We study nonlinear relaxation of the excited state in a system with two levels and a continuum. The process is first simulated in a one-dimensional waveguide array described by the discrete nonlinear Schrödinger equation. The results are interpreted in terms of degenerate four-wave mixing between the eigenmodes and diffraction properties of the array. We also show analytically that the role of the continuum can be played by a third bound state, with linear loss that replaces the diffraction in the continuum. This model enables derivation of the energy transfer rate and other parameters of the process.

• Received 26 January 2006
• Corrected 16 June 2006

DOI:https://doi.org/10.1103/PhysRevA.73.063811