Modal analysis of a highly multimoded microstructured optical fibre using a deflated nonlinear eigenvalue solver

We detail a new approach to the calculation of many leaky modes of a Microstructured Optical Fibres (MOF). A general Dirichlet-to-Neumann NRBC is used which leads to a nonlinear eigenvalue problem (NLEP). This NLEP is solved using residual inverse iteration and previously calculated modes are deflated from each iterate. This technique is fast, does not require the tuning of parameters of the boundary condition and finds unique modes that are orthogonal with respect to an orthogonality relation consistent with the NLEP. All modes found were unique; on the other hand, when an eigensolver without orthogonalisation is used 30% of all modes found were modes that had already been calculated. In conjunction with the development of more sophisticated numerical methods for NLEP this method promises to be an automatic and efficient way to reliably calculate large numbers of modes in multimoded MOF.