Engineering Fano resonances in discrete networks

We study transmission properties of discrete networks composed of linear arrays coupled to systems of N side defects, and demonstrate the basic principles of the resonant scattering management through engineering Fano resonances. We find exact solutions for the wave transmission coefficient and reveal the conditions for the perfect reflections and transmissions due to either destructive or constructive interferences. We associate these reflections and transmissions with Fano resonances, and demonstrate how they can be tuned by introducing nonlinear defects into the network.