Fig. 1
From: Ultrafast perturbation maps as a quantitative tool for testing of multi-port photonic devices
Illustration of the problem. An m-th ingoing waveguide mode \(\widetilde {\bf{\Phi }}_m^ +\) excites an arbitrary photonic system containing a perturbation Δ\({\bf{\epsilon }}\), yielding the total field \({\bf{E}}_m^ +\). The transmission coefficient to the n-th outgoing mode \(\widetilde {\bf{\Phi }}_n^ -\) is \(t_{mn} = t_{mn}^0 + C_{mn}\), where \(t_{mn}^0\) is the transmission coefficient in the unperturbed system and C mn the coupling coefficient induced by scattering by the perturbation. The perturbation map is obtained by scanning the perturbation over the photonic system
