The asymmetric solitons in two-dimensional parity–time-symmetric potentials

We investigate the properties in two-dimensional (2D) special parity–time (PT) symmetric complex potentials. The linear case of this special 2D PT-symmetric complex potential and self-focusing nonlinear cases are discussed. For linear case, the eigenvalues and eigenfunction for different loss or gain level of the PT-symmetric complex potentials are obtained numerically. For nonlinear cases, the existence of asymmetric solitons and PT-symmetric solitons is studied in this PT symmetric system. The eigenvalue for linear case is equal to the critical propagation constant bc of existing PT-symmetric solitons. When the PT-symmetric soliton's propagation constant reaches a certain threshold bc1, a branch of asymmetric solitons can bifurcate out from the branch of PT-symmetric solitons.