Manipulation of the resonance interaction in Mach-Zehnder-Fano interferometers

We study tunable interaction of the resonances in the Mach-Zehnder-Fano interferometers (MZFIs). A discrete Mach-Zehnder interferometer (MZI) with balanced arms supports bound states in the continuum. We demonstrate that doping an impurity in conventional MZIs gives rise to robust high-Q Fano resonances with asymmetric line shapes. By means of the modified Fano-Anderson model and the scattering-matrix approach, we show that the transmission and the intensity spectra of the whole system are very sensitive to both the location and the strength of the impurity. The side-coupled Fano defects induce an interaction with different eigenmodes of the pure MZI loop. We explore this interaction by tuning the parameters of the Fano defects. The observed resonance interaction can be attributed to the Fano-Feshbach resonance. We further provide with a particular physical example of photonic crystal circuit the applicability of our concept.