Yingji He

Gap solitons in parity-time complex periodic optical lattices with the real part of superlattices

We report the existence and stability of gap solitons in parity-time (PT) complex periodic optical lattices with the real part of superlattices. These solitons can stably exist in the semi-infinite gap. We have studied the effects of different relative strengths of the superlattices and different amplitudes of the imaginary part on soliton propagation. It was found that the relative strength of the superlattices and the amplitude of the imaginary part significantly affect the PT symmetry and the stability of solitons in the PT complex periodic optical lattices.

Two-dimensional multipeak gap solitons supported by parity-time-symmetric periodic potentials

We report on the existence and stability of the two-dimensional multipeak gap solitons in a parity-time-symmetric periodic potential with defocusing Kerr nonlinearity. We investigate the multipeak solitons with all the peaks of the real parts in-phase. It is found that these solitons can be stable in the first gap. The system can support not only the stable solitons with even number peaks, but also the stable solitons with odd number peaks. The transverse energy flow vector of these solitons is also studied.

Nonlocal multihump solitons in parity-time symmetric periodic potentials

We report on the existence and stability of nonlocal multihump gap solitons in one-dimensional parity-time symmetric periodic potentials. They can exist in the first gap in defocusing nonlocal nonlinearity and in the semi-infinite gap in focusing nonlocal nonlinearity. These solitons can be stable in the defocusing nonlinearity but are unstable in the focusing nonlinearity. For the multihump solitons, the shapes of the nonlinear contribution to refractive index are also multihump. The stability and shapes of the intensity distribution of these solitons will be changed by the degree of nonlocality. We also study the transverse power flow of these solitons.

Defect gap solitons in real linear periodic optical lattices with parity-time- symmetric nonlinear potentials

We report on the existence and stability of defect gap solitons in real linear periodic optical lattices with parity-time (PT)-symmetric nonlinear potentials. For uniform real periodic optical lattices and for a positive defect, the fundamental solitons exist in the semi-infinite gaps, and they are stable in wide regions. For a negative defect, solitons can exist in the semi-infinite gap and in the first gap. In the semi-infinite gap, solitons are also stable in a wide region, but are unstable in the region near the Bloch band. In the first gap, solitons are stable. With an increase of the amplitude of the imaginary part of the PT-symmetric nonlinear optical potentials, the stable region in the semi-infinite gap is shrunk; solitons are only stable in the moderate power region. In the first gap, solitons are unstable in the high-power region; they are only stable in the low-power region.

Defect gap solitons in self-focusing Kerr media with parity-time symmetric linear superlattices and modulated nonlinear lattices

We report the existence and stability of defect solitons (DSs) in a dissipative system with a parity-time (PT) symmetric linear superlattice and modulated periodical nonlinearity based on self-focusing Kerr media. It is found that for positive defects, the DSs can exist stably in the semi-infinite gap. For negative defects, the DSs can exist stably in both the semi-infinite and the first gap. The DSs in high power regions are unstable. If the defect strength increases, the stable regions shrink rapidly and eventually disappear. If the PT-symmetry is broken, all DSs are unstable.

Mixed-gap vector solitons in parity-time-symmetric mixed linear–nonlinear optical lattices

We report on the existence and stability of mixed-gap vector solitons in parity-time (PT)-symmetric mixed linear–nonlinear optical lattices. The first component is single-peaked, and the propagation constant is in the semi-infinite gap. The second component is the out-of-phase dipole mode; its propagation constant belongs to the first finite gap. The imaginary part and the depth of the PT-symmetric nonlinear optical lattice will significantly affect the existence and stability domains of these vector solitons. The propagation constant of the first component can also influence the existence and stability of the vector solitons. Finally, we also study the effect of the PT-symmetric linear optical lattice on the vector solitons’ stability.