One-dimensional PT -symmetric eigenmodes in k-wave number Scarf II potential with defocusing nonlinearity

Abstract

Abstract The stationary states and dynamical evolution of one-dimensional eigenmodes in self-defocusing nonlinear Kerr medium under transverse parity-time (   ) symmetric k-wave number Scarff-II potential have been analysed. We study the effect of the coefficient of the imaginary component of the   -symmetric potential on the eigenvalue spectra of the ground and first excited states in linear and nonlinear models. Symmetric eigenmodes with real eigenvalues are obtained in the unbroken   regime in both models. The linear stability analysis shows that the solutions are stable in the unbroken   regime. The stable propagation of the solutions in linear and nonlinear media supported by   -symmetric k-wave number Scarff-II potential is also investigated. The comparison of the solutions in the presence and the absence of nonlinearity reveals that in the self-defocusing Kerr medium nonlinearity suppresses the region of   -symmetry. The influence of the width of the complex k-wave number Scarff-II potential and the depth of the real potential function on the   -symmetry breaking have also been analysed.