Linear and nonlinear guided modes in a parabolic potential

V. V. Konotop and D. A. Zezyulin

University of Lisbon , Portugal

We describe the families of nonlinear modes of the nonlinear Schrodinger equation with the PT-symmetric harmonic potential. The found modes display a number of interesting features. In particular, even when they bifurcate from the different eigenstates of the underlying linear problem, they can belong to the same family of nonlinear modes. We also show that by proper adjustment of the gain/loss gradient it is possible to enhance stability of small-amplitude and strongly nonlinear modes comparing to the well-studied case of the real harmonic potential. Implications of the above properties for the guidance of optical beams, in particular for giant amplification of the guided modes will also be discussed. A part of this work is done in collaboration with V. S. Shchesnovich.