Huagang Li

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.

Gray solitons in parity-time symmetric potentials

We numerically study the gray solitons in parity-time (PT) symmetric potentials. Simulated results show that there are two kinds of gray solitons, the dip-shaped gray solitons and the hump-shaped solitons, and both of them can be stable. Hump-shaped solitons can always exist, but the grayness of a stable dip-shaped gray soliton should exceed a threshold value. More interesting, it is discovered that when propagating in PT symmetric potentials, the gray solitons have no transverse deviation, and this is a phenomenon different from the usual gray solitons.

Nonlocal bright spatial solitons in defocusing Kerr media supported by \chem{\cal {PT}} symmetric potentials

The bright spatial solitons in nonlocal defocusing Kerr media with parity-time () symmetric potentials are studied. The influence of the degree of nonlocality on the solitons and the transverse energy flow within the stable solitons are examined. We also find that these solitons can exist and be stable over a different range of the propagation constant and potential parameters. Interestingly, there exists a threshold value for the degree of nonlocality or potential parameters.

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.

Propagation of an Airy-Gaussian beam in defected photonic lattices

We investigate numerically that a finite Airy-Gaussian (AiG) beam varies its trajectory and shape in defected photonic lattices. Propagation properties and beam self-bending are controlled with modulation depth and period of photonic lattices, positive and negative defects, beam distribution factor and nonlinearities. For positive defects, the pseudo-period oscillation and localization of the AiG beam may form under a certain condition, while the beam diffuses in negative defects. Moreover, the solitons may appear during the propagation when the self-focusing nonlinearity is introduced.

Discrete dark solitons in parity–time-symmetric waveguide arrays with gain and loss

We demonstrate that discrete dark solitons can be self-trapped in binary self-defocusing parity–time-symmetric waveguide arrays with gain and loss. The discrete dark solitons appear in the form of a localized dip on the Bloch-wave background. When the appropriate boundary condition is satisfied in such finite arrays, the analytical and numerical solutions of discrete dark solitons exist and can both be stable in the one-dimensional case; the stable fundamental discrete vortex solitons can be numerically gained in the two-dimensional case. Interestingly, such one-dimensional discrete dark solitons do not exhibit displacement properties.

Surface defect gap solitons in optical lattices with nonlocal nonlinearity

We show that stable surface fundamental defect solitons can exist in different gaps of an optical lattice with focusing nonlocal Kerr nonlinearity. For positive defect, solitons stably exist in the semi-infinite gap. For negative defect, solitons are stable in the semi-infinite gap and the first gap. Increasing the negative defect depth, the existent regions of defect solitons in the semi-infinite gap and in the first gap will be changed. The degree of the nonlocality will affect the profiles of these solitons.

Transmission of nonparaxial nonlocal lattice solitons at nonlinear interfaces

We report on transmission of nonparaxial nonlocal lattice solitons at an arbitrary angle of incidence to the interface separating two nonlinear media with transverse periodic modulation of the refractive index. The energy distribution of solitons in two media can be varied by the degree of nonlocality, the nonlinear refractive index mismatch parameter at the interface, the nonparaxial parameter, the angle of incidence and the lattice parameters. Importantly, the modulation period and depth can introduce different regimes of soliton propagation in the media including refraction and trapping.