Modal Analysis of Composite Optical Fibers by a Vectorial Extended Integral Equation Method

We have developed a vectorial solution of coupled-integral representations (IRs) based on the extended integral equation (EIE) method, for the modal analysis of composite optical fibers (OFs). The method of solution is fully vectorial and it is based on the expansion of the electric and magnetic fields and Green's function (GF) in cylindrical vector wave functions (CVWFs). To correctly construct the determinantal equation for the calculation of the propagation constants, we apply a scheme on the electric and magnetic fields, appearing in the kernels of the IRs, where we satisfy the continuity of their tangential components at the dielectric surfaces of the OF. The developed solution allows for the calculation of the propagation constants in the general case, i.e, not within the weakly guiding approximation (WGA). Non circular core-cladding OFs, as well as composite core-shell-cladding structures, are examined. The method is exhaustively validated with analytical techniques, the literature and the HFSS commercial software. The numerical convergence and the computational performance are also discussed. The developed solution is utilized to study how the orbital angular momentum (OAM) modes change their modal characteristics under geometrical imperfections of core-cladding OFs, and how the fundamental mode is affected due to imperfect core offset in anti-resonant tube terahertz core-shell-cladding OFs.