Comparative modal analysis in micro–nano-optical fiber tapers using spectral parameter power series method and exact modes method

This work presents a comparative theoretical analysis of spatial modal evolution in micro/nano-optical fiber (MNF) tapers. The study proposes the use of the Spectral Parameter Power Series (SPPS) Method and compares its performance with results from the so-called Exact Modes Method (EMM) and the Finite Element Method (FEM) (the method employed by the COMSOL© software in which the computations were implemented). By using these techniques, the modal analysis and intensity evolution are discussed along different sections of the optical fiber taper. Furthermore, the data are compared considering experimental values from a real micro/nano-optical fiber taper sample. The SPPS method offers a competitive accuracy and versatility to deal with graded index profiles, its computational costs are low, and its implementation is relatively easy. The results from the SPPS method fit to those of the EM method, which sometimes involves intricated models, and those of the FEM, which may require more computational time. The SPPS method offers an average relative error of less than 5% with respect to the exact method with less computational cost compared to the FEM method for radii bigger than 2 μm at 1550 nm.