Numerical simulation for SNAP based on the Numerov method.

Surface nanoscale axial photonics (SNAP) microresonators are optical resonators characterized by nanoscale effective radius variations (ERV). In this work, we developed a numerical framework based on the Numerov method for modeling SNAP microresonators. The accuracy of the approach is validated by comparison with analytical solutions for specified ERV profiles. We further apply the method to a long semiparabolic ERV structure designed for advanced group delay applications, for which no analytical solution exists. The results demonstrate high accuracy and at least a twenty-fold improvement in computational efficiency. This work provides an efficient and reliable approach for modeling SNAP devices with arbitrary ERV profiles.