Reconfigurable multiport switch in coupled mode devices

We consider a coupled mode system where the effective propagation constants of localized modes are amenable to modulation. Starting from an unmodulated system where power transfer is heavily suppressed, we demonstrate that small, periodic modulation of the propagation constants enhance power transfer using a slowly varying envelope approximation for the field mode amplitudes. We calculate an approximate modulation frequency enabling complete transfer between otherwise negligibly coupled elements. The ability to control these modulations by electrical or thermal effects allows for reconfigurable multiport switching. We use an array of coupled silica waveguides and the thermo-optic effect to test our predictions in the telecom C-band. However, realistic parameters require spatial frequency modulation in the order of $10^{3}~\mathrm{rad/m}$ to produce total power transfer at spatial frequencies of the order $10^{2}~\mathrm{rad/m}$ that are unrealistic for integrated photonic applications. Nevertheless, our results are valid for devices described by an equivalent coupled mode matrix for space or time propagation; for example, arrays of microring or terahertz resonators, microwave cavities, radio frequency antennas, or RLC circuits.