Efficient Higher Order Spectral Element Method for Analyzing Modal Fields in Anisotropic Metamaterial Fibers

We present an efficient higher-order spectral element method formulated in cylindrical coordinates for analyzing electromagnetic fields in anisotropic metamaterial fibers. The formulation employs higher-order two-dimensional basis functions associated with the zeros of the completed Lobatto polynomial to represent the electromagnetic fields and uses a complex coordinate-stretched perfectly matched layer to mimic a radially unbounded surrounding air medium. We apply our technique to model anisotropic graded-index, strongly biaxial anisotropic, lossless, and lossy hyperbolic metamaterial fibers. The results show that the SEM requires less than 1% of the degrees of freedom (memory cost) used by FEM while providing solutions with similar accuracy. In addition, the computation time required by SEM is approximately 1/3 of that needed by FEM for the examples considered. A highly efficient and flexible modeling method, such as the proposed SEM, is highly desirable for synthetic data generation and training of machine learning methods and for rapid design of anisotropic and metamaterial fibers, offering potential applications in optoelectronics and advanced material design.