Poles and zeros of electromagnetic quantities in photonic systems

We present an approach to investigate poles and zeros in resonant photonic systems. The theory is based on contour integration of electromagnetic quantities and allows to compute the zeros, to extract their sensitivities with respect to geometrical or other parameters, and to perform modal expansions in the complex frequency plane. The approach is demonstrated using an example from the field of nanophotonics, an illuminated metasurface, where the emergence of reflection zeros due to the underlying resonance poles is explored.