Design algorithms of driving-induced nonreciprocal components

We utilize an effective Hamiltonian formalism, within the Floquet scattering framework, to design a class of driving-induced non-reciprocal components with {\it minimal} complexity. In the high driving-frequency limit, where our scheme is formally applicable, these designs demonstrate a leading order non-reciprocal performance which is inverse proportional to the driving frequency. Surprisingly, the optimal non-reciprocal behavior persists also in the slow driving regime. Our approach highlights the importance of physical loops in the design of these driven non-reciprocal components.