RPExpand (Q706)

Summary The software RPExpand is designed for efficient evaluations of electromagnetic quantities based on rational approximants whose summands can be attributed to eigenmodes of the physical system. Based on contour integration methods [1], eigenfrequencies are determined that, together with corresponding residues, are used to reconstruct the target quantity at any frequency inside the contour [2]. Furthermore, its zeros can be retrieved and, optionally, derivative information along the contour can be used to compute derivatives of eigenfrequencies and zeros [3,4]. The target quantity does not need to be linear in the electric or magnetic field but can be based on quadratic forms and derived from the far field [5]. The results can be visualized with a built-in plot function. For a comprehensive control of the error, expansions are compared to direct solutions at selected frequencies and to results with reduced numbers of integration points. The number of modes present in the spectral region of interest and coupling to the specified source can be large. Then, it can be preferable to use eigenvalues and corresponding normalized eigenvectors from external solvers to perform expansions based on quasinormal modes (QNMs) and polynomial interpolation [6]. The resulting modal contributions are equivalent to the residue based approach described above and quantities quadratic in the electric field can be expanded directly without cross terms [7]. One advantage of contour integral methods is parallelizability. This has been extensively exploited in the design of the interface to the finite element method (FEM) solver [JCMsuite](https://jcmwave.com/). The interface handles the parallel submission of jobs keeping the interaction with the solver as easy as possible while allowing advanced users to access its full range of functionalities. References [1] A. P. Austin et al., SIAM J. Numer. Anal. 52, 1795 (2014). [2] L. Zschiedrich et al., Phys. Rev. A 98, 043806 (2018). [3] F. Binkowski et al., Commun. Phys. 5, 202 (2022). [4] F. Binkowski et al., Phys. Rev. B 109, 045414 (2024). [5] F. Binkowski et al., Phys. Rev. B 102, 035432 (2020). [6] T. Wu et al., J. Opt. Soc. Am. A 38, 1224 (2021). [7] F. Betz et al., Phys. Status Solidi A 220, 2200892 (2023).