Study on High Precision and Stable Finite Element Beam Propagation Method Based on Incomplete Third Order Hybrid Edge/Nodal Element

It has been reported that the full vectorial finite element beam propagation method (FV-FE-BPM) is not always stable. In this paper, we propose a stabilized FV-FE-BPM using a linear filter to suppress unstable modes. Moreover, aiming for improving the computational accuracy of FV-FE-BPM for longitudinally varying optical waveguides, we employ incomplete third order hybrid edge/nodal elements to reduce interpolation error which occurs in finite element mesh update process at each propagation step. The validity and effectiveness of this approach are verified through several numerical examples of uniform waveguides and longitudinally varying waveguides.