Derivation of the Transient and Steady Optical States from the Poles of the S‐Matrix

The electromagnetic response of optical systems can be described by scattering operators, S, that link the incoming fields onto the system to the outgoing fields emerging from it. Considerable efforts have been devoted to retrieve the spectral response of the optical systems by expanding the S-matrix in terms of its singularities. Here a planar optical cavity that allows to derive analytical expressions of poles (in the case of lossless materials) and residues, and reflection/transmission Fresnel coefficients in the harmonic domain is considered. This singularity expansion is used to derive the impulse response function (IRF) of the cavity with respect to the poles of the S-matrix. The singular expression of the IRF consists of contributions oscillating at the excitation frequency and exponentially decaying contributions that impact signals only during the transient regimes. The convergence of this approach is thoroughly discussed in the case of a dispersive and metallic slab. The convergence is achieved by increasing the number of poles in the singularity expansion. It can also be achieved by considering only the poles within the spectral range of interest plus a fictive resonant term encapsulating the contribution of the singularities outside this spectral range.