SEMPO - Retrieving Complex poles, residues and zeros from arbitrary real spectral responses

Overview & Synopsis

The Singularity Expansion Method Parameter Optimizer -SEMPO -is a toolbox to extract the complex poles, zeros and residues of an arbitrary response function acquired along the real frequency axis. SEMPO allows to determine this full set of complex parameters of linear physical systems from their spectral responses only, without prior information about the system. The method leverages on the Singularity Expansion Method of the physical signal. This analytical expansion of the meromorphic function in the complex frequency plane motivates the use of an accuracy-driven improved version of the Cauchy method constrained by properties of physical systems, as well as an auto-differentiation-based optimization approach. Both approaches can be sequentially associated to provide highly accurate reconstructions of physical signals in large spectral windows. The performances of SEMPO are assessed and analysed in several configurations that include the dielectric permittivity of materials and the optical response spectra of various optical metasurfaces. SEMPO's performances are thoroughly analyzed and benchmarked with other state-of-the-art methods to highlight its capability to retrieve the natural poles of a physical system.