Abstract
Transmission through a complex network of nonlinear one-dimensional leads is discussed by extending the stationary scattering theory on quantum graphs to the nonlinear regime. We show that the existence of cycles inside the graph leads to a large number of sharp resonances that dominate scattering. The latter resonances are then shown to be extremely sensitive to the nonlinearity and display multistability and hysteresis. This work provides a framework for the study of light propagation in complex optical networks.
- Received 10 November 2010
DOI:https://doi.org/10.1103/PhysRevA.83.033831
©2011 American Physical Society