H1(curl) tangential vector finite element method for modeling anisotropic optical fibers

For the purpose of modeling anisotropic optical fibers, accurate and efficient description of how electromagnetic waves propagate in these structures of arbitrary geometry is required. This paper presents a full-wave analysis of anisotropic waveguides which are characterized simultaneously by both off-diagonal second rank symmetric [ε] and [μ] tensors. By using the H₁(curl) tangential vector finite element method, electromagnetic characteristics of propagating modes in the fibers are obtained without the occurrence of spurious modes. In this procedure, a formulation in terms of vector and scalar potentials is adopted and the eigenvalue of the final matrix equation corresponds to the propagation constant itself. Furthermore, the direct matrix solution technique with minimum degree of reordering has been combined with the modified Lanczos algorithm to solve for the resultant sparse generalized eigenmatrix equation efficiently. To demonstrate the strength of the present method, numerical results are verified and agreements with other published results are achieved