The optical properties of two-dimensional Scarff parity–time symmetric potentials

• The PT-breaking points with 2D Scarff parity–time are obtained.
• The relation with linear modes and solitons is reported.
• Fundamental and dipole solitons are studied.

We investigate the optical properties with two-dimensional (2D) Scarff parity–time (PT) symmetric potentials, including linear case, and self-focusing and self-defocussing nonlinear cases. For linear case, the PT-breaking points, the eigenvalues and eigenfunction for different modulated depths of 2D Scarff PT symmetry complex potential are obtained numerically. The PT-breaking points increase linearly with increasing the real part of the modulated depths of PT potential. Below the PT-breaking points, the eigenvalues of linear modes are real, however, eigenvalues of linear modes are complex above the PT-breaking points. For nonlinear cases, the existence of fundamental and multipole solitons is studied in self-focusing and self-defocussing media. The eigenvalue for linear case is equal to the critical propagation constant bcbc of soliton existing.