectors of plane waves. Through a series of complicated manipulations applied to the derivation of Helmholtz equations, we can attain ordinary differential equation of electric fields that merely exist in a certain direction and then compute four different eigenvalues in different MFAM regions. Under 3-D cases, meanwhile, concrete expressions of other fields can be obtained by given electric fields in the fixed direction. The ETC of electromagnetic fields in the tangential continuity is mainly considered in the TMM, and hence, the transferring matrix of electromagnetic field between MFAM regions can be constructed to achieve reflection and transmission coefficients. With various plane-wave modes such as transverse electromagnetic (TEM), transverse electric (TE), and transverse magnetic (TM) field modes, respectively, computational results of MFAM models are solved and adopted to compare with those from the commercial software of COMSOL. Finally, to discuss deeply and efficiently achieve color images, we acquire those reflection and transmission coefficients of more complicated fully anisotropic materials under the different transverse- k vectors. Our work can be an efficient and reliable solver for excavating prospective applications to predict ETC of models with single-layered/multilayered materials possessing fully anisotropy.