Non-trivial Bifocal and Optical Vortex Generation of DNG Materials Unveiled by Generalized Transfer Matrix Method and Matrix Fourier Optics

Abstract: The investigation and analysis of exotic physical phenomena facilitated by metamaterials have emerged as a compelling area of interest in physics, material science, and engineering. However, there remains a lack of suitable theoretical tools for scrutinizing light-matter interactions in metamedia, particularly those involving distinct constitutive tensors, such as polarization cross-coupling or non-reciprocal propagation induced by bianisotropy. In this research, we apply the generalized transfer matrix method and matrix Fourier Optics to devise a novel hybrid methodology adept at efficiently tracing an optical beam as it propagates through transverse-homogeneous, longitudinal-inhomogeneous bianisotropic media. Our proof-of-concept demonstration elucidates the interaction between a nonparaxial Gaussian incident beam with various linear/circular polarizations and a mismatched anisotropic double-negative (DNG) metamaterial. We unveil the nontrivial bifocal effect and optical vortex (OV) generation and focusing phenomena in a three-dimensional environment, findings that have not been documented previously. Significantly, the proposed efficient methodology holds the potential for application in examining more promising physical phenomena exhibited by intricate metamaterials, enabling a more visually rigorous approach.