Optical solitons in the parity-time-symmetric Bessel complex potential

Optical solitons in the parity-time (PT)-symmetric Bessel complex potential are studied, including the linear case, and self-focusing and self-defocusing nonlinear cases. For the linear case, the PT-symmetric breaking points, eigenvalues and the eigenfunction for different modulated depths of the PT-symmetric Bessel complex potential are obtained numerically. The PT-symmetric breaking points increase linearly with increasing the real part of the modulated depths of the PT potential. Below the PT-symmetric breaking points, the eigenfunctions of linear modes are symmetrical; however, the symmetries of the eigenfunction break above the PT-symmetric breaking points. For nonlinear cases, the existence and stability of fundamental and multipole solitons are studied in self-focusing and self-defocusing media. The eigenvalue for the linear case is equal to the critical propagation constant b(c) of the existing soliton. Fundamental solitons are stable in the whole region and multipole solitons are stable with the propagation constants being close to b(c) both for self-focusing and self-defocusing nonlinearities. The range of solitons' stability decreases with an increase of the number of the intensity peaks of the solitons.