A Numerical Mode Matching (NMM) Method for Optical Fibers with Kerr Nonlinearity

Recently, the reshaping of the transverse light field profile in nonlinear multimode fibers (MMFs) has attracted great attentions. However, the electromagnetic (EM) fields in such nonlinear media cannot be easily and accurately calculated by using the traditional computational electromagnetics methods due to the nonlinearity of Kerr optical materials in graded-index (GRIN) MMFs. The iterative division method based on the 2.5-D spectral element numerical mode matching (SNMM) method is developed to address this problem. The SNMM method is a semi-analytical method, which can effectively reduce the computational costs to obtain highly accurate solutions. Starting from the numerical results of SNMM, the iterative division method solves electromagnetic fields of the linear-to-nonlinear transition process together iteratively. In this work, several improvements are proposed to extend the SNMM for Kerr optical nonlinear MMFs. The governing equations with anisotropic permittivity with Kerr optical nonlinear media are established in the cylindrical coordinate system. The absorbing boundary condition (ABC) is introduced to replace the perfectly matched layer (PML) so that the eigenmodes of a waveguide can be obtained accurately. Numerical results show the validity, accuracy and advantages of the proposed method in simulated MMFs.