Wave dynamics in optically modulated waveguide arrays.
A model describing wave propagation in optically modulated waveguide arrays is proposed. In the weakly guided regime, a two-dimensional semidiscrete nonlinear Schrödinger equation with the addition of a bulk diffraction term and an external "optical trap" is derived from first principles, i.e., Maxwell equations. When the nonlinearity is of the defocusing type, a family of unstaggered localized modes are numerically constructed. It is shown that the equation with an induced potential is well-posed and gives rise to localized dynamically stable nonlinear modes. The derived model is of the Gross-Pitaevskii type, a nonlinear Schrödinger equation with a linear optical potential, which also models Bose-Einstein condensates in a magnetic trap.
Ablowitz
Mark J
MJ
Department of Applied Mathematics, University of Colorado, Campus Box 526, Boulder, Colorado 80309-0526, USA.
Julien
Keith
K
Musslimani
Ziad H
ZH
Weinstein
Michael I
MI