Spectral photonic response functions for temporal and broad band applications

Information extracted from a system’s quasi-normal modes—obtained via numerical solvers—should provide a means to reconstruct spectral expansions of photonic response functions (like the T -matrix). These spectral representations provide broad-band frequency predictions which should, in principle, even provide efficient time-domain simulations. However, time-domain implementations are typically constrained by the practical requirement of truncating the infinite spectral expansion, which introduces non-physical predictions, particularly at frequencies far from the region of interest. In this work, we show how physical and mathematical bounds on the response functions can be used to systematically adjust the spectral residues, thereby compensating for the effects of truncation.