Homoclinic nonlinear band gap transmission threshold in discrete optical waveguide arrays

We show for the first time that supratransmission threshold can be found in discrete nonlinear Schrödinger equation modelling the optical waveguide arrays with Kerr nonlinearity using two-dimensional map approach. Called homoclinic nonlinear band gap threshold, this amplitude is in agreement with the numerical one even for the strongly discrete aspect of the waveguide and for the large frequencies.