Nonlocal solitons supported by non-parity-time-symmetric complex potentials

We report on the existence and stability of fundamental and out-of-phase dipole solitons in nonlocal focusing Kerr media supported by one-dimensional non-parity-time (PT)-symmetric complex potentials. These fundamental and dipole solitons bifurcate from different discrete eigenvalues in the linear spectra. Below the phase transition of the non-PT-symmetric complex potentials, these solitons are stable in the low power region. While above the phase transition, they are stable in the moderate power region. The eigenvalues in linear-stability spectra of solitons appear as conjugation pairs (delta, delta*). The transverse power flow and the nonlinear contribution to refractive index are asymmetric functions. Moreover, the degree of nonlocality can also influence the stability of these solitons.