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We investigate the existence and stability of nonlocal surface solitons at the interface between linear media and nonlocal nonlinear media with two-dimensional (2D) parity-time ( PT )-symmetric optical lattices. We analytically obtain the nonlinearity-induced change of the refractive index by introducing a reasonable step function with the method of Fourier transform, and carry out the linear stability analysis for the surface solitons based on the response function of the infinite nonlocal medium. Numerical results show that nonlocal PT surface solitons can exist and be stable in 2D PT -symmetric optical lattices.

A method for the generation of tunable multi-degree-of-freedom rotations of vector beams on demand along a propagation direction is theoretically proposed. This generation can be achieved by a suitable vector superposition of three monochromatic non-coplanar beams, including a plane wave with elliptical polarization and two Bessel–Hermite–Gauss (BHG) beams with orthogonal polarization, the parameters of which were systematically chosen to obtain the different longitudinal characteristics of the field, i.e., the state of polarization (SoP), phase, and intensity. On one hand, both the incidence angles of the two BHG beams and the additional phase of the plane wave affect the rotation of the beam intensity and phase, but the incidence angle does not affect the rotation of the SoP. Moreover, the additional phase can lead to a change of the rotation angle of the SoP. On the other hand, the weight coefficients of the two BHG beams periodically change the beam intensity distribution along the propagation direction. Interestingly, the beam is non-diffracting, which means that energy is only exchanged internally and is conserved as a whole. This approach may find applications in dynamic multi-beam optical tweezers, atom guiding, materials processing, microscopy, and optical communications.

We investigate the “inverted” solitons in spin-orbit-coupled Bose-Einstein condensate with one-dimensional spatially periodic Zeeman field. Soliton existence depends on the exact invert for the condensate components in the spatially periodic Zeeman field. And the position and the total pseudomagnetization density of the solitons can be controlled by the spatially periodic Zeeman field. Simulated results show that the inverted solitons can be stable for the interatomic attractive interactions.

We report on the existence and stability of fundamental and out-of-phase dipole gap solitons in parity-time (PT)-symmetric mixed linear-nonlinear optical lattices with a fourth-order diffraction. These solitons exist in the semi-infinite gap. For fundamental gap solitons, they can bifurcate from the higher edge of the first Bloch band, solitons are stable in the low power region. For dipole gap solitons, they cannot bifurcate from the higher edge of the first Bloch band, they can stably exist in the moderate power region. The coupling constant of the fourth-order diffraction can influence the stability of these gap solitons.

We investigate the nonlocal gray solitons in parity-time (PT)-symmetric potentials with spatially modulated nonlinearity. If the nonlinear modulated function (nonlinear potential) is real, the coefficient of the function can control the grayness and the existence domain of these gray solitons. Especially, if the coefficient of the nonlinear modulated function is below a threshold, the gray solitons will be changed into anti-dark solitons. The effects of the degree of the nonlocality and the imaginary part of the PT-symmetric potentials on the grayness and the existence of the gray solitons are also discussed. If the nonlinear modulated function is also PT symmetric, the imaginary part of the function will obviously affect the existence and stability of the nonlocal gray solitons.

We study the existence of discrete solitons in saturable nonlinearity media with parity-time symmetric lattices. We find that there exist two kinds of discrete solitons, they share the same parameters but different energy flows. The degree of saturable nonlinearity can influence the properties of such discrete solitons. Stable discrete solitons are found near the anti-continuum limit.

We address two-dimensional surface solitons occurring at the interface between a semi-infinite linear medium and a semi-infinite nonlocal nonlinear medium. We find that there exist stable single and dipole surface solitons. The properties of the surface solitons can be affected by the degree of nonlocality. Interestingly, only when the degree of nonlocality is greater than a critical value, the surface solitons can exist.

We investigate numerically surface-wave solitons occurring at the interface between semi-infinite linear and thermal nonlinear optical media, with the refractive index of the linear medium being greater than that of the nonlinear medium (in the absence of light). We find that the threshold energy flows of the existence of the surface solitons depend on the linear refractive index difference of the two media. Their fitting empirical formula has been obtained. Furthermore, we elucidate that the optical beams propagating in thermal nonlinear optical media, either as a single surface soliton or as a dipole surface soliton, can be attracted to the surface, even when launched from far away.