Geometrical approach to stationary waves in a shallow grating

摘要

A geometrical analysis of the monochromatic solutions near the first band gap for a shallow Kerr grating is presented. The analysis is based on the coupled mode formalism and on Stokes variables. We investigate the electric field for nonzero energy flow, in particular we consider the phase difference between the counter-propagating coupled modes. Phase portraits for zero and nonzero energy flow are topologically different, and we clarify the way in which they are connected, thus identifying families of trajectories for nonzero flow that disappear when the flow goes to zero. References: 10