Calculated threshold of supratransmission phenomena in waveguide arrays with saturable nonlinearity

In this work, we consider a semi-infinite discrete nonlinear Schrödinger equation with saturable nonlinearity driven at one edge by a driving force. The equation models the dynamics of coupled photorefractive waveguide arrays. It has been reported that when the frequency of the driving force is in the forbidden band, energy can be transmitted along the lattices provided that the driving amplitude is above a critical value. This nonlinear tunneling is called supratransmission. Here, we explain the source of supratransmission using geometric illustrations. Approximations to the critical amplitude for supratransmission are presented as well.